One leg of a right triangle is 21 inches longer than the other leg, and the hypotenuse is 39 inches.
Find the lengths of the legs of the triangle

Answers

Answer 1

Answer:

One leg - 15 inches

Second leg - 36 inches.

Step-by-step explanation:

One leg - x inches.

Second leg - (x + 21) inches.

Hypotenuse - 39 inches.

Using Pythagorean theorem

x² + (x + 21)² = 39²

x² + x² + 2*21x  + 21² = 39²

2x² + 42x - 39² + 21² = 0

2x² + 42x - 1080 = 0

x² + 21x - 540 = 0

(x - 15)(x + 36) = 0

x = 15, x = - 36

We can use only positive value.

One leg - x inches = 15 inches

Second leg - (x + 21) inches = 15+21=36 inches.


Related Questions

PLEASE PLEASE PLEASE HELP

Answers

Step-by-step explanation:

I rectangle measures⅛(width)by 1/5(length). You have been asked to shade whose area is 3/5(w

length)by ⅞(width)

1)width=⅞÷1/8=7rectangles

2)length=3 /5÷1/5=3rectangles

thus shade 7rectangles along the width(sideways) and 3 rectangles along the length(downwards)

What is the sum of the infinite geometric series? Sigma-Summation Underscript n = 1 Overscript 3 EndScripts (1.3) (.8) Superscript n minus 1

Answers

Answer:

Sigma-Summation Underscript n = 1 Overscript 3 EndScripts (… ... Underscript n = 1 Overscript 3 EndScripts (1.3) (.8) Superscript n minus 1 ... To get the sum to infinity of the geometric series, we need to get its first term

Step-by-step explanation:

which inequality is represented by this graph ?

Answers

Answer:

D

Step-by-step explanation:

The point is on 4 so it cannot be A or B, and it is a closed circle not an open circle so it cannot be C.

Answer:

x≥4

Step-by-step explanation:

There is a closed circle at 4  which means there is an equal to sign and the lines goes to the right which means greater than

x≥4

the sum of two numbers is 90 .the larger number is 14 more than 3 times the smaller number.

Answers

Answer:

The numbers are 19 and 71.

Step-by-step explanation:

Let x and y represent the two numbers.  Then x + y = 90.  

Also, if we assume that the larger number is y, then y = 3x + 14.

We must solve this system of linear equations.  Since we already have the result of solution for y  (y = 3x + 14), let's use the substitution method to find the solution:

x + y = 90 becomes x + 3x + 14 = 90, or:

4x = 76.  Thus, x = 76/4, or 19.       If x = 19, then y = 3(19) + 14, or y = 71.

The numbers are 19 and 71.

Note that these add up to 90, as they must, and that 71 is 14 more than 3 times 19.

whats 2+2 ? ( This is worth 60 points go get them )

Answers

2+2 = 4

Very easy, just add them lol gotem

                       

Answer:

4

Step-by-step explanation:

2 + 2

Add the numbers.

= 4

Mr.Brown is planting trees in a field that is one mile long and 2 miles wide. How much is his field.

Answers

Answer:

Step-by-step explanation:

Wtwtettete

Answer:

2 miles squared.

Step-by-step explanation:

A= length times width

A= 1 mile times 2 miles

A= 2 miles squared

Allie and Samuel are rock climbing

*Allie climbs 5 1/2 meters in the first 1/4 hour.

*Samual climbs 14 1/4 meters in the first 3/4 hour.


each person's rate stays the same for the first hour they climb.


Part A


Which statements are true?


Select all that are Correct.

A. Samuel climbs at a rate of 19 hours per hour

B. Allie takes 1/22 of an hour to climb one meter.

C. Allie climbs at a rate of 1/22 meter per hour

D. Samuel climbs at a rate of 1/19 meter per hour

E. Samuel takes 1/19 of an hour to climb one meter

Answers

Answer:

A and E

Step-by-step explanation: I done this before

The statements that are true are:

Allie takes 1/22 of an hour to climb one meter.

Samuel takes 1/19 of an hour to climb one meter.

Options B and E are correct.

What is a fraction?

A fraction is written in the form of a numerator and a denominator where the denominator is greater that the numberator.

We have two types of fractions.

Proper fraction and improper fraction.

