X and Y intercepts of y=1/3x

Which of the following is a factor of 64x^3 +343

Lyrx [107]

Answer:

(4x + 7) or

(16x^2 - 28x + 49)

Step-by-step explanation:

This is the sum of cubes. If you have choices you really should list them because often the way we write answers is not in agreement with what you are given.

Step One

Factor 64x^3 and 343 into prime factors.

64x^3: 4*4*4*x * x *x

343: 7 * 7 * 7

Step Two

Factor using the sum of cubes.

(4x + 7)([4x]^2 - 7*4x + 7^2)

(4x + 7)(16x^2 - 28x + 49)

7 0

3 years ago

Read 2 more answers

Find the slope of the line shown

Oduvanchick [21]

Answer:

<h2>The slope m = -1</h2>

Step-by-step explanation:

Look at the picture.

The formula of a slope:

$m=\dfrac{y_2-y_1}{x_2-x_1}$

From the graph we have the points (-5, 2) and (-3, 0). Substitute:

$m=\dfrac{0-2}{-3-(-5)}=\dfrac{-2}{2}=-1$

8 0

3 years ago

A person is standing close to the edge on a 56 foot building and throws the ball vertically upward. The quadratic function h(t)=

Romashka [77]

Answer:

Part 1)

225 feet.

Part 2)

7 seconds.

Step-by-step explanation:

The height h(t) of the ball above the ground after t seconds is modeled by the function:

$h(t)=-16t^2+104t+56$

Part 1)

We want to determine the maximum height of the ball.

Notice that the function is a quadratic with a negative leading coefficient, so its maximum will be at its vertex point.

The vertex of a parabola is given by:

$\displaystyle \text{Vertex} = \left(-\frac{b}{2a}, f\left(-\frac{b}{2a}\right)\right)$

In this case, a = -16, b = 104, and c = 56.

Find the x- (or rather t-) coordinate of the vertex. So:

$\displaystyle t=-\frac{(104)}{2(-16)}=\frac{104}{32}=\frac{13}{4}=3.25\text{ seconds}$

In other words, the ball reaches its maximum height after 3.25 seconds.

To find the maximum height, substitute this value back into the function. Hence:

$\displaystyle h(3.25)=-16(3.25)^2+104(3.25)+56=225\text{ feet}$

The maximum height of the ball is 225 feet in the air.

Part 2)

We want to find the amount of time it took for the ball to hit the ground.

When the ball hit the ground, its height above the ground is zero. Therefore, we can set h(t) to 0 and solve for t:

$0=-16t^2+104t+56$

We can simplify a bit. Divide both sides by -8:

$0=2t^2-13t-7$

We can factor. Find two numbers that multiply to 2(-7) = -14 and add to -13.

-14 and 1 works! Therefore, split the second term into -14 and 1:

$\displaystyle 0=2t^2-14t+t-7$

Factor out a 2t from the first two terms and group the last two terms:

$0=2t(t-7)+(t-7)$

Factor by grouping:

$0=(2t+1)(t-7)$

Zero Product Property:

$2t+1=0\text{ or } t-7=0$

Solve for each case:

$\displaystyle t=-0.5\text{ or } t=7$

Since time cannot be negative, we can ignore the first case.

Therefore, it takes seven seconds for the ball to hit the ground.

6 0

3 years ago

In the set of ordered pairs a function?

MakcuM [25]

Answer:

because each output has exactly one input

3 0

3 years ago

After college you start a job earning $40,000 a year. You get a 6% raise each year.

alex41 [277]

Answers: A) $44,944
B) $50,499.0784

Math: Using the percentage calculator linked below 6% of $40,000 is $2,400. Since you're getting your second raise after your first and since it is a 6% raise from what you're getting paid at that time we add pay raise 1 to your starting pay before calculating the 6% for pay raise 2. $40,000+$2,400=$42,400. 6% of $42,400 is $2,544. $42,400+$2,544=$44,944, Since that is two pay raises that would be your earnings at the end of year two (answer A).
We continue calculating 6% then adding that onto the total before calculating it for the next year for problem B.
6% of $44,944 is $2,696.64. $44,944+$2,696.64=$47,640.64.
6% of $47,640.64 is $2,858.4384. $47,640.64+$2,858.4384=$50,499.0784. That's answer B.

Hopefully you can figure out C on your own! I feel a little bad for giving a partial answer but I think you can do this!

Percentage calculator used-https://percentagecalculator.net/
Note: can't handle commas, remove all commas before entering data in.

7 0

3 years ago