Sharon hits a golf ball off the ground. The function h represents the height of the golf ball, in feet, t seconds after it is hit. h(t) = -16(t − 3)2 + 144 Which of the following statements describes this situation correctly?
Answers
The statement which best describes the situation correctly is that the golf ball is on the ground at 0 and 6 seconds.
Given that:
Sharon hits a golf ball off the ground.
The function h represents the height of the golf ball, in feet, t seconds after it is hit.
h(t) = -16(t - 3)² + 144, which is a quadratic function.
Since the options contain the time when the ball hits the ground, it is required to find the time when the ball hits the ground.
When the ball is on the ground, the height is 0.
So, h(t) = 0
-16(t - 3)² + 144 = 0
-16(t - 3)² = -144
Divide both sides by -16.
(t - 3)² = 9
Take the square root on both sides.
t - 3 = ±√9
t - 3 = ±3
So, t = 3 + 3 and t = -3 + 3
So, t = 6 and t = 0
Hence, the ball hits the ground when t = 0 and t = 6, which is option B.
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The complete question is given below.
Related Questions
The Smiths spend 7% of their budget on entertainment. Their total budget this year is $1,000 more than
last year, and this year they plan to spend $3,150 on entertainment. What was their total budget last year?
Their total budget last year was
Answers
Answer:
Their total budget last year = $44,000
Step-by-step explanation:
Let last year's budget be x
let total budget this year be y
we are given the following information
y = 1000 + x - - - (1) (Their total budget this year is $1,000 more than last year)
7% of y = $3,150
7/100 × y = 3,150
0.07y = 3,150
y = 3,150 ÷ 0.07 = $45,000
Therefore, budget this year = $45,000
from equation 1
y = 1000 + x - - - (1)
∴ x = y - 1000
x = 45,000 - 1000 = $44,000
Therefore their total budget last year = $44,000
Final answer:
To find the Smiths' total budget last year, divide the amount they plan to spend on entertainment this year ($3,150) by 7% to calculate this year's budget ($45,000), then subtract the $1,000 increase from last year to reach the total budget for last year ($44,000).
Explanation:
To determine the Smiths' total budget last year, we need to work backwards from the amount they plan to spend on entertainment this year, which is $3,150. Given that entertainment costs represent 7% of their total budget, we can calculate their total budget for this year by dividing the entertainment expenditure by 7% (or 0.07). Once we have their budget for this year, we can subtract the $1,000 increase to find their budget for last year.
Let's calculate the total budget for this year:
Total budget this year = $3,150 / 0.07 = $45,000
Now, to find last year's budget, we subtract the $1,000 increase:
Total budget last year = $45,000 - $1,000 = $44,000
Therefore, the Smiths' total budget last year was $44,000.
A wheel whose diameter is 3 feet rolls a distance of 45 feet without slipping. Through what radian angle did the wheel rotate? 1) 30 2) 25 3 30 pi 4) 12 pi
Answers
Answer:
1) 30
Step-by-step explanation:
We need the radius of the wheel, we know that the radius is half the diameter, therefore:
r = d / 2 = 3/2 = 1.5
the angle is equal to the distance traveled (s) divided by the radius, thus:
° A = s / r =
° A = 45 / 1.5
° A = 30 radians
Through the radiation angle of 30 radians the wheel turned
therefore the answer is 1) 30
The radian angle at which the wheel rotated is; 1: 30
What is the angle of rotation?
We are given;
Diameter of wheel; d = 3 ft
Radius; r = d/2 = 3/2 = 1.5 ft
Now, the formula for the radian angle at which the wheel rotated is;
θ = s/r =
where;
s is distance
r is radius
Thus;
θ = 45/1.5
θ = 30 radians
Thus the angle at which the wheel rotated is 30 radians
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Ulissa is making a birthday card and wants to put a border made of pink ribbon all the way around the front of the card. The card is a rectangle 7 inches long and 4 inches wide. How long will the pink border be?
