Allison is making treat bags for Valentine's Day. She uses 7 sheets of stickers

There is $500 in Holly's bank account. She takes out $50 from her account each month but doesn't put money back in. What is the

galina1969 [7]

Answer:

The rate of change or slope m = -50

Step-by-step explanation:

The slope-intercept form of the line equation

$y = mx+b$

where

m is the rate of change or slope

b is the y-intercept

Given that there is $500 in Holly's bank account.

Thus, the y-intercept b = 500

It is stated that she takes out $50 from her account each month but doesn't put money back in.

It means the rate of change or slope is decreasing.

Thus, the rate of change or slope m = -50

<u>EXTRA BONUS!</u>

We can also determine the line equation by substituting m = -50 and b = 500 in the slope-intercept form

$y = mx+b$

y = -50x + 500

Here:

The slope m = -50

The y-intercept = 500

3 0

3 years ago

Find the solution to the system of equations given below using substitution. PLEASE ANSWER QUICKLY

irinina [24]

Answer:

option D

D. x = 5, y = 2

Step-by-step explanation:

Given in the question two equation,

Equation 1

5.3x + y = 28.5

Equation 2

4.2x + 3.1y = 27.2

rearrange equation 1 in terms of y

y = 28.5 - 5.3x

Substitute the value of y in equation 2

4.2x + 88.35 - 16.43x = 27.2

4.2x - 16.43x = 27.2 - 88.35

-12.23x = -61.15

x = 61.15/12.23

x = 5

put value of x in any of the equation

y = 28.5 - 26.5

y = 2

5 0

3 years ago

Find the measures of the angles of the triangle whose vertices are A = (-3,0) , B = (1,3) , and C = (1,-3).A.) The measure of ∠A

alekssr [168]

Answer:

$\theta_{CAB}=128.316$

$\theta_{ABC}=25.842$

$\theta_{BCA}=25.842$

Step-by-step explanation:

A = (-3,0) , B = (1,3) , and C = (1,-3)

We're going to use the distance formula to find the length of the sides:

$r= \sqrt{(x_1-x_2)^2+(y_1-y_2)^2+(z_1-z_2)^2}$

$AB= \sqrt{(-3-1)^2+(0-3)^2}=5$

$BC= \sqrt{(1-1)^2+(3-(-3))^2}=9$

$CA= \sqrt{(1-(-3))^2+(-3-0)^2}=5$

we can use the cosine law to find the angle:

it is to be noted that:

the angle CAB is opposite to the BC.

the angle ABC is opposite to the AC.

the angle BCA is opposite to the AB.

to find the CAB, we'll use:

$BC^2 = AB^2+CA^2-(AB)(CA)\cos{\theta_{CAB}}$

$\dfrac{BC^2-(AB^2+CA^2)}{-2(AB)(CA)} =\cos{\theta_{CAB}}$

$\cos{\theta_{CAB}}=\dfrac{9^2-(5^2+5^2)}{-2(5)(5)}$

$\theta_{CAB}=\arccos{-\dfrac{0.62}}$

$\theta_{CAB}=128.316$

Although we can use the same cosine law to find the other angles. but we can use sine law now too since we have one angle!

To find the angle ABC

$\dfrac{\sin{\theta_{ABC}}}{AC}=\dfrac{\sin{CAB}}{BC}$

$\sin{\theta_{ABC}}=AC\left(\dfrac{\sin{CAB}}{BC}\right)$

$\sin{\theta_{ABC}}=5\left(\dfrac{\sin{128.316}}{9}\right)$

$\theta_{ABC}=\arcsin{0.4359}\right)$

$\theta_{ABC}=25.842$

finally, we've seen that the triangle has two equal sides, AB = CA, this is an isosceles triangle. hence the angles ABC and BCA would also be the same.

$\theta_{BCA}=25.842$

this can also be checked using the fact the sum of all angles inside a triangle is 180

$\theta_{ABC}+\theta_{BCA}+\theta_{CAB}=180$

$25.842+128.316+25.842$

$180$

6 0

3 years ago

Read 2 more answers

Need help with 2&3 please .

Vsevolod [243]

Answer:

brainly.com/question/12500028

Step-by-step explanation:

brainly.com/question/12500028

5 0

3 years ago

If the range is 52 and the lowest score is 29, what is the highest score?

shepuryov [24]

Answer:

81

Step-by-step explanation:

Range = maximum - minimum so here, we'd have:

52 = max - 29

Add 29 to both sides to solve.

7 0

3 years ago