Mathematics High School

Use the Pythagorean theorem to find x, in simplest radical form

Answers

Answer 1

Answer:

[tex]4\sqrt{21}[/tex]

Step-by-step explanation:

Pythagorean theorem is [tex]a^{2} +b^{2} =c^{2}[/tex].

Which in this case:

'c' is hypotenuse. (hypotenuse = 20)

'a' and 'b' are the other sides. (a = x, b = 8)

[tex]a^{2} +b^{2}= c^{2}[/tex] [tex]x^{2} +8^{2} =20^{2}[/tex] [tex]x^{2} + 64 = 400[/tex] [tex]x^{2} = 336[/tex]

Now we should just take square root from the both sides.

and the answer will be [tex]\sqrt{336}[/tex] or [tex]-\sqrt{336}[/tex], but a side of a triangle can not be a negative number! so the answer will be [tex]\sqrt{336}[/tex].

As you see [tex]\sqrt{336}[/tex] is not the simplest radical.

We can write [tex]\sqrt{336}[/tex] as [tex]\sqrt{16 * 21}[/tex].

And from the laws of radical we can write [tex]\sqrt{16*21}[/tex] as [tex]\sqrt{16} * \sqrt{21}[/tex].

[tex]\sqrt{16} * \sqrt{21} = \sqrt{16}\sqrt{21} = 4\sqrt{21}[/tex]

I hope it helps you. Please choose my answer as the brainliest.

Related Questions

The length of Chen’s office is 15.5 feet and the width is 7.8 feet. Use the formula P = 2ℓ + 2w to find the perimeter of the office.

Answers

46.6 feet

Step-by-step explanation:

P = 2ℓ + 2w

P = 2(ℓ + w)

P = 2(15.5 + 7.8)

P = 2(23.3)

P = 46.6 feet

3. In the diagram below AB' is the image of AB after a reflection in AC. If mBAC4x7 and mBAB '  64 , then which of the following is the value of x?
(1) 6.25 (3) 14.25 (2) 12.5 (4) 18.75

Answers

When a line or shape or point is reflected, it must be reflected over a line.

The value of x is (b) 14.25

Reflection is a rigid transformation;

This means that:

[tex]\mathbf{\angle AC = \angle AB}[/tex]

So, we have

[tex]\mathbf{4x + 7 = 64}[/tex]

Subtract 7 from both sides

[tex]\mathbf{4x = 57}[/tex]

Divide both sides by 4

[tex]\mathbf{x = 14.25}[/tex]

Hence, the value of x is (b) 14.25

Answers

Answer:

Step-by-step explanation:

solve Kx + 12 = 3kx for x

Answers

Answer:

Here’s the link to the answer

https://brainly.com/question/4954271

The number of different cars sold in some country rose from 205 in 1997 to 280 in 2007. Find the percent increase. Round to the nearest whole percent.
The percent increase is ____%

Answers

Answer:

the answer is 37 percent

[tex]\sf 600+303+400[/tex]

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Answer: Is this like simple addition problem? Because if it is that would be 1303 ‍♀️

1,303 if it addition

Pleaseeee help asappp!

Answers

Answer: A and C

Step-by-step explanation:

plugging the ordered pairs into the suction on a graph is a good way to find them!

Answer:

I answered in comments but it was the first and last one :)

Step-by-step explanation:

Define :-
a). Monomial
b). Binomial
c). trinomial

Answers

a). Monomial

A expression having only one term is called monomial.

[tex]Eg:- 3x, { - 4y}^{2} , \frac{3}{2} yz [/tex]

b). Binomial

A expression having two terms is called Binomial.

[tex]Eg: 2x - 3y \: , {4x}^{2} + 5zx[/tex]

c). trinomial

A expression having three terms is called trinomial.

[tex]Eg: - 3p + 5q - \frac{2}{5} pq[/tex]

find the length of the hypotenuse of the right triangle. leave your answer in simplest radical form. not drawn to scale.

Answers

Two ways to solve this:
1) Notice that this is a 45-45-90 triangle, meaning the ratio of sides and hypotenuse is 1:1:sqrt(2)

Since the legs are 4, that would mean the hypotenuse would be 4*sqrt(2)

2) Pythagorean theorem: a^2 + b^2 = c^2

4^2 + 4^2 = 32
Sqrt(32) = 4*sqrt(2)

Answer:

it need to =90

Step-by-step explanation:

After enlarging his "U" in problem 3-26, Al has an idea. He drew a 60° angle, as shown in Diagram #1 at
right. Then, he extended the sides of the angle so that they are twice as long, as shown in Diagram #2.
"Therefore, the new angle must have measure 120°," he explained. Do you agree? Discuss this with your
team and write a response to Al.

Answers

When extending both sides of an angle, you are not changing the angle, so dat man wrong....

Answer: Don't agree

I need help with 9-11 I’ll mark
Brainliest

Answers

Answer: it is 26

Step-by-step explanation:

When Professor Winchester grades class tests, he gives an A to the fourth (top) quartile, a B to the third quartile, a C to the second quartile, and a D to the first quartile. The box plot shows the distribution of scores on a test. What is the range of scores for the students who received As?

