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3 years ago

Solve using the guess-and-check strategy.

Mathematics

2 answers:

Nadya [2.5K]3 years ago

7 0

The answer is 12. Matthew would be 12 & Elizabeth would be 7. 12+7=19. So C is your answer.

Ksivusya [100]3 years ago

4 0

The simplest way to do this would be to first subtract 5 from the total, because Matthew is going to be five years older than her.

19 - 5 = 14

14 will divide evenly by 2, making them each 7, but since Matthew is 5 years older, and 5 back to 7 to get his age.

7 + 5 = 12.

Matthew is 12 and Elizabeth is 7. Check your work.

12 + 7 = 19

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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

6 0

3 years ago

2x + 1 ≤ 7 and -2x + 1 ≤ 9

djyliett [7]

Answer:

Step-by-step explanation:

6 0

3 years ago

Complete the calculation.<br> 1,192<br> X 8

Alex17521 [72]

Answer: 9,536 = 1,192 x 8

Step-by-step explanation: 1,192

x 8

——————-

9,536

8 0

3 years ago

The table shows the volume V (in cubic feet) of a cube with a side length of x feet. Does the table represent a linear or nonlin

Reika [66]

Answer:

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3 years ago

Find the area of a regular hexagon with a radius of 6 in

s344n2d4d5 [400]

Hexagon is a total of 6 triangle
Let find area of one triangle the multiplying with 6
Area of a triangle is A=1/2bh
We know b=6 and h= (6(square root of 3))/2
A= 1/2x6x(6(square root of3))/2=9(square root of 3)
Where square root of 3= 1.732
Area of a triangle=9x1.732 =15.588
Area of Hexagon equals 6 area of triangle so
Area of Hexagon= 6x 15.588=93.53

4 0

4 years ago