Three pieces of wood measure 20 cm, 41 cm and 44 cm. If the same amount is cut off each piece, the remaining lengths can be formed into a right triangle. What is the length that is cut off?

Answers

Answer 1

5 cm or 29 cm

Step-by-step explanation:

Let x length is cut off from each measurements.

Thus, the new measurements would be: 20 - x, 41 - x, 44 - x, which forms the sides of a right triangle.

Here, (44 - x) will be hypotenuse and (20 - x) and (41 - x) will be perpendicular legs of the triangle.

Therefore, by Pythagoras theorem:

[tex] {(41 - x)}^{2} + {(20 - x)}^{2} = {(44 - x)}^{2} \\ \\ \therefore \: {(41)}^{2} - 82x + {x}^{2} + {(20)}^{2} - 40x + {x}^{2} \\ = {(44)}^{2} - 88x + {x}^{2} \\ \\ \therefore \: 1681 - 122x + 2 {x}^{2} + 400 \\ = 1936 - 88x + {x}^{2} \\ \\ \therefore \: 2081 - 122x + {x}^{2} = 1936 - 88x \\ \\ \therefore \: {x}^{2} - 122x + 88x + 2081 - 1936 = 0 \\ \\ \therefore \: {x}^{2} - 34x + 145 = 0 \\ \\ \therefore \: {x}^{2} - 29x - 5x+ 145 = 0 \\ \\ \therefore \: x(x - 29) - 5(x - 29) = 0 \\ (x - 5)(x - 29) = 0 \\ x - 5 = 0 \: or \: x - 29 = 0 \\ \\ \therefore \: x = 5, \: 29[/tex]

So, the length that is cut off will be either 5 cm or 29 cm.


Related Questions

I need help ASAP!!Please help me

Answers

Answer:

Below

Step-by-step explanation:

To find the volume of a rectangular prism find the area of a face and multiply it by the height

V = lwh

  = (12)(5)(12)

  = 720 km^3

Hope this helps!

given: y=8-3x find the slope and y intercept

Answers

Answer:

Step-by-step explanation:

