The values of p and q are 1 and 3, respectively.
Given the equation x^2-4x + 1 = (x-p)- q, we can compare the coefficients of the corresponding terms on both sides of the equation.
We compared the coefficients of the x^2 terms on both sides of the equation. The coefficient of the x^2 term on the left-hand side is 1, and the coefficient of the x^2 term on the right-hand side is 1. This means that the two terms are equal, and therefore p = 1.
We compared the coefficients of the x terms on both sides of the equation. The coefficient of the x term on the left-hand side is -4, and the coefficient of the x term on the right-hand side is -1. This means that the two terms are equal, and therefore q = 3.
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Find the product of each pair of complex conjugates.
(3 + 8i)(3 – 8i) =
(4 + 5i)(4 – 5i) =
Answer:
The product of each pair of complex conjugates is:
(3 + 8i)(3 – 8i) = (9 - 8^2) + i(9 + 8^2) = (-81) + i(99) = (-81) + i(11) = (-81) + 11i
And
(4 + 5i)(4 – 5i) = (16 - 25) + i(16 + 25) = (-9) + i(41) = (-9) + 41i
So, the products are:
(-81) + 11i
and
(-9) + 41i
Answer:
73
41
Step-by-step explanation:
Figure 1 has been transformed to produce figure 2.
N
O A.
O B.
c.
O D.
76
8
6-
2-
ON
60
Which notation describes this transformation?
(z,y)= (z+ 9,y - 2)
(z,y)= (-y, z)
(z',y)= (z - 9,y + 2)
(z,y)= (-z, y)
8
X
The notation of the transformation of the polygons is (x, y) = (x - 9, y + 2)
Describing the notation of the transformationFrom the question, we have the following parameters that can be used in our computation:
The polygons 1 and 2
In the graph, we can see that
Polygon 1 is shifted up by 2 unitsPolygon 2 is shifted left by 9 unitsusing the above as a guide, we have the following:
(x, y) = (x - 9, y + 2)
This means that the transformation of the polygons is (x, y) = (x - 9, y + 2)
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NO LINKS!! URGENT HELP PLEASE!!!
NOT MULTIPLE CHOICE!!
8. a. Finish the table
b. Name the type of sequence
c. Find the equation for the following sequence
Answer:
7: 63
8: 73
arithmetic sequence
y = 10x - 7
or f(n) = 10x -7
or
[tex]a_{n}[/tex] = 3 + (n-1)10
Step-by-step explanation:
the output increases by 10 every time that the input increases by 1. That gives us our common difference or slope. The y intercept is -7. That is the value is you worked backwards until you get to n = 0. The initial value is 3. That is when n is 1.
When n is 3, f(n) is 23
When n is 2, f(n) is 13
When n is 1, f(n) is 3
When n is 0, f(n) is -7
I am not sure if this is clear. I am assuming that you have a lot of knowledge of linear equations and how to write arithmetic sequence. If my explanation is confusing it is me and not you.
Answer:
a. 63,73
b. Arithmetic sequence
c.t(n)=10n-7
Explanation:
a. Here is the completed table:
n | t(n)
4 | 33
5 | 43
6 | 53
7 | 63
8 | 73
b.
The type of sequence is arithmetic.
An arithmetic sequence is a sequence of numbers where the difference between any two consecutive terms is constant.
In this case, the difference between any two consecutive terms is 10.
c.
The equation for the arithmetic sequence is:
t(n)=a+(n-1)d
where:
t(n) is the nth term in the sequencen is the term numberd is the common differencea is the first termFor Question:
d=43-33=10a=?Now
equation becomes:
t(4) = a+(4-1)10
33=a+30
a=33-30
a=3
Now, the Equation becomes
t(n) = 3+(n-1)10
t(n) = 3+10n-10
t(n)=10n-7
The length of a rectangular banner is 5 feet longer than its width. If the area is 66
square feet, find the dimensions.
Answer:
The length should be 11 feet and the width should be 6 feet. 11 feet is 5 feet more than 6 feet. 11 feet times 6 feet is 66 square feet.
Step-by-step explanation:
What is Navems manufacturing cycle efficiency (MCE) for its elevators
Navern Corporation's manufacturing cycle efficiency (MCE) for its elevators is approximately 11.36%.
How to calculate the valueValue-added time is the time spent on activities that directly add value to the product.
Value-added time: Process time = 5 days (the process of manufacturing the elevators)
Total cycle time: Wait time + Inspection time + Process time + Move time + Queue time
= 12 days + 12 days + 5 days + 6 days + 9 days
= 44 days
MCE = (Value-added time / Total cycle time) * 100
= (5 days / 44 days) * 100
≈ 11.36%
Therefore, Navern Corporation's manufacturing cycle efficiency (MCE) for its elevators is approximately 11.36%.
