9. The three squares below join together to form a right triangle. The area and the perimeter for two of the squares is shown. Find the side length of the largest square. Х Area: 81 in 2 Perimeter: 48 in.

Answers

Answer 1

We are given the area and perimeter of two squares that form a right triangle. We are asked to find the length of the bigger square. To do that we may use the Pythagorean theorem. Let "a" and "b" be the sides of a triangle and "c" the length of the hypothenuse, we have the following relationship:

$c^2=a^2+b^2$

Now, "a" and "b" are the size of the given squares. For the square which area is given, we can use the following formula for the area of a square:

$A_{\text{square}}=a^2$

We can solve for "a" by taking square root on both sides, like this:

$a=\sqrt[]{A_{square}}$

Replacing the value given for the area, we get:

$\begin{gathered} a=\sqrt[]{81in^2} \\ a=9in \end{gathered}$

Now, for the square which perimeter is given, we can use the fact that the perimeter of a square is the sum of all its sides, like this:

$\begin{gathered} P_{\text{square}}=b+b+b+b \\ P_{\text{square}}=4b \end{gathered}$

solving for "b" we get:

$b=\frac{P_{\text{square}}}{4}$

Replacing the known value for the perimeter, we get:

$b=\frac{48in}{4}=12in$

Now that we have both sides "a" and "b" we may replace this in the Pythagorean theorem, like this:

$\begin{gathered} c^{2^{}}=a^2+b^2 \\ c^2=9^2+12^2 \end{gathered}$

Solving the operations:

$\begin{gathered} c^2=81+144 \\ c^2=225 \end{gathered}$

Now we solve for "c" by taking square roots on both sides, like this:

$\begin{gathered} c=\sqrt[]{225} \\ c=15 \end{gathered}$

Therefore, the side length of the largest square is 15 in.

Related Questions

please answer both tysm

Answers

Answer:

B for 2

A, C, D, and F for 1

5 Ethan scored x points in a game. His younger sister scored 8 points when she
played the same game. Their combined score was y points.
a) Write an equation relating x and y.
b) Copy and complete the table to show the relationship between x and y.
Ethan's Scores (x points)
10
11
12
13
14
15
Combined Scores (y points)
?
?
?
12
이
?
?

Answers

The remaining values will be 19, 20, 21, 22 and 23

System of equations

Given the following parameters

Ethan's score = x points

His younger sister's score = 8 points

If their total score is y points, hence the equation relating x and y is expressed as:

x + 8 = y

x = 8 - y

If x = 10

y = x + 8

y = 18

The ramining values will be 19, 20, 21, 22 and 23

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9. CONSTRUCT AN ARGUMENT Determine
if the following statement is true or false.
Construct an argument to defend your
response.
Proportions can only be used to solve
problems where the smaller values are
known and a larger value is unknown.

Answers

Answer:

Step-by-step explanation:

The correct answer is true. If you know that the relationship between quantities is proportional, you can use proportions to find missing quantities.

2x + 4y =8 solve for x variable

Answers

In order to solve this equation for x, we just need to isolate this variable:

$\begin{gathered} 2x+4y=8 \\ 2x=8-4y \\ x=\frac{8-4y}{2} \\ x=4-2y \end{gathered}$

So we have that x = 4 - 2y.

What is the equation of the line that passes through the point (-1, 8) and has a slope of -6?

Answers

Answer:

y = -6x + 2

Step-by-step explanation:

y = mx + b

m = slope

slope = m = -6

y = -6x + b

8 = -6(-1) + b

b = 2

y = -6x + 2

Answer:

y = -6x + 2

Step-by-step explanation:

We can use point slope formula, when we have a point and a slope.

y - 8 = -6(x + 1)

that's the equation.

If you want it in Slope intercept form, you simply distribute the -6 and move the 8 to the other side

y - 8 = -6x - 6

y = -6x +2

Each volleyball set costs $63.74.
Which equation represents the cost, c, of n sets?

Answers

The equation that represents the cost, c, of n sets is c = 63.74n

Which equation represents the cost, c, of n sets?

from the question, we have the following parameters that can be used in our computation:

Each volleyball set costs $63.74.

