Answer:
b) 2.45
Step-by-step explanation:
The Euclidean distance in 3-space is the root of the sum of the squares of the x-, y-, and z-differences between the points.
ApplicationFor the given points ...
[tex]x(3,2,5)=(x_1,y_1,z_1)\quad\textsf{and}\quad y(2,3,3)=(x_2,y_2,z_2)[/tex]
The distance between x and y is ...
[tex]d=\sqrt{(x_2-x_1)^2+(y_2=y_1)^2+(z_2-z_1)^2}\\\\d=\sqrt{(2-3)^2+(3-2)^2+(3-5)^2}=\sqrt{1+1+4}\\\\d=\sqrt{6}\approx2.45[/tex]
What is the factored form of 5x − 625x4
Options:
A. 5x(1 + 5x)(1 - 5x + 25x2)
B. 5x(1 - 5x)(1 + 5x + 25x2)
C. (1 - 5x)(1 + 5x + 25x2)
D. (1 + 5x)(1 - 5x + 25x2)
Answer:
B
Step-by-step explanation:
5x - 625[tex]x^{4}[/tex] ← factor out 5x from each term
= 5x(1 - 125x³) ← this factor is a difference of cubes and factors in general as
a³ - b³ = (a - b)(a² + ab + b²) , then
1 - 125x³
= 1³ - (5x)³
= (1 - 5x) (1² + 5x(1) + (5x)² )
= (1 - 5x) (1 + 5x + 25x²)
Then
5x - 625[tex]x^{4}[/tex] = 5x(1 + 5x + 25x²)
Money in a savings account is compounded continuously over time, t, and is modeled by the function f(t)=1000e0.047t. what is the rate at which the balance grows?
Compounded continuously the balance grows at a continuous rate of 1.7%.
What is compound interest ?
Compound interest is when you earn interest on both the money you've saved and the interest you earn. So let's say you invest $1,000 (your principal) and it earns 5 percent (interest rate or earnings) once a year (the compounding frequency).The model used for continuous compounding is
f(t) = Pe^(rt)
where P is the principal amount, and r is the interest rate being compounded. Assuming a typo in your given equation, you have
f(t) = 1000·e^(0.017t)
Matching the various parts of the equation, we see that P = 1000 and r = 0.017 = 1.7%.
Therefore, the balance grows at a continuous rate of 1.7%.
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The point-slope form of the equation of the line that passes through (–9, –2) and (1, 3) is y – 3 = one-half EndFraction(x – 1). What is the slope-intercept form of the equation for this line?
y = y equals StartFraction one-half EndFraction x plus 2.x + 2
y = y equals StartFraction one-half EndFraction x minus 4.x – 4
y = y equals StartFraction one-half EndFraction x plus StartFraction 5 Over 2 EndFraction.x +
y = y equals StartFraction one-half EndFraction x minus StartFraction 7 Over 2 EndFraction.x –
The slope-intercept form of given equation is y = 1/2x + 5/2.
According to the statement
we have given that the equation y-3 = 1/2(x-1) and the passing points are (–9, –2) and (1, 3).
And we have to find the slope-intercept form of the equation
slope-intercept form is the equation of a straight line in the form y = mx + b where m is the slope of the line and b is its y-intercept.
So, According to this
y-3 = 1/2(x-1)
convert this into y = mx +b form then
y-3 = 1/2x -1/2
here m is 1/2 and b is -1/2.
Then
y-3 = 1/2x -1/2
Add three on both sides then
y = 1/2x + 5/2
So, The slope-intercept form of given equation is y = 1/2x + 5/2.
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Answer:
its cccccccc
Step-by-step explanation:
A contractor is excavating a ramp into a trench for a construction project. How much dirt will the crew have to remove? To answer, find the volume of the triangular prism in the figure shown. Opening 4 x 6, ramp 8'deep
Use 3.14 for pi. ROUND FINAL ANSWER TO TENTHS!
2461,8
hope this helps!! just use the formulas and substitute
Does the graph represent a function?
