at a fourth of july celebration, a rocket is launched straight up with an initial velocity of 128 ft. The height of the rocket in feet above sea level is modeled by the expression 128t - 16t^2, where T is the time in seconds after the rocket is launched. (a) what is the gcf of each term of the expression? (b) write the factored form of the expression for the height of the rocket after T seconds. (c) well the height of the rocket be greater after four seconds or after six seconds?
Answers
Answer:
Step-by-step explanation:
Given
Height of the rocket is given by
\(h=128t-16t^2\)
\(h=8\times 16t-16t\times t\)
(a)Greatest common factor in each term is \(16t\)
(b)
\(h=8\times 16t-16t\times t\)
\(h=16t(8-t)\)
(c)
After \(t=4\ s\)
\(h=16\times 4(8-4)\)
\(h=256\ m\)
after \(t=6\ s\)
\(h=16\times 6(8-6)\)
\(h=192\ m\)
Thus after \(4\ s\) height of rocket is greater .
Related Questions
This work is way to hard and my work is stacking it would be nice to have some weight off my back
Answers
1) Popcorn unit price: 17.57/7 = $2.51
2.51 x 3 = 7.53
Three bags of popcorn would cost $7.53.
2) Old games unit price: 73.10/5 = 14.62
14.62 x 6 = 87.72
If they sold six games they would've made $87.72.
3) Lollipop unit price: 20.51/7 = %2.93
2.39 x 4 = 11.72
Four lollipops would cost $11.72
4) Hotdogs unit price: 82.86/3 = $27.42
Hamburgers unit price: 55.12/2 $27.56
Hotdogs have the lower unit price. $27.42 < $27.56
5) Packs of paper unit price: 12.74/7 = $1.82
1.82 x 2 = 3.64
Two packs of paper would cost $3.64
6) Pair of shoes unit price: 49.32/4 = $12.33
12.33 x 6 = $73.98
Six pairs of shoes would cost $73.98
7) Brand A unit price: 71.28/6 = $11.88
Brand B unit price: 59.15/5 = $11.83
Brand B has the cheaper price. $11.83 < $11.88
8) Pounds of seeds unit price: 37.62/2 = $18.81
18.81 x 6 = $112.86
Six pounds of seeds would cost $112.86
9) Red Grapes unit price: .82
Green Grapes unit price: .84
Green grapes are more expensive. .84 > .82
10) Book Store unit price : 21.69/3 = $7.23
Online unit price: 14.28/2 = $7.14
Online has a lower unit price. $7.14 < $7.23
Some students recorded how many minutes they spent on the phone in one day. They put the results in a Stem-and-Leaf Plot.
What is the mean number of minutes spent on the phone?
Answers
Explanation:
The data from the stem-and-leaf plot is:
10,
24,25,26,
30,30,32,33,
40,45,46
Add up those values
10+24+25+26+30+30+32+33+40+45+46 = 341
Then divide over n = 11 which is the sample size.
341/11 = 31 is the arithmetic mean.
Answer:
341/11 = 31 is the arithmetic mean.
Step-by-step explanation:
the ratio of the number of oranges to apples to bananas is 8:5:2. if there are 120 fruits in total, how many bananas are there
Answers
Answer:
Step-by-step explanation:
To find the number of bananas, we need to determine the proportion of bananas in the total number of fruits based on the given ratio.
Let's assume that the ratio of oranges, apples, and bananas can be represented by 8x, 5x, and 2x, respectively, where x is a common multiplier.
The sum of the parts in the ratio is 8x + 5x + 2x = 15x.
We know that the total number of fruits is 120. Therefore, we can set up the following equation:
15x = 120
To solve for x, we divide both sides of the equation by 15:
x = 120 / 15
x = 8
Now that we know the value of x, we can find the number of bananas by multiplying it by the corresponding part of the ratio:
Number of bananas = 2x = 2 * 8 = 16
So, there are 16 bananas in total.
We can add all the parts to the ratio and get 15. Out of 15 parts, 2 are bananas. Now we can calculate how many fruits are in one part. One fifteenth of 120 is 8, so there are 8 fruits in one part. 2 parts are bananas, so multiplying 8 with 2 gives us our answer, 16.
Sample Answer: Make a table with inputs showing the number of bottles of water and outputs showing the total cost of the water. Use 1, 2, 3, and 4 bottles for the inputs. Find the corresponding outputs. Plot the ordered pairs in the table of the form (input,output).
Which instructions did you include in your explanation? Check all that apply.
Identify the input.
Identify the output.
Create a table for four input values.
Plot the points from the table.
Answers
The instructions that you would include in your explanation are:
Identify the output.
Create a table for four input values.
Plot the points from the table.
The instructions to be includedIn the given question, a series of instructions are provided. To properly explain your process, you have to explain how you got the output. There is no need of explaining the input as they are already provided.
Next, you will Show how you created the table and why you created it in that way. Finally, indicate how the points were plotted on the table. An explanation such as this will help anyone to follow through.
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Answer:1 to 2
2 to 4
Step-by-step explanation:
write 5 pounds fro $2.49 as a unit rate. Round to the nearest hundred
Answers
HELLP IM GIVING BRAINLIEST
Answers
Answer:
64
Step-by-step explanation:
4 times 4 times 4= 64
Answer:
the answer is 64 because "4^3" is = 4*4*4 and that is =64
Step-by-step explanation:
A carnival has a duck-pond booth. You choose a rubber duck at random. The mark on the bottom of the duck tells you whether you won a small, medium, or large prize, or no prize at all. There are 73 ducks floating in the pond. There are 5 ducks marked as large-prize winners, 11 ducks marked as medium-prize winners, and 24 ducks marked as small-prize winners. Find the theoretical probability of winning a medium prize at the duck pond. Express your answer as a decimal. If necessary, round your answer to the nearest thousandth.
Answers
Let's break down this problem step by step.
First, let's understand what's happening here. There's a carnival game where you can pick one duck from a pond. Each duck has a mark under it that might make you a winner of a prize. Some ducks are marked with large prizes, some with medium, some with small, and the rest don't win you any prize.
The total number of ducks in the pond is 73.
Out of these 73 ducks:
- 5 are marked for a large prize,
- 11 are marked for a medium prize,
- 24 are marked for a small prize.
We are asked to find the theoretical probability of picking a duck that has a medium prize mark. The theoretical probability is basically a fraction that compares the number of ways something can happen with the total number of outcomes.
Here, the number of ways you can win a medium prize is equal to the number of ducks that have a medium prize mark, which is 11.
The total number of outcomes is just the total number of ducks you can choose from, which is 73.
The probability (P) of winning a medium prize is then:
P(medium prize) = (Number of medium-prize ducks) / (Total number of ducks)
= 11/73
To convert this fraction to a decimal, simply divide 11 by 73:
= 11 ÷ 73
≈ 0.1507 (rounded to the nearest thousandth)
So, the probability of winning a medium prize at the duck pond is about 0.151 or 15.1%. Imagine, for every 100 ducks you pick (if there were that many), about 15 of them would win you a medium prize.
The theoretical probability of winning a medium prize at the duck pond is ≈ 0.150
To find the theoretical probability of winning a medium prize at the duck pond, we need to determine the ratio of the number of medium-prize-winning ducks to the total number of ducks in the pond.
The total number of ducks in the pond is given as 73.
The number of medium-prize-winning ducks is given as 11.
Therefore, the probability can be calculated as follows:
Probability of winning a medium prize = (Number of medium-prize-winning ducks) / (Total number of ducks)
Probability of winning a medium prize = 11 / 73
To express the answer as a decimal, we divide 11 by 73:
Probability of winning a medium prize ≈ 0.150
Rounded to the nearest thousandth, the theoretical probability of winning a medium prize at the duck pond is approximately 0.150
To better understand how to find theoretical probability of winning medium prize at the duck pond:
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Which list orders the numbers from least to greatest?
Negative 2.4, negative 1.5, negative 2 and one-fourth, negative 3, negative 1 and one-eighth
A number line going from negative 4 to positive 4.
