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sammy [17]
3 years ago
12

Sale price: $32.45 Discount percent: 45%

Mathematics
1 answer:
Ber [7]3 years ago
4 0

Answer:

Original Price: $59

Step-by-step explanation:

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A juggler tosses a ball into the air . The balls height, h and time t seconds can be represented by the equation h(t)= -16t^2+40
malfutka [58]
PART A

The given equation is

h(t) = - 16 {t}^{2} + 40t + 4

In order to find the maximum height, we write the function in the vertex form.

We factor -16 out of the first two terms to get,

h(t) = - 16 ({t}^{2} - \frac{5}{2} t) + 4

We add and subtract

- 16(- \frac{5}{4} )^{2}

to get,

h(t) = - 16 ({t}^{2} - \frac{5}{2} t) + - 16( - \frac{5}{4})^{2} - -16( - \frac{5}{4})^{2} + 4

We again factor -16 out of the first two terms to get,

h(t) = - 16 ({t}^{2} - \frac{5}{2} t + ( - \frac{5}{4})^{2} ) - -16( - \frac{5}{4})^{2} + 4

This implies that,

h(t) = - 16 ({t}^{2} - \frac{5}{2} t + ( - \frac{5}{4}) ^{2} ) + 16( \frac{25}{16}) + 4

The quadratic trinomial above is a perfect square.

h(t) = - 16 ( t- \frac{5}{4}) ^{2} +25+ 4

This finally simplifies to,

h(t) = - 16 ( t- \frac{5}{4}) ^{2} +29

The vertex of this function is

V( \frac{5}{4} ,29)

The y-value of the vertex is the maximum value.

Therefore the maximum value is,

29

PART B

When the ball hits the ground,

h(t) = 0

This implies that,

- 16 ( t- \frac{5}{4}) ^{2} +29 = 0

We add -29 to both sides to get,

- 16 ( t- \frac{5}{4}) ^{2} = - 29

This implies that,

( t- \frac{5}{4}) ^{2} = \frac{29}{16}

t- \frac{5}{4} = \pm \sqrt{ \frac{29}{16} }

t = \frac{5}{4} \pm \frac{ \sqrt{29} }{4}

t = \frac{ 5 + \sqrt{29} }{4} = 2.60

or

t = \frac{ 5 - \sqrt{29} }{4} = - 0.10

Since time cannot be negative, we discard the negative value and pick,

t = 2.60s
8 0
3 years ago
Click or touch the graph to plot the points.
lina2011 [118]

Answer:

the answer is C

Step-by-step explanation:

the y intercept is on the right, so (x, y)

and the third option has (4,8) so 8 is on the y

4 0
3 years ago
Let g(x)=2x and h(x)=x^2+4 find the value. (hog)(a)
lisov135 [29]
In short, (h o g)(a) is just h(    g(a)    ).

so what we can do is simply get g(a) first and then plug that in h(x).

\bf \begin{cases}
g(x)&=2x\\
h(x)&=x^2+4\\
(h\circ g)(a)&=h(~~g(a)~~)
\end{cases}
\\\\\\
g(a)=2(a)\implies g(a)=2a
\\\\\\
h(~~g(a)~~)\implies h(~~2a~~)=(2a)^2+4
\\\\\\
h(~~2a~~)=(2^2a^2)+4\implies  h(~~2a~~)=4a^2+4
8 0
3 years ago
What is equivalent to -3(x-9)
ivolga24 [154]
-3(x-9)=-3\cdot x-3\cdot(-9)=-3x+27
6 0
3 years ago
Read 2 more answers
Use compatible numbers to estimate the quotient. <br> 522 divided by 6 please help!!!
Paladinen [302]
The compatible numbers are 5220 and 60 because 522/6 = 87

I GUESS I AM RIGHT AND I REALLY HOPE THIS HELPS!!!!
3 0
3 years ago
Read 2 more answers
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