All categories

3 years ago

Solve the system y = -x + 7 and y = 0.5(x - 3)2 explain the answer

Mathematics

1 answer:

ehidna [41]3 years ago

4 0

Answer:

x=5, x=-1

Step-by-step explanation:

Since both equations are equal to y, we can set them equal to each other

y = -x + 7 and y = 0.5(x - 3)2

-x + 7 = 0.5(x - 3)^2

Distribute the right hand side by Foiling

-x+7 =.5 ( x^2 -3x-3x+9)

Combine like terms

-x+7 = .5( x^2 -6x+9)

Distribute the .5

-x+7 = .5x^2 -3x+4.5

Add x to each side

-x+x+7 = .5x^2 -3x+x+4.5

7 = .5x^2 -2x+4.5

Subtract 7 from each side

7 -7= .5x^2 -2x+4.5-7

0 = .5x^2 -2x-2.5

Multiply by 2 to clear the decimals

0 = x^2 -4x -5

Factor

0 = (x-5) (x+1)

Using the zero product property

x-5=0 x+1 =0

x=5, x=-1

You might be interested in

Use function notation to represent the area of a circle whose circumference is 136cm

Nimfa-mama [501]

Answer:

$A(\frac{68}{\pi})=\frac{4624}{\pi}$

Step-by-step explanation:

The given circle has circumference 136cm.

The formula for circumference is $C=2\pi r$

This implies that:

$136=2\pi r$

$\frac{136}{2\pi}=r$

$\frac{68}{\pi}=r$

The area of a circle is given as $A(r)=\pi r^2$

When $r=\frac{68}{\pi}$

$A(\frac{68}{\pi})=\pi*(\frac{68}{\pi})^2$

$A(\frac{68}{\pi})=\pi*\frac{(68)^2}{\pi^2}$

$A(\frac{68}{\pi})=\frac{4624}{\pi}$

7 0

3 years ago

What is the factored form of 8X^2 +12X?

pogonyaev

The highest common factor of both terms is 4x, so take this out by dividing each term by 4x

8x^2 / 4x = 2x
12x / 4x = 3

So the factored form is:
4x(2x+3)

8 0

3 years ago

A bacteria culture begins with eight bacteria which triple in size every week. how many bacteria exist in the culture after four

bija089 [108]

Well, you would have to multiply 8 by whatever factorial of 3, in this case 4 for the number of weeks
The equation is 8 x 3^4 which equals 648

My only thing is that they only triple in SIZE, and not multiply (as in make more of themselves) so technically speaking, there would still be 8 bacteria, just much bigger

3 0

4 years ago

1 ten and 15 ones in word

wolverine [178]

25 in total what do you mean

4 0

4 years ago

Samir bought 3 pounds of cement to repair the cracks in his sidewalk.

r-ruslan [8.4K]

Answer:

16oz=1lbs

First you need to see how many ounces equals three pounds, so you wanna go 16*3=48

You bought 48 ounces

You now take 48/2=24

You can fill 24 cracks with 3 pounds of cement

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers