Mateo is doing an experiment for Physics class. He drops a bouncy ball off abalcony from a height of 12 meters. The ball's next bounce is always 75% of
the height of the previous bounce. Let n = bounce number. Before the ball is
dropped, n = 0, because the ball has not yet bounced. Which explicit formula
represents the height of the ball after n bounces?

Answers

Answer 1

Answer:

Final answer:

The height of the ball after n bounces is given by the formula a_n = 12 * 0.75^(n - 1). This formula represents a geometric sequence where each height is 75% of the previous height.

Explanation:

The height the bouncy ball reaches after each bounce is a geometric sequence, where each subsequent height is found by multiplying the previous height by the common ratio, 75%, or 0.75. The initial term is the original height from which the ball is dropped, which is 12 meters.

The explicit formula for a geometric sequence is a_n = a_1 * r^(n - 1). Replacing a_1 with 12 (the initial height), r with 0.75 (the common ratio), and n with the bounce number, the explicit formula to find the height of the ball after n bounces is a_n = 12 * 0.75^(n - 1).

Learn more about Geometric Sequence here:

brainly.com/question/34721734

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Answer 2

Answer:

Answer:

Max. height following bounce # n is 12(¾)n because each prior height is multiplied by three fourths.

Step-by-step explanation: it jus is

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9/35 x 7/16 x 20/21 =

show work

Answers

$(9)/(35)\cdot(\not7^1)/(16)\cdot(20)/(\not21_3)=(9)/(35)\cdot(1)/(\not16_4)\cdot(\not20^5)/(3)=(\not9^3)/(35)\cdot(1)/(4)\cdot(5)/(\not3_1)=(3)/(\not35_7)\cdot(1)/(4)\cdot(\not5^1)/(1)\n\n=(3)/(7)\cdot(1)/(4)\cdot(1)/(1)=(3\cdot1\cdot1)/(7\cdot4\cdot1)=(3)/(28)$

Isosceles triangle with one angle of 100. What would most likely be the other angles?

Answers

Isoceles triangles have one pair of congruent base angles opposite their congruent sides. Also, the angles in a triangle add up to 180°. Therefore, we can set up this equation:

100 + x + x = 180

(we know it's not the 100° angle that has a congruent match because that would cause the total angle measure to go above 180°)

100 + 2x = 180
Subtract 100 from each side.
2x = 80
Divide by 2.
x = 40°

Both of the other angles would be 40°.

There's no "most likely" about it.

==> Every isosceles triangle has two equal angles.
==> In this one, the 100-degrees angle is either one of the two equal angles,
or else it isn't.
==> If the 100 is one of the two equal angles, then the other one is also 100,
and the sum of the angles in this triangle ... even without the third one ...
is already more than 180 degrees.
==> So the 100 CAN'T be one of the equal angles. It must be the third angle.

-- Now there are 80 degrees left over to split between the other two angles,
which ARE equal.

-- The other two angles, which are not 100 degrees, MUST be 40 degrees each.

Not probably, not maybe, not could-be, and not "most likely". They must be.

1000 calls received 15% not answered

Answers

A really easy one, just divide the number of calls, 1000, by 15 to get the number of calls unanswered, which is 150. Also, if 150 is taken from 1000, you get the total answered calls via subtraction, which is 850.

Which is a solution to (x – 3)(x + 9) = –27?

x = –9
x = –3
x = 0
x = 6

Answers

If you would like to solve (x – 3)(x + 9) = –27, you can do this using the following steps:

(x – 3)(x + 9) = –27
x^2 + 9x - 3x - 27 = -27
x^2 + 6x - 27 + 27 = 0
x^2 + 6x = 0
x * (x + 6) = 0
1. x = 0
2. x = -6

The correct result would be x = 0.

By evaluating the quadraticexpression at each realnumber, we conclude that x = 0 is a solution (root) to (x - 3) · (x + 9) = -27. (Correct choice: C)

How to find the roots of a given polynomic expression

In this question we must find a solution for a polynomicexpression. There are several approaches to find them. Since we have a polynomicexpression as a product of binomials, we can determine the solution by evaluating at each choice:

x = 0

(0 - 3) · (0 + 9) = -27

(-3) · 9 = -27

-27 = -27

By evaluating the quadraticexpression at each realnumber, we conclude that x = 0 is a solution (root) to (x - 3) · (x + 9) = -27. (Correct choice: C)

To learn more on quadratic functions: brainly.com/question/5975436

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You are building a rectangular deck. The area of the deck should be 250 ft.² . You want the lengths of the deck to be 5 feet longer than twice its width. What should the dimensions of the deck be?

Answers

et the width be x
"the length of the deck to be 5 ft longer than twice its width" --- >length = 2x+5

then
x(2x+5) = 250
2x^2 + 5x - 250 = 0
(x - 10)(2x + 25) = 0
x = 10 or x is a negative, which makes no sense

width = 10
length = 25

check:
is the length 5 more than twice the width ?? yes
is the area 250 ? yes

0.083 repeding as a percentage?

Answers

0.083 as a percentage would be 8.3% with a horizontal bar on top of the three to indicate that it is repeating.

To find percentage, multiply a decimal by 100.

Hope it helps

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