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3 years ago

Which choice is equivalent to (4^2)(4^3)? A: 4^6 B:4^5 C:64 D:16

2 answers:

6 0

B. 4^5

When multiplying exponents with the same base, you can simply add them together and keep the base the same.
Many people accidentally multiply the exponents, so just be cautious of that :) hope this helps

Taya2010 [7]3 years ago

3 0

Correct me if i'm wrong, but i think it's b, since you add the exponents and keep the 4 the same.

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A model rocket is launched with an initial velocity of 200 ft per second. The height h, in feet, of the rocket t seconds after t

Solnce55 [7]

Answer:

2.10 s, 10.40 s.

Step-by-step explanation:

We know that the height of the rocket is given by the function:

$h=-16t^2+200t$

We are asked to find the time for which the height of the rocket will be 350 ft. So, for that moment, we know the height but we don't know the time; however, we know that the equation can help us to find the time, doing h=350:

$350=-16t^2+200t$

The last is a quadratic equation, which can be put in the form $at^2+bt+c=0$ and solved applying the formula:

$t=\frac{-b+-\sqrt{b^2-4ac} }{2a}$

So, let's put the equation on the form $at^2+bt+c=0$ adding $16t^2$ and subtracting $200t$ to each side of the equation; the result is:

$16t^2-200t+350=0$

So, we note that a=16, b=-200, and c=350.

Then,

$t_1=\frac{200-\sqrt{200^2-4*16*350} }{2*16}=2.10$

$t_2=\frac{200+\sqrt{200^2-4*16*350} }{2*16}=10.40$

According to the equation, that are the times for which the height will be 350 ft; that is because the rocket is going to ascend and then to fail again to the ground.

4 0

3 years ago

A car's wheels spins at 1000 revolutions per minute. The diameter of the wheels is 23 inches. You want to know how fast the car

ch4aika [34]

Answer:

72,220 inches per minute

Step-by-step explanation:

A car's wheels spins at 1000 revolutions per minute. The diameter of the wheels is 23 inches.

1 revolution = $2\pi$ radians

$\frac{theta}{tome}=\frac{1000 \ revolution}{1 \ minuite} = \frac{1000* 2\pi }{1} =\frac{2000\pi}{1 \ minute}$

Speed $V= \frac{r*theta}{t}$

r is the radius , theta is the angle and t is the time

We know diameter = 23 , then radius = 23/2

Speed $V= \frac{23}{2}*\frac{2000\pi}{1}$

Value of pi = 3.14

speed = 23000* 3.14= 72220 inches/ minute

3 0

3 years ago

Read 2 more answers

What is the solution of ?<img src="https://tex.z-dn.net/?f=%5Cfrac%7B5%7D%7B2%7D%20x-7%3D%5Cfrac%7B3%7D%7B4%7D%20x%2B14" id="Tex

Nonamiya [84]

Combine the terms by multiplying into a single fraction.

$\bf{\dfrac{5}{2}x-7=\dfrac{3}{4}x+14 }$

Find the common denominator.

$\bf{\dfrac{5x}{2}-7=\dfrac{3}{4}x+14 }$

Combine fractions with the lowest common denominator.

$\bf{\dfrac{5x(-7)}{2}=\dfrac{3}{4}x+14 }$

Multiply the numbers.

$\bf{\dfrac{5x-14}{2}=\dfrac{3}{4}x+14 }$

Combine the multiplied terms into a single fraction

$\bf{\dfrac{5x-14}{2}=\dfrac{3x}{4}+14 }$

Find the common denominator.

$\bf{\dfrac{5x-14}{2}=\dfrac{3x}{4}+\dfrac{4\cdot14}{4} }$

Combine fractions with the lowest common denominator.

$\bf{\dfrac{5x-14}{2}=\dfrac{3x+4\cdot14}{4} }$

Multiply the numbers.

$\bf{\dfrac{5x-14}{2}=\dfrac{3x+56}{4} }$

Eliminate the denominators of the fractions.

$\bf{4\cdot\dfrac{5x-14}{2}=4\cdot\dfrac{3x+56}{4} }$

Cancel the multiplied terms that are in the denominator.

$\bf{2(5x-14)=3x+56}$

To distribute.

$\bf{10x-28=3x+56 }$

Add 28 to both sides.

$\bf{10x-28+28=3x+56+28 }$

Simplify

$\bf{10x=3x+84 }$

Subtract 3x from both sides.

$\bf{10x-3x=3x+84-3x }$

Simplify

$\bf{7x=84 }$

Divide both sides by the same factor.

$\bf{x=\dfrac{84}{7} }$

Simplify

$\bf{x=12 \ \ \ === > \ \ \ Answer}$

↓

<h3>Verification</h3>

Let x=12.

$\bf{\dfrac{5}{2}\times12-7=\dfrac{3}{4}\times12+14 }$
$\bf{\dfrac{5\times12}{2}-7=\dfrac{3}{4}\times12+14 }$
$\bf{\dfrac{60}{2}-7=\dfrac{3}{4}\times12+14 }$
$\bf{30-7=\dfrac{3}{4}\times12+14 }$
$\bf{30-7=\dfrac{3\times12}{4}+14 }$
$\bf{30-7=\dfrac{36}{4}+14 }$
$\bf{30-7=9+14 }$
$\bf{23=9+14 }$
$\bf{23=23}$

Checked ✅

3 0

2 years ago

A parabola can be drawn given a focus of (6,-1) and a directrix of y = 9. What can be said about the parabola?

zavuch27 [327]

Answer:

Since the focus is at (-6,-11) and the directrix is at y=9:

The vertex is halfway between the focus and the directrix, so the vertex is at (-6,-1). (Draw this on graph paper if that doesn't make sense.)

The general form (conics form) of a parabola: 4p(y-k)=(x-h)^2 (vertex is (h,k) and "p" is the distance between the focus and vertex (or between vertex and directrix)).

(h,k) = (-6,-1)

p = 10 (distance between focus and vertex), so 4p = 40.

Therefore:

40(y+1)=(x+6)^2

Or if you need to rearrange to "vertex form": y=(1/40)(x+6)^2 - 1

Step-by-step explanation:

3 0

3 years ago

Which of the following relations is a function?

Rudik [331]

Answer:

Ans. C

Step-by-step explanation:

every domain has different image in C.

5 0

3 years ago

Read 2 more answers