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-) Find the equation of the line that passes through (1,0) and (3,6).
The equation of the line that passes through the points (1, 0) and (3, 6) is y = 3x - 3.
To find the equation of a line passing through two points, we can use the slope-intercept form of a linear equation: y = mx + b, where m is the slope of the line and b is the y-intercept.
Given points:
Point 1: (1, 0)
Point 2: (3, 6)
Step 1: Calculate the slope (m) using the formula:
m = (y2 - y1) / (x2 - x1)
Substituting the coordinates:
m = (6 - 0) / (3 - 1)
m = 6 / 2
m = 3
Step 2: Substitute one of the given points and the slope into the equation y = mx + b to find the y-intercept (b).
Using Point 1 (1, 0):
0 = 3(1) + b
0 = 3 + b
b = -3
Step 3: Write the equation of the line using the slope (m) and the y-intercept (b):
y = 3x - 3
Therefore, the equation of the line that passes through the points (1, 0) and (3, 6) is y = 3x - 3.
This equation represents a line with a slope of 3, indicating that for every increase of 1 unit in the x-coordinate, the y-coordinate increases by 3 units. The y-intercept of -3 means that the line crosses the y-axis at the point (0, -3). By substituting any x-value into the equation, we can determine the corresponding y-value on the line.
Hence, the equation of the line passing through (1, 0) and (3, 6) is y = 3x - 3.
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what is the answer, i need help.
The calculated value of x in the figure is 12
How to calculate the value of x in the figureFrom the question, we have the following parameters that can be used in our computation:
The figure
The scale is given as
A : B = 8 : 9
So, we have
48 : 2x + 30 = 8 : 9
Next, we have
(2x + 30)/48 = 9/8
This gives
2x + 30 = 48 * 9/8
2x + 30 = 54
This gives
2x = 24
So, we have
x = 12
Hence, the value of x in the figure is 12
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In 2020 there were 18,700 students at college a with a projected enrollment increase of 500 students per year in the same year there were 26,200 students at college B with a projected enrollment decline of 1000 students per year according to these projections when will the colleges have the same enrollment? What will be the enrollment in each college at that time?
In 2025, both colleges will have an enrollment of 21,200 students.
To determine when the colleges will have the same enrollment, we need to set up an equation based on the projected enrollment increases and declines.
Let's assume the number of years from 2020 is represented by 'x'.
For College A, the projected enrollment can be represented by: 18,700 + 500x.
For College B, the projected enrollment can be represented by: 26,200 - 1000x.
To find when the colleges will have the same enrollment, we need to solve the equation:
18,700 + 500x = 26,200 - 1000x
Combining like terms, we get:
1500x = 7,500
Dividing both sides by 1500, we find:
x = 5
Therefore, the colleges will have the same enrollment in 5 years, or in the year 2025.
To determine the enrollment at that time, we substitute x = 5 into either equation. Let's use College A's equation:
Enrollment in College A in 2025:
18,700 + 500(5) = 18,700 + 2500 = 21,200 students
Enrollment in College B in 2025:
26,200 - 1000(5) = 26,200 - 5000 = 21,200 students
Both colleges will have an enrollment of 21,200 students in the year 2025 when they have the same enrollment.
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Please use the following for the next 7 questions. A random sample of 172 students was asked to rate on a scale to from 1 (not important) to 5 (extremely important) health benefits as a job characteristic (note that the rating scale can also have decimals, i.e. a student can give a rating of 1.32). The sample mean rating was 3.31, and the sample standard deviation was 0.70. For a type I error of 1% (alpha), can you be reasonably certain that the average rating is more than 3 in the population?
1.State the null and alternative hypotheses.
a. H0: µ = 0, Ha: µ > 3.31
b. H0: µ = 0, Ha: µ < 3.31
c. H0: µ = 0, Ha: µ > 3
d. H0: µ = 0, Ha: µ ≠ 3
2. Specify the rejection region for = 0.01. Reject H0 if
a. z > 2.33
b. t > 2.32
c. z < 2.33
d. t < 2.32
3. Calculate the test statistic
a. 2.3
b. -5.8
c. 0.44
d. 5.8
4. What is your conclusion?
a. Reject H0
b. Fail to Reject H0
c. Reject Ha
d. Fail to reject Ha
5. Obtain the lower bound of a 99% confidence interval for the mean rating.
a. 0.31
b. 0.34
c. 3.44
d. 3.17
6. Obtain the upper bound of a 99% confidence interval for the mean rating.
a. 0.31
b. 0.34
c. 3.44
d. 3.17
7. What assumption(s) do you need to make in order to answer the above questions?
a. No assumptions are needed
b. The population distribution is assumed to be normal.
c. The population distribution is assumed to be t-distributed.
d. The sampling distribution of the sample is assumed to be normal.
State the null and alternative hypotheses.
c. H0: µ = 0, Ha: µ > 3
The null hypothesis (H0) states that the population mean rating is equal to 3, while the alternative hypothesis (Ha) suggests that the population mean rating is greater than 3.
Specify the rejection region for α = 0.01. Reject H0 if
a. z > 2.33
The rejection region for a one-tailed test with a significance level of 0.01 (α) is in the upper tail of the distribution. In this case, we reject the null hypothesis if the test statistic (z-score) is greater than 2.33.
Calculate the test statistic
c. 0.44
To calculate the test statistic, we use the formula:
z = (sample mean - population mean) / (sample standard deviation / √n)
Plugging in the given values, we get:
z = (3.31 - 3) / (0.70 / √172) ≈ 0.44
What is your conclusion?
b. Fail to Reject H0
Since the calculated test statistic (0.44) does not exceed the critical value (2.33) in the rejection region, we fail to reject the null hypothesis. Therefore, we do not have sufficient evidence to conclude that the average rating is significantly greater than 3 in the population.
Obtain the lower bound of a 99% confidence interval for the mean rating.
d. 3.17
To obtain the lower bound of a 99% confidence interval, we subtract the margin of error from the sample mean. The margin of error can be calculated by multiplying the critical value (obtained from the z-table for a 99% confidence level) with the standard error (sample standard deviation divided by the square root of the sample size).
The lower bound is given by:
3.31 - (2.33 * (0.70 / √172)) ≈ 3.17
Obtain the upper bound of a 99% confidence interval for the mean rating.
c. 3.44
To obtain the upper bound of a 99% confidence interval, we add the margin of error to the sample mean. Using the same calculation as above, the upper bound is given by:
3.31 + (2.33 * (0.70 / √172)) ≈ 3.44
What assumption(s) do you need to make in order to answer the above questions?
b. The population distribution is assumed to be normal.
To perform hypothesis testing and construct confidence intervals, it is typically assumed that the population distribution is approximately normal. Additionally, assumptions such as random sampling and independence of observations are generally made.
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Graph the line. y = -x - 3
Find the equation for the line tangent of the graph of the function g(x)=7x/x-3 at (6,14)
Answer: y = (-28)x + 14
Step-by-step explanation:
The equation for the line tangent at point (a, b) can be found using the formula y = mx + c, where m is the slope of the line and c is the y-intercept. At point (6, 14), we need to find the value of m.
We start by finding the derivative of the original function g(x). Its derivative is given by:
dg(x)/dx=7/(x^2-3x+1)
Then, substitute x = 6 into the derivative expression to obtain:
dg(6)/dx = d/dx [7 * ln|x-3| ] evaluated at x = 6 = 7/3
Next, evaluate the original function g(x) at x = 6 to get g(6) = 7 * ln |6 - 3| / (6 - 3) = 7 * ln 3.
Since we know the coordinates of the point of tangency (6, 14), we can substitute them into the general form of the linear equation y = mx + c:
14 = 7 * 6 + c
14 = 42 + c
c = -28
The final equation of the line tangent at point (6, 14) is therefore:
y = (-28)x + 14
Please awnser asap I will brainlist
Answer:
a) ∩
Step-by-step explanation:
set A : {6,8,10,12}
set B : {5,6,7,8,9}
set C : {6,8}
A ∪ B = {6,8,10,12} ∪ {5,6,7,8,9} = {5,6,7,8,9,10,12} ≠ C
A ∩ B = {6,8,10,12} ∩ {5,6,7,8,9} = {6, 8} = C
Therfore{6,8,10,12} ∩ {5,6,7,8,9} = {6, 8}
Solve the quadratic equation by using the square root property.
(2x + 3)2 = 81
Answer: x = 3 and x = -6
Step-by-step explanation:
the first step is to square root both sides of the equation to get rid of the exponent (2) on the left side of the equation, however lets break it down:
[tex](2x + 3)^2 = 81\\\\[/tex]
81 can be rewritten as 9^2
[tex](2x + 3)^2= 9^2[/tex]
and now lets square root both sides:
[tex]\sqrt{(2x+3)^2} =\sqrt{9^2}[/tex]
The squares (the exponent 2) cancels out with the square root:
2x + 3 = +/- 9
now lets isolate x by subtracting 3 from both sides:
2x + 3 = +/- 9
-3 -3
2x = -3 +/- 9
2x = -3 + 9
2x = 6
2x = -3 - 9
2x = 12
And after simplifying, you can divide two on both sides:
2x = 6
/2 /2
x = 3
2x = -12
/2 /2
x = -6
x = 3 and x = -6
NO LINKS!! URGENT HELP PLEASE!!!