A proper fraction is a fraction whose numerator is less than the denominator.

An improper fraction is a fraction where the numerator is greater than the denominator.

Example:

1/2, 1/3 is a fraction.

3/6, 99/999 is a fraction.

1/4 is a fraction.

We have,

For Allie.

She climbs 5(1/2) meters in 1/4 hour.

This means,

11/2 meters = 1/4 hour

22 meters = one hour

Rate = 22 meters per hour.

We can also say,

To climb one meter, she takes 1/22 of an hour.

For Samuel.

He climbs 14(1/4) meters in 3/4 hour,

This means,

57/4 meters = 3/4 hour

19 meters = one hour

Rate = 19 meters per hour.

We can also say,

To climb one meter, he takes 1/19 of an hour.

Thus,

Allie takes 1/22 of an hour to climb one meter is true.

Samuel takes 1/19 of an hour to climb one meter is true.

Learn more about fractions here:

https://brainly.com/question/24370499

#SPJ2

can someone help me??????​

Answers

Answer:

25.2

Step-by-step explanation:

Volume of container: 2x3x5=30

0.84x30=25.2

HELP ME PLZ NOT A TEST !!!!!!!!!!!!!!!!! ITS A REVIEW AND I DONT GET IT I NEED TO KNOW THE STEPS AND THE AWNSER

Answers

Answer: See below

Step-by-step explanation:

1. For this problem, you see that it's 5². The only problem that displays 5² is A². Now, there is a ×3 after that. That means there is 3 of 5². If you are still not sure, you can solve the problem.

5²×3=25×3=75

A shows 75.

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

2. You need to first distribute each factor and then combine like terms.

-14a+10b+20a-32b+2

6a-22b+2

B

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

3. You need to first distribute each factor and then combine like terms.

-6n+30+18n-12

12n+18

D

pls answer as quick as possible for brainliest!!

Answers

Answer:

15

Step-by-step explanation:

(2 1/2 + 1 1/2 + 3 1/2) = 7 1/2 * 2 = 15

Answer:

15

Step-by-step explanation:

2.5+1.5+3.5 = 7.5

7.5*2 = 15

Two times a number is equal to the absolute value of the quantity "sixty-three less than five times that number." What could the number be?

Answers

Answer:

The number is 21.

Step-by-step explanation:

First you need to solve for n.

So the equation would be 2n = |5n-63|

First you'd subtract 5n from each side, that would give you -3n=|-63|

Then you need to divide each side by -3 to get n=21.

                       ~~~~~

To check, you can just plug 21 back into the equation.

2(21) = |5(21) - 63|

42 = |105-63|

42 = |42|

42 = 42

Find the sum
[tex](4 {xy}^{2} - {3x}^{2}y - 5xy - 6 ) + ( - {5xy}^{2} - 2xy + 3)[/tex]

Answers

Answer:

[tex]-3x^2y-xy^2-7xy-3[/tex]

Step-by-step explanation:

[tex](4xy^2-3x^2y-5xy-6)+(-5xy^2-2xy+3)[/tex]

[tex]4xy^2-3x^2y-5xy-6-5xy^2-2xy+3[/tex]

[tex]-3x^2y-xy^2-7xy-3[/tex]

select the two valuse of x that are roots of this equation. x^2+2x-5=0

Answers

Answer:

1 + sqrt(6)

You can't factor this by itself so you have to use the quadratic formula

Step-by-step explanation:

When making a budget, a recommended goal is to spend 10% on utilities. In reality, household spending depends on economic levels. Households with incomes from $15,000 to $20,000 spend over 11% on utilities. Households with incomes from $50,000 to $70,000 spend 8.2% on utilities, while households with incomes above $150,000 spend only 4.8% on utilities. The McKinneys' annual income is $65,000. How much should they budget annually for utilities? Enter the answer as a whole dollar amount, such as $200.

Answers

Answer:

= $5530  

Finds us 8.2%

Step-by-step explanation:

if 8.2 was recommended for utilities then we need to find 8.2% of $65,000

We take 65000 x 0.082 = 5530

Therefore the Mckinney's annual income is 65,000 less $5530 for utilities.

We write it as $5,530 in pen and type in whole amount as $ 5530.

