Answer:
20
Step-by-step explanation:
u add 13+7 and that gives you 20, so if you subtract 20 and 7 that gives you 13
a linear equation is an equation whose graph is a straight lina
The statement that a linear equation is an equation whose graph is a straight line is True.
What is a linear equation?A linear equation can be defined as an algebraic equation with each term having an exponent and the graphing of the equation results in a straight line.
From the definition, it can be deduced that the statement is True.
Thus, the statement that a linear equation is an equation whose graph is a straight line is True.
The complete question is:
True or false
A linear equation is an equation whose graph is a straight line.
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83
1 Show that I= {xy²w² dx + x²yw² dy + x²y²w dw} is independent of
the path of integration c and evaluate the integral from A (1, 3, 2) to
B (2, 4, 1).
2 Determine whether dz= 3x²(x² + y2) dx + 2y(x3 + y) dy is an exact
differential. If so, determine z and hence evaluate fedz from A (1, 2)
to B (2, 1).
1. Observe that
[tex]\nabla \dfrac{x^2y^2w^2}2 = \langle xy^2w^2, x^2yw^2, x^2y^2w\rangle[/tex]
is a gradient field, so the gradient theorem holds and the integral in question is indeed path-independent. Its value is
[tex]\dfrac{x^2y^2w^2}2\bigg|_{x=1,y=3,w=2}^{x=2,y=4,w=1} = 32 - 18 = \boxed{14}[/tex]
2. [tex]dz[/tex] is an exact differential if we can find a scalar function [tex]z=f(x,y)[/tex] such that
[tex]\dfrac{\partial f}{\partial x} = 3x^2 (x^2+y^2) = 3x^4 + 3x^2y^2[/tex]
[tex]\dfrac{\partial f}{\partial y} = 2y(x^3+y) = 2x^3y + 2y^2[/tex]
Integrating both sides of the first equation with respect to [tex]x[/tex] yields
[tex]f(x,y) = \dfrac35 x^5 + x^3 y^2 + g(y)[/tex]
Differentiating with respect to [tex]y[/tex] gives
[tex]\dfrac{\partial f}{\partial y} = 2x^3y + \dfrac{dg}{dy} = 2x^3y + 2y^2 \\\\ \implies \dfrac{dg}{dy} = 2y^2 \implies g(y) = \dfrac23y^3 + C[/tex]
and we ultimately find
[tex]f(x,y) = \boxed{z = \dfrac35 x^5 + x^3y^2 + \dfrac23 y^3 + C}[/tex]
(We can also use the same method here to determine the scalar function in part (1).)
Then the integral is path-independent, and its value is
[tex]f(2,1) - f(1,2) = \dfrac{418}{15} - \dfrac{149}{15} = \boxed{\dfrac{269}{15}}[/tex]
The following value 1.23456789 x 10-6
what is a answer?
Answer 1:
1.23456789 × (10-6) = 4.93827156
Answer 2:
(1.23456789 × 10) - 6 = 6.3456789
Answer 3:
1.23456789 × [tex]10^{-6}[/tex] = 0.000000123456789
Hope this helped! :)
The cost for hiring a car for 2 days in 2018 was Rs. 264 which was 20% more than in 2013. What was the cost of hiring a car for 2 days in 2013?
The cost of hiring a car for 2 days in 2013 is Rs. 316.8
How to find the cost of hiring in 2013 ?The cost for hiring a car for 2 days in 2018 was Rs. 264 which was 20% more than in 2013.
Therefore,
cost of hiring for 2018 = Rs. 264
Therefore,
let
cost of hiring in 2013 = 20%(264) + 264
cost of hiring in 2013 = 20 / 100 × 264 + 264
cost of hiring in 2013 = 1 / 5 × 264 + 264
cost of hiring in 2013 = 264 / 5 + 264
cost of hiring in 2013 = 52.8 + 264
cost of hiring in 2013 = 316.8
Therefore, the cost of hiring a car for 2 days in 2013 is Rs. 316.8.
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Suppose you want to have $300,000 for retirement in 25 years. Your account earns 8% interest. How much would you need to deposit in the account each month?
