If the hypotenuse of a right triangle is 10 inches long and one of its legs is 5 inches long, how long is the other leg?

Answers

Answer 1

Answer:

[tex]5\sqrt{3}[/tex] inches long is the other leg

Step-by-step explanation:

Given the statement: If the hypotenuse of a right triangle is 10 inches long and one of its legs is 5 inches long.

Hypotenuse side = 10 inches

Let length of other leg be x.

Pythagoras theorem states that in a right angle triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Then; by definition of Pythagoras theorem;

[tex]{\text}(Hypotenuse)^2 = (5)^2 + x^2[/tex]

[tex](10)^2 = 5^2 + x^2[/tex]

[tex]100 = 25 + x^2[/tex]

Subtract 25 on both sides we get;

[tex]100-25= 25 + x^2-25[/tex]

Simplify:

[tex]75 = x^2[/tex]

Simplify:

[tex]x = \sqrt{75} = 5\sqrt{3}[/tex] inches

Therefore, the sides of other leg is [tex]5\sqrt{3}[/tex] inches




Answer 2

Final answer:

Using the Pythagorean theorem, and knowing the length of the hypotenuse (10 inches) and one leg (5 inches), we calculate the other leg to be approximately 8.66 inches in length.

Explanation:

The question involves finding the length of the other leg of a right triangle when the lengths of the hypotenuse and one leg are known. By applying the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). The theorem is usually written as a² + b² = c².

In this case, the hypotenuse (c) is given as 10 inches, and one leg (a) is 5 inches. To find the length of the other leg (b), rearrange the Pythagorean theorem as b² = c² - a². Substituting the known values gives us b² = 10² - 5² leading to b² = 100 - 25. Therefore, b² = 75. Taking the square root of both sides to solve for b gives us b = √75 which simplifies to approximately 8.66 inches when rounded to two decimal places.

Thus, the length of the other leg in the right triangle is approximately 8.66 inches.


Related Questions

A student has 20 pencils at the beginning of the school year. After a week, the student has 18 pencils left. If the student continues to use pencils at the same rate, which equation will represent pencils left after w weeks?

Answers

Answer: p = -2w + 20

Step-by-step explanation:

If the student had 20 pencils but now has 18 pencils, he uses pencils at a rate of 2 per week.  So, m = -2  (negative because he is decreasing the amount of pencils).  The student started with 20 pencils so b = 20

Use the y = mx + b but replace "y" with "p" and replace "x" with "w" and input the m and b as stated above:

             p = -2w + 20

Write the equation of a line that passes through the points (0, -2) and (4, -5). Answer MUST be in standard form: Ax + By = C.

Answers

The slope-intercept form:

[tex]y=mx+b[/tex]

m - slope

b - y-intercept → (0, b).

We have the points (4, -5) and (0, -2) → y-intercept → b = -2.

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

Substitute:

[tex]m=\dfrac{-2-(-5)}{0-4}=\dfrac{-2+5}{-4}=\dfrac{3}{-4}=-\dfrac{3}{4}[/tex]

Therefore we have the equation of a line

[tex]y=-\dfrac{3}{4}x-2[/tex]

Convert to the standard form: [tex]Ax+By=C[/tex]

[tex]y=-\dfrac{3}{4}x-2\qquad\text{multiply both sides by 4}\\\\4y=-3x-8\qquad\text{add 3x to both sides}\\\\\boxed{3x+4y=-8}[/tex]

Steps:Slope-Intercept Form: y = mx + b (m = slope, b = y-intercept)Standard Form: Ax + By = C (A, B, & C are integers and A must be non-negative)Slope Formula: [tex]\frac{y_2-y_1}{x_2-x_1}[/tex] where (x₁,y₁) and (x₂,y₂) are coordinates.

So for this, I will be putting the equation into slope-intercept form then rearranging it into standard form. Firstly, we need to solve for the slope. To do this, take the 2 coordinates given to us and solve as such:

[tex]\frac{-5-(-2)}{4-0}=-\frac{3}{4}[/tex]

Now, one of the coordinates given to us is (0,-2), which is the y-intercept. With all this info, our slope-intercept equation is [tex]y=-\frac{3}{4}x-2[/tex] . From here we can solve for the standard form.

Firstly, add 3/4x onto both sides of the equation:

[tex]\frac{3}{4}x+y=-2[/tex]

Now, it may appear that we are finished. However, 3/4 is not an integer (Integers are whole numbers). To make it an integer, we need to multiply both sides by 4:

[tex]3x+4y=-8[/tex]

Answer:

In short, the standard form of this equation is 3x + 4y = -8.

