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3 years ago

5

Round your answer to the nearest hundredth 4.) A basketball is passed through the air. The height h of the ball in feet after th

e distance d In teet the ball travels horizontally is given by h= - + 124 + 6. How tar horizontally from the player passing the ball will the ball land on the ground? I

1 answer:

Leona [35]3 years ago

3 0

Answer:

10.48 feet

Step-by-step explanation:

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(07.01)<br> What is the 24th term of the arithmetic sequence where a1 = 8 and ag = 56?

san4es73 [151]

the 24th term of the arithmetic is 146

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3 years ago

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What is the value of 2x4 + 5x when x=6?

wlad13 [49]

This would be 2(6)^4 + 5*6

= 2592 + 30

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2 years ago

What would y=x^2 +x+ 2 be in vertex form

balu736 [363]

Answer:

$y = (x + \frac{1}{2} )^{2} + \frac{7}{4}$

Step-by-step explanation:

$y = {x}^{2} + x + 2$

We can covert the standard form into the vertex form by either using the formula, completing the square or with calculus.

$y = a(x - h)^{2} + k$

The following equation above is the vertex form of Quadratic Function.

<u>Vertex</u><u> </u><u>—</u><u> </u><u>Formula</u>

$h = - \frac{b}{2a} \\ k = \frac{4ac - {b}^{2} }{4a}$

We substitute the value of these terms from the standard form.

$y = a {x}^{2} + bx + c$

$h = - \frac{1}{2(1)} \\ h = - \frac{ 1}{2}$

Our h is - 1/2

$k = \frac{4(1)(2) - ( {1})^{2} }{4(1)} \\ k = \frac{8 - 1}{4} \\ k = \frac{7}{4}$

Our k is 7/4.

<u>Vertex</u><u> </u><u>—</u><u> </u><u>Calculus</u>

We can use differential or derivative to find the vertex as well.

$f(x) = a {x}^{n}$

Therefore our derivative of f(x) —

$f'(x) = n \times a {x}^{n - 1}$

From the standard form of the given equation.

$y = {x}^{2} + x + 2$

Differentiate the following equation. We can use the dy/dx symbol instead of f'(x) or y'

$f'(x) = (2 \times 1 {x}^{2 - 1} ) + (1 \times {x}^{1 - 1} ) + 0$

Any constants that are differentiated will automatically become 0.

$f'(x) = 2 {x}+ 1$

Then we substitute f'(x) = 0

$0 =2x + 1 \\ 2x + 1 = 0 \\ 2x = - 1 \\x = - \frac{1}{2}$

Because x = h. Therefore, h = - 1/2

Then substitute x = -1/2 in the function (not differentiated function)

$y = {x}^{2} + x + 2$

$y = ( - \frac{1}{2} )^{2} + ( - \frac{1}{2} ) + 2 \\ y = \frac{1}{4} - \frac{1}{2} + 2 \\ y = \frac{1}{4} - \frac{2}{4} + \frac{8}{4} \\ y = \frac{7}{4}$

Because y = k. Our k is 7/4.

From the vertex form, our vertex is at (h,k)

Therefore, substitute h = -1/2 and k = 7/4 in the equation.

$y = a {(x - h)}^{2} + k \\ y = (x - ( - \frac{1}{2} ))^{2} + \frac{7}{4} \\ y = (x + \frac{1}{2} )^{2} + \frac{7}{4}$

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3 years ago

Janet's Junk Shop is having its annual sale. Matt wants to buy a mixer that originally sold for $28.62 and is now on sale for of

Free_Kalibri [48]

$n\% \:\:off = (100 -n)\% \:\: of \:the\: original \:price$
$FinalPrice =$
$(Original Price \times(\frac{100\% - Discount}{100\%}))\times(\frac{100\% - Discount_2}{100\%}) =$
$\big(\$28.62\times(\frac{100\% - 25\%}{100\%})\big) \times(\frac{100\% - 15\%}{100\%}) =$
$\big(\$28.62\times(\frac{3}{4})\big) \times(\frac{17}{20}) \approx \$18.25$

Matt will pay $\$18.25$ for the mixer

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3 years ago

Jamie ordered 24 combo meals for $5 each for a party. The service charge for home delivery for the whole purchase was $6.

Alex17521 [72]

Ok so we know that each combo meal is $5. So 24 x 5 = $120
$6 service charge has to be divided by 120.
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5%

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2 years ago