Let the total number of sets be n

So we have

Cost of n = 63.74 * n

This gives

c = 63.74n

Hence, the equation is c = 63.74n

Answers

Answer:

associative property of multiplication

How would you make a dot plot out of these numbers? 75 80 82 41 92 98 79 83 100 87 85 73 70

Answers

Solution

To do that,

We draw a number line,

Arrange the numbers on the number line,

How would you make a dot plot out of these numbers? 75 80 82 41 92 98 79 83 100 87 85 73 70

Solve the following numerical problems. a. If a bus travels 6 km in 10 minutes, what distance does it travel in 1 secon

Answers

Answer:

10 meters

Step-by-step explanation:

c) The group is planning to build a fence around the garden. How many yards of
fencing materials do they need for the fence? Show your work. (3 points-2 points for
finding the value of side b and 1 point for finding the perimeter of the garden)
I

Answers

Based on the information, it should be noted that the perimeter that they need is 130 yds to build up the fence.

How to explain the value

Attached you can find a picture that will guide the explanation. We will assume that each line is supposed to be a fence. We will assume also that the diagonals that cross any subfield that has the same vegetable is unnecessary.

On the same fashion, the diagonal of the spinach-celery sector is 10. Recall that the field is a rectangle, so the perimeter of the outter fence is 2*(12+6)+2*(8+9) = 70 yds. Then, the total perimeter is given by

outter fence (70)+

fence spinach-watermelon (8) +

fence red peppers-watermelon(12)+

fence red peppers-carrots (15)+

fence carrots-tomatoes (9)+

fence celery-tomatoes(6) +

fence spinach-celery(10)

= 130 yds

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c) The group is planning to build a fence around the garden. How many yards offencing materials do they

the probability of an airline flight arriving on time at a certain airport is 84%, use a normal approximate to find the probability that more than 240 in a random sample of 400 commercial airline flights at the airport will arrive on time

Answers

The probability that more than 240 flights in a random sample of 400 commercial airline flights will arrive on time is approximately 1 or 100%.

To solve this problem using a normal approximation, we need to calculate the mean (μ) and standard deviation (σ) of the binomial distribution and then use the normal distribution to approximate the probability.

Given:

Probability of an airline flight arriving on time (success): p = 0.84

Number of trials (flights): n = 400

Number of flights arriving on time (successes): x > 240

First, we calculate the mean and standard deviation of the binomial distribution using the following formulas:

Mean (μ) = n * p

Standard Deviation (σ) = √(n * p * (1 - p))

μ = 400 * 0.84 = 336

σ = √(400 * 0.84 * 0.16) = √(53.76) ≈ 7.33

Now, we can use the normal distribution to find the probability that more than 240 flights will arrive on time. Since we're interested in the probability of x > 240, we will calculate the probability of x ≥ 241 and then subtract it from 1.

To use the normal distribution, we need to standardize the value of 240:

z = (x - μ) / σ

z = (240 - 336) / 7.33

z ≈ -13.13

Now, we can find the probability using the standard normal distribution table or a calculator. Since the value of z is extremely low, we can approximate it as:

P(x > 240) ≈ P(z > -13.13)

From the standard normal distribution table or calculator, we find that P(z > -13.13) is essentially 1 (close to 100%).

Therefore, the probability that more than 240 flights in a random sample of 400 commercial airline flights will arrive on time is approximately 1 or 100%.

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The volume of a sphere is 904.32 cubic millimeters. What is its radius?

Answers

Hello!

Answer:

$\boxed{ \bf The~radius~of~the~sphere~is~6~mm.}$

Explanation:

We know that:

V = $\frac{4}{3}$πr³

904.32 = $\frac{4}{3}$πr³

To figure out the radius, we have to undo the above. We can undo the fraction by multiplying by it's reciprocal:

$\frac{3}{4}$ × $\frac{904.32}{1}$ = $\frac{4}{3}$πr³ × $\frac{3}{4}$

678.24 = πr³

Next, we're going to divide both sides by pi:

$\frac{678.24}{\pi } = \frac{\pi r^{2} }{\pi }$

215.90 = r³

To undo the, we must find the cube root of 215.90.

r = 6

Answer:

$radius = 6mm$

Step-by-step explanation:

Volume of a sphere.

