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melomori [17]
3 years ago
9

6 points

Mathematics
1 answer:
kodGreya [7K]3 years ago
8 0

Answer:

y=-2\,(x+3)^2-3

Step-by-step explanation:

Notice that they are asking you to write the equation of the parabola in vertex form, that is using the coordinates of the vertex (x_v,y_v) in the expression:

y-y_v=a\,(x-x_v)^2\\y=a\,(x-x_v)^2+y_v

we can start by directly replacing the given vertex coordinates (-3, -3) in the expression, and then using the extra info on the point the parabola goes through in order to find the parameter a:

y=a\,(x-x_v)^2+y_v\\y=a\,(x+3)^2+(-3)\\y=a\,(x+3)^2-3\\-5=a\,(-2+3)^2-3\\-5=a\,(1)-3\\a=-5+3\\a=-2

So, now we can write the full expression for the parabola:

y=a\,(x+3)^2-3\\y=-2\,(x+3)^2-3

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Match each power of a power expression with its simplified expression.
VARVARA [1.3K]

Answer:

> (4^6)^{-3} = \frac{1}{4 ^ {18}}

> (4^{-3})^{-3} = 4 ^ 9

> (4^0)^{-9} = 4 ^0

> (-4^{-9})^2 = (-4) ^ {-18}

Step-by-step explanation:

We have to expand the powers of each of them:

> (4^6)^{-3} = 4^{(6 * -3)}

          = 4 ^ {-18}

(4^6)^{-3} = \frac{1}{4 ^ {18}}

> (4^{-3})^{-3} = 4 ^ {(-3 * -3)}

  (4^{-3})^{-3} = 4 ^ 9

> (4^0)^{-9} = 4 ^ {(0 * -9)}

  (4^0)^{-9} = 4 ^0

> (-4^{-9})^2 = -4 ^ {( -9 * 2)}

  (-4^{-9})^2 = -4 ^ {-18}

8 0
3 years ago
Read 2 more answers
Below an equation is modeled . What value of x makes this equation true?
Strike441 [17]
5x + 6 = 1
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5x = -5
Divide from both sides.
x = -1 (ANSWER)

hope this helps!!
5 0
3 years ago
Please Help? A circle has an arc length of 5π in. The central angle for this arc measures π/3 radians. What is the area of the a
Zielflug [23.3K]

Answer:

The area of the associated sector is \frac{25}{24}\pi \ in^{2}  

Step-by-step explanation:

step 1

Find the radius of the circle

we know that

The circumference of a circle is equal to

C=2\pi r

we have

C=5\pi\ in

substitute and solve for r

5\pi=2\pi r

r=2.5\ in

step 2

Find the area of the circle

we know that

The area of the circle is equal to

A=\pi r^{2}

we have

r=2.5\ in

substitute

A=\pi (2.5^{2})=6.25\pi\ in^{2}

step 3

Find the area of the associated sector

we know that

2\pi\ radians subtends the complete circle of area 6.25\pi\ in^{2}

so

by proportion

Find the area of a sector with a central angle of \pi/3\ radians

\frac{6.25\pi }{2\pi} =\frac{x}{\pi/3}\\x=6.25*(\pi/3)/2\\ \\x=\frac{25}{24}\pi \ in^{2}

8 0
3 years ago
Please help!!!
Evgesh-ka [11]
D because you need to make the denominators have a common multiple.
5 0
2 years ago
TEMA: Propriedade de Potência e Multiplicação de Números Negativos e Positivos.
GalinKa [24]
The correct answer is 34
7 0
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