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dezoksy [38]
3 years ago
7

The path of a baseball after it has been hit is modeled by the function h = – 0.0032d2 + d + 3, where h is the height in feet of

the baseball and d is the distance in feet the baseball is from home plate. What is the maximum height reached by the baseball? How far is the baseball from home plate when it reaches its maximum height?
Mathematics
1 answer:
aleksandr82 [10.1K]3 years ago
8 0

Answer:

the maximum height of the ball is 81.125 feet above the ground. when the ball is at its peak, the ball is 156.25 feet away from home plate.

Step-by-step explanation:

x = d

y = h

to find the x coordinate of the vertex of a parabola, use the equation

x = -b/2a

y = ax^2 + bx+ c

y = – 0.0032x^2 + x + 3

x = -1 / 2 • - 0.0032

x = 156.25

plug x into original equation to find the the y coordinate of the vertex

y = – 0.0032 • (156.25)^2 + (156.25) + 3

y = – 0.0032 • 24414.0625 + 159.25

y = – 78.125 + 159.25

y = 81.125

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Alexxx [7]

Answer: true because that’s what you get when you use the distributive property

Step-by-step explanation:

8 0
3 years ago
A paint-store chain produces and sells latex and semigloss paint. Based on long-range sales, the probability that a customer wil
Flauer [41]

Answer:

The probability that the paint  latex = 0.857

Step-by-step explanation:

From the given information:

Let consider X to be the event that the customer has purchased the latex paint

Let consider Y to be the event that the customer has purchased semigloss paint.

Now, the probability of X i.e. P(X) = 0.75

SInce X and Y are mutually exhaustive)

P(Y) = 1 - P(X)

P(Y) = 1 - 0.75

P(Y) = 0.25

Similarly, Let Consider Z be the event that the customer has purchased a roller.

We are being told that P(Z|X) = 0.6

P(Z|Y) = 0.30

P(X|Z) = \dfrac{P(Z|X)(P(X) }{P(Z|X)*P(X)+P(Z|Y)*P(Y)}

P(X|Z) = \dfrac{0.6 \times 0.75 }{(0.6 \times 0.75) +(0.3 \times 0.25)}

P(X|Z) = \dfrac{0.45 }{(0.45) +(0.075)}

P(X|Z) = \dfrac{0.45 }{0.525}

P(X|Z) = 0.857

Thus, the probability that the paint  latex = 0.857

4 0
3 years ago
CONSTRUCT ARGUMENTS Consider three points, (3, 7), (−6, 1), and (9, p) on the same line. Find the value of p. Justify your argum
gladu [14]

Answer:

p=11

Step-by-step explanation:

let A(3,7),B(-6,1),C(9,p) be the points.

or

B(-6,1),A(3,7),C(9,p) are the points in the same line.

let A divides BCin the ratio k:1

3=\frac{9k+1(-6)}{k+1} \\3k+3=9k-6\\3k-9k=-6-3\\-6k=-9\\k=\frac{-9}{-6} =\frac{3}{2}  \\so~ratio~is~\frac{3}{2} :1\\or\\3:2\\again\\7=\frac{3p+2(1)}{3+2} \\5*7=3p+2\\3p=35-2=33\\p=\frac{33}{3} =11

3 0
3 years ago
The sum of five times a number, and 1, is equal to four times the number
larisa86 [58]

Answer:

5x + 1 = 4x

You can really put any letter for "a number":

5n + 1 = 4n

7 0
3 years ago
9. The temperature of a liquid that is increasing can be represented by the equation
34kurt

Answer:

92°F

Step-by-step explanation:

in degrees Fahrenheit,

t=7

f(7)=64 + 4(7)

=92

6 0
3 years ago
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