Use this formula

$v = \frac{4}{3} \pi {r}^{3} $

Now solve for r

\(r = (3 \frac{v}{4\pi} ) ^{ \frac{1}{3} } \\ = (3 \times \frac{904.32}{4 \times \pi} ) ^{ \frac{1}{3} } \\ ≈

5.99899mm

Represent the following sentence as an algebraic expression, where "a number" is the letter x. The difference of 4 and a number

Answers

The algebraic expression "difference of 4 and a number" where the number is letter x is represented as 4 - x.

What is an algebraic expression

Algebra is an elementary branch of mathematics that deals with the numbers and the basic mathematics operations of addition, subtraction, division and multiplication. Algebraic expression involves arithmetic where the use of unknown quantities along with numbers.

From the question, we have the mathematical statement "difference of 4 and a number" and the number is "a number" is represented with the letter x.

the word difference in mathematics implies Subtraction (-)

Therefore, the mathematical statement "difference of 4 and a number" is represented as 4 - x.

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How is adding mixed numbers with unlike denominators the same as adding fractions with unlike denominators? How is it different?

Answers

To add a mixed number you must first convert it into a heavy headed fraction eg. 12/4
Then you must find a common denominator for all of the fractions like you normally do for regular addition of fractions
After you have added them you must convert the heavy headed fraction back into a mixed number by seeing how many times the numerator goes into the denominator

gustavo ronaldo says, if you subtract 11 from my number and multiply the difference by -3, the result is -51 . what is s number?

Answers

Answer:

Step-by-step explanation:

-3 * (x-11) = -51

x-11 = 17

x = 28

Find cos(a) in the triangle,

Answers

Cos (a) = 35/37
.....

The graph of a cube root function f is shown.

The graph of g is a vertical shrink by a factor of 1/2 of the graph of f. Graph the function g.

Answers

A graph of the cube root function g(x) = 1/2x³ is shown in the image below.

What is a dilation?

In Geometry, a dilation is a type of transformation which typically transforms the dimension (size) or side lengths of a geometric object, without affecting its shape.

This ultimately implies that, the dimension (size) or side lengths of the dilated geometric object would be stretched or shrunk depending on the scale factor that is applied.

When the parent cube root function f(x) = x³ is vertically shrunk by a scale factor of 1/2, the transformed function g(x) is given by;

g(x) = kf(x)

g(x) = 1/2f(x)

g(x) = 1/2x³.

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With a discount of 60 percent, the cost of a bracelet is $17.99. What is the price before the discount

Answers

Answer:
28.78

Explanation:

5,10,15,20,25 what is the common difference

Answers

Answer:

The common difference in the given sequence is 5.

Step-by-step explanation:

The common difference in the sequence is 5 because they all add by 5 each time for example 5 + 5= 10 and 10+5=15

Suppose that the mean GRE score for the United States is 500 and the standard deviation is 75. Use the 68-95-99.7 (empirical) rule to determine the percentage of students likely to get a score below 275? Is a score below 275 significantly different from the mean

Answers

1) The percentage of students who will get a score below 275 is; 0.15%

2) Yes, any score below 275 is significantly different from the mean.

How to use the Empirical rule in statistics?

The empirical rule states that for a normal distribution, 68% of the distribution are within one standard deviation from the mean, 95% are within two standard deviation from the mean and 99.7% are within three standard deviations from the mean.

The formula for z-score is;

z = (x' - μ)/σ

where;

x' is sample mean

μ is population mean

σ is standard deviation

1) We are given;

Population mean; μ = 500

Sample mean; x' = 275

standard deviation; σ = 75

Thus;

z = (275 - 500)/75

z = -3

This is 3 standard deviations from the mean. Thus;

The percentage of students who will get a score below 275 is;

(100 - 99.7)/2 = 0.15%

2) Yes, any score below 275 is more than 3 standard deviations away from the mean and can be considered significantly different from the mean.

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Calc question — related rates

Answers

The rate at which the depth of the liquid is increasing when the depth of the liquid reaches one-third of the height of the bowl is 1.25 cm s⁻¹.

How to determine rate?

The volume of the liquid in the bowl is given by the following integral:

$V = \int\limitsx_{0}^{h} \, \pi r^{2}(y) dy$

where r = radius of the bowl and y = height of the liquid.

