Mrs.Peterson dropped a ball from the top of a tower. At the same time, her son, Drake, launches a rocket from a different level of the tower.
The height of the tennis ball in feet after t seconds can be represented by the quadratic function: b(t)=-t^2-2t+26.
The height of Drakes rocket after t seconds can be represented by the linear function: p(t)=-2t+10.
What are the two solutions to this system? Show your work.
Explain which solution is not reasonable in this situation.
After how many seconds do the rocket and the ball reach the same height.
Answers
9514 1404 393
Answer:
two solutions: t = -4, t = 4t = -4 is not reasonable4 secondsStep-by-step explanation:
A graphing calculator shows the two solutions to be ...
(t, h) = (-4, 18) and (4, 2)
__
The two heights will be equal when ...
p(t) = b(t)
-2t +10 = -t^2 -2t +26
t^2 -16 = 0 . . . . subtract the right side expression
(t -4)(t +4) = 0 . . . factor the difference of squares
t = 4 or -4 . . . . values of t that make the factors zero
At these times, the heights will be ...
p(t) = -2{4, -4} +10 = {-8, 8} +10 = {2, 18}
The solutions are ...
(t, height) = (-4, 18) and (4, 2).
__
We generally discount solutions for negative time, because we start counting time when the objects are launched. t = -4 is an extraneous solution.
__
The rocket and ball reach the same height after 4 seconds.
Related Questions
You have 10 pounds of aquafaba. You need 6 oz to make one serving of consomme. How many servings can you make? Whole servings only - round down rather than using partial servings.
Answers
Using the principle of proportional relationship, the number of whole serving that can be made is 26.
Recall :
1 pound = 16 ozTotal amount of aquafaba in ounces :
16 × 10 = 160 ozAmount of aquafaba required per serving of consomme :
1 serving = 6 oz
x servings = 160 oz
Cross multiply
6x = 160
Divide both sides by 6
x = 160/6
x = 26.667
Hence, the amount of whole serving that can be made is 26.
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The product of a number is 221. sum of no. is 30. Find the number. . p
Answers
Answer: 13 and 17
Would appreciate brainly <3
Please look at picture for question.
Answers
Answer:
2/5m - 1/5
Step-by-step explanation:
what is 7 1/2 inches as a decimal of 1 foot
Answers
Answer:
7 1/2 inches as a decimal of 1 foot is 0.625ft
Answer:
7 1/2 inches = 0.625 ft
Step-by-step explanation:
7 1/2 inches = 7.5 inches
1 ft = 12 inches
7.5/12 = 0.625
7 1/2 inches = 0.625 ft
31 divided by 943.89
Answers
Answer:
0.032
Step-by-step explanation:
Answer: 0.03284281007
Step-by-step explanation:
maya used a drwaing to divide 86 she made groups of 17 with 1 left over. Draw a picture to determine how many groups may made.
Answers
Check the picture below.
The number of groups that may make will be 5.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
Maya utilized a drawing to partition 86 she made gatherings of 17 with 1 remaining over.
Then the number of the groups that may make will be given as,
⇒ (86 - 1) / 17
Simplify the expression, then we have
⇒ (86 - 1) / 17
⇒ 85 / 17
⇒ 5
The number of groups that may make will be 5.
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#SPJ2
tap the word that "they" refers to
a. birds
b. frogs
c. feets
Answers
Step-by-step explanation:
we would a small text, or give us a picture so we can read it, then we can answer this question, without it, I'd have to guess
Suppose y varies directly with x. If y=16 when x= 8, find x when y=10
Answers
Answer:
5
Step-by-step explanation:
By question,
=> y = kx
When y = 16 , x = 8
=> 16 = x(8)
=> x = 2
When y = 10 ,
=> 10 = 2x
=> x = 5
Answer:
5
it is the correct answer
The cash price of a used sedan is $18,750. Arthur Dennis cannot pay
cash, so he is making a down payment of $2,750 and 60 monthly
payments of $325 each. How much more does it cost to buy the vehicle this way?
