A rock is thrown straight up from the top of a bridge that is 75 ft high with an initial velocity of 32 ft/s. The height of the object can be modeled by the equation s(t) = -16t2 + 32t + 75. Determine the time(s) the ball is lower than the bridge in interval notation.
In two or more complete sentences, explain why (-∞,0) is not included in the solution.
Answers
The ball is lower than the bridge at the interval [2, 3.385] and (-∞,0) contains negative values
How to determine the time the balloon lower than the bridge?The equation of the function is given as
h(t)= -16t^2 + 32t + 75
The above equation is a quadratic equation
When the balloon is less than the bridge i.e. a height of 75 feet, we have
h(t) < 75
So, we have the following equation and inequality
h(t)= -16t^2 + 32t + 7
h(t) < 75
Next, we plot the equation and inequality on a graph (see attachment)
The equations intersect at
t = 0 and t = 2
Remove when t = 0
t = 2
The ball hits the ground at t = 3.385
So, the interval is [2, 3.385]
Also, (-∞,0) is not included in the solution because time cannot be negative
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Related Questions
what is the interest earned in a savings account after 12 months on a balance of $2000 if the interest rate is 1.5% APY compounded yearly? round your answer to the nearest hundredth.
Interest = $ [?]
Answers
Answer:
$30
Step-by-step explanation:
2000 x .015 = 30
The interest earned in the savings account after 12 months on a balance of $2000 if the interest rate is 1.5% APY compounded yearly is $30
How to calculate compound interest's amount?If the initial amount (also called as principal amount) is P, and the interest rate is R% per unit time, and it is left for T unit of time for that compound interest, then the interest amount earned is given by:
[tex]CI = P\left(1 +\dfrac{R}{100}\right)^T - P[/tex]
The final amount becomes:
[tex]A = CI + P\\A = P\left(1 +\dfrac{R}{100}\right)^T[/tex]
For this case, we're specified that:
Initial amount = P = $2000Interest rate 1.5% annually (compound interest), or R = 1.5Time for which interest will be compounded = 12 months = 1 year = T (converted time to year as interest is being compounded annually).Thus, we get the amount of interest as:
[tex]CI = 2000\left(1 +\dfrac{1.5}{100}\right)^1 - 2000\\\\CI = 2000\times \dfrac{1.5}{100} = 30 \: \rm (in \: dollars)[/tex]
Thus, the interest earned in the savings account after 12 months on a balance of $2000 if the interest rate is 1.5% APY compounded yearly is $30
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Money in a particular savings account increases by about 6% after a year. How much money will be in the account after one year if the initial amount is $100?
Answers
Brooke has scores of 84, 72, 90, 95, and 87 on her first five quizzes. After taking the sixth quiz, Brooke's mean score increased. Which could be Brooke's sixth quiz score? Select three options. 85 90 83 86 92
Answers
Step-by-step explanation:
Mean average = (84 + 72 + 90 + 95 + 87) / 5 = 85.6
For the mean score to increase, the new score must be greater than 85.6.
Hence the correct options are 90, 86 and 92.
Answer:
b, d, and e
Step-by-step explanation:
You manage an appliance store that currently has excess warehouse inventory. You decide to offer a price reduction on washer-dryer combination sets. As a result of the price reduction, the company sells 36 combination sets, and this reduces their inventory by 25%. How many washer-dryer combination sets are in the warehouse after the sale? 27 70 108 144 864
Answers
Answer:
108Step-by-step explanation:
Let the amount of washer-dryer combination sets that are in the warehouse after the sale be x
Initial amount in the ware house is y
y - 36 = 75% of y
y - 36 = 0.75y
0.75y - y = -36
-0.25y = -36
y = 36/0.25
y = 144
The initial amount of wash dryer before sale is 144
After sale the amount of set in the house x = 144 - 36 = 108
Hence there 108 washer-dryer combination sets are in the warehouse after the sale
I need help with this.
Answers
Answer:
[tex]x + (3x - 9) = 5x - 30 \\ x + 3x - 9 = 5x - 30 \\ 4x - 9 = 5 x - 30 \\ - 9 + 30 = 5x - 4x \\ 21 = x \\ so..value \: of \: x \: is \: 21 \\ so. \\ <ACD = 5 \times 21 - 30 = 105 - 30 = 75° \\ < ACB = 180° - 75° = 115°[/tex]
<ACB = 105°
it is correct✅ ans.❤❤❤❤❤❤❤❤❤
plazzz mark is as a brilliant ansfind x it is multiple choice.