y = mx + b

"m" is slope ; "b" is y-intercept.

~~~~~~~

y = - 3x + 8

m = - 3

b = 8

Can anyone help me with this please and thank you

Answers

Answer:

x=0, 7

Step-by-step explanation:

x^2-3x=4x

x^2-7x=0

x(x-7)=0

x=0 or 7

Answer:

x=0  x=7

Step-by-step explanation:

x^2 -3x = 4x

Subtract 4x from each side

x^2 -3x-4x=0

x^2 -7x = 0

Factor out an x

x(x-7) =0

Using the zero product property

x=0  x-7 =0

x=0  x=7

CX is an altitude in triangle ABC.
Which statements are true? Select two options. .

Answers

Answer:

Does the answer help you?

A. 4
B.-1/4
C. 4
D. 1/4

Answers

The answer should be 1/4

Who can do 20 assignments in math for me rn needs to b finish in 5 hours?

Answers

u need to finish 4 assignments in 1 hour

HELP ASAP

Write the equation of the line passing through the points (-5,8) and (-8,5).

Answers

Answer:

y=-5/8x+0

Step-by-step explanation:

Find the area of the circle.
Use 3.14 for it. Do not round your answer.
Hint: A = Tira
14 inches
Area = [?] inches?
Enter the number that
belongs in the green box.

Answers

Use the formula given. R is half the diameter

R = 14/2 = 7 inches.

Area = 3.14 x 7^2

Area = 153.86 inches^2

Answer:

Does the answer help you?

2y + x = 7 and y = -x + 5 find the solution of the following system of equations ok​

Answers

Answer:

(3, 2)

Step-by-step explanation:

Solve for the first variable in one of the equations, then substitute the result into the other equation.

Point Form:

(3, 2)

Equation Form:

x = 3

y = 2

For the Parabolay = (x + 7)2 – 3. the equation for the Line Of Symmetry is

Answers

Answer:

Hello

Step-by-step explanation:

Axis of symmetry is vertical:

x=-7 (since (-7,-3) is the vertex)

Answer:

x = -7

Step-by-step explanation:

y = (x+7)^2 -3

This is in vertex form

y =a(x-h)^2+k  where (h,k) is the vertex and the line of symmetry for a vertical parabola is x=h

y = (x- -7)^2 -3

x = -7

Brainliest if you can help me!!

Answers

Step-by-step explanation:

I guess option 1 is correct answer

The bar graph shows the median income for families in the United States from 1993 through 2000.
Which two consecutive years saw the largest increase in median income?

A. 1994–1995

B. 1997–1998

C. 1998–1999

D. 1999–2000

Answers

I think the answer is C

Consecutive years that saw the largest increase in median mode is C. 1998-1999.

What is median ?

Median is the the middle term when data are arranged in ascending or descending order when we have odd number of terms and median is sum of the mean of the middle term and the next term when we have even number of terms.

According to the figure and statement given a bar graph hows the median income for families in the United States from 1993 through 2000.

We have to determine which two years saw the largest increase in median income.

If we observe the graph carefully and go through options we can conclude that 1998-1999 has the largest increase in median income which is of 1500 dollars.

learn more about median here :

https://brainly.com/question/28060453

#SPJ2

Simplify the expression to a polynomial in standard form:
(2x - 1)(-x^2+ 4x + 6)

Answers

Answer:

[tex](2x - 1)( - {x}^{2} + 4x + 6) \\ = 2x \times - {x}^{2} + 2x \times4x + 2x \times 6 \\ - 1 \times - {x}^{2} - 1 \times 4x - 1 \times 6 \\ = - 2 {x}^{3} + 8 {x}^{2} + 12x + {x}^{2} - 4x - 6 \\ = - 2 {x}^{3} + 9 {x}^{2} - 8x - 6 \\ thank \: you[/tex]

Mr lim had just enough money to buy 6 similar lamps. However, he bought 3 such lamps and had $950 left. How much money did mr lim have at first?

Answers

Let the cost of a lamp = x

6 lamps would cost 6x

He bought 3 lamps at 3x plus Thad 950 left.

3 lamps plus the 950

Would be the same amount as 6 lamps:

Set up an equation and solve for x:

3x + 950 = 6x

Subtract 3x from both sides:

950 = 3x

Divide both sides by 3:

X = 316.67

Each lamp was $316.67

Multiply the price of a lamp by 6:

316.67 x 6 = 1900

He had $1900

Answer: $1900

Step-by-step explanation:

Mr Lim had enough money to buy 6 similar lamps. However he only bought 3 such lamps. That means he had only spent half of his money (6-3=3).

So, if he take money remaining with him = x = $950

Amount of money he first had = 2x =$950×2 = $1900

5. Which property was used to simplify the expression?


a) distributive property

b) commutative property

c) associative property

d) inverse property

Answers