Answers
Answer:
19,500
Step-by-step explanation:
You multiply 325 x 60 and you get 19,500
13 If CDEF is a rhombus, find m FED.
Answers
Answer:
36
Step-by-step explanation:
8x-20=5x+1
-5 -5
3x=-20+1
+20 +20
3x=21
3 3
x=7
8(7)-20
FED=36
Quick Computing installed its previous generation of computer chip manufacturing equipment 3 years ago. Some of that older equipment will become unnecessary when the company goes into production of its new product. The obsolete equipment, which originally cost $40 million, has been depreciated straight-line over an assumed tax life of 5 years, but it can be sold now for $18 million. The firm’s tax rate is 35%. What is the after-tax cash flow from the sale of the equipment?
Answers
The company's after-tax cash flow is a measure of the company's cash
generation ability.
The after-tax cash flow from the sale of the equipment is $16.1 millionReasons:
The given parameter are;
Original cost of the equipment = $40 million
The type of depreciation = Straight line depreciation
Number of years of depreciation = 5 years
Current price at which it can be sold = $18 million
The tax rate of the firm = 35%
Required:
The after-tax cash flow from the sale of the equipment.
Solution:
The Cash Flow After Tax, CFAT, is given as follows;
CFAT = Net income + Amortization + Depreciation + Other non-Cash Cash Charges
The annual depreciation is given as follows;
[tex]Annual \ depreciation = \dfrac{\$40 \ million - \$18 \ million}{5 \ years} = \$4.4 \ million \ per \ year[/tex]
Selling the equipment gives;
The Earnings Before Tax (EBT) = $18 million
The Net Income = Income - Tax = $18 million - (35% × $18 million)
The Net Income = $11.7 million
Cash Flow After Tax CFAT = Net income + Depreciation
∴ CFAT = $11.7 million + $4.4 million = $16.1 million
The after-tax cash flow = $16.1 millionLearn more here:
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what is the percent of $300,000=$75,000
Answers
Answer:
25%
Step-by-step explanation:
75000/30000=75/300=25/100=25%
Answer:
25%
Step-by-step explanation:
(75,000/300,000) (100)
(0.25) (10)
= 25
Subtract.
7 1/5−(−3/5)
Enter your answer in the box as mixed number in simplest form.
Answers
Cause I’m smort
Answer:
7 4/5
Step-by-step explanation:
when you subtract, keep the first value then change subtract to addition and, finally, change the sign of the second value
this problem, 7 1/5 -(-3/5) is the same as this addition problem:
7 1/5 + 3/5
this equals 7 4/5
what is the prime number of 30 to 59
Answers
Answer:
the prime numbers between 30 and 59 are 31, 37, 41, 43, 47, 53
Select the correct answer. What is the solution to the equation? 2(x+7)^2/3 = 8 A. -15 and 1 B. -15 C. 1 D. no solution
Answers
Answer:
The answer has no solution because it is infinite and that's your vairiable
Answer:
-15 and 1
Step-by-step explanation:
Hurry help plz
Solve for an angle in right triangles
Answers
[tex]\cos \angle B = \dfrac{2}{7}\\\\\implies \angle B = \cos^{-1} \left( \dfrac{2}{7} \right) = 1.28^{\circ}[/tex]
Which description represents the expression 5x – 9?
ANSWERS
A. 9 is subtractive from the product of 5
and
B. 5 times the difference of a number 9
C. 9 is subtracted from the sum of 5 and a number
D. 9 more than the product of 5 and a number
Answers
Which expressions are equivalent to (1/3x+2x−5/3x)−(−1/3x+5) ? Select all correct expressions. −4x+5+3x 5−x 4x−5−3x x−5
Answers
Answer:
its x-5 and 4x-5-3x
Step-by-step explanation:
I took the test
(1.2 times 10^9) divided by (3 times 10^5) in scientific notation
Answers
Answer:
[tex]4x \times {10}^{3} [/tex]
Step-by-step explanation:
[tex] \frac{1.2}{3} \times \frac{ {10}^{9} }{ {10}^{5} } [/tex]
[tex]0.4 \times {10}^{9 - 5} [/tex]
[tex]0.4 \times {10}^{4} [/tex]
[tex] = 4 \times {10}^{3} [/tex]
Evaluate the expression.
−12 ⋅ 1/3
Group of answer choices
4
-4
36
-36
Answers
Answer:
Option B. -4
Step-by-step explanation:
-12 x (1/3)
=> -12 ÷ 3
=> -4
Therefore, -4 is our answer.
