Use the Pythagorean Theorem to find the length of the leg in the triangle shown below. The figure shows a right triangle with one leg marked 20. The hypotenuse is marked 52.

Answers

Answer 1

Answer:

48

Step-by-step explanation:

The Pythagorean Theorem is:

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

where [tex]a[/tex] and [tex]b[/tex] are the legs of the right triangle. [tex]c[/tex] is the hypotenuse of the triangle.

In this right triangle, we know that one leg is 20 and the hypotenuse is 52. Therefore,

[tex]a=20[/tex]

[tex]c=52[/tex]

Since we don't know the other leg, we can leave it as [tex]b[/tex]. Substitute the values into the theorem.

[tex]20^2+b^2=52^2[/tex]

Evaluate the exponents first.

⇒ 20²=20*20=400

⇒ 52²= 52*52= 2704

[tex]400+b^2=2704[/tex]

Since we want to find [tex]b[/tex], we must isolate [tex]b[/tex]. First, subtract 400 from both sides of the equation.

[tex]400-400+b^2=2704-400[/tex]

[tex]b^2=2704-400[/tex]

[tex]b^2=2304[/tex]

[tex]b[/tex] is being squared. The inverse of a square is a square root. Take the square root of both sides of the equation.

[tex]\sqrt{b^2}=\sqrt{2304}[/tex]

[tex]b=\sqrt{2304}[/tex]

[tex]b=48[/tex]

The length of the other leg is 48


Related Questions

Is there a known infinite product for e? What I mean is, it’s similar to an infinite series.

Answers

"e" is an irrational number because it cannot be seen as a quotient of two integers. In the bright side, it can be shown as a continued fraction. "e" may also be used as an infinite product, infinite series, and any other limit to any sequence.

Best of Luck!

For Elizabeth's lemonade recipe, 4 lemons are required to make 2 cups of lemonade. At what rate are lemons being used in cups of lemonade per lemon?

Answers

Answer:

2 lemons per cup

Step-by-step explanation:

4/2 is two.

Answer:

2 lemons per cup

Step-by-step explanation:

Which number is a reasonable estimate for 553 +363?
A 1,300
B 1,000
600
D 200

Answers

its b because you can round 363 to 400 and 553 to 600 400 + 600 = 1000

answer choice b! the correct answer is 1,000!

Simplify:
(4xy^-6)^-3

[tex](4xy^{-6} )^{-3}[/tex]

Answers

Answer:

(4^-3)(x^-3) y^(18)

or

y^18/ (64 x^3)

Step-by-step explanation:

(4xy^-6)^-3

Distribute the exponent to all terms in the parentheses

(4^-3)(x^-3) (y^-6)^-3

a^ b^c = a^ (b*c)

(4^-3)(x^-3) y^(-6*-3)

(4^-3)(x^-3) y^(18)

If we do not want negative exponents

a ^ -b = 1/ a^b

y^18/( 4^3 x^3)

y^18/ (64 x^3)

Solve the equation. -10x + 1 + 7x = 37

A. X = -15
B. X =-12
C. X = 12
D. X = 15​

Answers

Answer:

B. X =-12

Step-by-step explanation:

- 10x + 1 + 7x = 37

-10x + 7x = 37 - 1

-3x = 36

x = 36/-3

x = - 12

AWARDING BRAINLIEST!!
Beth is solving this equation: 1/x+3=3/x
She says “I can multiply both sides by x and get the linear equation 1 + 3x = 3, whose solution is x = 2/3.”
Which of the following statements makes this a correct argument, or shows that it is incorrect? Select all that apply.

Question 1 options:

After multiplying both sides by x you need to subtract 1 from both sides


You can assume x ≠ 0 because both sides are undefined if x = 0.


You cannot multiply both sides by x because you do not know what x is.


The equation is not linear, so you cannot use the methods normally used for solving linear equations.

Answers

Answer:

1. After multiplying both sides by x you need to subtract 1 from both sides

2. You can assume x ≠ 0 because both sides are undefined if x = 0.

Step-by-step explanation:

Given

[tex]\frac{1}{x} + 3 = \frac{3}{x}[/tex]

Required

Which of the options shows the validity of Beth's action

The first option answers the question and the reason is as follows;

Multiply both sides by x

[tex]x * (\frac{1}{x} + 3) = \frac{3}{x} * x[/tex]

Open the bracket

[tex]1 + 3x = 3[/tex]

As stated in option 1; Subtract 1 from both sides

[tex]1 - 1 + 3x = 3 - 1[/tex]

[tex]3x = 2[/tex]

Divide both sides by 2

[tex]x = \frac{2}{3}[/tex]

Another correct option is the option 2

Because the expression is undefined if x = 0

See Proof by substituting 0 for x

[tex]\frac{1}{0} + 3 = \frac{3}{0}[/tex]

Division by 0 is undefined.

