Answer:
18 feet
Step-by-step explanation:
After each bounce, the ball reaches only a percentage of the maximum height it reached before.
The first height is 36 feet, after the first bounce, it will be 36*r, where r is the ratio of the height the ball can still reach by the previous maximum height.
In the second bounce, the height is 36*r^2
In the third bounce, the height is 36*r^3
In the fourth bounce, the height is 36*r^4, and this value is 2.25 ft, so:
36*r^4 = 2.25
r^4 = 2.25/36
r^4 = 0.0625
r = 0.5
So, after the first bounce, the height is:
36*r = 36*0.5 = 18 feet
The height should be 18 feet.
Given that,
You drop a ball from a stair case that is 36 ft high. By the time you get down the stairs to measure the height of the bounce, the ball has bounced four times and has a height of 2.25 ft after its fourth bounce.Based on the above information, the calculation is as follows:
The first height is 36 feet.
Now after the first bounce, it will be 36r
Here r is the ratio of the height
In the second bounce, the height is [tex]36\times r^2[/tex]
In the third bounce, the height is [tex]36\times r^3[/tex]
In the fourth bounce, the height is [tex]36\times r^4[/tex], and this value is 2.25 ft, so:
Now
[tex]36\times r^4 = 2.25\\\\r^4 = 2.25\div 36\\\\r^4 = 0.0625[/tex]
r = 0.5
Now
So, after the first bounce, the height is:
= 36r
= 36(0.5)
= 18 feet
Therefore we can conclude that The height should be 18 feet.
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9-18
Use what you have learned about triangles and angles to write an equation that represents each situation. Then find each of the missing angles in the triangles below.
9-19.
Additional Challenge: Use what you know about triangles and angle relationships to find the missing angles in the triangles below.
Answers and Step-by-step explanations:
9-18.
a) All the angles of a triangle add up to 180, by definition. So, we can write the expression: 30 + 115 + x = 180.
Then, we can just solve for x by subtracting 30 and 115 from both sides:
x = 180 - 115 - 30 = 35 degrees
b) Again all three angles should add up to 180, so:
x + x + x = 180 ⇒ 3x = 180 ⇒ x = 180/3 = 60 degrees
9-19.
a) These angles add up to 180:
2x + x + 30 = 180 ⇒ 3x + 30 = 180 ⇒ 3x = 150 ⇒ x = 50
2x = 50 * 2 = 100
The missing angles are 100 degrees and 50 degrees.
b) Again, these add up to 180:
x + 10 + x + 90 = 180 ⇒ 2x + 100 = 180 ⇒ 2x = 80 ⇒ x = 40
x + 10 = 40 + 10 = 50
The missing angles are 50 degrees and 40 degrees.
Hope this helps!
Answer:
9-18
a)
x = 180 - (115 + 30) = 180 - 145 = 35°
b)
3x = 180 => x = 180 : 3 => x = 60°
9-19
a)
180 = x + 2x + 30
180 - 30 = 3x
3x = 150
x = 50°
b)
180 = x + 10 + x + 90
180 - 10 - 90 = 2x
2x = 80
x = 40°
Consider the steps to solve the equation. 2 5 ( 1 2 y + 20 ) − 4 5 = 9 20 (2y − 1) Distribute: 1 5 y + 8 − 4 5 = 9 10 y − 9 20 What is the next step after using the distributive property? Use the multiplication property of equality to isolate the variable term on one side of the equation. Use the multiplication property of equality to isolate the constant on one side of the equation. Combine the like terms on the right side of the equation. Combine the like terms on the left side of the equation.
Answer: It’s D
Step-by-step explanation:
Just took assignment
Answer:
-DStep-by-step explanation:
I got 100% on this assignmentTwo new puzzle apps have 2,000 downloads on their first days. Jigsaw Junction
is downloaded 10,000 times each day after that, while Impossible Puzzles
double in total number of downloads each day. How many days will it take for
Impossible Puzzles to have more downloads than Jigsaw Junction?