Using the future value formula, it is found that you would need to deposit $272.95 in the account each month.
What is the future value formula?It is given by:
[tex]V(n) = P\left[\frac{(1 + r)^{n-1}}{r}\right][/tex]
In which:
P is the payment.n is the number of payments.r is the interest rate.For this problem, considering that there are monthly compoundings, the parameters are:
r = 0.08/12 = 0.0067, V(n) = 300000, n = 25 x 12 = 300.
Hence we solve for P to find the monthly payment.
[tex]V(n) = P\left[\frac{(1 + r)^{n-1}}{r}\right][/tex]
[tex]300000 = P\left[\frac{(1.0067)^{299}}{0.0067}\right][/tex]
1099.12P = 300000
P = 300000/1099.12
P = $272.95.
You would need to deposit $272.95 in the account each month.
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B
Given: ∠1=∠2
If AC3, BC = 5, and AB=7, find AD.
020
04
040
2/3
Answer:
Option 3
Step-by-step explanation:
[tex]\frac{5}{3}=\frac{AD}{7-AD} \\ \\ 35-5AD=3AD \\ \\ 35=8AD \\ \\ AD=4 \frac{3}{8}[/tex]
Do the 1. In a class of 60 students, a survey was conducted, 30 students had applied for Addis Ababa University, 25 students applied for Bahir Dar University and 24 students applied for Wachemo University. 11 students applied for both Addis Ababa and Bahir Dar Universities, 6 applied for both Addis Ababa and Wachemo Universities, 9 applied for both Wachemo and Bahir Dar Universities while 4 applied neither of the aforementioned universities. Find i. 11. 111. iv. number of students that applied for all the universities. number of students that applied for at least two of the universities. number of students that applied at most two universities. number of students that applied for Addis Ababa but not Bahir Dar University. 13Z 2. Solve the equation: = 11-3i, Z E C, where Z = x + iy, x&y E R. Z+1 3. Given that Z & W are complex numbers. 2 Prove that IZ + W1²-|Z - W² = 4Re(Z)Re(W). 4. Solve the equation: 2² + 4z +20 + iz(A + 1) = 0 where A is a constant, has complex conjugate root. If one of the roots of this quadratic is Z = B + 2i, where B is a real constant, find the possible values of A.
The number of students that applied for all universities is 3, the number of students that applied for at least two of the universities is 20, the number of students that applied for at most two of the universities is 53, and the number of students that applied for Addis Ababa but not Bahir Dar University is 5.
Given that there are 60 students out of which 30 students had applied for Addis Ababa University, 25 students applied for Bahir Dar University and 24 students applied for Wachemo University. 11 students applied for both Addis Ababa and Bahir Dar Universities, 6 applied for both Addis Ababa and Wachemo Universities, 9 applied for both Wachemo and Bahir Dar Universities while 4 applied neither of the aforementioned universities.
Let A, B, and W denote the sets of students apply to Addis Ababa Uni (A), Bahir Dar Uni (B), or Wachemo Uni (W). Let U denote the universal set of all students in the class.
We're given the cardinalities of several sets:
total number of students n(U)=60, A applicants is n(A)=30, B applicants n(B)=25, W applicants n(W)=24, A and B applicants n(A∩B)=11, A and W applicants n(A∩W)=6, B and W applicants n(B∩W)=9 non-applicants n(U\(A∪B∪W))=4
The last cardinality tells us n(A∪B∪W),60-4=56 students applied anywhere at all.
We want to find n(A∩B∩W), the number of students that applied to each of the three universities.
By the inclusion/exclusion principle,
n(A∪B∪W)=n(A)+n(B)+n(W)-n(A∩B)-n(A∩W)-n(B∩W)+n(A∩B∩W)
56=30+25+24-11-6-9+n(A∩B∩W)
n(A∩B∩W)=3
Now, we will find the number of students that applied for at least two of the universities.
