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3 years ago

What is the simplet form of 7 — 12?

Mathematics

1 answer:

inysia [295]3 years ago

6 0

Answer:

-5

Step-by-step explanation:

7−12

=7−12

=7+−12

=−5

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the vertex of this parabola is at (-5,-2). when the x-value is -4, the y-value is 2. what is the coefficient of the squared term

Anon25 [30]

Answer:

<u>First case</u> The coefficient of the squared term is 4

<u>Second case</u> The coefficient of the squared term is 1/16

Step-by-step explanation:

I will analyze two cases

First case (vertical parabola open upward)

we know that

The equation of a vertical parabola in vertex form is equal to

$y=a(x-h)^{2}+k$

where

a is the coefficient of the squared term

(h,k) is the vertex

we have

(h,k)=(-5,-2)

substitute

$y=a(x+5)^{2}-2$

Find the value of a

Remember that

when the x-value is -4, the y-value is 2.

substitute

For x=-4, y=2

$2=a(-4+5)^{2}-2$

$2=a(1)-2$

$a=2+2=4$

the equation is equal to

$y=4(x+5)^{2}-2$

therefore

The coefficient of the squared term is 4

Second case (horizontal parabola open to the right)

we know that

The equation of a horizontal parabola in vertex form is equal to

$x=a(y-k)^{2}+h$

where

a is the coefficient of the squared term

(h,k) is the vertex

we have

(h,k)=(-5,-2)

substitute

$x=a(y+2)^{2}-5$

Find the value of a

Remember that

when the x-value is -4, the y-value is 2.

substitute

For x=-4, y=2

$-4=a(2+2)^{2}-5$

$-4=a(4)^{2}-5$

$-4+5=a(16)$

$a=1/16$

the equation is equal to

$x=(1/16)(y+2)^{2}-5$

therefore

The coefficient of the squared term is 1/16

to better understand the problem see the attached figure

8 0

3 years ago

Please help me with this problem!!!

Lilit [14]

$3 {}^{4x - 5} = ( \frac{1}{27} ) {}^{2x + 10} \\ note \: \: that = \\ ( \frac{1}{27} ) = ( \frac{1}{3 {}^{3} } ) = 3 {}^{ - 3} \\ \\ 3 {}^{4x - 5} = (3 {}^{ - 3} ) {}^{2x + 10} \\ 3 {}^{4x + 5} = 3 {}^{ - 3(2x + 10)} \\ equal \: \: bases = > equal \: exponents$