5 Days
O 6 Days
7 Days
8 Days
Answer: 6 days
Step-by-step explanation: 6 days= 62,000 for jigsaw junction and 64,000 for impossible puzzles
i hope this helps
Impossible Puzzles will have more downloads than Jigsaw Junction in 1 day.
Explanation:To find out how many days it will take for Impossible Puzzles to have more downloads than Jigsaw Junction, we need to set up an equation and solve for the number of days.
Let's assume that the number of downloads for Impossible Puzzles on the first day is x. Since it doubles in total number of downloads each day, the number of downloads on the second day would be 2x, on the third day would be 4x, and so on.
On the other hand, Jigsaw Junction is downloaded 10,000 times each day after the first day. So, for n number of days, the number of downloads for Jigsaw Junction would be [tex]10,000 * n.[/tex]
We want to find the number of days when the number of downloads for Impossible Puzzles is greater than the number of downloads for Jigsaw Junction. So, we can set up the equation [tex]4x > 10,000n.[/tex]
To find the value of x, we can substitute 2,000 (the number of downloads on the first day for Impossible Puzzles) into the equation: [tex]4(2000) > 10,000n.[/tex]
Putting all the information together, we can set up the equation [tex]8,000 > 10,000n.[/tex]
To solve for n, we can divide both sides of the equation by[tex]10,000: 8,000/10,000 > n[/tex]. This simplifies to 0.8 > n.
Since n represents the number of days, we round up to the nearest whole number. Therefore, it will take 1 day for Impossible Puzzles to have more downloads than Jigsaw Junction.
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In a class of 666, there are 444 students who are secretly robots.
If the teacher chooses 222 students, what is the probability that neither of them are secretly robots?
Answer:
1/15
Step-by-step explanation:
2/6 for the first one the first the second is 1/5, so 2/6=1/3, so 1/3 x 1/5 = 1/15 your answer is 1/15
Mrs. Maldonado has $3,000 she wants to invest for the next 4 years. Her credit union offers a 5.96% interest rate compounded yearly, while a new bank will pay a 7.27% annual simple interest on her investment. Assume Mrs. Maldonado makes no additional deposits or withdrawals over the 4-year period.
Step 2: Use the correct formula to calculate the interest earned for the offer at the bank.
Please help me with these Square Root problems. Part 2. Please Show and check the work.
[tex]5. \sqrt{x+4} = 3 - \sqrt{x} \\\\6. \sqrt{x+4} =3 + \sqrt{x} \\\\7. \sqrt{x+ 3} = \sqrt{5x+6} - 3\\\\8. \sqrt{2x+1} = x - 1[/tex]
Answer:
5. 25/36
6. 25/36
7. -3/4 or 6
8. 0 or 4
Step-by-step explanation:
5. Square both sides: x + 4 = 9 - 6[tex]\sqrt{x}[/tex] + x
Subtract x from both sides and subtract 9 from both sides:
-5 = -6[tex]\sqrt{x}[/tex]
Square both sides again: 25 = 36x
Divide both sides by 36: x = 25/36
6. Square both sides: x + 4 = 9 + 6[tex]\sqrt{x}[/tex] + x
Subtract x and 9 from both sides: -5 = 6[tex]\sqrt{x}[/tex]
Square both sides: 25 = 36x
Divide both sides by 36: x = 25/36
7. Square both sides: x + 3 = 5x + 6 - 6[tex]\sqrt{5x+6}[/tex] + 9
Add 6[tex]\sqrt{5x+6}[/tex] to both sides and isolate it: 6[tex]\sqrt{5x+6}[/tex] = 4x + 12
Divide both sides by 2 and then square both sides again:
3[tex]\sqrt{5x+6}[/tex] = 2x + 6
9 * (5x + 6) = 4x^2 + 24x + 36
45x + 54 = 4x^2 + 24x + 36
4x^2 - 21x - 18 = 0
Factorize: (4x + 3)(x - 6) = 0 ⇒ x = -3/4 or x = 6
8. Square both sides: 2x + 1 = x^2 - 2x + 1
Move all the terms to one side and combine like terms: x^2 - 4x = 0
Factorize: x(x - 4) = 0 ⇒ x = 0 or x = 4
Hope this helps!