Negative 1 and one-eighth, negative 1.5, negative 2 and one-fourth, negative 2.4, negative 3
Negative 3, negative 2.4, negative 2 and one-fourth, negative 1.5, negative 1 and one-eighth
Negative 3, negative 2 and one-fourth, negative 2.4, negative 1 and one-eighth, negative 1.5
Negative 1.5, negative 1 and one-eighth, negative 2.4, negative 2 and one-fourth, negative 3
Answers
Negative 3, negative 2.4, negative 1.5, negative 2 and one-fourth, negative 1 and one-eighth
Hope my answer helps you✌️
Consider the functions below -
Answers
Answer:
y-intercept
Step-by-step explanation:
In all cases, when x = 0, f(0) = a or b or c.
Answer: y-intercept
I NEED HELP ASAP with a science experiment give me ideas what experiments (mini-labs) I could do based on the task! READ THE SCREENSHOT
Answers
Answer: You should do a representation of how the heat and light waves reach humans on earth and keep us warm.
Step-by-step explanation:
all your answers are already in the task introduction.
1. Make earth out of styrofoam ball (buy at a dollar store) and paint. (blue and green). (If you want to make humans out of popsicle sticks)
2. Use velvet pipe cleaners (blue for cold air and red for hot air) to represent convection and conduction.
3. Use yellow pipe cleaners for solar energy to represent radiation.
4. Rest is up to you for how you want it to look.
During one team’s season, the ratio of the number of games the team won to the number of games the team played was 4 to 12. The team played 42 games. How many games did the team win?
Answers
Answer:
noob noob noob noob noob noob noob noob
Please answer the question
Answers
The height of the dead tree is 16 feet
The direction in which the tree should fall is Northeast, Northwest, Southeast, Southwest.
How to solveFrom the given question, since the ray is straight, AC is parallel to DF
Meanwhile triangles ABC and DEF are right angles,
AB/DE =BC/EF
AB/6 = 8/3
AB= 16 feet.
Thus, the height of the tree is 16 feet.
Since 16 ft> 15ft> 14ft> 13ft> 12ft
Therefore, the direction which the tree is falling is Northeast, Northwest, Southeast, Southwest.
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HELP!!!!!!!!!
Your school is raising money for a non-profit organization. The local chapter of the non-profit organization keeps 80% of the money raised, and 20% goes to the national chapter of the non-profit organization. Four of your friends each donate the same amount. The total money you raise for the local chapter of the non-profit organization is is $51.20. How much does each friend donate?
Answers
Answer:
$16
Step-by-step explanation:
Let x = friends' donations
y = local chapter funds
4x = y
.8y = 51.2
Divide both sides by 0.8 for the second equation
.8y/.8 = 51.2/.8 = 64
Plug in the new y in the first equation
4x = 64
Divide both side by 4
4x/4 = 64/4
x = 16
Expiation:
A pear weighs 7/8 pound. A case contains 12 pears. If each pear weighs the same, how much does the case of pears weigh?
Answers
Answer:
67
Step-by-step explanation:
Answer:
10.5 pounds
Step-by-step explanation:
\(\frac{7}{8} *12=10.5 lbs\)
-3 + 6x. Which expression shows the correct factorization?
Here are the ones to pick from
1. -2 + -2 +6 +x
2. 6(-2 +x)
3. 6(-2 +x)
4. -3 (1 - 2x)
Answers
Answer:
Option #4
Step-by-step explanation:
Expand option #4
=-3(1-2x)
=-3 -2x*-3
=-3+6x which is what your original equation was.
You mix 23.385 grams of sugar and 12.873 grams of baking soda in a glass container for an experiment. You place the container on a scale to find that the total mass is 104.2 grams. What is the mass of the container
Answers
104.2-36.258=67.942
Answer=67.942
The mass of the container is 67.942 grams.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that amount of sugar is 23.385 grams, the amount of soda is 12.873 and the total mass is 104.2 grams.
The weight of the container will be calculated as below:-
Total weight of sugar and sods = 23.385+12.873=36.258
Weight of container = 104.2-36.258=67.942
Weight of container = 67.942 grams
Therefore, the mass of the container is 67.942 grams.