Answers
Answer:
22 inches
Step-by-step explanation:
7 + 7 = 14
4 + 4 = 8
14 + 8 = 22
which statement is true about the potential solutions to log3(2x^4 +8x^3) -3log3x =2log3x please help!
Answers
Answer:B
Step-by-step explanation:
Answer:
b. Only x = –2 is an extraneous solution.
Step-by-step explanation:
edge 2021
(:
If you help me get this right i will give you brainly, and 5 stars!
Answers
Answer:
all 3 statements are true
Step-by-step explanation:
domain is the x value or the first number in the parentheses
range is the y value or the second number in the parentheses
Answer:
1. True.
2. True.
3. True.
Step-by-step explanation:
The domain contains X coordinates, and the range contains Y coordinates. From the given list of coordinates, the domain contains numbers 2, 3, 5, and 6.
The range contains numbers 1, 4, 5, and 7, making questions 1 and 2 true.
Both the domain and range contain the number 5, so question 3 is also true.
I woke up at 6:47 a.M. I spent 25 minutes showering and getting dressed then I walked down stairs. I got downstairs at _______. I then ate breakfast and read a book for ____ minutes before leaving the house at 7:42 a.M.
Answers
Answer:
You got down stairs at 7:12, and you ate breakfast and read a book for 30 minutes.
Step-by-step explanation:
6:47 + 25 = 7:12
7:42 - 7:12 = 30 minutes
Hope this help
The first four terms of a sequence are shown below.
2,9,40.5,182.25 ...
what is the next number in the sequence?
Answers
Answer:
820.125
Step-by-step explanation:
2*4+2/2=9
9*4+9/2=40.5
40.5*4+40.5/2=182.25
182.25 * 4 + 182.25/2 = 820.125
What is 0.313131 as a fraction
Answers
Answer
the answer for this question is 31/99
x = 0.3131313...
100x = 31.31313...
99x = 31
x = 31/99
Kayla’s work to find the surface area of a composite solid formed when a rectangular prism and rectangular pyramid are joined at their bases is shown below. SA = 2 ((5) (7)) + 2 ((6) (7)) + 2 (one-half (5) (9.3)) + 2 (one-half (6) (9.2)) = 255.7 square units What statement best describes Kayla’s error? She used the wrong expression for the lateral faces of the solid. She should have simplified 2 (one-half (5) (9.3)) + 2 (one-half (6) (9.2)). She left out one of faces of the solid. She should have simplified 2 ((5) (7)) + 2 ((6) (7)) + 2 (one-half (5) (9.3)) + 2 (one-half (6) (9.2)) + (5) (6). She used the wrong expression for the lateral faces of the solid and left out the base of the figure. She should have simplified 2 (one-half (5) (9.3)) + 2 (one-half (6) (9.2)) + (5) (6). She included the face where the pyramid and prism are joined together. She should have simplified 2 ((5) (7)) + 2 ((6) (7)) + 2 (one-half (5) (9.3)) + 2 (one-half (6) (9.2)) minus 2((5) (6)). SA = 2 ((5) (7)) + 2 ((6) (7)) + 2 (one-half (5) (9.3)) + 2 (one-half (6) (9.2)) = 255.7 square units
What statement best describes Kayla’s error?
She used the wrong expression for the lateral faces of the solid. She should have simplified 2 (one-half (5) (9.3)) + 2 (one-half (6) (9.2)).
She left out one of faces of the solid. She should have simplified 2 ((5) (7)) + 2 ((6) (7)) + 2 (one-half (5) (9.3)) + 2 (one-half (6) (9.2)) + (5) (6).
She used the wrong expression for the lateral faces of the solid and left out the base of the figure. She should have simplified 2 (one-half (5) (9.3)) + 2 (one-half (6) (9.2)) + (5) (6).
She included the face where the pyramid and prism are joined together. She should have simplified 2 ((5) (7)) + 2 ((6) (7)) + 2 (one-half (5) (9.3)) + 2 (one-half (6) (9.2)) minus 2((5) (6))
Answers
Answer:
Option B
Step-by-step explanation:
The reason is because the surface area is not including the base of the pyramid and the top of the prism.