Answer:
5. x = 25/36
6. No real solutions
7. x = 6
8. x = 4
Step-by-step explanation:
5. sqrt(x + 4) = 3 - sqrt(x)
Square both sides
x + 4 = 9 - 6sqrt(x) + x
6sqrt(x) = 5
sqrt(x) = 5/6
x = 25/36
6. sqrt(x + 4) = 3 + sqr(x)
x + 4 = 9 + 6sqrt(x) + x
6sqrt(x) = -5
sqrt(x) = -5/6
Not possible. A + square root can not be negative
7. sqrt(x + 3) + 3 = sqrt(5x + 6)
Square both sides
x + 3 + 6sqrt(x + 3) + 9 = 5x + 6
6sqrt(x + 3) = 4x - 6
3sqrt(x + 3) = 2x - 3
Square both sides
9(x + 3) = 4x² - 12x + 9
4x² - 21x - 18 = 0
Using quadratic formula:
x = [21 +/- sqrt(21² - 4(4)(-18)]/(2×4)
x = [21 +/- 27]/8
x = 6, -¾
x = -¾ is rejected because it doesn't satisfy the initial equation
8. sqrt(2x + 1) = x - 1
2x + 1 = (x - 1)²
2x + 1 = x² - 2x + 1
x² - 4x = 0
x(x - 4) = 0
x = 0, 4
0 is rejected because it doesn't satisfy the initial equation
Express your answer in the form (a + bi)
(21 + 2i) + (13 + 8i) =
Answer:
The answer to your question is (34 + 10i)
Step-by-step explanation:
Data
(21 + 2i) + (13 + 8i) =
To solve this operation, just sum up the whole numbers and get a result then, sum up the imaginary numbers and get another result. Finally, write the result.
-Whole numbers 21 + 13 = 34
-Imaginary numbers 2i + 8i = 10i
Result (34 + 10i)
Answer:
34 +10i
Step-by-step explanation:
( 21 + 2i) + (13 + 8i) =
Add the real numbers
21+13 = 34
Add the imaginary numbers
2i+8i = 10i
The complex number is the real plus the imaginary number
34 +10i
find perimeter and area of figure
The vertex form of h(x) = x2 – 14x + 6 is h(x) = (x -
)2-
Answer:
(X-7)2-43
Step-by-step explanation:
Answer:
7
43
Step-by-step explanation:
An oblique prism is created using rohmbuses with the edge lengths of 25 units. The area of one rhombus is 600 square units. The perpendicular distance between the bases is 24 units.
What is the volume of the prism?
Given:
The length of each edge of rhombus = 25 unit
The area of one rhombus is 600 square units.
The perpendicular distance between the bases is 24 units.
To find the volume of the prism.
Formula
The volume of the prism
[tex]V = Bh[/tex]
where, B is area of one rhombus
h be the height.
Now,
Putting, B = 600 , h = 24 we get,
[tex]V = (600)(24)[/tex] cube unit
[tex]or, V = 14400[/tex] cube unit
Hence,
The volume of the prism 14400 cube unit.
Jeremy caught 8 fish in a contest.
The mean weight of the fish was 4.3125 kg.
He forgot to make his own record of the weight of the last fish,
but the first 7 were: 4.3 kg, 5.3 kg, 6.8 kg, 2.6 kg, 3.2 kg, 4.4 kg and 4.8 kg.
What was the weight of the last fish?
kg [2]
Answer:
Step-by-step explanation:
4.3 kg + 5.3 kg + 6.8 kg + 2.6 kg + 3.2 kg + 4.4 kg + 4.8 kg
4.3+5.3+6.8+2.6+3.2+4.4+4.8
= 31.4 ÷ 7
= 4.4857142857
Approx. 4.5kg
ABCD is a square. BD = 21.21 in. Find the perimeter to the nearest whole number.