It is true that the graph represents a function
How to determine if the graph represent a function?For a graph to represent a function, the following must be true
Each x value on the graph must point to exactly one
The above means that the function must pass the vertical line test
The given graph would pass the vertical line test
This is so because:
Each x value on the graph points to exactly one
Hence, the graph represents a function
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When a graphed line is vertical it indicates that the relation:
1. is a function and begins with y =
2. is not a function and begins with x =
3. is a function and begins with x =
4. is not a function and begins with y =
Answer:
y does not depend on x - it is not a function
That leaves (2) or (4)
Since one does not need y in the equation (4) is eliminated
(2) is the only possible result
For example: x = 5
Simplify 10 times the square root of quantity 3 x end quantity plus 4 times the square root of quantity 3 x end quantity plus 5 times the square root of quantity 3 x end quantity. 9 times the square root of quantity 3 x end quantity 9 times the square root of quantity 6 x end quantity 19 times the square root of quantity 3 x end quantity 19 times the square root of quantity 9 x cubed
The square root of the quantity x plus 7 end quantity minus 1 equals x=2.
What is square root?A number's square root is the factor that can be multiplied by itself to yield that number. Square root of, end square root is the symbol for square root. Finding an integer's square root is the inverse of squaring a number.To find the square root:
√(x + 7) − 1 = x√(x + 7) = x + 1x + 7 = (x + 1)²x + 7 = x² + 2x + 10 = x² + x − 60 = (x + 3) (x − 2)x = -3 or 2Check for extraneous solutions:
√(-3 + 7) − 1 = -3√4 − 1 = -32 − 1 = -31 = -3x ≠ -3√(2 + 7) − 1 = 2√9 − 1 = 23 − 1 = 22 = 2x = 2Therefore, the square root of the quantity x plus 7 end quantity minus 1 equals x = 2.
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The correct question is given below:
The square root of the quantity x plus 7 end quantity minus 1 equals x
what is the answer for x+$4.30 =$15.00
Answer:
x = 10.7
Step-by-step explanation:
Many newspapers carmy a certain purzile in which the reader must unsoramble leers to form words how many warys cam the letters of whyrot be aranged? Deny the coret unscrambling, then detemine the probability of getting that result by randomly selecting one amangement of the given lts how may ways can the lefters of whyrot be armanged 720. What is the cormect unscrambling of whyrot o a worthy o c. Rothwy o d. Thyrow.
The correct unscrambling of whyrot is worthy.
What is unscrambling?A word unscrambler is essentially a gadget that you feed all the letters into and it rearranges them to reveal all potential word combinations.Some might be concerned that this is a cheating method. However, if everyone playing the game has the option of using a word unscrambler, then the playing field is unquestionably even.A player may opt not to use the word generator and instead come up with their own list of terms. Having said that, they might want to utilize it afterward to assess their performance and review the entire list of terms they could have used.To learn more about unscrambling with the given link
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Practising
and Applying
1. Write each radial in simplified form.
a) √48
b) √ 1000
Answer:
[tex]\Large\boxed{a)~4\sqrt{3} }[/tex]
[tex]\Large\boxed{b)~10\sqrt{10} }[/tex]
Step-by-step explanation:
Question a). √48Given term
[tex]\sqrt{48}[/tex]
Factorize 48 inside the radical sign
[tex]\sqrt{2\times2\times2\times2\times3}[/tex]
Combine terms to form squares
[tex]\sqrt{2^2\times2^2\times3}[/tex]
Simplify the radical sign
[tex](2\times2)\sqrt{3}[/tex]
[tex]\Large\boxed{4\sqrt{3} }[/tex]
Question b) √1000Given term
[tex]\sqrt{1000}[/tex]
Factorize 1000 inside the radical sign
[tex]\sqrt{2\times2\times2\times5\times5\times5}[/tex]
Combine terms to form squares
[tex]\sqrt{2^2\times5^2\times2\times5 }[/tex]
Simplify the radical sign
[tex](2\times5)\sqrt{2\times5}[/tex]
[tex]\Large\boxed{10\sqrt{10} }[/tex]
Hope this helps!! :)
Please let me know if you have any questions
Which of the graphs below would result if you made the leading term of the following function negative?