Option b. she left out one of the faces of the solid she should have simplified 2((5)(7))+2((6)(7))+2[1/2(5)(9.3)]+2[1/2(6)(9.2)]+(5)(6)
Step-by-step explanation:
we know that
The surface area of the composite figure is equal to the surface area of the pyramid not including the base plus the surface area of the prism not including the top
so
SA= 285.7 units squared
Answer:
B
Step-by-step explanation:
Which transformations are needed to change the parent cosine function to the cosine function below?
vertical stretch of 2, horizontal stretch to a period of 2 pi, phase shift of StartFraction pi Over 2 EndFraction units to the right, vertical shift of 1 unit up
vertical compression of 2, horizontal stretch to a period of StartFraction pi Over 4 EndFraction, phase shift of StartFraction pi Over 4 EndFraction units to the left, vertical shift of 2 units down
vertical compression of 2, horizontal compression to a period of 4 pi, phase shift of StartFraction pi Over 3 EndFraction units to the left, vertical shift of 1 unit down
vertical stretch of 2, horizontal compression to a period of StartFraction pi Over 2 EndFraction, phase shift of Pi units to the right, vertical shift of 1 unit down
Answers
Question:
1. vertical stretch of 2, horizontal stretch to a period of 2 pi, phase shift of StartFraction pi Over 2 EndFraction units to the right, vertical shift of 1 unit up
2. vertical compression of 2, horizontal stretch to a period of StartFraction pi Over 4 EndFraction, phase shift of StartFraction pi Over 4 EndFraction units to the left, vertical shift of 2 units down
3. vertical compression of 2, horizontal compression to a period of 4 pi, phase shift of StartFraction pi Over 3 EndFraction units to the left, vertical shift of 1 unit down
4. vertical stretch of 2, horizontal compression to a period of StartFraction pi Over 2 EndFraction, phase shift of Pi units to the right, vertical shift of 1 unit down
Answer:
The correct option is;
4. Vertical stretch of 2, horizontal compression to a period of π/2, phase shift of π units to the right, vertical shift of 1 unit down
Step-by-step explanation:
Here, we have the parent cosine function given by y = cos(x)
A plot of the above function is attached
By comparison, it is observed that the transformation required to change the parent function includes;
1. Vertical stretch from the parent function of amplitude 1 to amplitude 2
2. A horizontal compression so that the period of one complete revolution is π/2 rather than 2·π in the parent cosine function
3. Phase shift of pi units to the right such that cos(π) = 1 rather than cos(2π) = 1 as it applies to the parent function
4. Shift of the y values from the symmetrical x-axis origin downwards by 1 unit such that the maximum y value of the doubly stretched transformation is 1 rather than 2
What are the solutions of x2 + 10x + 16 = 0?
x2 + 10x + 16 = 0
(x + 2)(X + 8) = 0
x + 2 = 0 or X + 8 = 0
and x =
1. Write the equation in standard form.
2. Factor the polynomial.
3. Apply the zero product property.
4. Solve the resulting equations.
Answers
Answer:
-2 and -8
Step-by-step explanation:
on edge
Answer:
x = -2 and x = -8
Step-by-step explanation:
I don't know if you can see the screenshot but I got it right on edge. Good luck :)
Find each percentage of 60.
3% of 60
Answers
Answer:
1.8
Step-by-step explanation:
We want 3% of 60 = 0.03 * 60 = 1.8
= 1.8
3% of 60 is 1.8
If sin Θ = 2 over 3 and tan Θ < 0 , what is the value of cos Θ?
Answers
[tex]\sin \theta = \dfrac 2 3[/tex]
[tex]\tan \theta < 0[/tex]
Positive sine, negative tangent, means we have a negative cosine. We're talking about the second quadrant.