Answer:
60 in
Step-by-step explanation:
BD² = s² + s²
21.21² = 2s²
s² = 224.93205
s = 14.997734829
Perimeter = 4s
= 59.990939316
Cecil recivies $15 per week for complting chores. He spend $12 on a video game. What percent of his monthly allowence did cecil spend on teh video gmae
Final answer:
Cecil spent 20% of his monthly allowance on the video game, calculated by dividing the $12 spent on the game by his $60 monthly allowance and then multiplying by 100 to get the percentage.
Explanation:
To find out what percent of his monthly allowance Cecil spent on the video game, we first need to calculate his total monthly allowance. Cecil receives $15 per week for completing chores. There are typically 4 weeks in a month, so Cecil's monthly allowance is 15 dollars/week * 4 weeks/month = $60 per month.
Next, we will calculate the percentage of his allowance that was spent on the video game. Cecil spent $12 on a video game. To find this percentage, we use the formula:
Percentage spent = (Amount spent / Total allowance) * 100
Percentage spent = ($12 / $60) * 100
Percentage spent = 0.2 * 100
Percentage spent = 20%.
Therefore, Cecil spent 20% of his monthly allowance on the video game.
A writer’s last four articles and fees paid have been recorded below. What is the rate of change in the writer’s fee from writing a 700-word article to an 800-word article
Answer:
i don't think anyone an answer this without the picture below.
Step-by-step explanation:
a cereal box has a length of 8 inches, a width of 1.75 inches, and a height of 12.25 inches. What is the volume of the cereal box?
Answer:
171.5
Step-by-step explanation:
Answer:
The answer to your question is Volume = 171.5 in ³
Step-by-step explanation:
Data
length = 8 in
width = 1.75 in
height = 12.25 in
To find the volume of this box, look for the formula to get the volume of a rectangular prism, substitute the values and simplify.
Formula
Volume = length x width x height
Substitution
Volume = 8 x 1.75 x 12.25
Simplification
Volume = 171.5 in ³
Twin brothers, Mike and Mark, are both offered jobs at grocery stores. Mike is offered a job at Fresh Foods making $10 per hour. Mark is offered a job at Groovy Groceries making $8 per hour plus a one-time hiring bonus of $100. Each twin believes he has been offered the better job. It's your responsibility to determine which brother has been offered the better job.
Answer: Mike offer is the best.
Step-by-step explanation:
Assuming he work for 30hrs per week in a month he gets
30hrs x 10 = $300 x 4 = $1200
If Mark work 30hrs per week he gets
30hrs x $8 = $240 x 4 = $960 + Bonus $100 = $1,060
Therefore, Mike makes more money.
1. 2x + y = 7 and 6x + 5y = 27*
Your answer
2x-5y=-1;6x-5y=27
Solution :
{x,y} = {7,3}
System of Linear Equations entered :
[1] 2x - 5y = -1
[2] 6x - 5y = 27
Graphic Representation of the Equations :
-5y + 2x = -1 -5y + 6x = 27
Solve by Substitution :
// Solve equation [2] for the variable x
[2] 6x = 5y + 27
[2] x = 5y/6 + 9/2
// Plug this in for variable x in equation [1]
[1] 2•(5y/6+9/2) - 5y = -1
[1] - 10y/3 = -10
[1] - 10y = -30
// Solve equation [1] for the variable y
[1] 10y = 30
[1] y = 3
// By now we know this much :
x = 5y/6+9/2
y = 3
// Use the y value to solve for x
x = (5/6)(3)+9/2 = 7
Solution :
{x,y} = {7,3}
Hope I helped! :)
A silver bracelet has a mass of 52.45g and volume of 5cm³ find the density of silver bracelet
Answer:
10.49 g/cm³
Step-by-step explanation:
d = m/V = 52.45g/5cm³ = 10.49 g/cm³
Answer:
10.49g/cm3
Step-by-step explanation:
mass=52.45g
volume=5cm3
density=mass divided by volume
52.45 divide by 5=10.49
Find the domain of the following function:
y = x^3 − 8
_________
x^2 + 9
Select the appropriate response:
A) 483xy
B) domain: all values of y
C) all values of x
D) Not possible to solve
Answer:
C) all values of x
Step-by-step explanation:
Domain is the set of values of input 'x'
Since the denominator is not 0 for any x, there's no domain restriction
Helga signs up to coach hockey. she wants to make at least $775 during the season. she gets $200 at the start of the season and $50 for each practice session she has. how many practice sessions does Helga need to have this season?
