Write fourteen billion in scientific notation

4) The line -3x + 4y = 8 is transformed by a dilation centered at the origin. Which linear equation could represent its image?

Dimas [21]

Answer:

4) The linear equation which could represent its image is y = $\frac{3}{4}$ x + 8 ⇒ (2)

5) The equation of the image of the line is y = $\frac{3}{2}$ x - 3 ⇒ (4)

Step-by-step explanation:

Dilation does not change the slope of a line but changes the y-intercept

Dilation of a line segment is longer or shorter by ratio that equal to the scale factor of dilation

4)

The slope-intercept form of the linear equation is y = m x + b, where m is the slope of the line and b its y-intercept

Let us put the given equation in the slope-intercept form to find its slope

∵ The line -3x + 4y = 8 is transformed by a dilation centered at

the origin

- Add 3x to both sides

∴ 4y = 3x + 8

- Divide both sides by 4

∴ y = $\frac{3}{4}$ x + 2 ⇒ the equation of the line before dilation

- By comparing it with the form above, then m = $\frac{3}{4}$ , so the

equation after dilation has the same slope

∵ The slope of the line before dilation is $\frac{3}{4}$

∴ The slope of the line after dilation is $\frac{3}{4}$

∵ The equation that has the slope $\frac{3}{4}$ is y =

∴ The equation of the image of the line is y = $\frac{3}{4}$ x + 8

The linear equation which could represent its image is y = $\frac{3}{4}$ x + 8

5)

∵ The equation of the line is y = $\frac{3}{2}$ x - 4

∵ The scale factor of dilation is $\frac{3}{4}$

- Dilation dose not change the slope of the line

∴ The slope of the image after dilation is $\frac{3}{2}$

- Dilation changes the y-intercept, to find it multiply the scale

factor of dilation by the y-intercept of the line before dilation

∵ The y-intercept of the line is (0 , -4)

- Multiply it by $\frac{3}{4}$

∵ $\frac{3}{4}$ × -4 = -3

∴ The y-intercept of the image is (0 , -3)

∴ The equation of the image of the line is y = $\frac{3}{2}$ x - 3

3 0

3 years ago

division equation where 13 is quotient with the dividend a whole number and a unit fraction is the divisor

lys-0071 [83]

The division equation that has a quotient of 13 is 1/1/13 = 13

<h3>How to determine the equation?</h3>

The given parameters are:

Quotient = 13
Dividend = Whole number
Divisor = Unit fraction i.e. 1/n where n is an integer.

A division equation is represented as:

Dividend/Divisor = Quotient

Substitute 13 for the Quotient

Dividend/Divisor = 13

Recall that:

Unit fraction = 1/n

So, we have:

Dividend/1/n = 13

Let n = 13.

So, we have:

Dividend/1/13 = 13

This gives

13 * Dividend = 13

Divide both sides by 13

Dividend = 1

So, we have:

1/1/13 = 13

Hence, the division equation is 1/1/13 = 13

Read more about division equations at:

brainly.com/question/1622425

#SPJ1

3 0

2 years ago

Francis went to the sporting goods store and spent $75.15 on 6 items.

MArishka [77]

Answer:

$6.03

Step-by-step explanation:

The question is asking us how much each pair of socks cost. With the information we are given, we know that there are 5 pairs and that they all cost the same amount. If the total were just the 5 socks, we could easily divide the total by 5 to get the price of each pair but that's not the case. The soccer ball is included in the final cost. To overcome this, we just have to subtract the soccer ball's cost ($45) from the total.

So we subtract $45 from $75.15, giving us $30.15, the total amount of all the socks. However we need to find out how much each pair costs and there are 5 of them, so we divide 30.15 by 5. This gives us the answer, $6.03.

Each pair of socks cost $6.03.

Simpler Explanation:

$75.15 - $45 = $30.15
$30.15 / 5 = $6.03

The answer is $6.03

5 0

3 years ago

8(3 – 2x)+ 4(3x – 2)=-16 <br>Can someone solve for x? please

castortr0y [4]

Answer: x = 8

Step-by-step explanation:

8(3-2x) + 4(3x - 2) = -16

expanding the equation , we have

24 - 16x +12x - 8 = -16

16 - 4x = -16

collecting the like terms

4x = 32

x = 32/4

x = 8

4 0

3 years ago

...............................

valkas [14]

I believe it’s 7/10

3 0

3 years ago