n(A∩B)=n(A∩B∩W)+n(A∩B∩W')
11=3+n(A∩B∩W')
8=n(A∩B∩W')
Similarly, we will find
n(A∩B'∩W)=3
n(A'∩B∩W)=6
n(A∩B'∩W')=16
n(A'∩B∩W')=8
n(A'∩B'∩W)=12
then the total number of students applied for at least two students is
n(A∩B∩W')+n(A∩B'∩W)+n(A'∩B∩W)+n(A∩B∩W)=20
Now, we will find the number of students that applied for atmost two universities, we get
n(A∩B∩W')+n(A∩B'∩W)+n(A'∩B∩W)+n(A∩B'∩W')+n(A'∩B∩W')+n(A'∩B'∩W)=53
now, we will find the number of students that applied for Addis Ababa but not Bahir Dar University is
n(A∩B')=n(A)-n(B)
n(A∩B')=30-25
n(A∩B')=5
hence, the total students is 60 and the number of students that applied for all universities is 3, the number of students that applied for at least two of the universities is 20, the number of students that applied for at most two of the universities is 53, and the number of students that applied for Addis Ababa but not Bahir Dar University is 5.
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Scenario 2 You are at a restaurant with three friends (party of 4) and need to estimate the amount of tip for your portion of the bill without using a calculator. Assume a 20% tip rate. For full credit, you will need the cost of your meal, an explanation of how you would calculate your 20% tip, and the total amount. Part B: Explain how you would solve this problem by organizing a sample calculation.
Assuming you had a bill of $120 when you went to the restaurant with your three friends, the 20% tip would come out to $24.
What would be the tip?First assume an amount that the meal you ate cost. Let's assume that amount if $120.
If the tip rate if 20%, it means that you need to find out what 20% of the bill of $120 is.
If you don't want to use a calculator, there are other ways you can calculate the tip.
An easy method would be to find 10% of the bill. To find 10%, all you have to do is to move the decimal point from right to left.
The decimal point in $120 is at the far right so the 10% amount would be:
= $12.0
Now that you have the 10% amount, remember that 20% is simply twice the amount of 10% so:
= 12 x 2
= $24
The total amount then becomes:
= 120 + 24
= $144
In conclusion, your tip amount would be $24.
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What is the smallest whole number larger than the perimeter of any triangle with a side of length 5 and a side of length 19?
Answer:
39
Step-by-step explanation:
In a triangle, the sum of any two side lengths must exceed the length of the remaining third side. Therefore these 3 inequalities must be true.
5 + 19 > x
5 + x > 19
19 + x > 5
We can ignore the third inequality because, for any positive value of x, the inequality is true.
x < 26
x > 14
Now we know that x, the length of the third side, must be greater than 14 but less than 26. Since we are asked for the smallest whole number possible, the third side would be length 15. Therefore the perimeter is 5 + 19 + 15 = 39.
Given the two similar octagons
shown below, find the perimeter
of the larger octagon.
28
Perimeter = 34
4
6 4
3
4
7
3
3
The perimeter of the bigger octagon that is similar to the smaller one is: 238 units.
What is an Octagon?An octagon can be described as a polygon that has 8 sides and 8 angles.
What are Similar Octagons?
Octagons are referred to as similar to each other if they have the same angle measure but corresponding sides that are proportional to each other. That is, they have the same shape but different sizes.
How to Find the Perimeter of Similar Polygons?
Given the two octagons in the diagram are similar, and:
Perimeter of the smaller octagon = 34 units
A side of the smaller octagon = 4 units
Perimeter of the bigger octagon = ?
A corresponding side of the bigger octagon = 28 units
Therefore:
Perimeter of the smaller octagon/Perimeter of the bigger octagon = side of the smaller octagon/corresponding side of the bigger octagon
Plug in the values
34/Perimeter of the bigger octagon = 4/28
Perimeter of the bigger octagon = (28 × 34)/4
Perimeter of the bigger octagon = 238 units.
In summary, the perimeter of the bigger octagon is: 238 units.
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Assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Enter a number. Round your answer to four decimal places.) = 8; = 2 P(7 ≤ x ≤ 11)
Using the normal distribution, the indicated probability is given as follows:
P(7 ≤ x ≤ 11) = 0.6247.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The mean and the standard deviation are given, respectively, by:
[tex]\mu = 8, \sigma = 2[/tex]
P(7 ≤ x ≤ 11) is the p-value of Z when X = 11 subtracted by the p-value of Z when X = 7, hence:
X = 11:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (11 - 8)/2
Z = 1.5
Z = 1.5 has a p-value of 0.9332.