Answer:
12
Step-by-step explanation:
Well 775-200 = 575
575÷50= 11.5
round up because you cannot got to a half of practice.
So 12 practices.
Find the distance between (2, -75) and (10, 235).
Answer:
2
Step-by-step explanation:
Answer:
Use the distance formula to determine the distance between two points.
Exact Form:
2 √ 24041
Decimal Form:
310.10320862
what are 3 equivalent ratios to 3/4?
Answer:
6/8, 9/12, 12/16
Step-by-step explanation:
Multiply the numerator and denominator by the same amount to maintain the same ration.
[tex]\frac{3}{4} =\frac{6}{8} = \frac{9}{12} =\frac{12}{16}[/tex]
answers to bad dog breakout
Without specific context or questions from 'Bad Dog Breakout', it's challenging to provide a specific answer. It's recommended to read the text carefully, breakdown the text, and note down important points such as characters, plot, and themes.
Explanation:I apologize but without the detailed context or exact questions from 'Bad Dog Breakout', it's challenging to provide a specific answer. 'Bad Dog Breakout' might be a literary work or a segment from an English curriculum, and the questions can vary greatly. However, I encourage you to read and comprehend the text carefully. Breaking it down paragraph by paragraph, identifying characters, noting down the plot, any significant themes and important details might help.
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A photo of an ant in a science book is increased 515% as large as the actual size. If the ant is 16 millimeters, what is the size of the ant in the photo
Answer:
82.4 millimeters is the size of the ant in the photo
Step-by-step explanation:
In this question, we are asked to calculate the size of an ant in a science book given the actual size of the ant and the percentage increase is the size of the ant in the book.
From the question, we can identify that the actual size is 16 millimeters
Now let’s find 515% of this to know the size to which it would be magnified in the science book.
That would be;
515/100 * 16 = 82.4 millimeters
Hence, this means the ant will have a size of 82.4 millimeters in the science book
Answer:
The size of the ant in the photo is 88 mm
Step-by-step explanation:
Here, we have the percentage increase = 515 %
Size of ant = 16 millimeters in real life,
Therefore, the size of the ant in the in the photo, is given by,
[tex]\frac{16 \, mm}{100} = \frac{y\, mm}{550} = \frac{16 \times 550}{100} = \frac{y \times 100 \, mm}{100} \rightarrow 88 \, mm = y[/tex]
y = 88 mm
The size of the ant in the photo = 88 mm.
if the radius of circle r is 7 and the radius of circle s is 9, what is the ratio of the circumference of circle r to circle s
Answer:
43.96 : 56.52
Step-by-step explanation:
Circumference = 2 * pi * Radius
Circumference = Diameter * pi
Circle R's Circumference = 43.96 (7 * 2 * 3.14)
Circle S's Circumference = 56.52 (9 * 2 * 3.14)
The ratio of the circumference of circle r to s = 43.96:56.52
Find the area of a circle with a circumference of \blueD{50.24}50.24start color #11accd, 50, point, 24, end color #11accd units.
Answer:
[tex]201 cm^2[/tex]
Step-by-step explanation:
The circumference of a circle is given by:
[tex]c=2\pi r[/tex]
where
r is the radius of the circle
For the circle in this problem,
c = 50.24 cm
Therefore the radius is:
[tex]r=\frac{c}{2\pi}=\frac{50.24}{2\pi}=8 cm[/tex]
The area of a circle is given by the formula
[tex]A=\pi r^2[/tex]
where r is the radius.
