Ask question

Ask question

All categories

3 years ago

12

Michael reads 12 pages of a book in 18 minutes, 8 pages in 12 minutes,and 20 pages in 30 minutes. Is this a proportional relatio

nship? If so, what is the constant of proportionality? What does it represent? Write an equation to represent this situation.

1 answer:

maria [59]3 years ago

7 0

Answer:

y = 2/3x

Step-by-step explanation:

<u>Reading rate is y pages per x minutes and proportional relationship formula is:</u>

y = kx

<u>The coefficient is:</u>

k = y/x

<u>Let's verify if the given numbers fit into the same relationship:</u>

12/18 = 2/3
8/12 = 2/3
20/30 = 2/3

We confirm all same and it means k = 2/3

<u>Required equation is:</u>

y = 2/3x

This represents that Michael reads 2 pages per 3 minutes and for x minutes he reads 2/3x pages

You might be interested in

The length of a rectangle is 5 centimeters longer than twice its width. If the perimeter of the rectangle is 88 centimeters, wha

fredd [130]

Answer:

The length of a rectangle is 5 centimetres longer than twice its width. If the perimeter of the rectangle is 88 centimetres, what is the width?

width=x

length=2x+5

perimeter=88=2L+2W

so half perimeter=44=L+W

x+2x+5=44

3x=39

x=13 cm width ANSWER

2x+5=31 cm length

8 0

4 years ago

Read 2 more answers

Find the point 3x - 7x₂ =5. of the lines x, - 5x2 = 1 and of intersection

tia_tia [17]

Answer:

( $\frac{9}{4},\frac{1}{4})$

Step-by-step explanation:

We are given that two lines

$x_1-7x_2=5$ and $x_1-5x_2=1$

We have to find the intersection point of two lines

Let $3x_1-7x_2=5$ (equation 1)

$x_1-5x_2=1$ (Equation 2)

Multiply equation 2 by 3 then subtract from equation 1

$-7x_2+15x_2=5-3$

$8x_2=2$

$x_2=\frac{2}{8}=\frac{1}{4}$

Substitute $x_2=\frac{1}{4}$ in the equation 1

Then, we get

$3x_1-7\frac{1}{4}=5$

$3x_1-\frac{7}{4}=5$

$3x_1=5+\frac{7}{4}=\frac{20+7}{4}=\frac{27}{4}$

$x_1=\frac{27}{4\times 3}=\frac{9}{4}$

Hence, the intersection point of two given lines is ( $\frac{9}{4},\frac{1}{4})$

6 0

3 years ago

Melanie is 5 years younger than twice Michael's age. Which expression represents Melanie's age? *

Sphinxa [80]

Answer: c) 2x-5

We can represent two times micheal’s age as 2x, and 5 years younger would be you subtract 5
So the answer is 2x-5

7 0

4 years ago

Complete the following statement. Round to the nearest hundredth .

RSB [31]

f(x) = 3/(x + 2) - √x - 3

f(7) = 3/(7 + 2) - √7 - 3

f(7) = 3/9 - √4

f(7) = 0.333 - 2

f(7) = -1.67

7 0

3 years ago

The hypotenuse of a right triangle is 52 in. One leg of the triangle is 8 in. More than twice the lenght of the other. What is t

shusha [124]

Call the short leg a. The Pythagorean Theorem says:

$a^2 + (8 + 2 a)^2 = 52^2$

$a^2 + 8^2 + 32 a + 4a^2 = 52^2$

$5a^2 + 32 a + 8^2-52^2 = 0$

$5a^2 + 32 a + (8-52)(8+52) = 0$

$5a^2 + 32 a - (44)(60) = 0$

$(5a + 132)(a - 20) = 0$

Only the positive root $a=20$ is relevant here.

The other side is $2a+8=48$

The perimeter is $20 + 48 + 52 = 120$ inches

3 0

3 years ago