A clerk is marking up merchandise 34% the original price of an item is 455 what will be the retail price

Answers

If we consider the original price to be 100% of the price and a markup is 34% this means 100%+34%=134%. In decimal 134%=1.34.

Therefore, we must multiply 1.34 by the original price and so:

455(1.34)=609.70

And so the retail price will be $609.70.

For a school drama performance, student tickets cost $5 each and adult tickets cost $10 each. The sellers collected $3,570 from 512 tickets sold. If c is the number of student tickets sold, which equation can be used to find the amount of tickets sold of each type?
10(512 – c) + 5c = 512
10(512 – c) + 5c = 3,570
5(512 – c) + 10c = 3,570
5(512 – c) + 10c 512

Answers

I think the right equation is 10(512 - c) plus 5c equals 3,570

Answer: [tex]10(512 – c) + 5c = 3,570[/tex]

Step-by-step explanation:

Given : The number of student tickets sold is represented by c.

For a school drama performance, student tickets cost $5 each and adult tickets cost $10 each.

The sellers collected $3,570 from 512 tickets sold.

Since , the total tickets sold = 512

Therefore , the number of adults ticket = [tex]512-c[/tex]

Now, cost of total child tickets : [tex]5c[/tex]

Cost of total adult tickets = [tex]10(512 – c)[/tex]

Now, according to the cost of the tickets , we have the following equation :-

[tex]10(512 – c) + 5c = 3,570[/tex]

There is a line whose slope is 0 and whose y -intercept is 9. What is its equation in slope-intercept form?

Answers

Answer:

y = 0x + 9

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y-intercept )

here m = 0 and c = 9, hence

y = 0x + 9

The equation of a horizontal line is normally written as y = 9

with the x- term omitted


The equation of a line with a slope of 0 and a y-intercept of 9 is y = 9, which represents a horizontal line on the graph.

The student is asking about the equation of a line in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. Given that the slope (m) is 0, and the y-intercept (b) is 9, the equation of the line is simply y = 0x + 9. Since any number multiplied by zero is zero, this simplifies to y = 9.

Therefore, the equation of the line with a slope of 0 and a y-intercept of 9 in slope-intercept form is y = 9. This represents a horizontal line that crosses the y-axis at 9.

Select the correct graph for the system of inequalities from the list of graphs. Indicate which graph represents the system, and list three possible solutions in the form of (x, y).
y greater or equal than minus 5 x plus 1 y greater than minus 4 x minus 2 y greater or equal than minus 2

Answers

Choose a graph from the list of graph, like in the picture.

A survey found that 12 out of every 15 people in the United States prefer eating at a restaurant over cooking at home. If 400 people selected eating at a restaurant on the survey, ow many people took the survey?

Answers

Answer:

It is 80

Step-by-step explanation:

This because of when we divided the number 400 by 15 we got 26.6' an infinite number this is how many times the survey 12/15 was taken then if we then times this by 3 we get 80 which is the amount of people who prefer their own dinner


Caiden earned $475 from mowing lawns last summer. He deposited this money in an account that pays an interest rate of 3.8% compounded annually. What will be his balance after 15 year?

Answers

Answer:

The balance after 15 year is  $831.25 .

Step-by-step explanation:

Formula

[tex]Amount = P (1 + r)^{t}[/tex]

Where P is the principle and r is the rate of interest in the decimal form and t is the time.

As given

Caiden earned $475 from mowing lawns last summer.

He deposited this money in an account that pays an interest rate of 3.8% compounded annually.

Here

P = $475

3.8% is written in the decimal form.

[tex]= \frac{3.8}{100}[/tex]

= 0.038

r = 0.038

t = 15 years

Put in the formula

[tex]Amount = 475 (1 + 0.038)^{15}[/tex]

[tex]Amount = 475 (1.038)^{15}[/tex]

[tex]Amount = 475\times 1.75(Approx)[/tex]

Amount = $831.25

Therefore the balance after 15 year is  $831.25 .

Final answer:

Caiden will have approximately $850.91 in his account after 15 years of interest compounded annually at a rate of 3.8%.

