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2 years ago

Nine less than twice x is three more than x what is the value of x

Mathematics

1 answer:

I am Lyosha [343]2 years ago

5 0

Answer:

Step-by-step explanation:

Nine less than twice x : 2x - 9

Three more than x : x + 3

2x - 9 = x + 3

2x -x - 9 = 3

2x -x = 3 + 9

x = 12

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A ball is thrown into the air from a height of 4 feet at time t = 0. The function that models this situation is h(t) = -16t2 + 6

katrin2010 [14]

Answer:

Part a) The height of the ball after 3 seconds is $49\ ft$

Part b) The maximum height is 66 ft

Part c) The ball hit the ground for t=4 sec

Part d) The domain of the function that makes sense is the interval

[0,4]

Step-by-step explanation:

we have

$h(t)=-16t^{2} +63t+4$

Part a) What is the height of the ball after 3 seconds?

For t=3 sec

Substitute in the function and solve for h

$h(3)=-16(3)^{2} +63(3)+4=49\ ft$

Part b) What is the maximum height of the ball? Round to the nearest foot.

we know that

The maximum height of the ball is the vertex of the quadratic equation

Convert the function into a vertex form

$h(t)=-16t^{2} +63t+4$

Group terms that contain the same variable, and move the constant to the opposite side of the equation

$h(t)-4=-16t^{2} +63t$

Factor the leading coefficient

$h(t)-4=-16(t^{2} -(63/16)t)$

Complete the square. Remember to balance the equation by adding the same constants to each side

$h(t)-4-16(63/32)^{2}=-16(t^{2} -(63/16)t+(63/32)^{2})$

$h(t)-(67,600/1,024)=-16(t^{2} -(63/16)t+(63/32)^{2})$

Rewrite as perfect squares

$h(t)-(67,600/1,024)=-16(t-(63/32))^{2}$

$h(t)=-16(t-(63/32))^{2}+(67,600/1,024)$

the vertex is the point (1.97,66.02)

therefore

The maximum height is 66 ft

Part c) When will the ball hit the ground?

we know that

The ball hit the ground when h(t)=0 (the x-intercepts of the function)

$h(t)=-16t^{2} +63t+4$

For h(t)=0

$0=-16t^{2} +63t+4$

using a graphing tool

The solution is t=4 sec

see the attached figure

Part d) What domain makes sense for the function?

The domain of the function that makes sense is the interval

[0,4]

All real numbers greater than or equal to 0 seconds and less than or equal to 4 seconds

Remember that the time can not be a negative number

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3 years ago

The points plotted below are on the graph of a polynomial. In what range of

Irina-Kira [14]

Answer:

the answer is 0 to 1 and 3 to 4

7 0

2 years ago

What is the area of this triangle?

Lapatulllka [165]

Area is 1/2•b•h so 25

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2 years ago

Jonathan says that when you add

sergij07 [2.7K]

oh ok alr thank you so much

8 0

2 years ago

Ella’s test grades in her history class are 89, 94, 82, 84, and 98. What score must Ella make on her next test to have a mean te

Stells [14]

Answer:

the answer is 93

Step-by-step explanation:

mean of x,y,z

x+y+z

3 terms

(x+y+z)/3=mean

represent next test score as x

89+94+82+84+98+x

count how many terms ther are (6 terms)

mean is 90

(89+94+82+84+98+x)/6=90

add the like terms

(447+x)/6=90

multiply both sides by 6 to clear fraction

447+x=540

subtract 447 from both sides

x=93

4 0

2 years ago