Answer:

$5,330

Step-by-step explanation:

Read this statement:

"The McKinneys' annual income is $65,000."

Now, read this statement:

"Households with incomes from $50,000 to $70,000 spend 8.2% on utilities"

Since $65,000 is between $50,000 and $70,000, the percent you need is 8.2%.

8.2% of $65,000 = 0.082 * $65,000 = $5,330

Which took place in 1853?
O The US made the Gadsden Purchase.
The US received payment from Mexico for Texas.
Mexico won the Mexican-American War.
Mexico paid the US for the Mexican Cession.

Answers

The first choice is the correct answer.

Answer:

The answer is a

Step-by-step explanation:

I hoped i helped

Jake took a handful of M&Ms from the candy dish on the coffee table.
gave half of them to his little sister. He sorted the M & Ms he had left and
put one third of them back in the dish because they were read and he do
not like red M & Ms. That left Jake with 6 M & Ms. How many did Jake hav
in his original handful?​

Answers

Answer:

36

I want brainliest

Step-by-step explanation:

6 x 3/1 or 6 x 3 = 18

put the reds back in

18 x 2 = 36

take the ones from his sister

Answer = 36

Step-by-step explanation:

6 x 3/1 or 6 x 3 = 18

reds go back in

18 x 2 = 36

take ones from the sister and there u go

A.3/4
B.4/3
C.-4/3
D.-3/4
I need help so bad pls

Answers

I’m pretty sure that it is b
The answer is B or C and if it’s not then my bad

Find the equation of the line that contains the given point and is perpendicular to the given line. Write the equation in​ slope-intercept form, if possible.
(8,1); y=-8x-1

Answers

Answer:

y= ⅛x

Step-by-step explanation:

Slope-intercept form

y= mx +c, where m is the gradient and c is the y-intercept.

Let's find the value of m first.

The product if the gradients of 2 perpendicular lines is -1.

Gradient of given line= -8

m(-8)= -1

m= -1 ÷(-8)

m= ⅛

y=⅛x +c

To find the value of c, substitute a coordinate.

When x=8, y=1,

1= ⅛(8) +c

1= 1 +c

c= 1 -1

c= 0

Thus, the equation if the line is y= ⅛x.

Plz help ASAP will give brainliest if answered correctly!!

Answers

Answer:

C

Step-by-step explanation:

Multiply 5/8 by 4 in which you get 2.5 which is 5/2 and simplify, then you get answer C

Which of the following is the explicit rule for a geometric sequence defined by a recursive formula of an=5an-1 for which the first term is 23?

Answers

Answer:

D

Step-by-step explanation:

The explicit rule for a geometric sequence is

[tex]a_{n}[/tex] = a [tex]r^{n-1}[/tex]

where a is the first term and r the common ratio

Here a = 23 and from the recursive formula

[tex]a_{n}[/tex] = 5[tex]a_{n-1}[/tex] , then r = 5 , thus explicit formula is

[tex]a_{n}[/tex] = 23 × [tex]5^{n-1}[/tex] → D

The correct option is D.

The calculation is as follows:

The explicit rule for a geometric sequence is

[tex]an = ar^{n-1}[/tex]

Here

a represents the first term

r represents the common ratio

So,

[tex]a_n = 5a_{n-1}[/tex]

So,

[tex]a_n = 23\times 5^{n-1}[/tex]

Learn more: brainly.com/question/17429689

PLEASE HELP! FIRST CORRECT ANSWER WILL MARK BRAINLIEST!
A grocer wishes to blend two different coffee brands in order to make a blend of 400 pounds to sell at $3.00 a pound. If he uses a brand of coffee worth $2.70 a pound with another brand worth $3.20 a pound, how many pounds of each does he use?

Answers

Answer:

160 pounds at 2.70

240 pounds at 3.20

Step-by-step explanation:

Let x be the pounds and 2.70 per pound

400-x is the pounds and 3.20 per pound

there will be 400 pounds and 3.00 per pound

2.70 x + (400-x) *3.20 = 400 *3

Distribute

2.70x +1280-3.20x = 1200

Combine like terms

-.5x +1280 = 1200

Subtract 1280 from each side

-.5x = -80

Divide each side by -.5

x = -80/-/5

x =160

160 pounds at 2.70

400-160 = 240 pounds at 3.20

Gregory spins the spinner once. What is P(vowel)?
PLEASE HELP ME!!!