Explanation:

In this problem, we're dealing with compound interest, not simple interest. The formula to calculate compound interest is: A = P (1 + r/n)^(nt), where A is the amount of money accumulated after n years, including interest; P is the principal amount (the initial money); r is the annual interest rate (in decimal); n is the number of times that interest is compounded per year; and t is the time the money is invested for in years. In this case, P equals $475, r equals 3.8/100 or 0.038 (transforming percentage to decimal), n is 1 (because the interest is compounded annually), and t is 15 years. Substituting these values into the formula gives: A = $475 (1 + 0.038/1)^(1*15). Calculate the bracketed part first, resulting in a figure around 1.038 and raise it to the power of 15, so we get a value around 1.7914. Multiply this by the initial amount of $475 to get the final balance after 15 years which will be approximately $850.91. Hence, Caiden will have $850.91 in his account after 15 years.

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Oceanside Bike Rental Shop charges 17 dollars plus 6 dollars an hour for renting a bike. Mike paid 71 dollars to rent a
bike. How many hours, h, did he pay to have the bike checked out? Write an equation and solve for h. Must show
your work to receive full credit.

Please show your work. Thank You.

Answers

Answer:

9 hours

Step-by-step explanation:

First off we need to subtract 17 from 71 in order to get rid of the initial cost. This will lead us to 54. The last thing we need to do is divide that by 6 since you pay 6 hours per hour. Mike paid 71 dollars to rent a bike for 9 hours.

The length of a rectangular is 5 centimeters less then it width. The perimeter of the rectangle is 26

Answers

Answer: length = 7 c, and width = 6 cm


Step-by-step explanation:


A number has the digits 1, 9 and 5 to the nearest 100 the number rounds to 600. What is the number?

Answers

Answer:

591

Step-by-step explanation:

the closest number to 600 out of every combo

195

159

951

915

519

591

Answer: 591

Step-by-step explanation:

From the digit 1, 9 and 5. The following numbers can be gotten if we use the 3 numbers.

159

195

519

591

915

951

Of all the numbers, the closest to 600 are 519 and 591.

To the nearest 100, 519 gives 500 while 591 gives 600. Therefore, the answer is 591.

What value of b will make the point (4,-3) lie on the line y=bx-2 in the standard (x,y) coordinate plane?

Answers

Plug the coordinates of the point in the equation and solve for b:

[tex] y=bx-2 \iff -3=4b-2 \iff 4b=-1 \iff b=-\dfrac{1}{4} [/tex]

A real estate aqent earns a commission on a house she sells. Her first commission is 5% on the first 500,000 of the sale price of the house. She then earns a 6% comission for the amount sbove 500,000 of the sale price of the house. How much commission did the agent earn if she sold the house for 585,000?

Answers

the agent earned $30,100 in commission.

you first have to break up the number 585,000 into 500,000 and 85,000.

next, you find the commission on the first $500,000. 5% of 500,000 is 25,000.

after finding the commission for the first 500,000, you need to find the commission to the $85,000 dollars we still have.

6% of $85,000 is $5,100.

$25,000 + $5,100 = $30,100 in commission. hope this helps !

The following is an example of a convex polygon



True

False

Answers

false it's concave polygon
The answer is false

FInd the slope of a line

Answers

Answer:

The answer is: undefined or infinite


Hope this helps.



We can use the points (-1, 3) and (-1, 1) to solve.

Slope formula: y2-y1/x2-x1

= 1-3/-1-(-1)

= -2/0

= 0

This line is straight so it's undefined.

Hope This Helped! Good Luck!

Find the slope-intercept form of the line passing through the point (7,-2) and parallel to the line y=-8x-4.

Answers

y=mx+b

-2= -8(7)+b

-2= -56+b

54=b

The answer is:

y= -8x+54

The slope-intercept form of the line passing through the point (7, -2) and parallel to the line y = -8x - 4 is y = -8x + 54. The required answer is y = -8x + 54.

To find the slope-intercept form of a line parallel to the given line, we need to determine the slope of the given line first.

The given line has a slope of -8 since it is in the form y = mx + b, where m represents the slope.

Since the line we are looking for is parallel to the given line, it will have the same slope of -8.

Now, we can use the point-slope form of a linear equation to find the equation of the line passing through the point (7, -2) with a slope of -8:

y - y1 = m(x - x1)

Substituting the values of the point and slope:

y - (-2) = -8(x - 7)

Simplifying:

y + 2 = -8x + 56

Rearranging the equation to the slope-intercept form:

y = -8x + 54

Therefore, the slope-intercept form of the line passing through the point (7, -2) and parallel to the line y = -8x - 4 is y = -8x + 54. The required answer is y = -8x + 54.

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The cost of a taxi ride is equal to $3.50 plus $0.25 for each mile. If a ride costs a total of $6.75 how long was the ride?

