The hypotenuse of a right triangle is 13ft long. The longer leg is 7ft longer than the shorter leg. Find the side lengths of the triangle.

Answers

Answer 1

Answer:

The side lengths are 5, 12, 13

Step-by-step explanation:

These are the side lengths we know before we have solved the problem.

a= x   b= x+7   c= 13

If we put this into the Pythagorean theorem, we get

[tex]13^{2} = x^{2} +(x+7)^{2}[/tex]

Expand

[tex]169 = 2x^2+14x+49\\[/tex]

Subtract 169 from both sides

[tex]0 =2x^2+14x-120[/tex]

Solve using the quadratic formula

a= 2   b= 14   c= -120

[tex]\frac{-14\pm \sqrt{14^2-4\cdot \:2\left(-120\right)}}{2\cdot \:2}[/tex]

[tex]x= \frac{-14\pm \:34}{2\cdot \:2}[/tex]  

If we separate the solutions we get

[tex]x= \frac{20}{4} = 5[/tex]

and

[tex]x= \frac{-48}{4} = -12[/tex]

Since this is a question about length, we can ignore the negative.

So the longer leg is 12ft and the shorter leg is 5ft

Answer 2

The shorter length is 5feet and the longer length is 12 feet

Let the shorter leg = x

Let the longer leg = x+7

Therefore,

x² + (x+7)² = 13²

x² + x² + 14x + 49 = 169

Collect like terms

2x² + 14x + 49 - 169 = 0

2x² + 14x - 120 = 0.

Divide by 2

x² + 7x - 60

By using quadratic equation

x² + 12x - 5x - 60

x(x + 12) - 5(x + 12)

Therefore, x - 5 = 0

x = 0 + 5.

x = 5

The shorter length is 5ft

Longer length = 5+7 = 12 feet

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Related Questions

Quincy rides his bicycle 1 mile in 4 minutes, and his sister Marissa runs 13,376 feet in 16 minutes. In miles per hour approximately how much faster is Quincy than Marissa? (Note: 1 mile = 5,280 feet)

Answers

Answer:

Quincy is 5.5 mi/h faster than Marissa

Step-by-step explanation:

Speed

It's required to compare the speed of Quincy and Marissa knowing that Quincy rides his bicycle 1 mile in 4 minutes.

The speed can be calculated as the distance by the time, but it's required to express the speed in miles/hour.

4 minutes is 4/60 = 0.0667 hours, thus Quincy's speed is:

[tex]\displaystyle \frac{1\ mile}{0.0667\ h}=15\ mi/h[/tex]

Quincy rides at 15 miles/hour.

Marissa runs 13,376 feet in 16 minutes. Since 1 mile=5,280 feet:

13,376 / 5,280 = 2.533 miles

16 minutes = 16/60 = 0.2667 hours

Marissa's speed is:

[tex]\displaystyle \frac{2.533\ mile}{0.2667 \ h}=9.5\ mi/h[/tex]

The difference is 15 - 9.5 = 5.5 mi/h

Quincy is 5.5 mi/h faster than Marissa

You want to buy 4 pens, each costing 27 cents. How many dollar bills should you take to the store? im not in college btw lol

Answers

Answer:

108c so 2 dollar bills.

Step-by-step explanation:

what is m% of n please help

Answers

m% of n would technically be some amount of n. To find m%, you would have to do n * 0.m to find your answer

ANYONE WANNNA HELP MATH!!!!! HRW BTW

Answers

Answer:

1/4 off

Step-by-step explanation:

1/4 is 0.25. 0.25 times 100 is 25. It would be 25% off. 25 is more than 20 and why buy 3 to get 1 free. Hope this helps!!!! Let me know if i'm right please.

Is this a function?