The radius of the bowl is equal to the distance from the curve y = (4/(8-x)) - 1 to the y-axis. This can be found using the following equation:

r = √{(4/(8-x)) - 1}² + 1²

The height of the liquid is equal to the distance from the curve y = (4/(8-x)) - 1 to the x-axis. This can be found using the following equation:

h = (4/(8-x)) - 1

Substituting these equations into the volume integral:

$V = \int\limitsx_{0}^{h } \, \pi {\sqrt{(4/(8-x)) - 1)^{2} + 1^{2} (4/(8-x))} - 1 dy$

Evaluate this integral using the following steps:

Expand the parentheses in the integrand.

Separate the integral into two parts, one for the integral of the square root term and one for the integral of the linear term.

Integrate each part separately.

The integral of the square root term can be evaluated using the following formula:

$\int\limits^{b} _{a} \, dx \sqrt{x} dx = 2/3 (x^{3/2}) |^{b}_{a}$

The integral of the linear term can be evaluated using the following formula:

$\int\limits^{b} _{a} \, {x} dx = (x^{2/2}) |^{b}_{a}$

Substituting these formulas into the integral:

V = π { 2/3 (4/(8-x))³ - 1/2 (4/(8-x))² } |_0^h

Evaluating this integral:

V = π { 16/27 (8-h)³ - 16/18 (8-h)² }

The rate of change of the volume of the liquid is given by:

dV/dt = π { 48/27 (8-h)² - 32/9 (8-h) }

The rate of change of the volume of the liquid is 7π cm³ s⁻¹. Also the depth of the liquid is one-third of the height of the bowl. This means that h = 2/3.

Substituting these values into the equation for dV/dt:

dV/dt = π { 48/27 (8-2/3)² - 32/9 (8-2/3) } = 7π

Solving this equation for the rate of change of the depth of the liquid:

dh/dt = 7/(48/27 (8 - 2/3)² - 32/9 (8 - 2/3)) = 1.25 cm s⁻¹

Therefore, the rate at which the depth of the liquid is increasing when the depth of the liquid reaches one-third of the height of the bowl is 1.25 cm s⁻¹.

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The triangle shown below has an area of 75^2
Find the missing side.

Answers

Answer:

Step-by-step explanation:

use pythagorean theorum and 75 is area. base is 2 and height is 2. base/2 ^2 = 1

1^2 + 2^2 = 5

To conserve water, many communities have developed water restrictions. The water utility charges a fee of $29, plus an additional $1.41 per hundred cubic feet (HCF) of water. The recommended monthly bill for a household is between $54 and $82 dollars per month. If x represents the water usage in HCF in a household, write a compound inequality to represent the scenario and then determine the recommended range of water consumption. (Round your answer to one decimal place.)

Answers

Answer:

I can lead you with this equation: 1.41x + 29 = Cost

I think it will be easy from here on for you.

Step-by-step explanation:

How many different sums of money can be made from 4coins of different denomination

Answers

Answer:

15 different sums

----------------------

There are various combinations of coins.

1 coin:4 options2 coins:4C2 = 4!/(2!2!) = 6 options3 coins:4C3 = 4!/(3!1!) = 4 options4 coins: 1 option

In total there are:

4 + 6 + 4 + 1 = 15 different sums

Aircraft A has 105 more seats than aircraft B. If their total number of seats is 519, find the number of seats for each aircraft.

Aircraft A has how many seats?

Answers

Aircraft A has 312 seats.

Let's assume that Aircraft B has x seats.

According to the given information, Aircraft A has 105 more seats than Aircraft B. So, the number of seats in Aircraft A can be expressed as x + 105.

The total number of seats in both aircraft is 519, which can be represented by the equation:

x + (x + 105) = 519

Simplifying this equation, we have:

2x + 105 = 519

Subtracting 105 from both sides, we get:

2x = 414

Dividing both sides by 2, we find:

x = 207

Therefore, Aircraft B has 207 seats.

To find the number of seats in Aircraft A, we substitute the value of x back into the expression x + 105:

Aircraft A = 207 + 105 = 312

Hence, Aircraft A has 312 seats.

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100 Points! Algebra question. Photo attached. Find the missing variable. Round your answers to the nearest hundredth. Please show as much work as possible. Thank you!

Answers

Using the z-score, mean and sample mean, the standard deviation of the sample is 7.57

What is z-score?

A z-score describes the position of a raw score in terms of its distance from the mean when measured in standard deviation units. The z-score is positive if the value lies above the mean and negative if it lies below the mean.

