Answer:
a) The height of the building is 12 metres.
b) The ball will take 6 seconds to hit the ground.
c) The maximum height of the ball is 16 metres and occurs 2 seconds after launch.
d) The ball have a height of 7 meters above the ground 5 seconds after launch.
Step-by-step explanation:
a) The roof of the building is represented by the initial height of the ball according to the function. If we know that [tex]t = 0\,s[/tex], the height of the building, measured in metres, is:
[tex]y = -(0\,s)^{2}+4\cdot (0\,s) + 12[/tex]
[tex]y = 12\,m[/tex]
The height of the building is 12 metres.
b) Let equalise the given polynomial and solve for [tex]t[/tex] to determine the time taken for the ball to hit the ground:
[tex]-t^{2}+4\cdot t +12 = 0[/tex] (1)
By the Quadratic Formula, we find the following solutions:
[tex]t_{1} = 6\,s[/tex] and [tex]t_{2} = -2\,s[/tex]
Since time is a positive variable, then the only solution that is physically reasonable is:
[tex]t = 6\,s[/tex]
The ball will take 6 seconds to hit the ground.
c) The maximum height of the ball occurs when speed is equal to zero. First, we differentiate the function and equalise to zero:
[tex]-2\cdot t + 4 = 0[/tex] (2)
[tex]t = 2\,s[/tex]
Lastly, we evaluate the function at given time:
[tex]y = -(2\,s)^{2}+4\cdot (2\,s)+12[/tex]
[tex]y = 16\,m[/tex]
The maximum height of the ball is 16 metres and occurs 2 seconds after launch.
d) We equalise the height formula to seven and solve the resulting polynomial:
[tex]-t^{2}+4\cdot t + 12 = 7[/tex]
[tex]-t^{2}+4\cdot t +5 = 0[/tex] (3)
By the Quadratic Formula, we get the following solutions:
[tex]t_{1} \approx 5\,s[/tex] and [tex]t_{2} \approx -1\,s[/tex]
The only solution that is physically reasonable is [tex]t = 5\,s[/tex].
The ball have a height of 7 meters above the ground 5 seconds after launch.
Use synthetic division and the Remainder Theorem to find f(4) if f(x) = – 2x3 + 9x2
2x3 + 9.c- 6x + 7
Step-by-step explanation:
Let's see. f(4) makes the divisor x-4
4|-2 9 -6 7
| 8 -68 296
-2 17 -74 2072
The quotient is -2x²+17x-74 with a remainder of 2072
Mariana jarred 42 liters of jam after 6 days. How much jam did Mariana jar if she spent 7
days making jam? Assume the relationship is directly proportional.
PLLLLZZZZZZZZZZZZZZ HELPPPP ASAP 10 POINTS!
AND PLZ do both if u can!! <3 :(
Answer:
13p and 4p+3
Step-by-step explanation:
Add similar elements: 12p+p=13p
Add/Subtract the numbers: 6-3=3
What is the slope of the line?
6x+10y=8
Answer:
First, get it into slope-intercept:
y = -3/5x + 4/5
The slope is -3/5
Step-by-step explanation:
Round your answer to the nearest hundredth BC=
Answer:
BC = 4.92
Step-by-step explanation:
cos 35° = [tex]\frac{?}{6}[/tex]
BC = 6 x cos 35°
BC = 6(.82) = 4.92
You carry a balance of $2065.00 on a credit card at a 17.25% APR for five months how much is your total payment by the fifth month $2213.14
A 2213.42
B 2077.37
C 2421.21
D 2094.68
The state of California takes about 8% of your income for income tax. How much of your money do you owe California in taxes each month?
Answer:
you can't answer it without knowing how much money they have to multiply it by the 8% to find out what you'll be paying out to California each month
Step-by-step explanation:
you have to know your monthly income to know how much you're paying out in California
Correct answer will get Brainlyist!
Answer:
Option B
Step-by-step explanation:
Question 7
1). √14 + 6.2 < 3π - 8.2
Since, 14 is the nearest whole square number to 16
√14 ≈ √16 ≈ 4
Similarly, π ≈ 3.14 ≈ 3
By substituting these approximate values in the inequality,
4 + 6.2 < 3(3) - 8.2
10.2 < 9 - 8.2
10.2 < 0.8
False.
2). [tex]\frac{17}{5}+\sqrt{64}>8+\pi[/tex]
[tex]\frac{17}{5}+8>8+\pi[/tex]
3.4 + 8 > 8 + 3.14
11.4 > 11.14
True.
3). 35 - √40 > 6π
[Since, nearest whole square integer to 40 is 36 and π ≈ 3]
35 - √36 > 6(3)
35 - 6 > 18
29 > 18
True.
Therefore, Option B is the correct option.
3x-7-8+5x2 -x given x=-3
Answer:
-46
Step-by-step explanation:
-9-7-8-15-6-1 equals -46
The equations of four lines are given. Identify which lines are perpendicular.
Line 1: y=-5
Line 2: g=12-1
Line 3: r=-6
Line 4: y+5= -4(2+1)
Jane scored 4 times as many points as Lenny did in basketball. The sum of their scores was 35. How many did each score?
Answer:
Jane scored 28 and Lenny scored 7
Step-by-step explanation:
What is 69+69 please fast I need for test
Answer:
138
Step-by-step explanation:
Thats the answer bcus yea
Answer:
you can't rickroll be with 69
Step-by-step explanation:
but it is 138
Please answer correctly and write explanation
Answer:
the 3rd choice, 10x + 5, looks good
Step-by-step explanation:
a coefficient is the number in front of a variable , so that's 10
a constant is a number w/o a variable ... so that's 5
I believe that the answer is 10x + 5.
Coefficents are also know as "multipliers". They pair with variables (in this case, that is x). Constants are simply numbers on their own.
Hope that makes sense.
solve for y.
-38=7y+17-12y
Answer:
y=11
Step-by-step explanation:
Im so 100 percent sure but thats mostly the right answer
Answer:
y = 11
Step-by-step explanation:
-38 = 7y + 17 - 12y
-38 = -5y + 17
-17 -17
-55 = -5y
divide both sides by -5
11 = y
or y = 11
Hope this helps!!!
Suppose you deposit $2,000 in a savings account that pays interest at an annual rate of 6%. If no money is added or withdrawn from the account, answer the following questions.
a. How much will be in the account after 4 years?
b. How much will be in the account after 17 years?
c. How many years will it take for the account to contain $2,500?
d. How many years will it take for the account to contain $3,000?
Answer:
a. $2480b. $4040c. 4 years and 2 monthsd. 8 years and 4 monthsStep-by-step explanation:
a. Account after 4 years:
2000 + 4*2000*0.06 = $2480b. Account after 17 years:
2000 + 17*2000*0.06 = $4040c. Time when account = $2500:
2000 + x*2000*0.06 = 2500120x = 500x = 500/120x = 4 20/120 = 4 2/12 years = 4 years and 2 monthsd. Time when account = $3000
2000 + x*2000*0.06 = 3000120x = 1000x = 1000/120x = 8 40/120 = 8 4/12 years = 8 years and 4 monthsFind the x-intercept and y-intercept of the line. -3x+6y=11
Answer:
x- intercept is at [tex]( - 3 \frac{2}{3} ,0)[/tex].
y- intercept is at [tex](0,1 \frac{5}{6} )[/tex].
Step-by-step explanation:
The x-intercept occurs when y=0.
Thus, substitute y= 0 into the equation to find the x- intercept.
-3x +6y= 11
When y= 0,
-3x +6(0)= 11
-3x= 11
x= 11 ÷ (-3)
[tex]x = - \frac{11}{3} \\ x = - 3 \frac{2}{3} [/tex]
The y-intercept occurs at x= 0.
When x= 0,
-3(0) +6y= 11
6y= 11
y= 11÷ 6
[tex]y = 1\frac{5}{6} [/tex]
If y varies inversely as x and y=10 when x= 5, find y when x= 5
Answer:
x = 10 when y = 5Step-by-step explanation:
Note: y = 10 when x = 5 is already given, must be find x for y = 5.