Answers

Answer:

yes

Step-by-step explanation:

Which of the following is an example of the distributive property?
1. 3(10 + 5) = 3(15)
2. 3(10 + 5) = (10 + 5)3
3. 3(10 + 5) = 30 + 15
4. 3(10 + 5) = 3(5 + 10)​

Answers

Answer:

3 - 30+15

Step-by-step explanation:

take the outside number and multiply it by each individual number in the parenthesis one at a time

The seventh grade class is having a dance. They are selling tickets for $8 each. How many tickets do they need to sell to pay for their expenses, which equal $256?​

Answers

Answer:

They need to sell 32 tickets

Step-by-step explanation:

256/8=32

Answer:

They need to sell 32 tickets to pay for their expenses.

assume that the variable under consideration has a density curve. it is given that 27.1% of all possible observations of the variable are less than 17. Determine the area under the density curve that lies to the right of 17.​

Answers

Answer:

72.9%

Step-by-step explanation:

Given that :

27.1% of all possible observation of a certain variable are less than 17 ;

That is ;

Let variable = y ;

Proportion of (y < 17) = 27.1% = (27.1 / 100) = 0.271

Proportion that lies to the right :

P(y > 17) = 1 - P(y < 17)

P(y > 17) = 1 - 0.271

P(y > 17) = 0.729 = 72.9%

Point R on the coordinate grid below shows the location of a car in a parking lot. A second car needs to park 6 units above R to leave room for a utility truck. What are the coordinates of the location of the second car?

Image of a coordinate grid with point R R located at negative 1, negative 3.
(3 points)

(−1, −3)
(−1, 3)
(5, −3)
(5, 3)

Answers

Answer:

Point R is located at the point (-1,-3)

The car needs to park 6 units above point R.

When you are moving something up or down on the coordinate grid, you are affecting the y- axis. So to find the coordinates we would keep the x value and add 6 to the y value.

Coordinates of the second car

(-1, -3 +6)

(-1 , 3)

The answer to this question is B

Adding a positive to a negative is the same as subtracting.

EX:

We were adding 6 and -3

Adding 6 and -3 is the same as subtracting 3 from 6.

Either way we get the same answer.

B is your answer

Hope this helps!

If Tim has 2/3 pizza to share with 6 friends how much does he friend get

Answers

Answer:

Each friend gets 1/9th of the pizza.

Step-by-step explanation:

Assuming Tim does not have any pizza, you would multiply 2/3 by 3 to get 6/9. 6/9 divided by 6 is 1/9.

In triangle XYZ, angle Y = 45º and angle Z = 60º. If XZ = 4, then what is XY?

Answers

Answer:

[tex]XY = 4.9[/tex]

Step-by-step explanation:

Given

[tex]XZ= 4[/tex]

[tex]\angle Y = 45[/tex]

[tex]\angle Z = 60[/tex]

Required

Determine the measure of side XY

To do this, we make use of sine law. This is as follows:

[tex]\frac{a}{\sin\ A} = \frac{b}{\sin\ B} = \frac{c}{\sin\ C}[/tex]

In this case:

[tex]\frac{4}{\sin(45)} = \frac{XY}{\sin(60)}[/tex]

Cross Multiply

[tex]XY * \sin(45) = 4 * \sin(60)[/tex]

[tex]XY * 0.7071 = 4 * 0.8660[/tex]

Make XY the subject

[tex]XY = \frac{4 * 0.8660}{0.7071}[/tex]

[tex]XY = \frac{3.4640}{0.7071}[/tex]

[tex]XY = 4.89888276057[/tex]

[tex]XY = 4.9[/tex] -- approximated

2.
Mrs Yusuf went shopping at a superstore.
The pie chart shows information about the money she spent on petrol, on clothes, on food and on
other items
Puro
bao
Food
Clothes
(a) What did she spend most money on?

Answers

Answer:

Dude First show the pie chart

Mrs. Yusuf spend the most money on Food.

Given is pie chart showing the information about the money Mrs. Yusuf spent on petrol, on clothes, on food and on other items,

We need to identify the portion which tell that she spend the most money on that item,

So, we know that the more portion one item has on the pie chart the more she had spend on that item,

Here in the pie chart we can see the food portion is largest.

So, we can say she spend her most money on food items.

Hence the correct answer is Food.

Learn more about Pie chart click;

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Find all missing angles

Answers

Answer:

m1=30

m2=41

m3=96

Step-by-step explanation:

m1=180-66-84

m2=180-96-43

m3=180-84

The perimeter of the square below is 36 yards. What is the length of each side?
yards

Answers

Answer:

9 yards

Step-by-step explanation:

36 divided by 4 = 9

The length of each side is 9 yards.