9. a. Finish the table
b. Name the type of sequence
c. Find an equation for the following sequence
Answer:
a. 0.9375, 0.46875
b. geometric sequence
c. equation: [tex] 7.5 * (\frac{1}{2})^(n-1)[/tex]
Step-by-step explanation:
a.
The table can be finished as follows:
n t(n)
1 7.5
2 3.75
3. 1.875
4. 0.9375
5 0.46875
b.
The type of sequence is a geometric sequence.
A geometric sequence is a sequence of numbers where the ratio between any two consecutive terms is constant.
In this case, the ratio between any two consecutive terms is 3.75/7.5=½ ,
so the sequence is geometric.
c.
The equation for the sequence is t(n) = 7.5 * (1/2)^n.
This equation can be found by looking at the first term of the sequence (7.5) and the common ratio (1/2).
t(1) = 7.5
t(2) = 7.5 * (1/2) = 3.75
t(3) = 7.5 * (1/2)^2 = 1.875
The equation can also be found by looking at the general formula for a geometric sequence,
which is [tex]t(n) = a*r^{n-1}[/tex]
In this case,
a = 7.5 r = 1/2.t(n) =[tex] 7.5 * (\frac{1}{2})^{n-1}[/tex]
This is the required equation.
Answer:
[tex]\textsf{a.}\quad \begin{array}{|c|c|c|c|c|c|}\cline{1-6}\vphantom{\dfrac12} n&1&2&3&4&5\\\cline{1-6}\vphantom{\dfrac12}t(n)&7.5&3.75&1.875&0.9375&0.4687\\\cline{1-6}\end{array}[/tex]
[tex]\textsf{b.} \quad \textsf{Geometric sequence.}[/tex]
[tex]\textsf{c.} \quad t(n)=7.5(0.5)^{n-1}[/tex]
Step-by-step explanation:
Before we can complete the table, we need to determine if the sequence is arithmetic or geometric.
To determine if a sequence is arithmetic or geometric, examine the pattern of the terms in the sequence.
In an arithmetic sequence, the difference between consecutive terms (called the common difference) remains constant.In a geometric sequence, the ratio between consecutive terms (called the common ratio) remains constant.Calculate the difference between consecutive terms by subtracting one term from the next:
[tex]t(2)-t(1)=3.75-7.5=-3.75[/tex]
[tex]t(3)-t(2)=1.875-3.75 = -1,875[/tex]
As the difference is not common, the sequence is not arithmetic.
Calculate the ratio between consecutive terms by dividing one term by the previous term.
[tex]\dfrac{t(2)}{t(1)}=\dfrac{3.75}{7.5}=0.5[/tex]
[tex]\dfrac{t(3)}{t(2)}=\dfrac{1.875}{3.75}=0.5[/tex]
As the ratio is common, the sequence is geometric.
To complete the table, multiply the preceding term by the common ratio 0.5 to calculate the next term:
[tex]t(4)=t(3) \times 0.5=1.875 \times 0.5=0.9375[/tex]
[tex]t(5)=t(4) \times 0.5=0.9375 \times 0.5=0.46875[/tex]
Therefore, the completed table is:
[tex]\begin{array}{|c|c|c|c|c|c|}\cline{1-6}\vphantom{\dfrac12} n&1&2&3&4&5\\\cline{1-6}\vphantom{\dfrac12}t(n)&7.5&3.75&1.875&0.9375&0.4687\\\cline{1-6}\end{array}[/tex]
To find an equation for the sequence, use the general form of a geometric sequence:
[tex]\boxed{\begin{minipage}{5.5 cm}\underline{Geometric sequence}\\\\$a_n=ar^{n-1}$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the first term. \\\phantom{ww}$\bullet$ $r$ is the common ratio.\\\phantom{ww}$\bullet$ $a_n$ is the $n$th term.\\\phantom{ww}$\bullet$ $n$ is the position of the term.\\\end{minipage}}[/tex]
In this case, the first term is the value of t(n) when n = 1, so a = 7.5
We have already calculated the common ratio as being 0.5, so r = 0.5.
Substitute these values into the formula to create an equation for the sequence:
[tex]t(n)=7.5(0.5)^{n-1}[/tex]
Two less than of a
number(x) is no more than 5
Seven subtracted from 4 times a
number (x) is more than 13.
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
Number Line Graph
-
The sum of two times a number (x)
and-2 is at least 8.
Four added to 3 times a number (x)
is less than 19.
Inequality
The valid numbers that satisfy all the given inequalities are -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6.
Let's solve each inequality step by step:
1. Two less than a number (x) is no more than 5:
The inequality is given as x - 2 ≤ 5. Adding 2 to both sides, we get x ≤ 7. This means that any number less than or equal to 7 satisfies the inequality.