F(x) = 5x³ + x-8
A. Graph A
B. Graph B
C. Graph C
D. Graph D
Answer: D
Step-by-step explanation:
If the leading coefficient is negative, then as [tex]x \to \infty[/tex], [tex]f(x) \to -\infty[/tex].
Eliminate A and B.If the leading coefficient is negative, then as [tex]x \to -\infty[/tex], [tex]f(x) \to \infty[/tex].
Eliminate C.This leaves D as the correct answer.
The function f(x) = –1∕3x2 is shifted down one unit. Which of the following function equations represents this translation? Question 6 options:
A) f(x) = –1∕3(x – 1)2
B) f(x) = –1∕3x2 + 1
C) f(x) = –1∕3x2 – 1
D) f(x) = –1∕3(x + 1)2
[tex]f(x) = y \: \: \ \: \: \: \: \: \: \: \: \: {normal \: function} \\ f(x) = y - 1 \: \: \: \: \: \: \: func\: shifted \: down[/tex]
[tex]f(x) = \frac{ - 1}{3} x {}^{2} \\ f(x) = \frac{ - 1}{3} x {}^{2} - 1[/tex]
Answer: CAnswer: F(x)= -1/3x2-1
Step-by-step explanation:
Can anyone help me solve these linear systems using substitution?
1. 3x-y=4
x+2y=6
2. 2x-y= -39
x+y= -21
3. 2x+y =11
6x-5y =9
Each question should demonstrate step by step on how to do it, as well as each step should show the final given points of each solution (x,y)
Answer:
1. (2,2)
2. (-20, -1)
3. (4,3)
Step-by-step explanation:
See attached images
Answer:
The solutions to the sets of equations may be found by either a substitution process or by graphing and looking for the point that the two lines formed by the quations intersect. Both approaches are described.
The "solution" to these sets of equations is the point at which the two lines intersect each other.
Step-by-step explanation:
1. 3x-y=4 and x+2y=6
x+2y=6
6x-2y=8 We can simply add these two equations since y will disappear, leaving just x.
7x = 14 [result of addition]
x = 2 [Solve]
Since x = 2, [Then use the solution for x to find y]
x+2y=6
(2)+2y=6
2y = 4
y = 2
(2,2) is the solution (where the lines intersect). See attached graph.
2. 2x-y= -39 and x+y= -21
2x-y= -39
x+y= -21 Add the two equations (since the y will be eliminated)
3x = -60
x = -20
Find y:
x+y= -21
(-20)+y= -21
y = -1
Solution is (-20,-1)
3. 2x+y =11 and 6x-5y =9
2x+y =11
-6x+-3y = -33 [Multiply by -3 and then add to other equation. This allows us to eliminate x]
6x - 5y = 9
-8y = - 24
y = 3
2x+y =11
2x+(3) =11
2x = 8
x = 4
Solution is (4,3)
==================
See attached graph for all the graphed solutions.
==================
The substitution process also works if we isolate one of the 2 variables in one equation and then use the resulting value in the second eqaution. For example, in problem 1:
3x-y=4
x+2y=6
Pick either equation and isolate the x or y. I'll pick the second equation and isolate for x:
x = 6-2y
Now use this value of x (6-2y) in the other equation:
3x-y=4
3(6-2y)-y=4
18 - 6y - y = 4
-7y = -14
y = 2
Then use y=2 to fiond x, using either equation:
x+2y=6
x+2(2)=6
x = 2
The solution is (2,2).
This same approach can be used on all these problems. It avoids trying to visualize what can be done to an entire equation to eliminate one of the variables, but it takes a bit more paper.
All solutions are graphed in the attachment.