Answers

Answer:

13 miles

Step-by-step explanation:

Write and solve an equation involving this information, using x as the distance traveled, in miles:

Cost(x) = $6.75 = $3.50 + ($0.25/mile)x

First, subtract $3.50 from both sides, obtaining:  $3.25 = ($.25/mile)x.

Next, divide both sides by $0.25/mile:

        $3.25

x = ------------------ = 13 miles

      $0.25/mile

The length of the taxi ride was 13 miles.

PLZ HELP!! The question is attached!

Answers

Answer:


Step-by-step explanation:

Subtract the 680 from 960, then divide the product by 52000 to get the answer

A Plummer is fixing a pipe with an interior diameter of 0.63 inches. He buys a replacement pipe that must fit inside the old pipe. He uses plumbing tape that will fill 0.15 inches off the space between the two pieces of pipe. The new pipe must be 0.1 inches smaller than the old pipe and tape so that it can fit inside. What is the largest interior diameter pipe he can buy that will still fit inside the old pipe?

Answers

.63 - .15 - .10 = .38 is the answer.
Final answer:

The largest interior diameter of the new pipe that would still fit inside the old one is 0.38 inches, after taking into account the thickness of the plumbing tape and additional space requirement.

Explanation:

The plumber is attempting to fit a new pipe into an old pipe with an interior diameter of 0.63 inches. We need to take into account the thickness of the plumbing tape that will add an extra 0.15 inches to the diameter, as well as the requirement that the new pipe must be 0.1 inches smaller to fit inside the old pipe.

To calculate the largest interior diameter the new pipe can have, we should do the following:

First, start with the old pipe's diameter, which is 0.63 inches. Deduct the thickness of the plumbing tape. This gives us 0.63 - 0.15 = 0.48 inches. Then, subtract the additional 0.1 inch requirement to provide space for the new pipe to fit. This gives us 0.48 - 0.1 = 0.38 inches.

So, the largest interior diameter of the new pipe that will fit in the old one is 0.38 inches.

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Find the distance between points M(-1,-10) and P(-12,-3) Round to the nearest tenth

Answers

Answer:

13.0 units

Step-by-step explanation:

To find the distance between two points, we use the formula

d = sqrt( (y2-y1)^2+ (x2-x1)^2)

    sqrt((-3--10)^2 + (-12--1)^2)

    sqrt( (-3+10)^2 + (-12+1)^2)

    sqrt( (7^2  + (-11)^2)

   sqrt( 49+121)

   sqrt( 170)

 13.038

Rounding to the nearest tenth

13.0

John is creating a Thanksgiving display at the store where he works, using only canned pumpkin and canned green beans. He needs to maintain a ratio of pumpkin to green beans of 5 to 1. If he wants to use a total of 114 cans, how many cans of green beans should he use?

Answers

Answer:

19

Step-by-step explanation:

The ratio of green beans (g) to pumpkin (p) is ...

... g : p = 1 : 5

Then the ratio of green beans to the total is ...

... g : (g+p) = 1 : (1+5) = 1 : 6

Since you have

... g/total = (1/6)

... g = total · 1/6

you can substitute 114 for the total to find ...

... g = 114 · 1/6 = 19

The probability that a student at certain high school likes art is 36%. The probability that a student who likes art also likes science is 21%. Find the probability that a student chosen at random likes science given that he or she likes art. Round to the nearest tenth of a percent.

Answers

Answer: Probability that a student chosen at random likes science given that he or she likes art is 58%

Step-by-step explanation:

Since we have given that

Probability that a student who likes art and science = 21%

Probability that a student who likes art = 36%

According to question,

we need to find the probability that a student chosen at random likes science given that he or she likes art.

So, we will use "Conditional Probability":

P(A) = 0.36

P(S ∩ A) = 0.21

[tex]P(S\mid A)=\frac{P(S\cap A)}{P(A)}\\\\P(S\mid A)=\frac{0.21}{0.36}\\\\P(S\mid A)=0.58\\\\P(S\mid A)=58\%[/tex]

Hence, Probability that a student chosen at random likes science given that he or she likes art is 58%.

the volume of this rectangular prism is 5x^3. what does the coefficient 5 mean in terms of the problem?

