Mathematics Middle School

The function y= -16t^2 +24t represents the height y (in feet) of a tennis ball bouncing straight up from the ground t seconds after it bounces. After how many seconds does the tens ball return to the ground?

Answers

Answer 1

Answer:

-16t² + 24t = 0

-8t(2t - 3) = 0

t = 1.5 seconds

The tennis ball returns to the ground in 1.5 seconds.

Answer 2

The tennis ball returns to the ground after [tex]$\frac{3}{2}$[/tex] seconds.

To find when the tennis ball returns to the ground, you need to determine when the height y is equal to zero. In the given function [tex]y = -16t^2 + 24t\)[/tex], set y equal to zero and solve for t:

[tex]\[ -16t^2 + 24t = 0 \][/tex]

Factor out 8t from both terms:

[tex]\[ 8t(-2t + 3) = 0 \][/tex]

Now, set each factor equal to zero:

1. 8t = 0: This gives t = 0.

2. -2t + 3 = 0: Solve for t.

[tex]\[ -2t = -3 \][/tex]

Divide both sides by -2:

[tex]\[ t = \frac{3}{2} \][/tex]

So, the two solutions are t = 0 and [tex]$t = \frac{3}{2}$[/tex]. However, $t = 0$ corresponds to the initial bounce, and we are interested in the time it takes for the ball to return to the ground after the first bounce.

Therefore, the tennis ball returns to the ground after [tex]$\frac{3}{2}$[/tex] seconds.

Related Questions

Need help with 3 and 4.

Answers

A) Problem 3

Answer: third option 11.5

Explanation:

1) Since this is a right triangle you can use the trigonometric ratios.

2) sin (α) = opposite-leg / hypotenuse

3) α = 35°; opposite-lge = x; hypotenuse = 20.

4) substitute values

sin(35°) = x / 20

5) Solve for x

x = 20 * sin (35°) = 11.47

6) Round to the nearest tenth: 11.5

Answer: third option 11.5

B) Problem 4

Answer: first option 8.3

Explanation:

1) Since it is a right triangle you can use trigonometric ratios

2) cos (α) = adjacent - leg / hypotenuse

3) α = 41°; adjacent - leg = x; hypotenuse = 11

4) Substitute values

cos (41°) = x / 11

5) Solve for x: x = 11 * cos (41°) = 8.30

6) Round to the nearest tenth: x = 8.3

Answer: 8.3

A square tile with sides of length 1 ft is divided into 4 equal sections as shown.

Write a multiplication equation showing how to calculate the area of the shaded square portion of the tile in square feet using fractions. Explain what each part of the multiplication represents in terms of the shaded square.

Answers

The shaded part represents 1/4 of the whole square, of which the area is 4/4 (1) ft^2. So, you need to find out 1/4 of 4/4. This can be done by doing 4/4 × 1/4 = 4/16 = 1/4. Therefore, the smareaof the shaded square is 1/4 ft^2.

Funny is studying a population of frogs. She determines that the population is decreasing at an average rate of 3% per year. When she began her study, the frog population was estimated at 1,200. Which function represents the frig population after years?

Answers

Each year the frog population is multiplied by (1-3%) = 97% = 0.97. The function that represents the frog population can be written as
.. p(t) = 1200*0.97^t

The surface area of the triangular prism is?

A. 540 Square Meters

B. 552 Square Meters

C. 576 Square Meters

D. 624 Square Meters

Answers

If I did my math right, the right answer should be that the surface area of this triangular prism is 576 square meters.

Final answer:

The area of a triangle with a base of 166 mm and height of 930.0 mm is found by converting the measurements to meters and using the formula A = 1/2 × base × height. It calculates out to be 0.07719 m² and should be reported as 0.0772 m² to match the least number of significant figures provided in the measurements.

Explanation:

To calculate the area of a triangle, you use the formula A = 1/2 × base × height. Given the base is 166 mm and the height is 930.0 mm, first, you need to convert the measurements to meters by dividing them by 1000 (since there are 1000 millimeters in a meter), which gives us 0.166 m for the base and 0.930 m for the height. Then you plug these values into the formula:

A = 1/2 × (0.166 m) × (0.930 m)

So the area of the triangle is:

A = 1/2 × 0.15438 m²

A = 0.07719 m²

This result should be reported with the proper number of significant figures. Given that the base was provided to three significant figures and the height to four, the area should also be reported to three significant figures since the number of significant figures in the answer is determined by the measurement with the fewest significant figures. Therefore:

Area = 0.0772 m²

how do you do the formula a2+b2=c2

Answers

In the formula a^2 + b^2 = c^2, a is (most often) the height of the triangle, b is the length of the triangle, and c is the last side-length connecting a and b, called the hypotenuse. The formula states that a and b must form a 90 degree angle, and that a^2 + b^2 = c^2.