Answers

Answer:

There is two vowels and 6 sections in total

2 wanted sections / 6 total sections = 1/3

1/3 chance or 33.33333%

Step-by-step explanation:

Find the difference quotient of​ f; that​ is, find StartFraction f left parenthesis x plus h right parenthesis minus f left parenthesis x right parenthesis Over h EndFraction comma h not equals 0 comma for the following function. f left parenthesis x right parenthesis equals negative 4 x plus 6

Answers

Answer:

-4

Step-by-step explanation:

Given the following function:

f(x) = -4x + 6

We have to find the difference quotient of​ f(x); that​ is,

[f(x + h) - f(x)]/h

So, we ned to compute f(x + h) as follows:

f(x+h) = -4(x+h) + 6 = -4x - 4h + 6

Replacing into the difference quotient, we get:

[f(x + h) - f(x)]/h = [-4x - 4h + 6 - (-4x + 6)]/h

[f(x + h) - f(x)]/h = [-4x - 4h + 6 + 4x - 6)]/h

[f(x + h) - f(x)]/h = [- 4h)]/h

[f(x + h) - f(x)]/h = -4

Help please! Will give brainly! A rock is dropped from the top floor of a 500-foot tall building. A camera captures the distance the rock traveled, in feet, after each second. Use the information in the image to answer the question.

Answers

Answer:

Step-by-step explanation:

1. No it does not as the rock will accelerate downwards (because of gravity) but we can also see that at the first second the rock fell 16 feet compared to the 2 to 3 seconds gap where it fell 80 feet (144-64).

2. All the way down to the ground. Each time gap is getting bigger and bigger (it's accelerating) and the gap between 5 and 6 s should be bigger than 4 to 5 and it is not as the rock cannot fall through the ground but only hit the ground

you may have to change the english a bit and english is not my first language

hope this will help

a garden has the lengths of 11m,8m,19m and 10m work out the area

Answers

Answer:

A(lawn) = 68 m²

Step-by-step explanation:

A(lawn) = Agarden - Aflower - Avegetables

= 10m×14m - 3m×8m/2 - (5m+7m)×10m/2

= 140m² - 12m² - 60m²

= 68 m²

A(rectangle) = w × h

A(triangle) = ½ × b × h

A(trapeze) = ½(B+b) × h

Evaluate 4 ÷ 5/6 Give your answer as a mixed number in its simplest form.

Answers

Answer:

4 ÷ 5/6

= 4 × 6/5

= 24/5

= 4 4/5

Hope this helps.

25 POINTS!!!!Which of the following statements are true? Select all that apply.


The product of B and D is negative.

The quotient of A and C is positive.

= A ∙

The quotient of 0 and F is undefined.

A ∙ D = -E ∙ D

Answers

Answer:

then 0 and f have to be positive.

Step-by-step explanation:

Mark me brainlest.

Answer:

Its A and C  and F

Step-by-step explanation:

I need help on this 10j< – 10

Answers

Answer:

j<-1

Step-by-step explanation:

10j<-10

divide both sides by 10 and get

j<-1

Answer:

[tex]j < - 1[/tex]

Step-by-step explanation:

[tex]10j < - 10 \\ \frac{10j}{10} < \frac{ - 10}{10} \\ = j < - 1[/tex]

hope this helps

brainliest appreciated

good luck! have a nice day!

Can you think of the integers for x, y, and z so that x³+y³+z³=8? Sure. One answer is x = 1, y = -1, and z = 2. But what about the integers for x, y, and z so that x³+y³+z³=42?​

Answers

Answer:

Well ,lets see∉ if you add theose numbers togetherФ it maybe it he answe ris 4=67 *64  ---4 67x54 5xe4t4 6x

Find the measure of an exterior angle of a regular hexagon

Answers

Answer: 60 degree angle

Step-by-step explanation:

The rule for polygons is that the sum of the exterior angles adds up to 360. Since there are 6 exterior angles on a 6 sided polygon (hexagon), then we can divide 360 by 6 to find the measure of an exterior angle. This means that one exterior angle of a hexagon is equal to 60 degrees.

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