[tex]\cos^2 \theta + \sin ^2 \theta = 1[/tex]
[tex]\cos^2 \theta = 1 - \sin ^2\theta[/tex]
[tex]\cos \theta = \pm \sqrt{1 - \sin ^2\theta}[/tex]
We know it's negative,
[tex]\cos \theta = - \sqrt{1 - (2/3)^2} =-\sqrt{5/9} = - \dfrac 1 3 \sqrt{5}[/tex]
Answer: -(1/3)√5
A sample of bacteria is growing at a rate of 8% per hour compound continuously. How many hours will it take for the sample to double? Round your answer up to the nearest whole number and do not include units
Answers
Answer:
The sample would double in 9 hours
Step-by-step explanation
The number of hours it will take for the sample to double can be found using the 72 rule.
The 72 rule is such that a growth rate would double itself by it is used in dividing the number 72 as shown below:
number of hours =72/8=9 hours
The number of hours it would take the sample to double is 9 hours as computed above.
78 is what percent of 450
Answers
Answer:
17.33
Step-by-step explanation:
plug 78/450 into your calculator
78 is 17.33% of percent of 450.
78 is what percent of 450?A percentage is defined as the ratio that can be expressed as a fraction of 100.
To calculate what percent of 450 is 78, we can use the following formula:
percent = (part / whole) * 100
In this case, the part is 78 and the whole is 450. Thus, we have:
percent = (78 / 450) * 100
percent = 17.33%
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Kevin is taking a two-part test in social studies
Part 1 is multiple choice and worth 60 points.
Part 2 is an essay portion and worth 40 points.
He must earn at least 86 points to pass the
class. If his teacher already graded Part 1
and he earned 54 points, how many points
will he need to earn on Part 2? Help asap!!!!!
Answers
Answer:
32
Step-by-step explanation:
subract the amount he needs by the number he has
There are 32 points will he need to earn on Part 2.
What is mean by Subtraction?Subtraction in mathematics means that is taking something away from a group or number of objects. When you subtract, what is left in the group becomes less.
We have to given that;
Kevin is taking a two-part test in social studies.
Part 1 is multiple choice and worth 60 points.
And, Part 2 is an essay portion and worth 40 points.
Here, He must earn at least 86 points to pass the class.
And, His teacher already graded Part 1 and he earned 54 points.
Hence, Number of points will he need to earn on Part 2 is,
⇒ 86 - 54
⇒ 32
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4. A cylinder has a height of 7 cm and a base with a diameter of 10 cm. Determine the volume, in cubic centimeters, of the cylinder in terms of pi
Answers
Answer:
[tex]549.8cm^{3}[/tex]
Step-by-step explanation
identify the variables - h = 7 d = 10
radius is half of the diameter - r = 5
V = πr2h use volume of a cylinder formula
V = π(5) (7) substitute variables into formula
V = 549.778714378 multiply
V = [tex]549.8cm^{3}[/tex] round to the nearest tenths place
Final answer:
To find the volume of a cylinder with a given height and base diameter, you need to use the formula V = πr²h. In this case, with a base diameter of 10 cm and a height of 7 cm, the volume is 275.75 cm³.
Explanation:
In this case, we are dealing with the volume of a cylinder with a given height and base diameter. The formula to find the volume of a cylinder is V = πr²h, where r is the radius and h is the height.
Given the base diameter of 10 cm, the radius (r) is half of the diameter, so r = 5 cm. Plugging in the values, we get V = 3.142 × (5 cm)² × 7 cm = 275.75 cm³.
Sylvia earns $7 per hour at her after school job. After working one week, she received a paycheck for $91.
a. Write and solve an equation to find the number of hours Sylvia worked to earn $91.
b. The greatest number of hours Sylvia can work in any week is 15. Write an inequality to represent this statement.
c. What is the greatest amount of money Sylvia can earn in one week?
please help
Answers
Answer:
a.) [tex]hours=13[/tex]
b.) [tex]h\leq 15[/tex]
c.) $[tex]$105[/tex]
Step-by-step explanation:
a.) If she earns $7 'per' hour, this multiplication. After a week, we need to see how many hours she worked to earn $91, so this goes behind the equal sign. Let h be the unknown number of hours:
[tex]7h=91[/tex]
Solve for h. Divide both sides by 7:
[tex]\frac{7h}{7}=\frac{91}{7}\\\\h=13[/tex]
Sylvia worked 13 hours at a rate of $7 an hour.