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Find the slope of the line that passes through (8, 5) and (3, 1)
PLEASE HELP
Answers
Answer: m = 4/5
Step-by-step explanation:
Use the slope formula
\(y_{2}-y_{1}/ x_{2} - x_{1}\)
Let's plug in the points:
5 - 1 / 8 - 3
4/5
So, m=4/5
Answer:
A) \(\frac{4}{5}\)
Step-by-step explanation:
Slope formula given 2 points:
\(\frac{y_{2}-y_{1}}{x_{2}-x_1}\)
Our points are (8,5) and (3,1)
Substitute:
\(\frac{1-5}{3-8} \\=\frac{-4}{-5}\)
negatives cancel out:
=\(\frac{4}{5}\)
Hope this helps! :)
Please help, thank you!!
Answers
Answer:
Step-by-step explanation:
Givens
TriangleBase = 11 inchesHeight = 12 inchesFormula
A = Base * height / 2
Solution
Area = 11 * 12/2Area = 132 /2Area = 66 square inches.Answer:
66
Step-by-step explanation:
Formula: bh1/2
Substitute: (11)(12)(1/2)
Solve: (11)(6)
66
(You could’ve also multiplied 11*12 first, gotten 132, then divided that by 2, also getting 66).
The grocery store is having a sale and sodas are on sale for “5 for $10.25”. At this rate what is the cost of one soda
Answers
Please help me I'm stressed and this is due tomorrow...:((
Answers
Answer:
A
Step-by-step explanation:
The line starts at 24 and ends with 34. The box starts at 25 and 32. The line in the middle shows 31.
Order the set of numbers from least to greatest: 2.71 repeating 71, 2 and 3 over 4, square root 5, 5 over 2 Group of answer choices 2.71 repeating 71, 2 and 3 over 4, square root 5, 5 over 2. 5 over 2, square root 5, 2.71 repeating 71, 2 3 over 4 square root 5, 5 over 2, 2.71 repeating 71, 2 3 over 4 2 3 over 4, 2.71 repeating 71, 5 over 2, square root 5
Answers
Answer:
C. Square root if 5, 5 over 2, 2.71 repeating 71, and 2+3 over 4.
Answer:
c
Step-by-step explanation:
The point B is at the centre of the circle.
The points P and Q are on the circumference of the circle.
Calculate the area of the shaded sector.
take π to be 3.142 in your working.
Give your final answer to 1dp
Answers
Answer:
24.7
Step-by-step explanation:
Calculation of the area of the shaded sector is 24.7:
Since
Line PQ = 5.413590865cm
BQ = 9cm
Now
cos(x) = 0.8190928022
x = 35.00591739˚
Now finally the
Area of sector = 24.7cm^2
So point B is at the centre of the circle, making the area of the shaded sector to be 24.7 .
April mails 3 packages.
The first weighs 14.125 pounds
The second weighs 12.35 pounds
The third weighs 17.4 pounds.
What is the total weight of the packages?
Don't forget to EXPLAIN your answer as well.
(I'm being graded on this)
Answers
Answer:
The total weight of the packages would be 43.875.
Step-by-step explanation:
The total weight of the packages would be 43.875 because all you have to do is add each amount to get the total. So, you would do 14.125 + 12.35 + 17.4 to equal 43.875.
12.35
17.4
Add zeros in place of blank number places
12.35 add a 0 in the thousandths place
17.4 add a 0 in the hundredths and thousandths place
(This just makes it easier to add)
