Which expression is equivalent to 5^10 times 5^5?

Suppose f(x)=x^2. what is the graph of g(x)=f(3x)?

Vitek1552 [10]

F(x)=x2,g(x)=f(3x)=(3x)2=9x2Now to graph y=9x2. This is a parabola (U-shape), vertex at (0, 0), symmetric aroung y axis. When x=1/3 or -1/3, then y=1.

3 0

3 years ago

Which is the standard form of the equation of the parabola that has a vertex of (–4, –3) and a directrix of x = 2?

Zielflug [23.3K]

Answer:

Equation of the parabola is $\left(y+3\right)^{2}=-24(x+4)$

Step-by-step explanation:

We have to find the equation of a parabola with vertex is (-4,-3) and a directrix x=2.

As vertex is (-4,-3) that means parabola is in third quadrant.

So the standard formula of the parabola will be y²= -4px through origin (0,0).

But when a parabola is shifted from origin to the left of y axis so the equation will be (y-shifting form y axis)² = -4(distance between vertex and directrix)(x-shifting from x axis)

$\left\{y-(-3)\right\}^{2}=(-4\times 6)\left\{x-(-4)\right\}$

$\left(y+3\right)^{2}=-24(x+4)$ .

5 0

4 years ago

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Star Wars land encompasses an area of 14.0 acres. [1.00 acre = 4046.86m2]. If Star Wars land were made into a circle, what would

Free_Kalibri [48]

Answer:

<h3>The answer is 134.29 m</h3>

Step-by-step explanation:

First of all we need to convert 14.0 acres to m²

1.00 acre = 4046.86 m²

14.0 acres = 14 × 4046.86 = 56656.04 m²

Area of a circle = πr²

where

r is the radius

To find the radius substitute the value for the area into the above formula and solve for the radius

That's

$56656.04 = \pi {r}^{2}$

Divide both sides by π

We have

${r}^{2} = \frac{56656.04}{\pi}$

Find the square root of both sides

$r = \sqrt{ \frac{56656.04}{\pi} }$

r = 134.29139

r = 134.29 m to 2 decimal places

Hope this helps you

3 0

3 years ago

Paul brought $37 to the art supply store. He bought a brush a sketchbook and a paint set. The brush was 1/3 as much as the strec

Lorico [155]

Answer: B = $ 3.25

S = $ 9.75

P = $ 19.5

Step-by-step explanation: Please find the attached file for the solution

8 0

3 years ago

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Complete the statements below that show y = x2 + 2x - 1 being converted to vertex form. Form a perfect-square trinomial. y = x2

marishachu [46]

Solution: The needed answer for first blank is 1 and the needed a for second blank is 1.

Explanation:

The given equation is $y=x^2+2x-1$ .

The form of perfect square is $(x+y)^2=x^2+2xy+y^2$ .

The given equation can be written as $y=(x^2+2x)-1$ .

To make the perfect square we can add or subtract $(\frac{b}{2a})^2$ in the given equation. Where, a is coefficient of $x^2$ and b is coefficient of x. In the parenthesis the coefficient of $x^2$ is 1 and coefficient of x is 2.

$(\frac{b}{2a})^2=(\frac{2}{2(1)})^2=1$

So, the given equation is written as $y=(x^2+2x+1)-1-1$

$y=(x+1)^2-2$

Therefore, the needed answer for first blank is 1 and the needed a for second blank is 1.

4 0

3 years ago

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