Answers
Answer:
25
Step-by-step explanation:
What Ps the value
of (100)^o
Answers
Answer:
(100)^0=1
Step-by-step explanation:
This follows the laws of indices
What is the value of X?
A: 15
B: 27
C: 45
D: 12
Answers
Answer:
D
Step-by-step explanation:
A.) what is the domain?
B.) what is the range?
C.) is this relation a function?
Answers
Answer:
The Domain is the set of all points over which a function is defined.
The range is the set of values the function takes on as output.
What’s the slope and y intercept of (3,4) and (0,-3)
Answers
Slope: 7/3
Y intercept: -3
use the diagram below to find the lengths of the following answer question 18-25. Be sure to include all necessary work. Leave your answer in the simplest radical form when necessary.
Answers
Answer:
18. AE = 6
19. BG = 6
20. CF = 5
21. GF = 2
22. CE = 3
23. AC = 3·√5
24. A_F = 10
25. DA = 3·(√5 - 1)
Step-by-step explanation:
Whereby the point C is the center of the circle, we have;
CB = CG = CE = 3 = The radius of the circle with center at C
CE = 3
CF = √(4² + 3²) = 5 by Pythagoras' theorem
CF = 5
GF = CF - CG = 5 - 3 = 2
GF = 2
BG = CB + CG = 3 + 3 = 6
BG = 6
Whereby, BC is a tangent to the circle with center, C, we have;
A_F = √(8² + 6²) = 10 by Pythagoras' theorem
A_F = 10
AE = A_F - EF = 10 - 4 = 6
AE = 6
AC = √(6² + 3²) = 3·√5 by Pythagoras' theorem
AC = 3·√5
DA = AC - CD = 3·√5 - 3 = 3·(√5 - 1)
DA = 3·(√5 - 1).
Plz, Help me with this question!!!!
Answers
Answer:
152y+125
Step-by-step explanation:
HELP ASAP!!!
If f(x) = -4x + 1, find f(2).
Enter the numerical value only
Answers
Answer:
-7
Step-by-step explanation:
-4(2)=-8
-8+1=-7........
Nathan earns $1500 a week. Calculate his new weekly wage if he receives a pay rise of 20%
Answers
Answer:
$1800
Step-by-step explanation:
1. Approanch
An easy way to calculate one's salary after they recive a raise is to, convert the percent that one's salary is increased into a decimal; divide the percent by 100. Then multiply the increase as a decimal by the original salary, to attain the amount the salary is raised by. Finally add the amount the salary is raised by to the original salary to find the new salary. A quicker way to do this is to convert the percent by the salary is increased into a decimal. Then add 1 to that number. Finally one will multiply that number by the original slary and get the new salary.
2. Solving
Original salary; 1500
Raise; 20%
a. convert the raise as a percent into a decimal, then add 1
20% = 0.2
0.2 + 1 = 1.2
b. multiply the number by the original salary
1.2 * 1500
1800
Answer:
$ 1800
Step-by-step explanation:
Rise in payment = 20% of 1500
[tex]= \frac{20}{100}*1500\\\\=20 *15\\\\= $300[/tex]
New weekly wage = 1500 + 300
= $ 1800
Urgent! Please help!
Solve the given equation:
3(x-2)^4/3 =243
Answers
Answer:
x is equal to 29.
Step-by-step explanation:
[tex]3(x - 2)^{\frac{4}{3}} = 243\\(x - 2)^{\frac{4}{3}} = 243 / 3\\(x - 2)^{\frac{4}{3}} = 243 / 3\\(x - 2) =( 243 / 3)^{\frac{3}{4}}\\x - 2 = 81^{\frac{3}{4}}\\x = 3^3 + 2\\x = 27 + 2\\x = 29[/tex]
Courtney works for the Red Cross and has been tasked with buying non-perishable items for families recently displaced by a hurricane. She finds a company willing to send her Meals-Ready-to-Eat (MREs) at a discounted price. Cases of small portion meals are $20.00 each and cases of large portion meals are $30.00 each. She buys a total of 20 cases and spends a total of $450.00.
Let x represent the number of small portion meals and let y represent the number of large portion meals. Write a system of equations, in terms of x and y, to model the situation. Enter your equations in the space provided.
Answers
9514 1404 393
Answer:
x + y = 2020x +30y = 450Step-by-step explanation:
The equation for the total number of cases is ...
x + y = 20
The equation for the total cost of the cases is ...