So, to find x in this triangle:

x^2 + 8^2 = 12^2
x^2 + 64 = 144
x^2 = 80
x = 8.94

Hope this helps!

81 times a number minus 77 is equal to -77 less than the number

Answers

81 times a number minus 77 is equal to -77 less than the number 81x-77=x-77

The people who "consume" or use the travel product are called _____.
A---suppliers
B---consumers
C---intermediaries
D---distributors

IM TERRIBLE AT MATH
HELP PLEASE

Answers

I believe its B.

Hope this helps!

Answer:

B. Consumers literally read the question?

Step-by-step explanation:

write the equation in slope intercept form 2x-3y=6

Answers

Slope is 2/3
Y Intercept is -2

hope this helps

Slope intercept form is y = mx + b.

-3y = -2x + 6
-y = -2/3x + 2
y = 2/3x -2

Hope this helps!

Jordan and Roman travel the same route to work. Jordan leaves work one morning and drives at a rate,r, of 56 mph. Roman leaves the house soon after, when Jordan has already traveled 2 mo. Roman drives at a rate of 60 mph. How long after Jordan leaves home well Roman catch up to her? How many miles into the commute Will this occur

Answers

60 mph................

Answer: Roman will catch up Jordan after 0.5 h, and they will be 30 miles into the conmute.

Explanation:

1) Data:

Jordan's speed: r1 = 56 mi / h

Roman's speed: r2 = 60 mi / h

Jordan's initial position: 2 miles

Roman's initial position: 0 miles

2) Formula:

Both motions are at constant speed, so rate = distance / time

Position = Initial position + distance run = initial position + rate * time

3) Solution:

Jordan's position, x1 = 2 mi + 56 mi / h * t

Roman's position, x2 = 0 mi + 60 mi/h * t = 60 mi / h

They start driving at the same time, so their times are equal.

When Roman catch up Jordan their position are equal => x1 = x2

=> 2 + 56t = 60 t

=> 60t - 56t = 2

=> 4t = 2

=> t = 2/4 = 0.5 hours

Now you can calculate the position of both in the commute:

From Jordan's rate: x1 = 2 mi + 56 mi /h * 0.5 h = 2mi + 28mi = 30 mi

From Roman's rate: x2 = 60 mi/h * 0.5 h = 30 mi

Answer: Roman will catch up Jordan after 0.5 h, and they will be 30 miles into the conmute.

how many 1/2 cups servings of cereal are in 2 cups of cereal ?

Answers

There are 4 1/2 cups of cereal in 2 cups

Find the volume of the bag and candle.Round to the nearest tenth

Answers

The volume of the bag will be found by multiplying the length times the width times the height. This would be 5.5 x 3 x 8. The volume of the bag is 20.9 cubic inches. The volume of the candle would be found by using the formula for finding volume of a cylinder. V =pi(approximately 3.14) x r^2 x h, where r is the radius( half the diameter) and h is the height. V = 3.14 x 1.25 x 1.25 x 6. The volume of the cylinder would be 29.4 cubic inches.

Angle JKL and MKQ are complementary angles.
The measure if angle JKL is twice the measure of angke MKQ.
Write one equation to find x, the measure if angle MKQ, and then solve for x
Enter your equation and your solution in the space provided

Answers

Hi, to answer this question you need to know that complementary angle will add up to 90 degrees. If the angle of MKW is x, then angle JKL is 2x (twice the measure). The sum of both of these would be 90°. You can show this as x + 2x=90. Simplify this to 3x=90. Then divide by 3 on both sides to get x=30 degrees.

The equation of the complementary angles can be represented as 2x + x = 90° and the measure of ∠MKQ is 30 degrees.

What are complementary angles?

Complementary angles are angles that sum up to 90 degrees. The angles complement each other.

Therefore,

∠JKL + ∠MKQ = 90°

let

∠MKQ = x

Hence,

∠JKL = 2x

Therefore,

2x + x = 90°

3x = 90

divide both sides by 3

3x / 3 = 90 / 3

x = 30

learn more on complementary angles here:https://brainly.com/question/5366669

#SPJ2

8. Which box-and-whisker plot shows the high temperatures in Philadelphia, Pennsylvania, during the first two weeks of March: 42, 51, 54, 46, 49, 53, 52, 37, 33, 36, 50, 41, 50, 38

Answers

Step 1: Arrange the data given in ascending order, that is from least to greatest.

