All Answers 357301 Answers

h = -16t^2 + 90t = -16(t^2 - 45/8 t) = -16((t - 45/16)^2 - (45/16)^2) = 2025/16 - 16 (t - 45/16)^2

The maximum height of the ball is 2025/16.

(The unit is missing from the question.)

Let L ft be the length of the shorter leg.

Length of longer leg = L + 9

Length of hypotenuse = (L + 9) + 9 = L + 18

By Pythagorean theorem,

L^2 + (L + 9)^2 = (L + 18)^2

2L^2 + 18L + 81 = L^2 + 36L + 324

L^2 - 18L - 243 = 0

(L - 27)(L + 9) = 0

L = 27 or L = -9 (rejected)

Therefore the shorter leg is 27 ft, longer leg is (27 + 9) ft = 36 ft, hypotenuse = (27 + 18) ft = 45 ft.

ty ily

It's actually 29, but thanks for helping! :D

Observe which part of the graph is below the x-axis.

Answer: -2 ≤ x ≤ 3

414 is divisible by 9

=> 414n is divisible by 9

=> 414n + 9 is divisible by 9

414n + 12 = (414n + 9) + 3

414n + 12 is 3 more than a multiple of 9. The required remainder is 3.

Let $\alpha, \beta$ be the roots.

Then the quadratic is $x^2 - (\alpha + \beta)x + \alpha \beta$.

Set $\begin{cases} \alpha = -(\alpha + \beta) - 2\\ \beta = \alpha\beta - 2 \end{cases}$.

Then $\begin{cases} \alpha = \dfrac{-\beta - 2}2\\ \beta = \alpha \beta - 2 \end{cases}$.

Substituting, we have

$\beta = \beta\left(\dfrac{-\beta-2}{2}\right) - 2\\ \beta = -\dfrac{\beta^2}2 - \beta - 2\\ \dfrac{\beta^2}2 + 2\beta + 2 = 0\\ \beta^2 + 4\beta + 4 = 0\\ (\beta + 2)^2 = 0\\ \beta = -2$

Now, $\alpha = \dfrac{-(-2) - 2}2 = 0$

The required quadratic is $x^2 - (0 + (-2))x + 0(-2)$

Simplifying, the required quadratic is $x^2 + 2x$

Let x be the length of CQ. Then DQ = 30 - x.

By power of points,

x(30 - x) = 72

x^2 - 30x + 72 = 0

(x - 15)^2 - 225 + 72 = 0

(x - 15)^2 = 153

$x = 15\pm \sqrt{153}$

Minimum length of CQ = $15 - \sqrt{153}$

You should know how to find u + v and uv.

Hint: u/v + v/u = (u^2 + v^2)/(uv) = ((u + v)^2 - 2uv)/(uv)

The rest is just substituting the values of u + v and uv into the expression.

The sum is 2200.

So you have 4 boxes.

In the first box, you have to choose which ball you want to put in. You have 4 choices.

In the second box, you have to choose which ball you want to put in. This time, you have 3 choices because you already put one in the first box.

In the third box, you choose a ball to put in. Now you only have 2 balls left.

In the final box, you only have one ball left.

Therefore the amount of ways you can distribute these 4 balls is 4x3x2x1=24 ways.

I hope this helps :)

plug in x=5 and see if it works

The equation y = -16t^2 + 28t + 180 describes the height (in feet) of a ball tossed up in the air at 28 feet per second from a height of 180 feet from the ground. In how many seconds will the ball hit the ground?

Hello Guest!

$vt-\dfrac{g}{2}t^2=-180\\ \dfrac{28ft}{s}\cdot t-\dfrac{9.80716.087m}{2\cdot sec^2}\cdot \dfrac{ft}{0,3048037064m}\cdot t^2+180ft=0\\ 28t-16.0874t^2+180=0$

$t=4,326575159634674\ s$

In 4.32 seconds will the ball hit the ground.

  !

I used mass points, and got that [PAB]/[QAB] = 5/4.

You can get 10 pieces.

The answer is (2,-3).

im 99% sure that second guest isnt bestzack66

There are 9*5*5 = 225 three-digit arrows.

sup flec

uhhh i usually dont use this website

but i tried to answer a couple peoples questions

do you know who i am

I think that it is 2^1008. The magnitude is sqrt(1^2 + 1^2), so sqrt(2)^2016 is 2^1008.

Let the number of quarters  =x  and the  number  of  dimes = 10  - x

So

Value of a quarter * their  number +  value of a dime  * their number =  1.45

.25 x  +  .10 (10 -x) =   1.45      simplify

.25x  +  1 - .10x  = 1.45

,25x  -.10x  =  1.45  - 1

.15x =  .45     divide  both sides  by  .15

x = 3  =   the number of quarters

10 - x  = 10 -  3  =  7   =  the number of dimes

10x   + 25(10-x) = 145

-15x = -105

x = dimes = 7

quarters = 10 -x = 3  

Using Quadratic Formula    x = 5/2 ± sqrt(21) / 2

 doing the math results in   x^4 + 1/x^4 = 527    for either of the roots !

The probability is 7/36.

If this has a double root, then the discriminant = 0 ....so....

b^2   - 4(16)(1)  = 0

b^2   -  64  =   0

b^2  = 64      take  both square roots

b =  8        or  b  =   - 8