What is perimeter?

A closed shape's perimeter is the sum of the lengths of its outside boundaries. The lengths of all the sides are added to determine the measurement.

Given:

The perimeter of the square below is 36 yards.

The length of each side,

= perimeter/ number of sides.

= 36/4

= 9 yards.

Therefore, each side is 9 yards.

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plz help! will give brainliest!

Answers

Answer:

B

Step-by-step explanation:

The graph shows 3 spaces up every our on the y axis I hope this helped you! im very good at these so I can help is u have more questions! can I have brainliest? I was the first

Answer: 3 miles per hour

Step-by-step explanation:

looking at the graph you have (1,3)  (2,6) and (3,9) and everytime its multiplying by 3... 1x3=3 , 2x3=6, 3x3=9

Therefore, your answer is 3 miles per hour

NEED HELP ASAP!!!! WILL MARK BRAINLIEST!!!!!

Which statement best compares the rate of change of the two functions?

O The rate of change of both functions is 2

O The rate of change of both functions is 3.

O The rate of change of function A is greater. than the rate of change of function B.

O The rate of change of function B is greater than the rate of change of function A.​

Answers

Answer: The rate of change is 2

Step-by-step explanation:

Divide the Y by X for each of them and they all are 2

Estimate 32% of 19.

Answers

Answer: 6.08.

Explanation: 32% × 19 = 6.08.

A partnership between two companies calls for company A to get a flat fee of $25,000 from Company B each month, plus 15% of all sales for the jointly developed product sold by company B. If Company B sells a total of $1,200,000 of the jointly developed product in the first twelve months, what will be the total amount owed Company A by Company B?

Answers

Answer:

no idea what the answer is, good luck!

Step-by-step explanation:

Coach Coleman is ordering thigh and knee pads for the football players. There are 20 players. Thigh pads come in packs of 2 and knee pads come in packs of 4. What is the least number of packs of thigh and knee pads can he order so that none will be left over?​

Answers

Answer:

100 or 80

Step-by-step explanation:

I HAD A SIMILAR QUESTION.

I'M SORRY IF ITS WRONG.

The data below gives the mean price (in cents) of a liter of regular gasoline at self-service filling stations at a sample of six urban centers in Canada in May 2011.

Urban area Price/liter
St. John, NL 137.1
Halifax 133.6
Montreal 136.2
Regina 132.3
Saskatoon 132.2
Yellowknife 138.9

Required:
a. Find the sample mean (in cents).
b. Find the sample standard deviation (in cents).
c. Find a 90% confidence interval for the mean gasoline price per liter across urban Canada in May 2011. Provide the lower and upper limits for your confidence interval.
d. Find a 95% confidence interval for the mean gasoline price per liter across urban Canada in May 2011. Provide the lower and upper limits for your confidence interval.

Answers

Answer:

135.05 ; 2.762 ; (133.201, 136.899) ; (132.840, 137.260)

Step-by-step explanation:

Given the data:

Urban area Price/liter

St. John, NL 137.1

Halifax 133.6

Montreal 136.2

Regina 132.3

Saskatoon 132.2

Yellowknife 138.9

Mean = (137.1 + 133.6 + 136.2 + 132.3 + 132.2 + 138.9) / 6

= 810.3 / 6

= 135.05

Standard deviation (σ) : √Σ(X - mean)²/n-1

(137.1 - 135.05)^2 + (133.6 - 135.05)^2 + (136.2 - 135.05)^2 + (132.3 - 135.05)^2 + (132.2 - 135.05)^2+ (138.9 - 135.05)^2 = 38.135

√(38.135 / (6 - 1))

= √7.627

= 2.7617023

= 2.762

C.)

90% confidence interval of the mean :

Mean ± Zcrit * σ/√n

Zcrit at 90% = 1.64

135.05 ± 1.64 * (2.762/√6)

135.05 ± 1.64 * 1.1275817

Lower Value = (135.05 - (1.64 * 1.1275817)) = 133.201

Upper Value = (135.05 + (1.64 * 1.1275817))) = 136.899

Confidence interval = (133.201, 136.899)

D.)

95% confidence interval of the mean :

Mean ± Zcrit * σ/√n

Zcrit at 95% = 1.96

135.05 ± 1.96 * (2.762/6)

135.05 ± 1.96 * 1.1275817

Lower Value = (135.05 - (1.96 * 1.1275817)) = 132.840

Upper Value = (135.05 + (1.96 * 1.1275817)) = 137.260

Confidence interval = (132.840, 137.260)

When the price of Xis RM4 and the price of Y is RM10, which of the following combinations would be the intercept of axes
(X,Y) if you have an income of RM 100?
Select one:
A. (25X, 10Y)
B. (20X, 5Y)
C. (10X, 25Y)
D. (5X, 20Y)

Answers

I would say C but I’m not completely 100% sure

What is the solution for this inequality?

need help fast please!​

Answers

Answer:

[tex]x\geq -4[/tex]

Step-by-step explanation:

[tex]-10x\leq 40[/tex]

divide by -10, which means you need to flip the inequality sign since youre dividing by a negative number

[tex]x\geq -4[/tex]

Answer:

The anwer is D

Step-by-step explanation:

up up up......

Devin volunteers at Big Pup Rescue. He is mixing up shampoo solution for the dog washing station. He needs 2 cups of shampoo concentrate for every 9 cups of water. Devin will use 36 cups of water.
How much shampoo concentrate should Devin add to the water to make the shampoo solution?

Answers

Answer:

8 cups of shampoo concentrate

Step-by-step explanation:

let x=how much shampoo concentrate Devin should add

[tex]\frac{2}{9} =\frac{x}{36}[/tex]

cross multiply

2*36=9x

72=9x

72/9=x

x=8

Devin should add 8 cups of shampoo concentrate to the water to make the shampoo solution.

A 5 lb. package of chicken costs $6.00. What is the cost per pound?

Answers

Answer:

$1.2

Step-by-step explanation:

Cost per pound = 6/5 = $1.2

Answer:

1.20 a pound

Step-by-step explanation:

Find the slope of the line that passes through the pair of points.
4. (1, 6), (6, -1)
7
a.
5
b.
5
7
c.
7
5
d.
5
7

Answers

Answer:

-7/5

Step-by-step explanation:

What is the y-intercept of the graph of 4y = 2x + 8?
4
2
6
00
N

Answers

Answer:

2

Step-by-step explanation:

4y = 2x + 8

First get the equation in slope intercept form  y= mx+b where m is the slope and b is the y intercept

Divide each side by 4

4y/4 = 2x/4 +8/4

y = 1/2x +2

The slope is 1/2 and the y intercept is 2

Answer:

2

Step-by-step explanation:

Manipulate your equation into slope-intercept form: y = mx + b, where b is the y-intercept.

To do this, divide 4 from both sides:

[tex]y=\frac{1}{2} x+2[/tex]

b = 2

What is the equation of the line shown in the graph below? *

Answers

Answer:

y=1/2x−2

Step-by-step explanation:

if you find the 2 point that touch the y and x-axis on the graph, (4,0) and (0,-2), and put it in y=mx+b formula, you get the answer.

please help
2×1,000+9×100+5×1+1×1100+3×11,000
2×1,000+9×10+5×110+1×1100+3×11,000
2×1,000+9×10+5×1+1×110+3×11,000

Answers

Answer:

37005

36740

35205

Step-by-step explanation:

Which equation has a slope of 2 and y-intercept of -3

Answers

y = 2x -3

fhfjdydtsfxbnpurwsgh

A group of students are standing in rows. There are as many students in a row as there are rows. If there are 64 students in the group, how many students are standing in pach row?
A. 4
B 6
C. 8
D 12.​

Answers

Answer:

B..im pretty sure

Step-by-step explanation:

First it cant be D because 12 x __ = 64. There is no whole number multiplied by 12 that equals 64. So cross that out. then it's not B because 6 x ___ = 64. So also cross that out. the only thing u have left is 4 and 8. Then u can cross out A because the group of students has to be the same number of rows. Which is 8 x 8 aka B. The answer is B

Answer:

B

Step-by-step explanation:

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