b.) She can work at most 15 hours a week. At 'most' can also mean less than or equal to. Let h be hours:
[tex]h\leq 15[/tex]
Sylvia can work less than or equal to 15 hours per week.
c.) If Sylvia can work 15 hours, plug in this value for h into an equation when she earns $7 per hour. Let the product of the hours and money equal t for total:
[tex]t=7(15)\\t=105[/tex]
The most money Sylvia can earn in a week is $105.
Finito.
A cube has an edge length of 2/3 inch . What is the volume of the cube ?
Answers
Answer:
The volume would be eight inches. I hope this helps.
Brainliest welcome
Step-by-step explanation:
Final answer:
The volume of a cube with an edge length of 2/3 inch is found by cubing the edge length, which results in a volume of 8/27 cubic inches.
Explanation:
To find the volume of a cube with an edge length of 2/3 inch, we use the formula for the volume of a cube, which is the edge length cubed (V = [tex]s^3[/tex]). Thus, the volume V is:
V = (2/3 inch) * (2/3 inch) * (2/3 inch)V = ([tex]2^3[/tex])/([tex]3^3[/tex]) cubic inchesV = 8/27 cubic inchesTherefore, the volume of the cube is 8/27 cubic inches.
A three-dimensional model of Lucia’s apartment is shown. To cool the whole apartment, an air conditioner must provide 2.5 BTUs per cubic foot. How many BTUs are needed to cool Lucia’s apartment? 19,600 BTUs 19,800 BTUs 20,400 BTUs 24,000 BTUs
Answers
Answer: c
Step-by-step explanation:
20,400
Factor x2 + 5x - 24 A) (x + 8)(x - 3) B) (x + 3)(x - 8) C) (x + 6)(x + 4) D) (x + 2)(x - 12)
Answers
Answer:
a) (x+8) (x-3)
Step-by-step explanation:
the 2 factors of -24 that equal 5 is 8 and -3 because 8×-3 is -24 and 8-3 is 5.
whole numbers greater than 15 but less than 16
Answers
Answer:
There are no whole numbers greater than 15 but less than 16... I am pretty sure it cant be 15 1/2 or something like that...
Step-by-step explanation:
Help me answer this please : The new cost of an iPhone 11 is $700. You decide to put this on your credit
card that earns 9% (0.09). When the bill comes in you pay off $200,
meaning you still owe $500. How much interest will you be charged? And what will your new total bill be?
Answers
Answer:
No I will never ever help you
To calculate the interest charged on the credit card, subtract the amount paid off from the new cost of the iPhone 11 and multiply it by the interest rate and time. The interest charged is $45. The new total bill will be $545.
Explanation:To calculate the amount of interest charged on the credit card, we need to find the difference between the new cost of the iPhone 11 ($700) and the amount you paid off ($200). This difference will be the initial principal amount on which interest is charged.
Interest is calculated using the formula: interest = principal x rate x time. In this case, the principal is $500 (the remaining amount owed), the rate is 0.09 (9% as a decimal), and the time is 1 year since the interest is calculated annually for credit cards.
Using this information, we can calculate the interest charged: interest = $500 x 0.09 x 1 = $45.
To find the new total bill, we add the interest charged to the remaining amount owed: new total bill = $500 + $45 = $545.
can someone help me with this
Answers
Answer:
A) 24 ft³
Step-by-step explanation:
The area of the right triangle base is ...
A = (1/2)(3)(4) = 6 ft²
The volume of the triangular prism is the product of the area of its base (6 ft²) and its height (4 ft).
V = Bh = (6 ft²)(4 ft) = 24 ft³ . . . . matches choice A
_____
Comment on the triangle
You know the 3-4-5 triangle is a right triangle, because you have seen those numbers many times in relation to the Pythagorean theorem. If you don't know that, then you can check to see by using the Pythagorean theorem:
5² = 3² +4²
25 = 9 + 16 . . . . . true; so the triangle is a right triangle
In any event, there are other means for finding the area of the triangle based on the lengths of its sides. You will get the same area result.