2. Seven subtracted from 4 times a number (x) is more than 13:
The inequality is given as 4x - 7 > 13. Adding 7 to both sides, we get 4x > 20. Dividing both sides by 4, we obtain x > 5. So any number greater than 5 satisfies the inequality.
3. The sum of two times a number (x) and -2 is at least 8:
The inequality is given as 2x - 2 ≥ 8. Adding 2 to both sides, we get 2x ≥ 10. Dividing both sides by 2, we have x ≥ 5. So any number greater than or equal to 5 satisfies the inequality.
4. Four added to 3 times a number (x) is less than 19:
The inequality is given as 3x + 4 < 19. Subtracting 4 from both sides, we get 3x < 15. Dividing both sides by 3, we obtain x < 5. So any number less than 5 satisfies the inequality.
Based on the above solutions, the valid numbers that satisfy all the given inequalities are -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6. These numbers can be represented on a number line graph by marking the appropriate points and shading the corresponding regions.
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the perimeter of a semicircle protractor is 14.8cm,find it's radius
The radius of the semicircle protractor is approximately 4.693 cm.
Given,Perimeter of a semicircle protractor = 14.8 cm.
To find:The radius of a semicircle protractor.Solution:We know that the perimeter of a semicircle protractor is the sum of the straight edge of a protractor and half of the circumference of the circle whose radius is the radius of the protractor.
Circumference of a circle = 2πrWhere, r is the radius of the circle.If the radius of the semicircle protractor is r, then Perimeter of a semicircle protractor = r + πr [∵ half of the circumference of a circle =[tex](1/2) × 2πr = πr]14.8 = r + πr14.8 = r(1 + π) r = 14.8 / (1 + π)r ≈ 4.693[/tex] cm.
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Match the equations of ellipses to their equivalent equations in standard form. bts Feserved 25x2150x +9y² = 0 4x² - 36y +9y² = 0 3² + (y-2)² 22 (x + 7)² 7² 6² + + (y + 4)² 42 16x2 +288y +36y² = 0 36x² +504x + 49y² = 0 || - = 1 1 (z − 3)² + ²/² = 1 - 32 22 - 2 HAMMA 49x² +686 +36y² = 0 9x²54x + 25y² = 0
Matching of the equations of the Ellipses to their equivalent equations in standard form are:
The general form of x²/3² + (y - 2)²/2² = 1 is 4x² - 36y + 9y² = 0
The general form of (x + 7)²/7² + y²/6² = 1 is 36x² + 504x + 49y² = 0
The general form of x²/6² + (y + 4)²/4² = 1 is 16x² + 288y + 36y² = 0
The general form of (x - 3)²/3² + y²/5² = 1 is 25x² - 150x + 9y² = 0
How to identify the equation of the Ellipse?The general form and the standard form of the ellipse are:
- The general form is: Ax² + Bxy + Cy² + Dx + Ey + F = 0
- The standard form is: (x - h)²/a² + (y - k)²/b² = 1
1) x²/3² + (y - 2)²/2² = 1
Expanding gives:
x²/9 + (y - 2)²/4 = 1
Multiply through by 36 to get:
4x² + 9(y - 2)² = 36
Expand bracket to get:
4x² + 9y² - 36y + 36 = 36
Subtract 36 from both sides to get:
4x² - 36y + 9y² = 0
The general form of x²/3² + (y - 2)²/2² = 1 is 4x² + 9y² - 36y = 0
2) (x + 7)²/7² + y²/6² = 1
(x + 7)²/49 + y²/36 = 1
Multiply through by 1764 to get:
36(x + 7)² + 49y² = 1764
Expand bracket to get:
36x² + 504x + 1764 + 49y² = 1764
Subtract 1764 from both sides to get:
36x² + 504x + 49y² = 0
The general form of (x + 7)²/7² + y²/6² = 1 is 36x² + 504x + 49y² = 0
3) x²/6² + (y + 4)²/4² = 1
x²/36 + (y + 4)²/16 = 1
Multiply through by 576 to get:
16x² + 36(y + 4)² = 576
Expand bracket to get:
16x² + 36y² + 288y + 576 = 576
Subtract 576 from both sides to get:
16x² + 288y + 36y² = 0
The general form of x²/6² + (y + 4)²/4² = 1 is 16x² + 288y + 36y² = 0
4) (x - 3)²/3² + y²/5² = 1
(x - 3)²/9 + y²/25 = 1
Multiply through by 225 to get:
25(x - 3)² + 9y² = 225
Expand the bracket power to get:
25x² - 150x + 225 + 9y² = 225
Subtract 225 from both sides
25x² - 150x + 9y² = 0
The general form of (x - 3)²/3² + y²/5² = 1 is 25x² - 150x + 9y² = 0
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Match the equations of ellipses to their equivalent equations in standard form.
25x² - 150x + 9y² = 0
16x² + 288y + 36y² = 0
49x² + 686 + 36y² = 0
4x² - 36y + 9y² = 0
36x² + 504x + 49y² = 0
9x² - 54x + 25y² = 0
x²/3² + (y - 2)²/2² = 1 ⇒
(x + 7)²/7² + y²/6² = 1 ⇒
x²/6² + (y + 4)²/4² = 1 ⇒
(x - 3)²/3² + y²/5² = 1 ⇒
Which equations represent the line that is parallel to 3x - 4y = 7 and passes through the point (-4,-2)? Select two
options.
Oy=-3x+1
03x-4y=-4
4x-3y=-3
Oy-2=-(x-4)
Oy+2=2(x+4)
The equations that represent a line parallel to 3x - 4y = 7 and passes through the point (-4, -2) are:
0 = 3x - 4y - 4
3x - 4y = 4
To determine which equations represent a line that is parallel to the given line and passes through the point (-4, -2), we need to find the equations that have the same slope as the given line.
The equation 3x - 4y = 7 can be rewritten in slope-intercept form as y = (3/4)x - 7/4. From this form, we can see that the slope of the given line is 3/4.
Now let's analyze the options:
Oy = -3x + 1: This equation has a slope of -3, which is not equal to the slope of the given line (3/4). Therefore, this option does not represent a line parallel to the given line.
0 = 3x - 4y - 4: This equation can be rewritten as 3x - 4y = 4. Comparing this to the given line, we can see that it has the same coefficients of x and y, which means it has the same slope of 3/4. Therefore, this option represents a line parallel to the given line.
4x - 3y = -3: This equation has a slope of 4/3, which is not equal to the slope of the given line (3/4). Therefore, this option does not represent a line parallel to the given line.
Oy - 2 = -(x - 4): This equation can be rewritten as y = -x + 2. The slope of this line is -1, which is not equal to the slope of the given line (3/4). Therefore, this option does not represent a line parallel to the given line.
Oy + 2 = 2(x + 4): This equation can be rewritten as y = 2x + 6. The slope of this line is 2, which is not equal to the slope of the given line (3/4). Therefore, this option does not represent a line parallel to the given line.
In conclusion, the equations that represent a line parallel to 3x - 4y = 7 and passes through the point (-4, -2) are:
0 = 3x - 4y - 4
3x - 4y = 4
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Ejemplos de Costos evitables
Avoidable costs are costs that can be eliminated if the activity that caused them is discontinued. The examples are listed.
What are list of avoidable costs?Direct materials: Direct materials are the materials that go into a product and can be easily traced to it. For example, the wood used to make a table is a direct material. If a company decides to stop making tables, it can avoid the cost of buying wood.
Direct labor: Direct labor is the labor that is directly involved in making a product. For example, the wages paid to the workers who assemble a car are direct labor. If a company decides to stop making cars, it can avoid the cost of paying direct labor.
Variable overhead: Variable overhead is the overhead costs that vary with the number of units produced. For example, the cost of electricity used to power a factory is a variable overhead cost. If a company decides to stop producing a product, it can avoid the variable overhead costs associated with that product.
Sunk costs: Sunk costs are costs that have already been incurred and cannot be recovered. For example, the cost of research and development for a new product is a sunk cost. If the company decides not to launch the product, it cannot recover the cost of research and development.
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NO LINKS!! URGENT HELP PLEASE!!!
10. Find the equation of the circle below.
Answer:
(x+3)^2 + (y+1)^2 = 16
Step-by-step explanation:
The equation of a circle is (x – h)^2 + (y – k)^2 = r^2, where h is the x value of the center, k is the y value of the center, and r is the radius.
We can see from the picture that the radius is at about (-3, -1) and the radius is about 4, so we can plug those in:
(x – (-3))^2 + (y – (-1))^2 = 4^2
Simplify:
(x+3)^2 + (y+1)^2 = 16
Answer:
Equation of circle:[tex](x + 3)^2 + (y + 1)^2 = 16[/tex]
Step-by-step explanation:
Given:
Center of the circle = (-3, -1)
Point on the circle = (1, -1)
In order to find the radius of the circle, we can use the distance formula.
distance =[tex] \boxed{\bold{\sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}}}[/tex]
where:
x1 and y1 are the coordinates of the center of the circlex2 and y2 are the coordinates of the point on the circleIn this case, the distance formula becomes:
radius = [tex]\sqrt{(-3 - 1)^2 + ((-1) - (-1))^2}= \sqrt{16}=4[/tex]
Therefore, the radius of the circle is 4 units.
Now that we know the radius of the circle, we can find the equation of the circle using the following formula:
[tex]\boxed{\bold{(x - h)^2 + (y - k)^2 = r^2}}[/tex]
where:
h and k are the coordinates of the center of the circler is the radius of the circleIn this case, the equation of the circle becomes:
=[tex](x + 3)^2 + (y + 1)^2 = 4^2[/tex]
=[tex](x + 3)^2 + (y + 1)^2 = 16[/tex]
This is the equation of the circle.
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The number of $10 tickets sold is 1210 tickets.
The number of $20 tickets sold is 1344 tickets.
The number of $30 tickets sold is 827 tickets.
How to determine the number of each type of tickets sold?In order to write a system of linear equations to describe this situation, we would assign variables to the number of each tickets sold, and then translate the word problem into an algebraic equation as follows:
Let the variable x represent the number of $10 tickets.Let the variable y represent the number of $20 tickets.Let the variable z represent the number of $20 tickets.Since the basketball team sold 3381 tickets overall, 134 more $20 tickets than $10 tickets and the total sales are $63,790, a system of three linear equations to model this situation is given by;
x + y + z = 3381
y - x = 134
10x + 20y + 30z = 63790 ⇒ x + 2y + 3z = 6379
Next, we would solve the system of three linear equations simultaneously as follows;
x + x + 134 + z = 3381
2x + 134 + z = 3381
z = 3247 - 2x
x + 2(x + 134) + 3(3247 - 2x) = 6379
x = 1210 tickets.
For the value of y, we have:
y = x + 134
y = 1210 + 134
y = 1344 tickets.
For the z-value, we have:
z = 3247 - 2x
z = 3247 - 2(1210)
z = 827 tickets.
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Complete Question:
A basketball team sells tickets that cost $10, $20, or, for VIP seats, $30. The team has sold 3381 tickets overall. It has sold 134 more $20 tickets than $10 tickets. The total sales are $63,790. How many tickets of each kind have been sold?
How many $10 tickets were sold?
How many $20 tickets were sold?
how many $30 tickets sold?
Nave Corporation manufactures and sells custom home elevators. From the time an order is placed until the time the elevator is installed in the customer's
averages 44 days. This 44 days is spent as follows
12 days
5 days
Help
What is Naven's manufacturing cycle efficiency (MCE) for its elevators?
Nave Corporation's manufacturing cycle efficiency (MCE) for its elevators is approximately 27.27%.
To calculate the manufacturing cycle efficiency (MCE) for Nave Corporation's elevators, we need to determine the ratio of value-added time to the total lead time.
Value-added time refers to the time spent on activities that directly contribute to the production or customization of the elevators, while lead time refers to the total time from order placement to installation.
Given the breakdown of time:
12 days for manufacturing and customization
5 days for waiting or non-value-added time
The value-added time is 12 days, and the total lead time is 44 days.
To calculate MCE, we divide the value-added time by the total lead time and multiply by 100 to express it as a percentage:
MCE = (Value-added time / Total lead time) x 100
MCE = (12 / 44) x 100
MCE = 27.27%
Therefore, Nave Corporation's manufacturing cycle efficiency (MCE) for its elevators is approximately 27.27%.
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A grid shows the positions of a subway stop and your house. The subway stop is located at (4,
-2), and your house is located at (-9,-6). What is the distance, to the nearest unit, between
your house and the subway stop?
A. 6
B. 9
C. 14
D. 15
Let Q be an orthogonal matrix with an eigenvalue λ1=1. Let x be an eighenvector beloinging to λ1. Show that x is also an eigenvector of QT
If Q is an orthogonal matrix with an eigenvalue λ1 = 1, then x, the eigenvector corresponding to λ1, is also an eigenvector of QT with an eigenvalue λ2 = λ1 * (QT * x).
To show that x is also an eigenvector of QT, we need to demonstrate that QT * x is a scalar multiple of x.
Given that Q is an orthogonal matrix, we know that QT * Q = I, where I is the identity matrix. This implies that Q * QT = I as well.
Let's denote x as the eigenvector corresponding to the eigenvalue λ1 This means that Q * x = λ1 * x.
Now, let's consider QT * x. We can multiply both sides of the equation Q * x = λ1 * x by QT:
QT * (Q * x) = QT * (λ1 * x)
Applying the associative property of matrix multiplication, we have:
(QT * Q) * x = λ1 * (QT * x)
Using the fact that Q * QT = I, we can simplify further:
I * x = λ1 * (QT * x)
Since I * x equals x, we have:
x = λ1 * (QT * x)
Now, notice that λ1 * (QT * x) is a scalar multiple of x, where the scalar is λ1. Therefore, we can rewrite the equation as:
x = λ2 * x
where λ2 = λ1 * (QT * x).
This shows that x is indeed an eigenvector of QT, with the eigenvalue λ2 = λ1 * (QT * x).
In conclusion, if Q is an orthogonal matrix with an eigenvalue λ1 = 1, then x, the eigenvector corresponding to λ1, is also an eigenvector of QT with an eigenvalue λ2 = λ1 * (QT * x).
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100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!
Answer:
Step-by-step explanation:
According to the triangle proportionality theorem (or thales theorem), the lines are parallel if AD/BD = AE/CE
15/12= 1.25
10/8 = 1.25
Because the ratios are equal, the lines are parallel to each other.
100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!
The scaled triangle will be larger than the initial size by a factor 2.
The scaled square will be smaller than the initial side by a factor 4
What is dilation?Dilation refers to a transformation that changes the size of a geometric figure without altering its shape.
Dilation involves scaling an object by a certain factor, that might result in enlarging or reducing its dimensions uniformly in all directions.
Based on the given diagram, the new length and size of the object is calculated as follows;
For the triangle, (measure the length with ruler)
new lengths = 2 times the original lengthoriginal length = 2 cm, new length = 4 cmthe new size of the triangle will increase by a factor 2For the square; (measure the length with ruler)
new lengths = 0.25 times the original lengthoriginal length = 4 cm, new length = 2 cmthe new size of the square will decrease by a factor 4Learn more about dilation here: https://brainly.com/question/20482938
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A man standing in front of a house built on top of a rock 70m away from the rock observes that the angle of elevation of the top and foot of the house are 63degrees and60 degrees respectively.Find the height of the house
Answer: 33.7
Step-by-step explanation:
Let the height of the house be h, and the distance from the foot of the rock to the house be x.
From the given information, we have the following diagram:
```
*
/ \
/ \
/ 63° \
/ \
/θ \
A ----------------------- B
70m x
Angle A = 60° (complementary to the angle of elevation of the foot of the house)
Angle B = 63° (angle of elevation of the top of the house)
Using trigonometry, we have:
tan(63°) = h/x ----(1) (for triangle AOB)
tan(60°) = h/(x + 70) ----(2) (for triangle ABD)
Solving equations (1) and (2) simultaneously, we get:
h = (70 tan(63°) - 70 tan(60°)) meters
h ≈ 33.7 meters (rounded to one decimal place)
Therefore, the height of the house is approximately 33.7 meters.
Find the two
solutions. y=x+2, y=x^2. PLEASE HELP ASAP WILL MARK AS BRANLIEST
Answer: The two solutions are (2, 4) and (-1, 1).
Step-by-step explanation:
The given is a system of equations, y = x + 2, and, y = x^2
A system of equations comprises two or more equations and seeks common solutions to the equations.
To solve you can use substitution. And by doing so you can replace y of one equation with what the other equation equals:
y = x + 2
y = x^2
-> x + 2 = x^2
Now lets get all variables and constant to one side of the equation, set it equal to zero.
x + 2 = x^2
-x -2 -x -2
x^2 -x -2 = 0
Lets factor to find the solution
Factoring is used to simplify an algebraic expression by finding the greatest common factors that are shared by the terms in the expression.
We can factor, x^2 -x -2 = 0, into:
(x - 2)(x + 1) = 0
-------
SIDE NOTE:
If confuse on factoring please see attached image.
------
with (x - 2)(x + 1) = 0 we can find the solution by setting each component in the parentheses to 0:
x - 2 = 0
x + 1 = 0
Now you must solve for x.
x - 2 = 0
+2 +2
x = 2
x + 1 = 0
-1 -1
x = -1
x = 2 and x = -1
However, we are not done yet, we need to find what y is, and by doing so we can plug in the x values we got to find the corresponding y value to create points (coordinates).
-
When x = 2
y = x + 2
y = (2) + 2
y = 4
(2, 4)
-
When x = -1
y = x + 2
y = -1 + 2
y = 1
(-1, 1)
-
The two solutions are (2, 4) and (-1, 1).
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Answer: true
Step-by-step explanation:
What is the complete factorization of the polynomial x^3+2x^2+x+2
The complete factorization of the polynomial x³+2x²+x+2 is(x-1)(x+1)(x+2).
To factorize the polynomial x³+2x²+x+2 completely, one may use the rational root theorem, and synthetic division method.
Therefore, first we list the factors of 2 and divide it by the factors of 1 as the leading coefficient:Factors of 2 = ±1, ±2Factors of 1 = ±1Therefore, the possible rational roots for the given polynomial equation are± 1, ±2From the given polynomial, x³+2x²+x+2,
we can easily see that there is no remainder when divided by (x-1). Hence, (x-1) is a factor of the polynomial and we can use synthetic division to factorize the polynomial.x³+2x²+x+2 = (x-1)(x²+3x+2)Now we can use the quadratic formula or factoring to find the remaining factors. We get,x²+3x+2 = (x+1)(x+2).
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