Answer:

a

Step-by-step explanation:

distributive property

How do I solve part A

Answers

You have to put them into order, then multiple the two sides kf the triangle then put them together

Answer:

you have to put them in order

please help me !! :)

Answers

Answer:

I believe it is D

Step-by-step explanation:

Find the value of ( 1+cosA) (1-cosA)

Answers

Answer:

sin^2 A

Step-by-step explanation:

first expand the trigonometry

1(1-cosA)+cosA(1-cosA)

=1-cosA+cosA-cos^2 A

= 1-cos^2 A

from trigonometric identity sin^2 A + cos^2 A= 1

sin^2 A= 1- cos^2 A

=sin^2 A

45. A crew member on a boat releases a camera 2 feet above the surface of a lake. The
camera falls 6 feet, where it is caught by a diver. How many feet below the surface of
the lake is the diver?
A. 6 feet below
B. 8 feet below
C. 4 feet below
D. 12 feet below

Answers

Answer:

C. 4 feet below

Step-by-step explanation:

A crew member on a boat releases a camera 2 feet above the surface of a lake. That is +2 feet

The camera falls 6 feet. -6

+2+(-6)

2-6

-4

Below 4 feet

I have been trying to find the answer for 10 minutes now..Please help!

Answers

Plugging in the values, we see that object 1 has more potential energy (the ball to the left)

Pls help me it’s algebra

Answers

Answer:

x^2 + 13x + 2

Step-by-step explanation:

The perimeter is all of the sides added up.

11 + 3x + x^2 + 2 -(-6x+5) + 2/5(10x-15)

11 + 3x + x^2 + 2 + 6x -5 + 4x - 6

x^2 + 13x + 2

Basically, we combine like terms and you will get a final answer of:

x^2 + 13x + 2.

This is the simplified expression! I hope this helped.


What is the volume of the cylinder?
5767 cm3
2887 cm3
967 cm3
1921 cm3

Answers

Calculate the area of the base circle: pigreco • r^2 = 3,14 • (6)^2 = 3.14 • 36 = 113 cm2
Now you have to moltiplicate to the high, so: 113 • 16 = 1808 cm3

If 4x – 5 = 96, what is the value of 4x + 12?

Answers

Answer:

113

Step-by-step explanation:

Solving the first equation, 4x - 5 = 96, we get x = 25.25:

4x - 5 = 96

add 5 to both sides

4x = 101

divide both sides by 4

x = 25.25

Then we plug that into 4x + 12.

We already know 4x = 101, so 101 + 12 = 113

The value of the expression will be equal to 113.

What is an expression?

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Solving the first equation, 4x - 5 = 96, we get x = 25.25:

4x - 5 = 96

Add 5 to both sides.

4x = 101

Divide both sides by 4.

x = 25.25

Then we plug that into 4x + 12.

4x = 101,

Substitute the value of 4x into the expression.

101 + 12 = 113

Therefore, the value of the expression will be equal to 113.

To know more about expression follow

https://brainly.com/question/723406

#SPJ2

Please help!!! Find the length of MK

Answers

Answer:

HK = 42

HM = 23

MK = ??

23 + MK = 42

MK = 19

^^^ so you're correct :)

Let me know if this helps!

Can you help please answer will give Max points

Answers

Answer: 256/9 or 28 and 4/9

Answer:

28 4/9

Step-by-step explanation:

5 1/3 times 5 1/3

paul leaves for school at 7:25 am he returned home at 3:15 pm how long was paul away from home?

Answers

Answer:

8 hours 10 minutes

I hope this answers your question

Answer: paul has been away from home for 7 hours and 50 minutes.

Step-by-step explanation:


FIND AC! PLS HELP!!

Answers

Answer:

AC = 7.3 in

Step-by-step explanation:

tan(51°) = 9/AC

1.24 = 9/AC

AC = 9/1.24

AC = 7.26

There are 10 boys and 6 girls. How many ways are there to choose 8 people to get at most girls

Answers

Answer:

2 ways

Step-by-step explanation:

6G and 2B

5G and 3B

help me pleaseeee <333 .

Answers

Answer:

3 one

Step-by-step explanation:

Answer:

3 option is correct

Step-by-step explanation:

gd afternoon

have a lovely day

Write an
equivalent expression by distributing the
""
"sign outside the parentheses:
-(-9.1d - 6f +9.1)
Answer:
Submit Answer

Answers

Answer:

[tex] - ( - 9d - 6f + 9.1) \\ = 9d + 6f - 9.1 \\ thank \: you[/tex]

Other Questions