Austin is a human resources executive for a technology company. He is deciding between two types of plans for vacation allowance for the employees of the company: Unlimited and Traditional, Austin wants to deterrine, for workers in the tech Industry, if the yearly mean number of vacation days taken by workers with an Unlimited plan is greater than the yearly mean number of vacation days taken by workers with a Traditional plan Austin surveys a random sample of 17 workers who have the Unlimited plan and a random sample of 15 workers who have the Traditional plan. (These samples are chosen independently.) For each worker, he records the number of vacation days taken last year. For the workers with an Unlimited plan, the sample mean is 18.9 with a sample variance of 30.8. For the workers with a Traditional plan, the sample mean is 17.4 with a sample variance of 6.1 Assume that the two populations of vacation days taken are approximately normally distributed. Can Austin conclude, at the 0.10 level of significance, that the population mean of the yearly number of vacation days taken by workers with an Unlimited plan is greater than the population mean of the yearly number of vacation days taken by workers with a Traditional plan? Perform a one-talled test. Then complete the parts below. Carry your intermediate computations to three or more decimal places, (If necessary, consult a list of formulas.) (*) State the null hypothesis and the alternate hypothesis (a) Determine the type of test statistic to use (a) state the null hypothesis H, and the alternate hypothesis (b) Determine the type of test statistic to use. (c) Find the value of the test statistic (Round to three or more decimal places.) (d) Find the critical value. (Round to three or more decimal places) (e) At the 0.10 level of significance, can Austin conclude that the yearly mean number of vacation days taken by workers with an Unlimited plan is greater than the yearly mean number of vacation days taken by workers with a Traditional plan?
The question requires that we have to state the hypothesis:
null hypothesis;H0: u1 < u2, the alternate hypothesis;H1: u1 > u2. The one tail test is what is to be used.
A. How to state the hypothesisH0: u1 < u2
H1: u1 > u2
The one tail test statistic is what is to be used here
B. standard error[tex]\sqrt{\frac{30.8}{17} +\frac{6.1}{15} }[/tex]
= 1.49
The df = 17 + 15 - 2
= 30
test statistic = 18.9 - 17.4 / 1.49
= 1.007
We have the critical value on excel as T.INV(0.9,30)
= 1.310
E. At 0.1, we can conclude that t-value (1.007) does not lies in the rejection area. We fail to reject the null hypothesis. Hence we conclude that the mean vacation with the unlimited plan is greater.
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The Library is having a book sale. Hardcover books sell for $4 each, and paperbacks sell for $2 each. If Connie spent $26 on 8 books, how many hard covers did she buy?
Please show work with a system of equations!!!!!!!!!!!!!
If Connie spent $26 on 8 books, The number of hard covers she buy is 5 hard cover.
Number of hardcover boughtLet h represent hard cover
Let p represent paperbacks
Formulate an equation
h + p= 8.......(1)
4h + 2p= 26......(2)
Multiply equation (1) by -2
-2h + -2p = -16
4h + 2p = 26
2h + 0p =10
2h = 10
Divide both side by 2h
h=10/2
h =5 hard covers
Paper backs
P=5-2
P=3 paper backs
Therefore If Connie spent $26 on 8 books, The number of hard covers she buy is 5 hard cover.
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Find the missing length indicated.
The value of the missing length in the image shown using the Pythagoras theorem is x = 1500
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Let h represent the missing red line. Using Pythagoras:
x² = h² + 900²
h² = x² - 900²
Also:
r² = h² + 1600²
r² = x² - 900² + 1600²
And:
(1600 + 900)² = r² + x²
(1600 + 900)² = (x² - 900² + 1600²) + x²
x = 1500
The value of the missing length in the image shown using the Pythagoras theorem is x = 1500
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Use part 1 of the fundamental theorem of calculus to find the derivative of the function. g(x) = x t3 t5 dt 0
Using the fundamental theorem of calculas the derivative of function g(x)=[tex]xt^{3}+t^{5}[/tex] at x=0 is [tex]t^{3}[/tex].
Given a function g(x)=[tex]xt^{3}+t^{5}[/tex].
We are required to find the derivative of the function g(x) at x=0.