Hence, option 2 is also correct

The other options (3 and 4) are incorrect

if a dog food costs 0.75 per pound, and dog bones cost 1.75 each, what is the cost of 2 bones and 25 pounds of dog food?

Answers

Answer:

2 bones and 25 pounds of dog food would cost $22.25

Step-by-step explanation:

the outdoor temperature was 8 degrees at midnight the. temperature declined 5 degrees during each. of the next 3 hours what was the temperature at 3 A.M.

Answers

-7 degrees would be the answer

Which problem can be solved by division of decimals? How much money does Jon need to buy 10.3 gallons of gas that costs $3.79 a gallon? What grade does Maria need on her next test to achieve a total of at least 400 points if she had 4 previous tests that had grades of 75.3, 92.1, 78.6, and 81.0? Helena saved $45.00 toward a dress that costs $78.00. How much more does she need to save? Mica spent $45.50 on 7 indoor baseball sets. How much does it cost for one set?

Answers

Answer:

Mica spent $45.50 on 7 indoor baseball sets. How much does it cost for one set?

Step-by-step explanation:

Answer:

ITS D I TOOK THE TEST

Step-by-step explanation:

Oliver reads 28 ½ pages of a book in 1 1/6 hours. Express his speed in pages per hour?

Answers

Answer:

Answer: The speed of Oliver is 24\dfrac{1}{3}24

3

1

pages per hour.

Step-by-step explanation: Given that Oliver reads 28\dfrac{1}{2}28

2

1

pages of a book in 1\dfrac{1}{6}1

6

1

hours.

We are to express his speed in pages per hour.

We will be using the UNITARY method to solve the given problem.

Number of pages read by Oliver in 1\dfrac{1}{6}=\dfrac{7}{6}1

6

1

=

6

7

hours is

=28\dfrac{1}{2}=\dfrac{57}{2}.=28

2

1

=

2

57

.

Therefore, the number of pages read by Oliver in 1 hour is given by

\dfrac{57}{2}\times\dfrac{6}{7}=24\dfrac{3}{7}.

2

57

×

7

6

=24

7

3

.

Thus, the speed of Oliver is 24\dfrac{1}{3}24

3

1

pages per hour.

Step-by-step explanation:

Plz Mark me as brainliest

Perform the indicated operation. 11(-2), 22, 9, -22, -9 which one us it

Answers

Answer:

-22

Step-by-step explanation:

When numbers are placed closed like that, and have a parenthesis, you will multiply.

11(-2) = 11 * -2 = -22

-22 is your answer.

~

Answer:

[tex]\Huge \boxed{-22}[/tex]

[tex]\rule[225]{225}{2}[/tex]

Step-by-step explanation:

[tex]11(-2)[/tex]

Multiplying,

[tex]\Longrightarrow \ \ 11*-2[/tex]

[tex]\Longrightarrow \ \ -22[/tex]

[tex]\rule[225]{225}{2}[/tex]

write a quadratic equations given the roots 5/2 and 9

Answers

Answer:

(x-5/2)(x-9).

x^2-5/2x-5/2x+45/2.

Multiply the number by 2.

which is 2(x^2-5/2x-5/2x+45/2).

2x^2-5x-5x+45.

2x^2-10x+45.

What is the domain of the given function?

Answers

Answer:

Domain = 3, 6, -1, 5, -4

Step-by-step explanation:

The Domain is the first coordinate of a coordinate set so it is x

Hope This Helps :)

Which refers to the rate of change in velocity?

Answers

Answer:

acceleration refers to the rate of change in velocity

Acceleration is defined as the rate of change of velocity. Velocity is a vector, which means it contains a magnitude (a numerical value) and a direction. So the velocity can be changed either by changing the speed or by changing the direction of motion (or both).

1) What does the equation x = 4 represent in R^2? a) a circle.b) a plane.c) a line.d) a pointWhat does it represent in R^3? a) a plane.b) a line.c) a circle.d) a point.2) What does the equation y + 3x = 2 represent in R^3? a) a plane.b) a circle.c) a line.d) a point.What does z - 4y = 8 represent? a) a line.b) a circle.c) a point.d) a plane.What does the pair of equations y = 2, z = 8 represent? In other words, describe the set or points (x, y, z) such that y = 2 and z = 8. a) a line.b) a circle.c) a plane.d) a point.