X = 7:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (7- 8)/2
Z = -0.5
Z = -0.5 has a p-value of 0.3085.
0.9332 - 0.3085 = 0.6247.
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If AB = 58, and BC = 46, find the length of the radius to the nearest tenth. Assume BC is tangent to Circle A.
Applying the Pythagorean theorem, the length of the radius is: 35.3 units.
How to Apply the Pythagorean Theorem?According to the Pythagorean theorem, the sum of the squares of the shorter sides of a right triangle equals the square of the longest side. For example, if a and b are two smaller legs of a right triangle, and c is the longest leg (hypotenuse) of the right triangle, then the Pythagorean theorem states that:
a² + b² = c².
Given the following parameters of the right triangle:
Triangle ABC is a right triangle with angle ACB as the right angle according to the tangent theorem since segment BC is tangent to Circle A
Segment AB = 58 (hypotenuse of the right triangle)
Segment BC = 46 (small leg of the right triangle)
Radius = AC (small leg of the right triangle)
Using the Pythagorean theorem, we have:
AC = √(AB² - BC²)
AC = √(58² - 46²)
AC = 35.3 units (to the nearest tenth).
Therefore, by using the Pythagorean theorem, the length of the radius of the circle, which is segment AC, to the nearest tenth is: 35.5 units.
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If f (x) = 3x + 5 and g (x) = 2x - 3 then find the value of fg (x) and fg(2).
Answer:
f(g(x)) = f(2x - 3) = 3(2x - 3) + 5 = 6x - 9 + 5 = 6x - 4
f(g(2)) = f(2*2 - 3) = f(4 - 3) = f(1) = 3*1 + 5 = 3 + 5 = 8
The composite function values:
f(g(x)) = 6x- 4
f(g(2)) = 8.
What is a composite function?Any function that is created by combining two or more other functions is referred to as a composite function. To put it another way, given two functions, f, and g, the composite function of f and g, denoted as f(g(x)), is a new function that applies g to the input x before applying f to the output of g. (x).
To find the value of fg(x), we need to compute g(x) first and then substitute it into f(x).
g(x) = 2x - 3
Substitute g(x) into f(x):
f(g(x)) = 3(2x - 3) + 5
f(g(x)) = 6x - 4
Therefore, fg(x) = 6x - 4.
To find the value of fg(2), substitute 2 into fg(x):
fg(2) = 6(2) - 4
fg(2) = 8
Therefore, fg(2) = 8.
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find a number which decreased by 21 equals twice the opposite of the number
The required number is 7. The expression formed with the given information is x - 21 = 2(-x).
What is an expression?An expression is the combination of variables, constants, and coefficients.
If two expressions are related by an equal in between them, then that is said to be an equation.
Calculation:From the given data,
Consider the required number = x
The number is decreased by 21 i.e., x - 21
Twice the opposite of the number = 2(-x)
So, on equating,
x - 21 = 2(-x)
On simplifying,
⇒ x - 21 = -2x
⇒ x + 2x = 21
⇒ 3x = 21
∴ x = 7
Thus, the required number is 7.
Check:
7 - 21 = -14 and 2(-7) = -14.
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What is the slope of a line that is parallel to y=5x+3
The slope of a line that is parallel to y=5x+3 is 5x.
Two lines must have the same slope to be parallel to each other.
3-3x/4≥9 help please
Answer:
x ≤ −8
Step-by-step explanation:
Let's solve your inequality step-by-step.
3 - 3x/4 ≥ 9
Step 1: Simplify both sides of the inequality.
-3/4x + 3 ≥ 9
Step 2: Subtract 3 from both sides.
-3/4x + 3 - 3 ≥ 9 − 3
-3/4x ≥ 6
Step 3: Multiply both sides by 4/(-3).
(4/-3) * (-3/4x) ≥ (4/-3) * (6)
x ≤ −8
Answer:
x ≤ −8
If you chose an angle, how are the construction steps you completed similar to the steps you would have taken to construct and bisect a line segment? How are they different?