Function is relationship between two or more variables expressed in equal to form. The values entered in a function are part of domain and the values which we get from the function after entering of values are part of codomain of function. Differentiation is the sensitivity to change of the function value with respect to a change in its variables.
g(x)=[tex]xt^{3}+t^{5}[/tex]
Differentiating with respect to x.
d g(x)/dx=[tex]t^{3}[/tex]+0 [Differentiation of x is 1 and differentiation of constant is 0]
=[tex]t^{3}[/tex]
Hence using the fundamental theorem of calculas the derivative of function g(x)= [tex]xt^{3}+t^{5}[/tex] at x=0 is [tex]t^{3}[/tex].
The function given in the question is incomplete. The right function will be g(x)=[tex]xt^{3}+t^{5}[/tex].
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.
number 14 part 1 pls
Given
[tex]7 - px - x^2 = 16 - (q + x)^2[/tex]
expanding the right side gives
[tex]7 - px - x^2 = 16 - (q^2 + 2qx + x^2)[/tex]
[tex]7 - px - x^2 = 16 - q^2 - 2qx - x^2[/tex]
Two polynomials of equal degree are the same if their coefficients are identical. This means
[tex]\begin{cases}16 - q^2 = 7 \\ -2q = -p\end{cases}[/tex]
[tex]16 - q^2 = 7 \implies q^2 = 9 \implies q=\pm3[/tex]
[tex]-2q = -p \implies p = 2q = \pm6[/tex]
Both [tex]p[/tex] and [tex]q[/tex] are positive, so [tex]\boxed{p=6}[/tex] and [tex]\boxed{q=3}[/tex].
Sims waist is 30 inches. He wants to put on more weight and is hoping to gain enough weight to increase his waist size by 8%. How many inches does he want his waist to be?
Answer:
32.4 inches
Step-by-step explanation:
Sam wants the increase to be 8% of 30 inches.
IncreaseThe amount of increase Sam wants in his waist size is ...
8% × 30 in = 0.08×30 in = 2.4 in
Waist sizeAdding the wanted increase to his present size would make Sam's waist size be ...
30 in + 2.4 in = 32.4 in
Sam wants his waist size to be 32.4 inches.
__
Additional comment
The larger size can also be computed from ...
30 +8%×30 = (1 +8%)×30 = 1.08×30 = 32.4 . . . inches
The piecewise defined function f(x) is graphed below what is the value of f(5)
Considering the piecewise function, it is found that f(5) is given by:
f(5) = -1.
What is a piecewise function?A piecewise function is a function that has different definitions, depending on the input.
To find the value of f(5) looking at the graph, we have to find y when x = 5. Researching this graph on the internet, we have that, when x = 5:
There is an open circle at y = 3.There is a closed circle at y = -1.The definition is at the closed circle, hence f(5) is given by:
f(5) = -1.
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A Bank manager receives Rs. 18000 for a basic 36 hours per week Over time is paid at a time and a half. How many hours are worked in a week where his total wage is Rs. 23250? a) 43 hours b) 42 hours c) 41 hours d) 40 hours
He worked 43 hours to earn Rs. 23250
His basic pay is Rs. 18000 for a basic 36 hours a week. His salary is
Rs. 23250. This proves that he has worked extra time. So the amount earned in the extra hours equals Rs. 23250 - Rs. 18000 = Rs.5250.
Amount per hour earned in basic pay = 18000/36 = Rs.500 a hour.
∴ Amount per hour earned in extra hours = 1.5 x 500 = 750 per hour.
So number of hours he worked in extra time = Rs.5250/750 = 7 hours.
Thus total number of hours = 36 + 7 = 43 hours.
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Practical Problem 2
Provide a practical problem below that you will use to represent inverse variation. The problem should be written in complete sentences.
Steps and Work:
List each step for solving the inverse variation practical problem and the work that corresponds with each step.
Answer
Give the correct answer that the app user is being asked to find.