Answers

Answer:

The equation [tex]x=4[/tex] represents in R^2 c) a line

The equation [tex]x=4[/tex] represents in R^3 a) a plane

The equation [tex]y+3x=2[/tex] represents in R^3 a) a plane

The equation [tex]z-4y=8[/tex] represents d) a plane

The pair of equations [tex]y=2,z=8[/tex] represents a) a line

Step-by-step explanation:

Let's start by studying each question :

1)

In R^2 , [tex]x=a[/tex] with [tex]a[/tex] ∈ IR is the equation of all vertical lines

In this case, the only free variable is the variable ''y''

R^2 has two dimensions (x and y) so if we set [tex]x=4[/tex] we will have only one free variable in R^2 (which is a line in R^2). Therefore, [tex]x=4[/tex] represents a line in R^2

Now, in R^3 we have three dimensions (x, y and z) so if we set [tex]x=4[/tex] we will have only two free variables (y and z) and [tex]x=4[/tex] will represent a plane (which have two dimensions) in R^3.

2) The equation [tex]y+3x=2[/tex] in R^3 has the free variable ''z'' and given that we select a value (for example for ''x'') the another value from the variable ''y'' is determined. Finally, we have the free variables ''z'' and ''x'', and the variable ''y'' restricted for our choice of the variable ''x''.

The equation [tex]y+3x=2[/tex] in R^3 (given that we have two free variables) represents a plane.

Using the same reasoning, the equation [tex]z-4y=8[/tex] represents a plane (given that it has two free variables : ''y'' and ''x'')

Finally, the pair of equations [tex]y=2,z=8[/tex] set values for ''y'' and ''z'' leading us ''x'' as the free variable. With only one free variable we will have a ''one dimensional'' geometric form. The one dimensional forms in R^3 are lines.

The final answer is a) a line.

What is (6x10^6)(4x10^-1) ?

Answers

Answer:

Step-by-step explanation:

Multiply the 6 and 4 together. 6*4 = 24

The next part is a bit tricky. Add the powers on the base 10. Keep the base 10.

10^(6 - 1) = 10^5

Now put the two parts together. 24 * 10^5

The number in front of the 10 must be between 1 and 10.

So 24 can be written as 24 = 2.4 * 10^1

2.4 * 10^1 * 10^5 = 2.4 * 10^(5 + 1) = 2.4 * 10^6

what exponent will make this true? Enter your naswer in the box 10?=1,000​

Answers

Answer:

10 to the 2nd power

Step-by-step explanation:

Help please I don’t understand

Answers

Answer:

Answer is -6

Step-by-step explanation:

first do from small bracket -(-6)=+6

and then -6-6=-12

do-12+6=-6

1
What is an equivalent form of the following function?
f(x) = 4(x - 1)2 + 12
O A. f(x) = 4x2 - 8x + 16
O B. f(x) = 4x2 - 8x + 8
OC. f(x) = 4x2 - 2x + 16
OD. f(x) = 4x2 + 8x + 8

Answers

C. F(x)=4x2-2x+16 .....:...
Your answer is F(x)=-1/2 or -0.5

what are all the names that apply to 1/8 Irrational,Integer,Whole,Real, Or irrational

Answers

Answer:

Rational NumberReal numbers

Step-by-step explanation:

Solve for h : -37+h=-2

Answers

Answer:

h = 35

Step-by-step explanation:

Step 1: Write out equation

-37 + h = -2

Step 2: Add 37 to both sides

-37 + 37 + h = -2 + 37

h = 35

h = 35
The answer is

you roll a die what is the probability a prime number will come up?​

Answers

Answer:

1/2 or 50%

Step-by-step explanation:

Total numbers: 1 to 6

Prime numbers: 2, 3, 5

Possible outcomes= 6Favorable outcomes = 3

Probability

3/6 = 1/2 or 50%

HELP! WILL GIVE BRAINLIEST IF YOUR ANSWER IS RIGHT Maria lives in Mexico. Both of her parents are Mexican. Maria is a Mexican citizen. She was born in an American hospital when her parents were on a short vacation in San Diego, California. Was Maria an American citizen at birth? Explain your answer.

Answers

Yes, because she was born in America and if she was born in Mexico she would be a Mexican citizen.