Answers

it's C, assuming x always has the same value

Answer:

the length is 5 times the width of the prism

Step-by-step explanation:

the volume of this rectangular prism is [tex]5x^3[/tex]

volume of the prism = length * width * height

Length of the prism = 5x

Width = x

height =x

Length of the prism = 5x = 5* width of the prism

So, the length is 5 times the width of the prism

Zoe rounded 6 * 8493 to 6 * 8000. Andrew rounded 6 * 8493 + 6 * 9000 who will have an estimate closer to the actual product? How do you know? Explain another way to estimate 6 * 8493 that would give a better estimate

Answers

Answer: Zoe is closer to the actual product because 6.80 is closer to 6.8493 than 6.90 mathematically. Another way to estimate 6.8493 is to round to the nearest hundredth place: 6.85

Final answer:

Zoe will have an estimate closer to the actual product.

Explanation:

To determine who will have an estimate closer to the actual product, we can compare the rounding methods used by Zoe and Andrew. Zoe rounded 6 * 8493 to 6 * 8000, while Andrew rounded 6 * 8493 + 6 * 9000. In this case, Andrew's estimate will be closer to the actual product because he considered additional terms in his calculation.



Another way to estimate 6 * 8493 that would give a better estimate is to round each term separately before multiplying. For example, rounding 6 to 10 and 8493 to 8500, the estimate would be 10 * 8500 = 85,000.

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Trey drives an average of 36 miles per day. How many days will it take him to drive 3,240 miles?

Answers

Answer:

90 days

Step-by-step explanation:

That = 3240 / 36

= 90 days

Answer:

90 days

Step-by-step explanation:

Hello, I think I can help you with this

You can easily solve this by using a simple rule of three.

Step one

Define

if the drives an average 36 miles per day,the how many days(x)  will it take to drive 3240 miles :it is

1 day ⇔ 36 miles

x days ⇔ 3240  miles

the relation is

[tex]\frac{1\ day}{36\ miles}=\frac{x\ day}{3240\ miles}\\[/tex]

Step two

solve for x

[tex]\frac{1\ day}{36\ miles}=\frac{x\ day}{3240\ miles}\\\\x=\frac{1\ day*3240\ miles}{36\ miles}\\x=90\ days\\[/tex]

90 days

Have a great day.

A right triangle has legs that measure 7 cm and 6 cm. What is the length of the hypotenuse in meters?

Answers

Greetings!

Answer:

[tex]\sqrt{85}  or 9.22[/tex]

Step-by-step explanation:

You need to remember the following equation:

[tex]a^{2} + b^{2} = c^{2}[/tex]

Where a and b is the lengths of the two sides and c is the hypotenuse.

So simply plug these values into this:

[tex]6^{2} + 7^{2} = h^{2}[/tex]

36 + 49 = h^2

36 + 49 = 85

So the hypotenuse is the square root of 85:

[tex]\sqrt{85}  = 9.22[/tex]


Hope this helps!

Use the function below to answer the question.

[tex]f(x)=x^3+7x^2+16x+12=(x+2)(x+2)(x+3)[/tex]

What is the multiplicity of the root -3 ?

Answers

Answer:

1

Step-by-step explanation:

(x +3) appears only once as a factor, hence the multiplicity of the root x=-3 is 1.

At a basketball game, a vender sold a combined total of 223 sodas and hot dogs. The number of hot dogs sold was 57 less than the number of sodas sold. Find the number of sodas sold and the number of hot dogs sold.

Answers

Answer: 140 Hot dogs and 83 sodas.


Step-by-step explanation:

Alright, so we will say that h = hot dogs and s = sodas.

h + s = 223

I have used the guess and test strategy to get:

h = 140

140 - 57 = 83

s = 83

Check: 83 + 140 = 223

A pitcher of fruit punch holds 2 gallons. If 9 people share the entire pitcher equally, how much punch will each person get?

Answers

ans = 2/9 if a gallon.

Answer:

2/9

Step-by-step explanation:

2÷9=2/9

What is the third quartile of this data set 20,21,24,25,28,29,35,37,42,43,44

Answers

Answer:

42

Step-by-step explanation:

The median is 29 . The third quartile is the middle number of the last 5 numbers.

This is 42

Answer:

42

Step-by-step explanation:

We are given that a data set

20,21,24,25,28,29,35,37,42,43,44

We have to find the value of third quartile of the given data set.

To find the third quartile we will use the given below formula

[tex]Q_3=\frac{3}{4}\times (n+1)^{th} term[/tex]

Where n=Total number of term

We have n=11

By using the formula

[tex]Q_3=\frac{3}{4}\times (11+1)^{th}[/tex] term

[tex]Q_3=9^{th}[/tex] term

[tex]9^{th}[/tex] term=42

Hence, third quartile=42

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