20x +30y = 450
_____
Additional comment
The solution to these equations is (x, y) = (15, 5).
There are 40 questions in a test and you get 75 % correct. How many
questions do you get right?
Answers
Answer:
30
Step-by-step explanation:
To solve this problem the way I would do it would be:
75% = 3/4
40 ÷ 4 = 10 × 4
Since you have 75% or 3/4 you add 1/4 3 times. 1/4 of 40 is 10 so add 10 3 times.
10 + 10 + 10 = 30
Answer:
[tex]30[/tex]
Step-by-step explanation:
[tex]40 \times \frac{75}{100} = \\ 40 \times \frac{3}{4} = 30[/tex]
uhh.i dumb the screenshot is here
Answers
Answer:
40
Step-by-step explanation:
Just use a calculator. I didn´t need to. My brother helped me a little
What is the value of x in the solution of the system x+y=3
y=-6x+3
Answers
disssss tooo helllllllpppp shoals shzn
Answers
Answer:
3/2
Step-by-step explanation:
Use this formula y2-y1/x2-x1
PLUG IN YOUR POINTS
-3 - -9/ 8- 4 =
6/4 (simplify)
1.5 or 3/2
Hope this helps ya!!
Can someone help me please
Answers
I think this is right
Find the slope of the line passing through the points (3, 4) and (8,-3).
Answers
Answer:
-1.4
Step-by-step explanation:
all right guys help me out a little bit no jokes this is worth 13 points I need help with 432 / 73
Answers
Answer:
5.91780821918
Step-by-step explanation:
432/73 is the same as 432 ÷73=5.91780821918
Hope this helps ∞<3
What is the product of 10x4 y2 and 3xy3 ?
Answers
Answer:
30x^5y^5
Step-by-step explanation:
What is the product of 10x4 y2 and 3xy3 ?
30x^5y^5
Ted sells cleaning supplies. He earns a monthly salary of $850.00, plus commission. He earns 5% commission on the first $10,000 in sales, and 7% commission on any sales over $10,000. If he sold $14,000 worth of supplies this month, how much will his pay be this month?
Answers
Answer:
$1830Step-by-step explanation:
Step one:
Ted's monthly salary =$850.00
since he made sales over $10,000. that is he sold supplies worth $14,000
his commission will be 7% of $14,000
=7/100*$14,000
=0.07*$14,000
=$980
Required
His total earnings
Step two:
Hence his total earnings is, his monthly salary plus 7% commission of supplies worth $14,000
=$850.00+$980.00
=$1830
y=x+6
x+y=8
now graph 3 points on the line x+y=8
Answers
Answer:
y=2
Step-by-step explanation:
advgdsfh usb hey do f ft h
Find the equation to the line , Please help !!!!
Answers
Answer:
y= -3/2 + 3
Step-by-step explanation:
first to answer gets brainliest im being nice so what is 2+2 XD
Answers
Answer:
4
Step-by-step explanation:
what else o3o
Answer:
2+2=4
Step-by-step explanation:
tysm!!
You spend 3 hours every day practicing the piano. What fraction of the day do you spend practicing the piano? Give your answer in simplest form.
Answers
Answer:
1/8th
Step-by-step explanation:
since there are 24 hours in a day
Answer: 1/8
Step-by-step explanation:
a day is 24 hours long. If you spend 3 hours out of 24 hours a day to practice piano it would be 3/24. Then to get it in simpilest form, you divide 3 by 3 and 24 by 3 which would get you the answer 1/8.
Hope i helped have a good rest of your day!!
Error Analysis
On a math test a student, Jake, has to identify all the coefficients and constants of
the expression 7b+ m + 8. Jake says that 7 is a coefficient and 8 is a constant. Identify all the
coefficients and constants of the expression. What error might Jake have made?
The coefficient(s) of the expression is are __
Use a comma to separate answers as needed.)
The constant(s) of the expression is/are __
(Use a comma to separate answers as needed.)
What error might Jake have made?
A. Jake said 7 is a coefficient. It is actually a constant.
OB. Jake said 8 is a constant. It is actually a coefficient.
OC. Jake did not include the constant 1.
OD. Jake did not include the coefficient 1.
Click to select your answer's).
Answers
The coefficient(s) of the expression is/are 7, 1
Use a comma to separate answers as needed.)
The constant(s) of the expression is/are 8
(Use a comma to separate answers as needed.)
What error might Jake have made?
OD. Jake did not include the coefficient 1.
Click to select your answer's