For the circle in this problem,
r = 8 cm
So the area is
[tex]A=\pi \cdot 8^2 = 201 cm^2[/tex]
The area of the circle is 201 cm square.
Calculation of the area of the circle:Since we know that
Circumference of the circle = [tex]2\pi r[/tex]
So here radius should be
[tex]= c\div 2\pi \\\\= 50.24\div 2\pi[/tex]
= 8 cm
Now the area of the circle is
[tex]= \pi r^2\\\\= 3.14\times 8^2[/tex]
= 201
Hence, we can conclude that The area of the circle is 201 cm square.
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Which of the following statements are true about the angles in the figure? Select all that apply.
∠X and ∠Z are vertical angles.
∠X and ∠Y are a linear pair.
∠W and ∠Z are supplementary.
∠Y and ∠Z are supplementary.
∠W and ∠X are adjacent.
Answer:2 , 3 , and 5 would be your answer
Step-by-step explanation:
Answer:
B,C,E
Step-by-step explanation:
so the guy above me is right
Determine if each equation is a linear equation.
[Linear equation / Not a linear equation]
1) [tex]5x_1 + x_2 - 7x_3 = 4[/tex]
2) [tex]5x_1 + 4.6x_2 + 12x_3 = -5[/tex]
3) [tex]3x_1 - x_3 = -5x_2 + 7[/tex]
4) [tex]3x_1x_2 + x_3 = 5[/tex]
5) [tex]4x_1^3 + x_2 = 5[/tex]
6) [tex]6x_1 - 4x_2 + x_3 = 0[/tex]
Answer:
Linear-1,2,3,6
Nin-Linear-4,5
Step-by-step explanation:
A linear equation is an equation in which the highest power of the variable is 1.
Out of the given equations, the following are linear.
1) [tex]5x_1 + x_2 - 7x_3 = 4[/tex]
2) [tex]5x_1 + 4.6x_2 + 12x_3 = -5[/tex]
3) [tex]3x_1 - x_3 = -5x_2 + 7[/tex]
6) [tex]6x_1 - 4x_2 + x_3 = 0[/tex]
These equations on the other hand are nonlinear.
4) [tex]3x_1x_2 + x_3 = 5[/tex]
5) [tex]4x_1^3 + x_2 = 5[/tex]
No 4 contains a term which is the product of two variables therefore it is not linear.
No 5 contains a term whose highest power is 3. Such an equation is a Cubic Equation.
Fred has saved 3 quarters from washing cars how many cents does Fred have
Answer:75 cents
Step-by-step explanation:
one quarter is equal to 25 cents and since you have 3 of them you multiple 25 times 3 and get 75.
Fred has 3 quarters, and since each quarter is worth 25 cents, he has a total of 75 cents from washing cars.
Fred has saved 3 quarters from washing cars, and we need to determine how many cents he has. In U.S. currency, one quarter is equivalent to 25 cents. To find out the total number of cents Fred has, we can perform the following multiplication:
25 cents × 3 quarters = 75 cents
Therefore, Fred has a total of 75 cents.
whats 11/12 of a full rotation?
Pls mark Brainliest.
Answer:
330°
Step-by-step explanation:
A full rotation is 360°. Saying 11/12 of a full rotation is equivalent to saying 11/12 * 360°, which equals 330°.
We have that for the Question "whats 11/12 of a full rotation?" it can be said that 11/12 of a full rotation is
[tex]X=330 \textdegree[/tex]
From the question we are told
whats 11/12 of a full rotation?
Generally the equation for the Statement is mathematically given as
[tex]x=\frac{11}{12}[/tex]
Where
360° signifies full rotation
Therefore
11/12 of a full rotation is
[tex]\frac{11}{12}*360[/tex]
[tex]X=330 \textdegree[/tex]
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