4

8

14

28

Answers

Answer:

Step-by-step explanation:

Which is an equation of the line containing (1, –3) and (7, 15)?

y = 3x – 10

y = 3x

y = 3x – 6

y = –3x + 8

Answers

Answer:

y = 3x - 6

Step-by-step explanation:

(1, -3) (7, 15)

Step 1. Find the slope

Slope = 3

Step 2. Create the equation of the slope then use a point and plug it in as terms of x and y with a y-intercept at the end

y = 3x + b

(15) = 3(7) + b

15 = 21 + b

15 - 21 = b

b = -6

Thus, the equation of the line is y = 3x - 6

-3 3/5 divided by -1/2

Answers

Answer:

36/5 or 7 1/5 or 7.2

Step-by-step explanation:

-3 3/5 = -18/5

-18/5 * -2 = 36/5

A salesperson works 40 hours per week at a job where has two options for being paid. Option A is an hourly wage of 23$. Option B is a commission rate of 10% on weekly sales. How much does need to sell this week to earn the same amount with the two options

Answers

Answer:

$9200

Step-by-step explanation:

Since he works 40 hours a week and would make $23 for every hour with option A, we just multiply 40 by 23

40 x 23 = 920

This means 10% of the sales will need to equal to 920

Let x = sales

We multiply x by 0.1 to get 920

0.1x = 920

Divide both sides by 0.1

0.1x/0.1 = 920/0.1

x = 9200

What is the measure of the angle of rotation for the polygon?

Answers

Answer:

360 degrees divided by that order

Plz help I don’t understand

Answers

Answer:

send full question plzzz

Write an algebraic expression for each phrase?

Don’t know if those are right also

Answers

Answer & Step-by-step explanation:

1) 4x

2) y-8

3) 6/x

4) 12-y

5) y+9

6) 5^2

7) x^4

8) 9+n

9) 64-y

10) 12/n

11) x^2/7

12) x-8=22

13) 2a-b^2

14) 12-ab

Answer:

4xy - 86 / x12 - y9 + y5^2x^49 + x64 - y12 / xx^2 / 7x - 8 = 222a - b^212 - ( a × b )

Hopefully this helped!

Brainliest please?

What is the slope of the line on the graph?

Answers

Answer:

5/12

Step-by-step explanation:

It goes up 5 and over 12.

Find the slope of the secant line for f(x) = -x^2 + 20

Answers

Answer:

250

Step-by-step explanation:

State the angle relationship and state the measure of each angle indicated that makes lines u and v parallel

Answers

Answer:

5) Alternate Exterior angles 90º

6) Same side Interior angles. 132º if that says 48º on the page

7) Corresponding angles. too blurry but they are congruent

8) Alternating Exterior angles. too blurry but they are congruent

Step-by-step explanation:

Congruent means they are the same measurement just as a reminder :).

Please help me solve problem 2 and 3

Answers

2= 50
It’s because you have to first find the area which is 100 inches
Divide it by 2 inches with is 50 inch cubes

Rhythm Time sells music online. Last year, its customers downloaded a total of 697,900 songs. This year, they downloaded 467,593 songs. What is the percent of decrease in annual downloads?

Answers

LEGA HEB LEFA OOOOOOOOOOOOF

The quotient of a number x and five

Answers

Answer: fun fact : by reading what i just right u just lost 5 sec of ut life

Step-by-step explanation:

The triangles are congruent. Write the congruence statement

Answers

Answer:

answerr is d

beacause the middle congruence which is c shoild be in the middle

[tex]4,\pi ,8[/tex] how do i order from least to greatest

Answers

Answer:

[tex] \pi \: 4 \: 8[/tex]

Answer:

[tex]\pi, 4, 8[/tex]

Step-by-step explanation:

Note that [tex]\pi\approx3.14[/tex]. As [tex]3<3.14<4[/tex], [tex]\pi[/tex] comes before [tex]4[/tex].

Clearly [tex]4<8[/tex], so [tex]4[/tex] comes before [tex]8[/tex].

The only possible ordering is [tex]\boxed{\pi, 4, 8}[/tex]

You collect 3 dimes, 2 dimes and then 4 dimes. How

much money do you have as a fraction of a dollar.

Here’s a easy questions for some points

Answers

9 dimes is this the correct answer?

It would be 90/100 but you can simplify and it would be 9/10

a substance is kept at -3. 1*F it's temperature is raised by 2.5 what is the new temperature

Answers

Answer:

.6 degrees

Step-by-step explanation:

-3.1+2.5=.6

plsssssss help no nonsense pls
Two cars traveled equal distances in different amounts of time. Car A traveled the distance in 2.4 h, and Car B traveled the distance in 4 h. Car A traveled 22 mph faster than Car B.

How fast did Car A travel?

(The formula R⋅T=D , where R is the rate of speed, T is the time, and D is the distance can be used.)

Enter your answer in the box.

Answers

Answer:

We let x the distance traveled by Car A and y the distance traveled by car B. The speed of car A can be represented as x/2.4 and for Car B is y/4. From the statement given, we can write an equation relating the speed of both cars.

x/2.4 = 22 + y/4

Since y = x, then:

x/2.4 = 22 + x/4

Solving for x, we obtain:

x= 132 meters traveled by both cars

Therefore, Car A has a speed of 55 mph.

Step-by-step explanation:

Answer:

Step-by-step explanation:

x/2.4 = 22 + y/4

Since y = x, then:

x/2.4 = 22 + x/4

x= 132 meters traveled by both cars

Therefore, Car A has a speed of 55 mph.

help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

WHAT IS THE BLANK The formula C = πd gives you the ______ of a circle.

Answers

Circumference give me brainliest pls

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