y = k/x is the formula, using the given values finding the constant:
10 = k/5k = 10*5k = 50So for y=5 we have:
5 = 50/xx = 50/5x = 10Washington High School is building a new running track. The track is constructed from a rectangle and two semicircles. 51 ft 250 ft Part A Determine the distance the runners run around the edge of the track. Round to the nearest whole number. Use 3.14 for T. feet Part B The inside of the track will all be grass. Determine the area of grass needed to fill in the track. Round to the nearest whole number. Use 3.14 for it. square feet
Answer:
660 ft
Step-by-step explanation:
I got it right ✅ khhgu y jnj
Answer:
660ft
Step-by-step explanation:
-14-3x-9-12x=15
Combine Like Terms
Answer:
-15x - 23 = 15
General Formulas and Concepts:
Algebra I
Combining Like TermsStep-by-step explanation:
Step 1: Define Equation
-14 - 3x - 9 - 12x = 15
Step 2: Simplify
Combine like terms (x): -15x - 14 - 9 = 15Combine like terms (Z): -15x - 23 = 15A bird is flying 10 feet above the water.A fish is swimming 4 feet below the water
Answer:
-4 for fish
+10 for birds
Step-by-step explanation:
CHECK THE COMPLETE QUESTION BELOW
A bird is flying 10 feet above the water, a fish is swimming 4 feet under the water. What number represents the location of the fish on the number line. Iready lesson
A number line can be regarded as a straight line having a number with equal interval with both positive and negative sides
The number that represents the location of the fish on the number line is -4 while that of bird is +10
CHECK THE ATTACHMENT FOR THE NUMBER LINE
Answer: it should be -4
Step-by-step explanation: Hope this help
Question1 of 10
Which is the best definition of an equilateral triangle?
O A. A triangle that has at least two congruent sides
OB. A triangle that has three congruent sides
O C. A triangle in which no two sides are congruent
SUBMIT
determine if the triangle is sss, sas, asa, or aas or none.
Which of the numbers given below is an irrational number ?
0
2.14
2.14367.....................
Answer:
2.14367............. is a irrational number.Kia buys a shirt that costs $12.50 and some pairs of socks that are $2.50 each. She pays a total of $27.50 How many pairs of socks did Kia buy? Write your solution in a complete sentence.
Answer:
6
Step-by-step explanation:
Given that:
Cost of shirt = $12.50
Cost per socks = $2.50
Total amount paid = $27.50
How many pairs of socks was purchased =?
Let Number of socks purchased = x
Total amount paid = cost of shirt + (cost per socks * number of socks)
27.50 = 12.50 + (2.50 * x)
27.50 = 12.50 + 2.50x
27.50 - 12.50 = 2.50x
15 = 2.50x
x = 15 / 2.50
x = 6
Number of pairs purchased = 6
please help!!! worth 15 pts
Answer:
clue 1 with graph 3, Clue 2 with graph 4, clue three with graph 1, and clue 4 with graph 2
Step-by-step explanation:
Hope this helps :)
Wendy spends 3/5 of her money on 3 bowls and 8 plates. With the rest of your money, you can buy another 6 bowls. If you spend all your money just on plates, how many plates can you buy?
answer: 16 plates
I apologize if this is an incorrect answer,however, I believe that the fraction was added to throw you off. so if you divide the number of bowls you get 2 and then you multiply 8 by 2
If you spend all your money just on plates. Then the number of plates that you can buy will be 20.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
Wendy spends 3/5 of her money on 3 bowls and 8 plates. With the rest of your money, you can buy another 6 bowls.
Let 'x' be the cost of each bowl, 'y' be the cost of each plate, and 'T' be the total amount of money. Then the equations are given as,
3x + 8y = (3/5) T ...1
6x = (2/5) T
x = (1/15) T ...2
From equations 1 and 2, then the cost of each plate is calculated as,
3(1/15)T + 8y = (3/5)T
8y = 2/5
y = (1/20)T
If you spend all your money just on plates. Then the number of plates that you can buy will be given as,
⇒ T / (T / 20)
⇒ 20
More about the solution of the equation link is given below.
https://brainly.com/question/545403
#SPJ2
What is 0.1x30 I need help for this problem in math
Answer:
3
Step-by-step explanation:
Answer:
3
Step-by-step explanation:
Which expression is equivalent to 16+8?
A.2{8+4}
B.4{4+8}
C.4{4+1}
D.2{8+5}
Answer:
A
Step-by-step explanation:
Which one is greater 0.05 or 0.050
They are both equal
0.05 = 0.050
Hope this helps
Answer:
equal
Step-by-step explanation:
0.05 = 0.050
if the relationship is proportional, what is the missing value from the table? -18 -15 15 18
Answer:
B
Step-by-step explanation: