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3 years ago

What is an equation of the line that passes through the point (5,8) and is parallel to the line 4x−5y=45?

1 answer:

3 0

4x-5y=45
4x-45=5y

(4/5)x+9=y

A line parallel to this one would have the same gradient (since the lines won't get closer or go farther) and maybe a different y intercept ("maybe" because a line would be parallel to itself)

So'
y= (4/5)x + c

Line passes through (5,8)
Plug in the x and y values into the equation to find c:
(4/5)(5) + c =8
4+c=8
Therefore, c = 8-4 = 4

So the new equation is y= (4/5)x+4

Now, we could put this back into the same format as the question because why not.
We find the common denominator of the right hand side of the equation:
y= (4/5)x +(20/5) = (4x+20)/5
Multiply both sides of the equation by 5:
5y = 4x+20
Therefore 4x-5y = -20.

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A researcher wants to estimate the percentage of all adults that have used the Internet to seek pre-purchase information in the

Lubov Fominskaja [6]

Answer:

The required sample size for the new study is 801.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$ .

The margin of error is:

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

25% of all adults had used the Internet for such a purpose

This means that $\pi = 0.25$

95% confidence level

So $\alpha = 0.05$ , z is the value of Z that has a pvalue of $1 - \frac{0.05}{2} = 0.975$ , so $Z = 1.96$ .

What is the required sample size for the new study?

This is n for which M = 0.03. So

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

$0.03 = 1.96\sqrt{\frac{0.25*0.75)}{n}}$

$0.03\sqrt{n} = 1.96\sqrt{0.25*0.75}$

$\sqrt{n} = \frac{1.96\sqrt{0.25*0.75}}{0.03}$

$(\sqrt{n})^2 = (\frac{1.96\sqrt{0.25*0.75}}{0.03})^2$

$n = 800.3$

Rounding up:

The required sample size for the new study is 801.

4 0

3 years ago

12000 pennie s equal

Arlecino [84]

There are 100 pennies in a dollar. We can divide 12000 pennies by 100 to find out how much they are worth in dollars.

12000/100 = $120

8 0

3 years ago

Read 2 more answers

How do I solve these?

makkiz [27]

1) The number is 12.

2) There are 7 passengers in a row.

3) Carol, Xavier and Keela drank 580, 1160 and 1260 mL of water, respectively.

<h3>How to resolve word problems involving linear equations</h3>

In this question we find word problems involving linear equations, in each case we need to understand the statement, derive mathematical equations and looking for corresponding solutions by algebraic means. Now we proceed to solve for each case:

Case 1

A variable is found herein and we need to resolve on this linear equation: (x - A number)

(x + 8) / 4 = 1 + (1 / 3) · x

(1 / 4) · x + 2 = 1 + (1 / 3) · x

1 = (1 / 12) · x

x = 12

The number is 12.

Case 2

A variable is found herein and we need to resolve on this linear equation: (x - Number of passengers per row)

30 · x + 12 = 222

30 · x = 210

x = 7

There are 7 passengers in a row.

Case 3

Three variables are found herein and we need to resolve on these linear equations: (x - Water consumed by Carol, y - Water consumed by Xavier, z - Water consumed by Keela)

z = 2 · x (1)

y = z + 100 (2)

x + y + z = 3000 (3)

Finally, we find the solution of this system:

x + (z + 100) + z = 3000

x + 2 · z = 2900

x + 4 · x = 2900

5 · x = 2900

x = 580 mL

z = 1160 mL

y = 1260 mL

Carol, Xavier and Keela drank 580, 1160 and 1260 mL of water, respectively.

To learn more on systems of linear equations: brainly.com/question/21292369

#SPJ1

3 0

2 years ago

Explain why you cannot square each side of the equation when verifying a trigonometric identity.

Sergeu [11.5K]

This is because when we do verification of an identity, we must work separately on both sides, and to see in the end if we can get an equality. Because if we square both sides, that already means that we assume that the equality exist in the beginning, so no need to verify the identity.

8 0

3 years ago

Read 2 more answers

Brenna is

soldi70 [24.7K]

Write a C program to compute Matrix Multiplication of two matrices. Use one dimensional array to store each matrix, where each row is stored after another. Hence, the size of the array will be a product of number of rows times number of columns of that matrix. Get number of row and column from user and use variable length array to initialize the size of the two matrices as well as the resultant matrix. Check whether the two matrices can be multiplied or not. Write a getMatrix() function to generate the array elements randomly. Write a printMatrix() function to print the 1D array elements in 2D Matrix format. Also, write another function product(), which multiplies the two matrices and stores in the resultant matrix. With SEED 5, the following output is generated.

Sample Output

Enter the rows and columns of Matrix A with space in between: 3 5

Enter the rows and columns of Matrix B with space in between: 5 4

Matrix A:

8 6 4 1 6

2 9 7 7 5

1 3 1 1 2

Matrix B:

9 5 4 5

9 9 8 1

4 4 3 5

2 6 2 1

4 5 2 4

Product AxB:

168 146 106 91

161 186 125 81

50 52 37 22

In conclusion, the answer is 5x1

Please give Brainliest answer thanks! :)

6 0

3 years ago

Read 2 more answers