The formula is given as;

z = x - μ / σ

z = z -scoreμ = mean x = sample meanσ = standard deviation

Substituting the values into the formula;

-2.13 = 19.3 - 29 / σ

Cross multiply both sides;

-2.13σ = 19.3 - 29

-2.13σ = -9.7

Divide both sides by the coefficient;

-2.13σ / -2.13 = -9.7 / -2.13

σ = 7.57

The standard deviation is 7.57

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Determine the component representation and magnitude of the vector having the initial point P and the terminal point Q.
P(-3,2) and Q(5,17)
The component representation of the vector having the initial point P and the terminal point Q is....
The magnitude of the vector having the initial point P and the terminal point Q is ....

Answers

The magnitude of the vector having the initial point P and the terminal point Q is 17.

What is magnitude ?

Simply said, "distance or amount" is the definition of size. In terms of motion, it shows the absolute or relative size, direction, or movement of an item. It is used to describe something's size or scope. Magnitude in physics often refers to a size or amount.

Given: p (- 3,2) , q (5,17)

vector = (17-2)i + (5+3)j

= 15i + 8j

Magnitude = $\sqrt{(15^{2}+8^{2} ) }$

magnitude =17

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2
Select the correct answer from each drop-down menu.
Triangle ABC is shown in the coordinate plane. It is translated 6 units left and 4 units down. Then it is dilated by a scale factor of 3 centered about the
origin. Complete the statements.
-6 -4
v.
6
4-
2-
lo
-2-
-4-
-6-
The translation of triangle ABC
A
2
с
6
B
Reset
The dilation of triangle ABC
Next

Answers

For the transformations of the triangle, we have that:

1. The translation of triangle ABC preserves side lengths and angles.

2. The dilation of triangle ABC preserves angles but not side lengths.

Hence the correct options are, respectively, C and B.

A translation involves shift left, shift right, shift down, or shift up, meaning that just the coordinates of the figure change, not the angles or the side lengths,

1. The translation of triangle ABC preserves side lengths and angles.

For a dilation, the coordinates of the vertices are multiplied by a constant, hence the side lengths change while the angles remain constant, thus:

2. The dilation of triangle ABC preserves angles but not side lengths.

Hence the correct options are, respectively, C and B.

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2Select the correct answer from each drop-down menu.Triangle ABC is shown in the coordinate plane. It

Which of the following are solutions to the system of inequalities y<−x+5 and y≥3x+1?
A)
(1,0)

cross out

B)
(−2,2)

cross out

C)
(1,6)

cross out

D)
(0,1)

cross out

E)
(1,4)

cross out

F)
(−2,7)

Answers

From the graph attached below, the solution to the system of linear inequalities are (1, 4)

What is the solution to the system of linear inequalities?

A system of linear inequalities is a collection of linear inequalities in the same variables. The solution is any ordered pair that satisfies each of the inequalities.

In the problem given;

y < - x + 5 ...eq(i)

y ≥ 3x + 1 ...eq(ii)

To determine the solution to the system of linear inequalities, it is easier for us to use graphical method. This is simply done by plotting the points and determine the coordinate at which both inequalities intersect.

From the graph of the system of linear inequalities, the solution to this is (1, 4) which is option E

Kindly find attached graph below

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Which of the following are solutions to the system of inequalities y<x+5 and y3x+1? A)(1,0)cross outB)(2,2)cross

You still work at Dockery Manufacturing (still exciting!), and your organization still requires a lead time between 18 and 23 days for supplied items. After further investigating the supplier’s process, you determine their current lead times are normally distributed with a process mean of 21 days and a standard deviation of 1.90. What is the percent likelihood that a randomly observed lead time by the supplier would be too short per your firm’s specifications? Group of answer choices 5.71% 14.69% 20.58% 35.13% 44.29%

Answers

Answer:

The probability is of 14.69%

Step-by-step explanation:

According to the given data we have the following:

Lead time mean = 21 days

Standard deviation = 1.90

To calculate the percent likelihood that a randomly observed lead time by the supplier would be too short per your firm’s specifications we will calculate first the z statisticsas follows:

z= (X- mean)/ Standard deviation

z = (23-21)/ 1.90

z = 1.05

Then Looking at z table, we will find probability corresponding to z = 1.05. The probability is 0.8531 but the area for z > 1.05 will be 1- 0.8531= 0.1469

Therefore, the probability is of 14.69%

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