Hoped this helped.
My kid already tried 3x7x7x7x7 = 3 x 7 to the power of 4 but it says it’s wrong, help please!
Answers
Answer:
[tex]7^{4} * 3[/tex]
Step-by-step explanation:
The staff at a company went from 40 to 29 employees. What was the percent change in the number of staff?
Answers
Answer: 27.5% decrease in the staff
Step-by-step explanation:
4/5 - 1/2 plz help i neeeeeeeeeed to know plz plz plz plz
Answers
Answer:
3/10
Step-by-step explanation:
Find a common denominator for both fractions.
4/5 - 1/2 = 8/10 - 5/10
On a particular stretch of highway, the State Police know that the average speed is 62 mph with a standard deviation of 5 mph. On a busy holiday weekend, the police are concerned that people travel too fast. So they randomly monitor speeds of a sample of 50 cars and record an average speed of 66 mph. Use central limit theorem to calculate
Answers
Using the normal distribution and the central limit theorem, it is found that there is a 0% probability of a sample of 50 cars recording an average speed of 66 mph or higher.
In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It measures how many standard deviations the measure is from the mean. After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X. By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].In this problem:
Mean of 62 mph, hence [tex]\mu = 62[/tex].Standard deviation of 5 mph, hence [tex]\sigma = 5[/tex].Sample of 50 cards, hence [tex]n = 50, s = \frac{5}{\sqrt{50}} = 0.7071[/tex]The probability of a sample of 50 cars recording an average speed of 66 mph or higher is 1 subtracted by the p-value of Z when X = 66, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{66 - 62}{0.7071}[/tex]
[tex]Z = 5.66[/tex]
[tex]Z = 5.66[/tex] has a p-value of 1.
1 - 1 = 0.
There is a 0% probability of a sample of 50 cars recording an average speed of 66 mph or higher.
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hii, i need help with this word problem :)
Answers
Multiply the amount per week by the number of weeks (x) and add that to the starting amount they had. Set those to equal each other and solve for x:
222 + 10x = 148 + 12x
Subtract 10x from both sides:
222 = 148 + 2x
Subtract 148 from both sides
74 = 2x
Divide both sides by 2
X = 37
Answer: 37 weeks
how do i do this?
y=- 1/2x + 3
Answers
Answer: y-intercept would be (0,-1/3)
Step-by-step explanation:
I might be wrong
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
You buy clothing at a sale. You buy a sweater at
7
10
of its original price of $35. Answer each question and show all your work.
a. How much money did you spend?
b. How much money did you save?
c. What fraction of the total original price did you save?
Answers
The amount that will be spent is $24.50, the amount saved will be $10.50, and the percentage saved will be 30%.
The amount that will be spent will be:
= 7/10 × $35 = $24.50
The amount that will be saved will be:
= $35 - $24.50 = $10.50
The fraction of the original price that is saved will be:
= 10.50/35 × 100
= 30%
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Who is the general information of acounting
Answers
Answer:
General accounting essentially refers to general ledger collection and accounting activities that include account charges in credits and debits and documenting financial statements for a quarter, calendar or fiscal year.
g(x) = 2x
f(x) = -2x + 2x
Find g(x) + f(x)
Answers
Step-by-step explanation:
f(x) = 0
-2x + 2x is always 0.
so, g(x) + f(x) = g(x) + 0 = g(x) = 2x.
long proof :
g(x) + f(x) = 2x + -2x + 2x = 2x
Write 34% as a fraction in simplest form
Answers
Answer:
The answer is that the simplest fraction form of 34% is 17/50
Step-by-step explanation:
Both the numerator and denominator of the fraction 34/100 can only be divided by 2, to satisfy creating its simplest form.
34% = 17/50
Have an awesome day! :D
Answer:
[tex]\frac{17}{50}[/tex]
Step-by-step explanation:
To write any fraction as a percent, remember perCENT means per 100. Think of 100 cents in a dollar. So 34 perCENT means 34 of 100, which you write as [tex]\frac{34}{100}[/tex].
Simplest form means to reduce, so you see if there is any number you can divide out of the top and the bottom.
[tex]\frac{34}{100}[/tex] = [tex]\frac{17*2}{50*2}[/tex]= [tex]\frac{17}{50}[/tex]