Given data:

[tex] 42, \; 51, \; 54, \; 46,\; 49, \; 53,\; 52, \; 37, \; 33, \; 36, \; 50, \; 41,\; 50,\; 38\\ \\ [/tex]

Data in ascending order:

[tex] 33, \; 36, \; 37, \; 38, \; 41, \; 42,\; 46, \; 49,\; 50, \; 50,\; 51,\; 52,\; 53, \; 54 [/tex]

Step 2: Find the median (Q2). The median is the value exactly in the middle of an ordered set of numbers .If there is an even number of items in the data set, then the median is found by taking the mean (average) of the two middlemost numbers.

Since in our problem we have 14 datas, we need to pick the middle most numbers and find the average of the same.

[tex] Median =\frac{46+49}{2} =\frac{95}{2} =47.5 [/tex]

The median is called Q2 and equal to 47.5

Step 3: Find the lower quartile (Q1). Considering the values to the left of the median(Q2), the median to those values is the Q1 and called as Lower quartile.

[tex] Q1=38 [/tex]

Step 4: Find the upper quartile (Q3). Considering the values to the right of the median(Q2), the median to those values is the Q3 and called as Upper quartile.

[tex] Q3=51 [/tex]

Conclusion:

Using the above details we need to plot the box and whisker plot attached with this problem.

Pythagorean Theorem in Cones. Please help

Answers

3^2 + height^2 = 9^2

9 + height^2 = 81
height ^2 = 72

height = sqrt(72)

The area of a square is 144 in². What is the length of the square in feet?

Answers

the answer should be 1

The answer would not be 1. All you need to do is divide 144 by 12 to get 12. There is no possible way for it to be 1.

What is 2 * 4 + 8/7 - 2/5 (3 + 8)

No calculator plzz!!!

Answers

Hey there Banana!

[tex]simplify \ \frac{2}5} \\ \\ (8+ \frac{8}{7})-( \frac{2}{5} *11) \\ \\ simplify \ \frac{8}{7} \\ \\ \frac{8*7+8}{7} = \frac{64}{7} \\ \\ \\ \frac{L \ Mult \ *R \ num}{L.C.M} * \frac{64*5}{35} \\ \\ \frac{64*5-(22-7)}{35} = \frac{166}{35} \\ \\ (final \ result) \\ \\ \boxed{\boxed{ \frac{166}{35} =(4.74286)}} \\ \\ Hope \ this \ helps \ you![/tex]

2 * 4 + 8/7 - 2/5 (3 + 8) =

= 8 + 8/7 - 2/5 * 11

= 8 + 8/7 - 22/5

The LCD is 35.
We multiply the first fraction by 35/35, the second fraction by 5/5, and the third fraction by 7/7 to have a common denominator.

= 280/35 + 40/35 - 154/35

= 166/35

= 4 26/35

How to define, “Greatest common factor.” Please Help.

Answers

The greatest common The greatest common factor in my words: The greatest of the common factors of two or more numbers.

Which number is an irrational number?

A: 0.12

B: 0.1257486

C: 0.12121212

D: 0.111111

Answers

An irrational number is a number that can not be expressed as a rational number(a whole number, repeating decimal number, and a fraction that is rational.)
So 0.1257486 is the answer.

Final answer:

The irrational number in the given options is C: 0.12121212, as it repeats the sequence '12' infinitely without any pattern.

Explanation:

An irrational number is a number that cannot be expressed as a simple fraction (i.e. a ratio of two integers) and has an infinite number of non-repeating decimal places. Out of the given options, the number C: 0.12121212 is an irrational number because it repeats the sequence '12' infinitely without any pattern. The other options, A: 0.12, B: 0.1257486, and D: 0.111111, can all be expressed as fractions and have either a finite decimal representation or a repeating decimal pattern.

Sheila works for a fishing company. She is paid $20 per day and an additional $2 for each lobster she catches. She wants to know how many lobsters she must catch in order to earn a total of at least $130 after five days of working.

Create an inequality on the number line with the tools provided which represents the number of lobsters that Sheila could catch to earn at least $130.

Answers

In five days, she would get $100 no matter what meaning she needs $30 in lobsters. 30/2 = 15 so the number of lobsters she needs to catch could be represented as x >= 15

Data Set 1 has a mean of 54 and a MAD of 4. Data Set 2 has a mean of 60 and a MAD of 2.

What can be concluded about the two distributions?

Select each correct answer.

The distributions are somewhat similar.

The means-to-MAD ratio is 1.5.

The distributions are similar.

The means-to-MAD ratio is 3.

Answers

Hello,

B.
The means-to-MAD ratio is 1.5.D.
The distributions are somewhat similar.

mark brainiest mate!