There are different ways to construct an angle. The steps used in making a line segment are; First, you have to put the compass at one specific end of the line segment. Then you shift the compass slowly a little bit so it will be longer than half the length of the line segment. Then you have to draw arcs up and down the line. while using the same compass width, you then draw arcs from one specific end of the line. and thereafter you put your ruler at the point where the arcs cross, and you then draw the line segment. The difference is that to bisect an angle, one has to divide the shape or angle into two congruent parts while in the construction of a line segment, there are differences in length. What is the construction process of Angles? This entails a good construction process in making angles. They are step-by-step processes used to produce detailed and exact geometric figures.
The area of a circle is 28.26 square miles. What is the circle's diameter?
Use 3.14 for л.
miles
A = 28.26 miz
14. In a right triangle, if one acute angle has measure 10x + 6 and the other has measure 2x + 7, find the larger of these two angles.
Answer:
421/6 degrees
Step-by-step explanation:
The acute angles of a right triangle are complementary, so
[tex]10x+6+2x+7=90 \\ \\ 12x+13=90 \\ \\ 12x=77 \\ \\ x=\frac{77}{12}[/tex]
So, the acute angles measures 421/6 degrees and 119/6 degrees, and thus the larger angle is 421/6 degrees.
Find m/1 and m/2 in the kite.
help asap
The measure of angle 1 (m ∠1) is 28° and the measure of angle 2 (m ∠2) is 62°
Calculating anglesFrom the question, we are to determine the measure of angle 1 and the measure of angle 2
The given diagram is a kite and the diagonals intersect at right angles
Thus,
m ∠2 + 28° + 90° = 180°
m ∠2 = 180° - 28° - 90°
m ∠2 = 62°
Hence, the measure of angle 2 is 62°
For the measure of angle 1
Consider ΔADB
ΔADB is an isosceles triangle
Thus,
In the triangle, m ∠D = m ∠B
Then, we can write that
m ∠1 + 62° + 90° = 180°
m ∠1 = 180° - 62° - 90°
m ∠1 = 28°
∴ The measure of angle 1 is 28°
Hence, the measure of angle 1 (m ∠1) is 28° and the measure of angle 2 (m ∠2) is 62°
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how many significant figures are in this number 6.01x10^3
Answer:
3
Step-by-step explanation:
6.01 has 3 sig fig
I think that's how I do it
what is 4,928 will rounded to the nearest hundred
Answer:
The answer is 4900, because the next number is less than five, due to that we don't have to add a number (+1).
---
Thank you so much for participate in the community of Brainly.com
I hope help you :)
Kind regards, Antonio.
Two debt payments of $2000 each are due now and nine months from now. If money is worth 8%, what single payment six months from now is required to settle the debt?
The single payment six months from now is required to settle the debt will be $4042.
How to calculate the amount?The interest rate monthly will be 8/1200.
The number of time period given is 6 months.
Therefore, the future value will be:
= 2000(1 - 8/1200)^6
= 2081.35
The present value will be:
= 2000(1 - 8/1200)^3
= 1960.53
Therefore, the single payment will be:
= 2081.35 + 1960.53
= 4042
In conclusion, the correct amount is $4042.
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Nereo and Azeneth start recording video at the same time. Nereo's phone starts with 1,000 megabytes
(MB) of free space and uses 7 MB of space per second of video.
Azeneth's phone has 1,255 MB of free space and uses 10 MB of space per second of video.
How much free space will they have when they first have the same amount of space left?
Jennifer has 25 coins with a total value of $4.25. The coins are quarters and nickels. How many of each does she have?
Answer:
15 quarters, 10 nickels
Step-by-step explanation:
[tex]q+n=25[/tex]
[tex]0.25q+0.05n=4.25[/tex]
multiply the first equation by -0.25 and add the second equation to it
[tex]-0.25q-0.25n=-6.25\\0.25q+0.05n=4.25[/tex]
________________
[tex]-0.2n=-2[/tex]
[tex]n=\frac{-2}{-0.2} =10[/tex] has 10 nickels
[tex]q=25-n=25-10=15[/tex] has 15 quarters
10(.05) +15(0.25) = 0.5 + 3.75 = 4.25
Hope this helps
Suppose you are still committed to owning a $190,000 BMW (see Question 9). If you believe your mutual fund can achieve a 12% annual rate of return and you want to buy the car in nine years on the day you turn 30, how much must you invest today?
