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3 years ago

Write the function in vertex form. y=-x^2-8x-9

Mathematics

1 answer:

xeze [42]3 years ago

4 0

Answer:

y = -(x+4)² +7

Step-by-step explanation:

I find it convenient to factor the leading minus sign from the first two terms, then work with what's left.

... y = -(x² +8x) -9

Now, add the square of half the x-coefficient inside parentheses. Add the opposite of that amount outside parentheses.

... y = -(x² +8x +4²) -9 +4²

... y = -(x +4)² +7 . . . . . . . . . rewrite parentheses as a square; collect terms

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How do you simplify this? x²y+xy² / y²+2/5 × xy

polet [3.4K]

$\huge \boxed{\mathbb{QUESTION} \downarrow}$

How do you simplify this?
x²y+xy² / y²+2/5 × xy

$\large \boxed{\mathbb{ANSWER\: WITH\: EXPLANATION} \downarrow}$

$\sf\frac{ { x }^{ 2 } y+x { y }^{ 2 } }{ { y }^{ 2 } + \frac{ 2 }{ 5 } \times xy } \\$

Factor the expressions that are not already factored.

_____

How to factorise :-

NUMERATOR $\downarrow$

$\sf \: x ^ { 2 } y + x y ^ { 2 }$

Factor out xy.

$\sf \: xy\left(x+y\right)$

DENOMINATOR $\downarrow$

$\sf{ y }^{ 2 } + \frac{ 2 }{ 5 } \times xy \\$

Factor out 1/5.

$\sf \: {\frac{1}{5}y\left(2x+5y\right)} \\$

_____

Continuing...

$\sf\frac{xy\left(x+y\right)}{\frac{1}{5}y\left(2x+5y\right)} \\$

Cancel out y in both the numerator and denominator.

$\sf\frac{x\left(x+y\right)}{\frac{1}{5}\left(2x+5y\right)} \\$

Expand the expression.

$\sf\frac{x^{2}+xy}{\frac{2}{5}x+y} \\$

This can further simplified to as $\downarrow$

$= \boxed{\boxed{\bf\frac{5x\left(x +y\right)}{2x+5y}}}$

3 0

3 years ago

Hello I need help thanks!

prisoha [69]

Answer:

$36

Step-by-step explanation:

ok so first you want to find out how much she makes per hour and to do that you would take $27 / 3hrs = $9. So now we know that Kayla makes $9 per hour. If she babysits for 4 hours you would then do $9 x 4hr = $36.

8 0

3 years ago

When does the graph of a quadratic function open upward of downward

sveticcg [70]

It opens upward when X is an even power. It would be for X squared or X raised to the 4th power.

6 0

3 years ago

Every person has blood type O, A, B, or AB. A random group of people are blood-typed, and the results are shown in the table. A

S_A_V [24]

Answer:

3/25 for type B, 1/25 for type AB, and 4/25 for both

Step-by-step explanation:

O goes to 22

A goes to 20

B goes to 6

AB goes to 2

22+20+6+2 = 50, so (number of people with a certain blood type)/50 = the answers for each question.

4 0

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The Table Shows The Number Of Rows Of Bricks A Worker Can Lay In Different Numbers Of Hours

klemol [59]

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3 years ago