Rewrite each expression using each base only once.

(-6)^12 * (-6)^3 * (-6)^2

2^2 * 2^7 * 2^0

Simplify each expresion.

5c^4 * c^6

(-2.4n^4)(2n^-1)

(4c^4)(ac^3)(-3a^5c)

a^6b^3 * a^2b^-2

Answers

Rewrite each expression using each base only once.

(-6)^12 * (-6)^3 * (-6)^2
(-6)^(12+3+2)
(-6)^(17)
Answer:
(-6)^(17)

2^2 * 2^7 * 2^0
(2)^(2+7+0)
(2)^(9)
Answer:
(2)^(9)

Simplify each expresion.

5c^4 * c^6
5*c^(4+6)
5*c^(10)
Answer:
5*c^10
(-2.4n^4)(2n^-1)
(-2.4*2)(n^4)(n^-1)
(-2.4*2)(n^(4+(-1))
(-4.8)(n^(4-1))
(-4.8)(n^(3))
Answer:
(-4.8)(n^(3))

(4c^4)(ac^3)(-3a^5c)
((4)*(-3))*(c^(4+3+1))*(a^(1+5))
(-12)*(c^(8))*(a^(6))
Answer:
(-12)*(c^8)*(a^6)

a^6b^3 * a^2b^-2
(a^(6+2))*(b^(3+(-2)))
(a^(8))*(b^(3-2))
(a^(8))*(b^(1))
(a^8)*(b)
Answer:
(a^8)*(b)

I neeeeed help please

Answers

17. You are supposed to use the perimeter formula for a rectangle. Your text has apparently written that formula as
.. P = 2w +2l
You are given values for P and l. Put them in the formula.
.. 6 = 2w +2*1
Solve in the usual way. First, subtract 2.
.. 4 = 2w
Then, divide by 2
.. 2 = w
You have found w, and it is 2.

_____
Personally, I like to write the perimeter formula for a rectangle as
.. P = 2(w +l)
Usng this version, we can fill in values and get
.. 6 = 2(w +1)
Dividing by 2 gives
.. 3 = w +1
Subtracting 1, we get
.. 2 = w

Rounding 9 1\3 to the nearest whole number

Answers

The answer is 9 because one third is closer to 0 then 1

The answer is 28/3
Have an nice day

Algebra 1
The sum of two numbers is 186. The difference between the same numbers is 32. what are the two numbers?

Answers

[tex]x + y = 186 \\ y - x = 32 \\ 2x = 186 - 32 \\ 2x = 154 \\ x = 77 \\ y = 77 + 32 = 109[/tex]
X is 77
Y is 109

The ratio of vertical change to the horizontal change is called _________.
A. The slope
B. Translation
C. The y intersept

Answers

I think the ratio of a vertical change to the horizontal change is called slope.

Answer:

slope

Step-by-step explanation:

justin can type w words per minute. melvin can type 4 times as many words as justin. write an expression that represents the rate at which Melvin can type

Answers

m = Words per min that Justin can type
w = Words per min that Melvin can type
w = m*4

Melvin's typing rate can be expressed as 4w words per minute by multiplying Justin's rate by 4.

To determine how many words Melvin can type per minute, we need to use Justin's typing rate as a reference.

Since Justin can type w words per minute, and Melvin can type 4 times as many words as Justin, we multiply Justin's rate by 4.The expression for Melvin's typing rate is 4w words per minute.

For example, if Justin types 50 words per minute (w = 50), then Melvin would type 200 words per minute (4 * 50 = 200).

The function f(x)=square root -x is shown on the graph. Which statement is correct?

Answers

The domain of the the function f(x)=sqrt (-x) which has been shown in the graph is:
Domain:
{x ∈ R: x≤0}

This means that the domain is all non-positive real numbers.

The answer is:
d] The domain of the function is all real numbers less than or equal to 0.

Answer:

Step-by-step explanation:

i just did the test and got it right.

Which equation can solve for x

Answers

I would say answer D hopefully it is correct.

Answer Choice B is correct
And if you finished solving the x value is 2

Hope this helped you :)

Need some help. Find the distance of the line PQ.

I tried multiplying the radius by 2 but that’s not the answer :/ simple equation but I’m blanking

Answers

distance = sqrt (x2-x1)^2 + (y2-y1)^2

distance = 5

Can someone plz help me with this question

Answers

A = L*W
A = (2r+3)*(r -4)
Use the distributive property, three times in total.
.. = 2r(r -4) +3(r -4)
.. = 2r^2 -8r +3r -12
Collect terms.
A = 2r^2 -5r -12

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