Which sentence uses an objective tone?-"We will plant the best garden of any school in the area."-"The new campus garden will surely be envied by other schools."-"A garden would provide numerous benefits to the students."-"You will probably agree that gardens have many benefits." 9sin()-7=0. Solve the trigonometric equation A rectangle has a perimeter of 53 feet and a base of 7.1 feet. What is the height? Simplify 132-12x12-124:31 Send Photo do in full process Why are scientific models important? 9x+5y=34 8x-2y=-2What are the values of x and y? Please explain the steps. Figure A AA is a scale image of Figure B BB. 12 12 6 6 x x 9 9 Figure B Figure B Figure A Figure A What is the value of x xx? In Shakespeare's "Romeo and Juliet," the main focus is the tragic love story betweenRomeo and Juliet. However the play also tells the story of fighting between theMontagues and Capulets. What is this called? Can someone answer the question I uploaded yesterday, subject is social studies. All you have to do is read an article and answer questions. Giving brainliest. Create a parent class called Shape with width and height parameters of type double and a function that returns the area of the shape, which simply returns 0. Then define two subclasses, Rectangle, and Triangle, that override the area function to return the actual area (width*height for Rectangle and 1/2*width*height for Triangle).The code must be in java What is the equation and the answer? please help me in solving this Can someone PLEASE answer the Algebra Question CORRECTLY BELOW!Thank you, I will mark brainiest! EX1: Fill in the missing prepositions:71. Out .... sight , out ,,,, mind 72. The sun rises .... the east , and sets ..... the west73. Were your friends successful .... getting a loan from the bank74. I'm sure the explanation in the book will be quite clear ... you75. Miss White was upset ... the news of her father's death 76. I'm not familiar ... his name77. We were very grateful ... our friends ... all of their assistance78. Don't you think you should try to be friendly .... your classmate79. Mr Green is respnsible ... hiring employees80. That type of music is quite popular ... teenage boys and girls81. My daily expenses are just about equal ... my income82. Fred is capable ... doing better work than he is doing at present 83. We were very doubtful .... his ability84. Ken was proud ... his good marks on English85. My plan is similar ... yours , but it is different ... Ken's86. Piere said he had become quite fond ... American hamburgers87. We are still hopeful ... hearing from our friends before Saturday88. That fashion magazine is full .... advertising for women's clothes 89. This gloves aren't very suitable ... that kind of work90. They were happy ... the result of the election91. It was cartainly kind ..... you to help me92. Mrs Brown is often worried ... money93. Her parents are very pleased ... her French94. I'm not interested ... politics95. She was sad because he was rude ... her96. She was angry .. Tom97. Traveling by air is preferable ... traveling by train98. Thank you You are kind ... me99. Everybody was surprised ... the news100. I was delighted ... the present you gave meEX2: Choose the best option to complete the following sentences13. She is older than meA. I'm more younger than her B. I'm as younger as herC.I'm more young than her D. I'm younger than her14. The test is not ..............A. as difficult as it was last month B. So difficult as it was last monthC. more difficult as it was last month D. Both A & B are correct16. ................ we read , ............ we knowA. The most/the most B. The more /the moreC. Most/most D. more/more17. It gets ................... Let's go swimming A. hot and hot B. The more hotC. More and more hot D. Hotter and hotter18. Peter usually drivers .............. MaryA. more fast B. More fast than C. more fast D. faster19. The problem seems to be ...........A. more serious B. more serious thanC.more serious as D.more and more serious20. Peter can not earn ...... his wife A. as many money as B. as much money as C. as many money than D. as much money than21. Prices get................A. high and high B. highest and highestC. more and more high D. higher and higher22. the more manufactures advise , ..... they sellA. the most products B. the products more C. the more products D. most products Sagarmatha is our national pride. Justify the statement. please I need a step by step explanation ASAP thank you explain this statement "I can set limits and still be a loving person" what is national heritage The ratio of men to women working for a company is 5 to 3. If there are 200 employees total, how many women work for the company? which of the following equations is an example of inverse variation between the variables x and y?