Then add
14.125
12.350
17.400
Your answer will be 43.875
Add: a² + b² + c² – 3abc and a² – b² + c² + abc
2. Add: xy² + 4x²y – 7x²y - 3xy² + 3 and x²y + xy²
3. Add: 5x² + 7y - 6z² ; 4y + 3x² ; 9x² + 2z² - 9y and 2y - 2x².
4. From the sum of 3x - 2y + 4z and 3y – 2z, subtract x - y - z.
5. Subtract a – 2b – c from the sum of 3a – b + c and a + b – 3c.
6. The sum of two expressions is 3x2 + 2xy – y2. If one of them is 2x2 + 3y2, find the other.
7. From the sum of 4b2 + 5bc, -2b2 – 2bc – 2z2 and 2bc + 4c2, subtract the sum of 5b2 – c2 and -3b2 + 2bc + c2.
8. What should be subtracted from 3x + 5y + 9 to get - 2x + 3y + 15?
9. Subtract 2m – 5q + 7 from 4p + 2q and add your result to m2 – 3m3 + m - 1.
10. Subtract 2a2b – 3b2 from 3a2 – 5ab2 + 2b2 and subtract your result from the sum of the two expressions 3ab2 + 5b2 – 2a2b and a2b + 5a2 – 3ab2
Answers
Answer:
Here is your ans.
Step-by-step explanation:
I have few time Because I am too late to school.. So I had solved only up to q.no 5. . Hope you understand it. If you Like then Plz give a five star rating to my ans. And One thing sorry for rough handwriting and mistake
2. -xy^2-2x^2y+3
3. 15x^2+4y-4z^2
4. 2x+2y+3z
5. 3a-c+2b
6. x^2+2xy-4y2
7. Sum of 4b2+5bc ; -2b^2-2bc-2c^2 ; 2bc+4c^2 is (2b^2+2c2)
Sum of 5b^2-c^2 and -3b^2+2bc +c^2 is (2b^2-2bc)
And the subtract of two answers is (2c^2-2bc)
8. 5x+2y-6
9. 3m+6-7q-4p+m^2-3m^3
10. Subtract of (3a^2-5ab^2+2b^2) and (2a^2b-3b^2) is (3a^2-5ab^2-b^2-2a^2b)
Sum of (3ab^2+5b^2-2a^2b) and (a^2b+5a^2-3ab^2) is (5b^2-a^2b+5a^2)
And the subtract of two answers is (6b^2+a^2b+2a^2+5ab^2)
I hope this helped! And if you need to see the solution here it is. I can’t upload other pics (5-7)
If a loan is taken out for $40.54 at 0.9% and costs $1.09, how long was the loan for?
Answers
Answer:
2 YEAR AND 9 MONTHS
Step-by-step explanation:
solution,
given,
principle [p]=40.54
rate [r]=0.9
interest=1.09
time[t]=?
now,
t=I*100/P*R
109/40.54*0.9
109/36.48
=2.9
last try I don't get this-
Answers
Answer:
The answer is -7
Step-by-step explanation:
-5d = 35
/-5 /-5
d = 7
Plss show work :( thank u....
Answers
Answer:
Only if show feet
Step-by-step explanation:
pls
Evalute 8a -1+0.5b when a =1/4 and b= 10 how dose this work i need help..
Answers
8a -1+0.5b
Replace a nd b with the given values:
8(1/4) -1 + 0.5(10)
8 x 1/4 = 2
0.5 x 10 = 5
Now you have:
2 -1 + 5
2-1 = 1 +5 = 6
Answer is 6
Answer:
6
Step-by-step explanation:
Substitute the value of the variable into the expression and simplify.
I don't know B. :⊂ Find the answer for me please?
Answers
Answer:
For A: The answer is (79-2x) degrees
For B: The answer is (169-2x) degrees
I hope this answer helped you out!
Step-by-step explanation:
I took the test!!!
Hevesh wants to make 2 lines of dominoes that are both 21 inches long. Each line has dominoes spaced 1 and 1/2 inches apart. How many dominoes will she need for both lines?
Answers
Answer: 30 dominoes in total.
Step-by-step explanation:
Each line is 21 inches long.
the space between dominoes is 1 + 1/2 inches.
(assuming that the distance includes the domino itself) Now, we need at least two dominoes to see this distance,
The we have N + 1 dominoes per line, and the distance is:
N*(1 + 1/2)inches = 21 inches
If we find N, we can find the number of domineoes in each line:
N = 21/(1 + 1/2) = 14
This means that we have 14 + 1 = 15 dominoes in each line, and we have two lines, so we have 30 dominoes in total.