Using Heron's formula, s = (a+b+c)/2 = (3+4+5)/2 = 6.
A = √(s(s -a)(s -b)(s -c)) = √(6(3)(2)(1)) = √36 = 6 . . . . area of base triangle
if√y - 2 = 8 then y =
Answers
Answer:
100
I want brainliest
Step-by-step explanation:
sqareroot of y -2=8
10-2=8
sqare root 10^2-2=8
y=100
Answer:
y = 100
Step-by-step explanation:
Assuming you mean sqrt(y) - 2 = 8
Add 2 to each side
sqrt(y) - 2+2 = 8+2
sqrt(y) = 10
Square each side
y = 10^2
y = 100
Mrs. Brown gives two tests to her class. 30% of the class passed both tests and 45% of the class passed the first test. What percent passed the second test given that they passed the first test?
Answers
66.67% of the students who passed the first test also passed the second test.
To find the percent of students who passed the second test given that they passed the first test, we need to calculate a conditional probability. Let's define the events:
A: Passing the first testB: Passing the second testWe are given:
Probability of both events happening (passing both tests), P(A ∩ B) = 30% or 0.30Probability of passing the first test, P(A) = 45% or 0.45The conditional probability P(B|A) can be calculated using the formula:
P(B|A) = P(A ∩ B) / P(A)
Substitute the given values into the formula:
P(B|A) = 0.30 / 0.45
When we divide 0.30 by 0.45, we get 0.6667 or approximately 66.67%.
Therefore, 66.67% of the students who passed the first test also passed the second test.
What is the area of a rectangle with a base of 12mm and a height of 1.4mm?
Answers
Answer: 16.8mm2
Step-by-step explanation:
12x1.4=16.8
solve some algebra problems using the properties of equality...
pls help i’m horrifyingly bad a math i understand nothing :(((
Answers
Answer:
a. Property 1
b. Property 2
Step-by-step explanation:
In this case, what we will do is say the properties of the equations, which are 4, the following:
Property 1: When a number is added or subtracted to both sides of equality, equality remains.
Property 2: When multiplied or divided by the same number, other than zero, on both sides of equality, equality remains.
Property 3: When both members of equality are raised to a nonzero power, equality remains.
Property 4: When the same root is extracted, on both sides of the equality, equality remains.
In other words, property 1 is used in part a and property 2 is used in part b.
can someone help me with this question please
Answers
Answer:
C. the vertical scale does not start at zero.
Step-by-step explanation:
The bars should be longer than they are drawn because the scale does not start at zero. As it is visual comparisons of the different months is misleading.
For example, it looks like the sales for February are about twice the March sales but that is not true.
AKS 18/19 A travel agent is arranging a private cruise. The agent can arrange for, at most, 40 people to go on the trip. The trip cannot be finalized unless there are at least 12 men and 15 women committed to the cruise. The agent will make $26 profit per man and $14 profit per woman. What are the constraints for this situation?
Answers
Answer:
M + W <= 40
M >= 12
M >= 15
Total profit = $26 * M + $14 * W
Step-by-step explanation:
Let the number of men be denoted by M
number of women be denoted by W
Maximum no of people that can go one trip = 40
Therefore representing it mathematically we have
M + W <= 40 -------------- CONSTRAINT 1
Minimum number of men needed on trip = 12
Therefore representing it mathematically we have
M >= 12 CONSTRAINT 2
Minimum number of women needed on trip = 15
Therefore representing it mathematically we have
M >= 15 CONSTRAINT 3
profit on 1 man = $26
profit on M men = $26 * M
profit on 1 woman = $14
profit on M men = $14 * W
Total profit combining for men and women =
$26 * M + $14 * W -------------CONSTRAINT 4
___________________________________________
writing together all the constraint
M + W <= 40
M >= 12
M >= 15
Total profit = $26 * M + $14 * W