The steps to solve the inverse variation will be:
Write the variation equation: y = k/x or k = xySubstitute in for the given values and find the value of kRewrite the variation equation: y = k/x with the known value of kSubstitute the remaining values and find the unknownHow to illustrate the variation example?The example will be y varies inversely with x and y = 2 when x = 5. Find y when x = 30
Step 1: Write the variation equation: y = k/x or k = xy:
k = xy
Step 2: Substitute in for the given values of x and y:
k = (2)(5) = 10
Step 3: Rewrite the variation equation: y = k/x with the known value of k (10):
y = 10/x
Step 4: Substitute the remaining values and find the unknown:
y = 10/30
y = 1/3
Therefore, y is 1/3 when x is 30.
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Use the diagram to answer each question.
m/A+m/B=
These are called
1
2 m2D+mz
These are called
= 180°
Use the diagram to answer each question.
3. If m/H=43⁰.
m/E=
m/G=
m/F=
4. If m/G= 132°.
m/H=
m/E=
m/F=
Molly is thinking of a number. twice her number take away seven is the same as her number plus five. what is her number?
Answer:
Number = 12
Step-by-step explanation:
2n-7=n+5 (+7 to both sides)
2n=n+12 (-n to both sides)
n=12
Suppose you receive a postcard from a good friend with a picture of the Golden Gate Bridge in San Francisco. The postcard is 3.5 inches high and 5.5 inches wide. The fine print on the postcard states that the scale of the picture is 1:19,600. Based on the scale, what's the actual length of the Golden Gate Bridge?
Question 19 options:
Based on the scale, the actual length of the Golden Gate Bridge is 68,600 inches.
What is the actual length of the Bridge?A scale drawing is a reduced form in terms of dimensions of an original image / building / object. The scale drawing is usually reduced at a constant dimension. An example of a scale drawing is a map.
The scale of a drawing is usually written in this format - length in the drawing, a colon (:), then the matching length on the original image. An example of a scale is 1 : 19,600. This scale means that 1 inch of the postcard represents 19.600 of the original Golden Gate Bridge.
Actual length of the Bridge = scale x length of the bridge in the postcard
19,600 x 3.5 = 68,600 inches
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1. There are only two numbers that are twice the sum of their
individual digits. One of them 0 and I am the other one. I am a
multiple of 9. Which number am I
Answer: 18
Step-by-step explanation: 18=1+8=9
its complicated but when you check something like
23= 2+3 =5
10 = 1+0=1
the individual digits of 18 are 1 and 8
Sum = 1+8=9
multiply 9 by 2 we get 18
18 is also a multiple of 9.
I hope this helps
Find the diameter of this circle.
a. sqrt 10
b. 4
c. 2
d. 2 sqrt 5
Answer:
3 sqrt 5
Step-by-step explanation:
diameter talks about the center of the circle..and the middle of the circle lies between 3 and 5
algebra 2: graph question
what is the value of a?
what is the value of b?
(graph attached)
Answer:
a = 3.14
b = 6.28
Step-by-step explanation:
The interval where the function is decreasing is where increasing x values result in decreasing y values. The y values peak at the point (3.14, 2) and decrease until the point (6.28, 0) where the function starts increasing again.
Simplify the expression to a single numerical value. a. 144 b. 432 c. 900 d. 5,184
The correct option is: (b)
=432.
What is simplification?By employing multiple processes, simplification refers to reducing the expression to a simpler form. Approximation is the process of making something less complicated and hence easier to accomplish or understand, or the object that arises from this process. The mathematical formula is simplified to its nearest value but is not exactly correct.
What is the simplified equation?Therefore, we must follow the order listed above when simplifying expressions. In the example before, we divide 8 by 4 and then add the result to 12 because, according to BODMAS, division (D) comes before multiples (M).
[tex]$3 \cdot 2^{3} \cdot 2 \cdot 3^{2}Calculate exponents $2^{3}: 8$$$=3 \cdot 8 \cdot 2 \cdot 3^{2}$$Calculate exponents $3^{2}: 9$$$=3 \cdot 8 \cdot 2 \cdot 9$$ $3 \cdot 8 \cdot 2 \cdot 9= 432$$$=432$$[/tex]
So. the value will be = 432
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I understand that the question you are looking for is :
Simplify the expression to a single numerical value.
3*2^3*2*3^2
(a)144
(b)432
(c)900
(d)5,184