The amount of money which you must invest today is equal to $68,517.85.
How to calculate the present value?Mathematically, the present value of an investment can be calculated by using this formula:
Present Value, PV = FV/(1 + r)^t
Given the following data:
Time, t = 9 years.
Future value, FA = $190,000.
Interest rate, r = 12% = 0.12.
Substituting the given parameters into the formula, we have;
PV = 190,000/(1 + 0.12)^9
PV = 190,000/(1.12)^9
PV = 190,000/2.7730
PV = $68,517.85.
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The sum of 2 numbers is 70.4. One number is 19 times the other and the smaller number is less than 5. What are the two numbers?
Answer: [tex]\Large\boxed{3.52~;~66.88}[/tex]
Step-by-step explanation:
Given information
One number is 19 times the other
The smaller number is less than 5
Sum = 70.4
Set variables
Let x be the smaller number
Let 19x be the larger number
Set equation according to the given information
Smaller number + Larger number = Sum
x + 19x = 70.4
Simplify by addition
20x = 70.4
Divide 20 on both sides
20x / 20 = 70.4 / 20
[tex]\Large\boxed{x=3.52}[/tex]
Substitute values into the variables to find the larger number
Larger number = 19x
= 19 (3.52)
[tex]\Large\boxed{=66.88}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
Answer:
smaller number 3.52
greater number 66.88
Step-by-step explanation:
Let x and y be two numbers ,where x < 5 and x ≤ y.
x + y = 70.4
y = 19x
By replacing y by 19x in the first equation we get :
x + 19x = 70.4
Then
20x = 70.4
Then
x = 70.4÷20
= 3.52
y = 19x
Then
y = 19 × 3.52 (just replace x by 3.52)
= 66.88
Find the equation to the line below.
y =
Answer:
[tex]y=\frac{-3}{4}x-3[/tex]
Step-by-step explanation:
This is a linear graph so the equation will be in the format of y=mx+b.
b, the y-intercept, will be -3, as that is where the line crosses the y-axis.
m, the slope, is [tex]\frac{-3}{4}[/tex], calculated from the change in y over the change in x from points (-4,0) to (0,-3).
Now substitute the values in our equation:
[tex]y=\frac{-3}{4}x-3[/tex]
Answer:
y= -3/4+[-3]
Step-by-step explanation:
Given h of x equals negative 2 times the square root of x minus 3 end root, which of the following statements describes h(x)?
The function h(x) is increasing on the interval (–∞, 3).
The function h(x) is increasing on the interval (–3, ∞).
The function h(x) is decreasing on the interval (–∞, 3).
The function h(x) is decreasing on the interval (3, ∞).
Answer:
The function h(x) is decreasing on the interval (3, ∞).
Step-by-step explanation:
Please take a look at the attached image.
You will see a graph of the given function h(x) = -2[tex]\sqrt{x-3}[/tex]. The function is decreasing.
The function starts at 3 and starts to go towards negative infinity on the x-axis. Therefore the function is decreasing on the interval (3, ∞).
The equation y equals 15 times 2 to the power of t shows the number of infected people from an outbreak of the measles. The variable y represents the number of infected people, and t represents time in weeks. In how many weeks will the number of infected people reach 1200?
It will take 6 weeks for the number of infected people to reach 1200
How to determine the number of weeks?The function is given as:
y equals 15 times 2 to the power of t
Rewrite the function properly as follows
y = 15 * 2^t
When the population is 1200, the equation becomes
15 * 2^t = 1200
Divide both sides by 15
2^t = 80
Take the logarithm of both sides
t * log(2) = log(80)
Divide both sides by log(2)
t = 6.3
Approximate
t = 6
Hence, it will take 6 weeks for the number of infected people to reach 1200
Read more about exponential functions at:
https://brainly.com/question/11464095
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