NEED HELP ASAP PLEASE

NO LINKS!! Use the method of substitution to solve the system. (If there's no solution, enter no solution). Part 11z

Roman55 [17]

Answer:

$(x,y)=\left(\; \boxed{-1,-8} \; \right)\quad \textsf{(smaller $x$-value)}$

$(x,y)=\left(\; \boxed{5,16} \; \right)\quad \textsf{(larger $x$-value)}$

Step-by-step explanation:

Given system of equations:

$\begin{cases}y=x^2-9\\y=4x-4\end{cases}$

To solve by the method of substitution, substitute the first equation into the second equation and rearrange so that the equation equals zero:

$\begin{aligned}x^2-9&=4x-4\\x^2-4x-9&=-4\\x^2-4x-5&=0\end{aligned}$

Factor the quadratic:

$\begin{aligned}x^2-4x-5&=0\\x^2-5x+x-5&=0\\x(x-5)+1(x-5)&=0\\(x+1)(x-5)&=0\end{aligned}$

Apply the <u>zero-product property</u> and solve for x:

$\implies x+1=0 \implies x=-1$

$\implies x-5=0 \implies x=5$

Substitute the found values of x into the <u>second equation</u> and solve for y:

$\begin{aligned}x=-1 \implies y&=4(-1)-4\\y&=-4-4\\y&=-8\end{aligned}$

$\begin{aligned}x=5 \implies y&=4(5)-4\\y&=20-4\\y&=16\end{aligned}$

Therefore, the solutions are:

$(x,y)=\left(\; \boxed{-1,-8} \; \right)\quad \textsf{(smaller $x$-value)}$

$(x,y)=\left(\; \boxed{5,16} \; \right)\quad \textsf{(larger $x$-value)}$

6 0

1 year ago

Read 2 more answers

Help please!

Alina [70]

Step-by-step explanation:

Given

f(x) = 8x - 9

Then

For a.

f(3y - 1 ) = 8(3y - 1 ) - 9

= 24y - 8 - 9

= 24y - 17

Now for b.

f(x) = - 23

or, 8x - 9 = - 23

8x = - 23 + 9

8x = - 14

x = - 14 / 8

x = - 7 / 4

Hope it will help :)

7 0

3 years ago

What is the volume of the sphere in terms of π? V = π in.3

svlad2 [7]

Answer:

The answer is 288

Step-by-step explanation:

I did the assinment

5 0

3 years ago

Read 2 more answers

Jared has some quarters and dimes that total $5.50. If he has 8 more quarters that dimes, how much dimes does Jared have?

MAXImum [283]

Answer: 10 dimes

Solve using system of equations.
q=number of quarters and d=number of dimes
.25q+.10d=5.50 because the total of dimes and quarters is $5.50
8+d=q because there are 8 more quarters than dimes
substitute 8+d for q into the first equation to get .25(8+d)+.10d=5.50
then simplify
2+.35d=5.50
.35d=3.50
d=10 he has 10 dimes

8 0

4 years ago

Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.

Hatshy [7]

Answer:

The change in the area of the rectangle is 0 square feet

Step-by-step explanation:

To solve this problem we have to calculate the area of the two rectangles that give us

first we have to know the formula to calculate the area of a rectangle

a = area

l = length = 12ft

w = width = 5ft

a = l * w

we replace the known walues

a = 12ft * 5ft

a = 60ft²

we do the same with the other rectangle, but first we have to calculate its sides

w = 5ft - (5ft * 20/100)

w = 5ft - 1ft

w = 4ft

l = 12ft + (12ft * 25/100)

l = 12ft + 3ft

l = 15ft

a2 = 15ft * 4ft

a2 = 60ft²

to calculate the change in the area we subtract (a - a2)

a - a2 =

60ft² - 60ft² = 0ft²

3 0

3 years ago