Yes, Maria was a "citizen" of America.

What is citizenship?

A legal status and relation between an individual and a state that entails specific legal rights and duties.

Given that, Maria lives in Mexico. Both of her parents are Mexican. Maria is a Mexican citizen. She was born in an American hospital when her parents were on a short vacation in San Diego, California.

The answer is yes,

A child born in American soil will be an American citizen.

Hence, Maria an American citizen at birth.

For more references on citizenship, click;

https://brainly.com/question/18099945

#SPJ2

Since cos(x) is the derivative of sin(x), then integral 16 sin^2(x) cos(x) dx can be done by substituting u = sin (x) sin (x) and du = cos (x) cos (x)^dx. With the substitution u = sin(x), we get integral 16 sin^2 (x) cos(x) dx = 16 integral u^2 du. which integrates to + C. Substituting back in to get the answer in terms of sin(x), we have integral 16 sin^2 (x) cos (x) dx = + C.

Answers

Complete

Find the integral of  [tex]f(x) =  16sin^2 (x ) cos(x) dx[/tex]

Answer:

The solution is    [tex]\frac{16}{3} sin^{3}x + c[/tex]

Step-by-step explanation:

So

   [tex]Let \  u  =  sin(x)[/tex]

=>  [tex]\frac{du}{dx}  =  cos (x)[/tex]

=>   [tex]du  =  cos(x)dx[/tex]

So

   [tex]\int\limits {16sin^2 (x ) cos(x) dx} \, \equiv \int\limits {16u^2  du}[/tex]

=>  [tex]\int\limits {16u^2  du} = 16 [\frac{u^3}{3} ] + c[/tex]

Now substituting sin(x) for u  

      [tex]\frac{16}{3} u^3 + c  =  \frac{16}{3} sin^{3}x + c[/tex]

So the  integral of  [tex]f(x) =  16sin^2 (x ) cos(x) dx[/tex]  is

      [tex]\frac{16}{3} sin^{3}x + c[/tex]

Mrs. Santiago wants to buy a new dining room table. She is trying to decide between a large table that costs $548.00 and a smaller table that costs $135.00. How much money will Mrs. Santiago save if she buys the smaller table?

Answers

Answer:

$413

Step-by-step explanation:

 548

- 135

413

Answer:

413.00

Step-by-step explanation:

Subtract.

548.00 minus 135.00 is 413.00.

That is the answer.

58 POINTS!!! The line contains the point (8,2) and is parallel to a line with a slope of -2/3 The equation of the line is

Answers

Answer:

The answer is

[tex]y = - \frac{2}{3} x + \frac{22}{3} [/tex]

Step-by-step explanation:

Equation of a line is y = mx + c

where

m is the slope

c is the y intercept

Since the lines are parallel their slope are also the same

So the slope of parallel line = - 2/3

So the equation of the line containing the point (8 , 2) and slope - 2/3 is

[tex]y - 2 = - \frac{2}{3} (x - 8) \\ y - 2 = - \frac{ 2}{3} x + \frac{16}{3} \\ y = - \frac{2}{3} x + \frac{16}{3} + 2[/tex]

We have the final answer as

[tex]y = - \frac{2}{3} x + \frac{22}{3} [/tex]

Hope this helps you

Slope intercept form: y = mx + b

Parallel lines have the same slope, so the slope is -2/3.

We can solve using point slope form.

y - 2 = -2/3(x - 8)

y - 2 = -2/3x + 16/3

y = -2/3x + 22/3

Best of Luck!

Solve the equation for a 62=a(25-0)(25-50)

Answers

...............................

Isabella left a 15% tip for a meal. The total cost of the meal, including the tip, was $23. What was the cost of the meal before the tip was added?

Answers

Answer:

the meal was $3.45

Step-by-step explanation:

Answer: cost before tip is $20

Step-by-step explanation:

Tip=20(0.15)

= 3

Total = Cost + Tip

= 20 + 3

= 23

Question Given the following functions f(x) and g(x), find (f ° g)(x).

f(x)=-x^2-x+7
g(x)=5x+4​

Answers

Answer:

Step-by-step explanation:

g(x) = 5x + 4

f(5x + 4) = (5x + 4)^2 - (5x + 4) + 7

25x^2 + 40x + 16 - 5x - 4 + 7

25x^2 + 35x + 19

Which list shows these numbers in ascending order?
-V6, 2, -23, 2.5

Answers

-v6,-23,2,2.5
Correct to ascending order
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