Find the unknown side length. Write your answer in simplest radical form.

Find The Unknown Side Length. Write Your Answer In Simplest Radical Form.

Answers

Answer 1

Answer: 1. x= 20 units,   2. x= [tex]5\sqrt{3}[/tex] units    3. x= [tex]4\sqrt{2}[/tex] units.

Step-by-step explanation:

In a right triangle,

[tex]Hypotenuse^2= Perpendicular^2+Base^2[/tex]  (Pythagoras theorem)

1. Hypotenuse = x , Base = 16, Perpendicular = 12

[tex]\Rightarrow\ x^2 =12^2+16^2\\\\ \Rightarrow\ x^2=144+256\\\\ \Rightarrow\ x^2=400\\\\ \Rightarrow\ x=\sqrt{400}=20[/tex]

2. Hypotenuse = 14 , Base = 11, Perpendicular = x

[tex]\Rightarrow\ 14^2=x^2+11^2\\\\\Rightarrow\ 196=x^2+121\\\\\Rightarrow\ x^2=196-121\\\\\Rightarrow\ x^2 = 75\\\\\Rightarrow\ x=\sqrt{75}=\sqrt{25\times3}=5\sqrt{3}[/tex]

3.  Hypotenuse = 9 , Base = x, Perpendicular =7

[tex]\Rightarrow\ 9^2=x^2+7^2\\\\\Rightarrow\ 81= x^2+49\\\\\Rightarrow\ x^2=81-49\\\\\Rightarrow\ x^2=32\\\\\Rightarrow\ x=\sqrt{32}=\sqrt{16\times2}\\\\\Rightarrow\ x=4\sqrt{2}[/tex]


Related Questions

Select the example of an inequality.
o 14y = 2
0 32 - 4
044 = 15
4y < 64

Answers

The last one is the answer

How can I calculate the zeros of x^3+3x^2-4?
I know the answers (x1= -2 and x2= 1) but I need to show why these are the zeros.

Answers

Answer:

x = 2

x = -1

The radius of a circle is represented by the expression x+3. Express the circumferend terms of x​

Answers

Answer:

The circumference of circle with radius x+3 is: [tex]2\pi x+6\pi[/tex]

Step-by-step explanation:

Given that

Radius = r =x+3

The circumference of a circle is the distance around boundary of the circle.

The circumference of circle is given by the formula.

[tex]C = 2\pi r[/tex]

Putting the value of r, we get

[tex]C = 2\pi (x+3)\\C = 2\pi x+6\pi[/tex]

Hence,

The circumference of circle with radius x+3 is: [tex]2\pi x+6\pi[/tex]

Subtract 28.9 − 9.25 =_____

Answers

Answer:

19.65

Step-by-step explanation:

Answer:

19.65

Step-by-step explanation:

..........

HELP WITH THIS WORD PROBLEM

While riding a train in New York City, you notice there are 125 passengers in the first carriage, 10 more passengers in the second carriage then there are in the first carriage, and 10 more passengers in the third carriage then there are in the second carriage. If this pattern continues, how may passengers are there in the fourth carriage?

Answers

Answer:

1 cart = 125

2 cart = 135

3 cart = 145

4 cart = 155

Step-by-step explanation:

write the ratio in simplest form 2 feet to 40 inches​

Answers

Answer:

2+5

Step-by-step explanation:

Ratio of 2feet to 40 inches = 3/5 = 3:5

What is ratio?

The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.

Given measurements,

2 feet and 40 inches

1 feet = 12 inches

2 feet = 24 inches

Ratio of 2 feet to 40 inches = 24/40

                                              = 3/5

Hence, 3/5 is the ratio of 2 feet to 40 inches.

Learn more about ratio here:

https://brainly.com/question/13419413

#SPJ5

can someone please help asap?!

Answers

Answer:

[tex]\displaystyle m=\frac{-1}{3}[/tex]

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Algebra I

Slope Formula: [tex]\displaystyle m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Step-by-step explanation:

Step 1: Define

Find points from graph.

Point (2, 0)

Point (5, -1)

Step 2: Find slope m

Simply plug in the 2 coordinates into the slope formula to find slope m

Substitute in points [SF]:                     [tex]\displaystyle m=\frac{-1-0}{5-2}[/tex][Fraction] Subtract:                              [tex]\displaystyle m=\frac{-1}{3}[/tex]

Factor the following polynomial fully.

10x^2 + 16x – 8

A. 2(5x – 4)(x + 1)
B. (2x + 4)(5x – 2)
C.(10x – 8)(x + 1)
D.2(x + 2)(5x – 2)

Answers

The correct answer is D
The answer to your question is D

Match each expression on the left with an equivalent expression on the right. Some answer choices on the right will not be used.​

Answers

Answer

6.038 times 100 = 603.8

603.8 / 10 = 60.38

60.38 / 1,000 = 0.06038

0.6038 times 10 = 6.038

Answer:

6.038 times 100 = 603.8

603.8 / 10 = 60.38

60.38 / 1,000 = 0.06038

0.6038 times 10 = 6.038

( Did it on college board)

Step-by-step explanation:

What’s the measure of <7

Answers

It’s 115 degrees.


Hope that helps

(4^3)² × 4^2
Please help

Answers

Answer:

65536

Step-by-step explanation:

=(642)(42)

=4096(42)

=(4096)(16)

i hope this helps if u need me to explain more i will be happy too <3

PLEASE HELPPPP
ITS EASY MY BRAIN JUST HURTS

Answers

500minute

Step-by-step explanation:

if anthony rides 32 miles in 160 minute then he will ride 1 mile in 5 minutes

I really need help with this

Answers

Answer:

1/2 or .5

Step-by-step explanation:

you find 2 points that the line goes through, then you find the rise/run. lastly you simplify if you can, then you have the answer

A child's ladder is made of 333 sections. Each section is \dfrac{3}{4} 4 3 ​ start fraction, 3, divided by, 4, end fraction meters long. How long is the ladder when all 333 sections are extended to make one ladder? meters

Answers

Answer:

[tex]Ladder = 2\frac{1}{4}\ m[/tex]

Step-by-step explanation:

Given

[tex]Sections = 3[/tex]

[tex]Length = \frac{3}{4}m[/tex] per section

Required

Determine the length of the ladder

The length of the ladder is calculated by multiplying the number of sections by the length of each section.

So, we have:

[tex]Ladder = 3 * \frac{3}{4}\ m[/tex]

[tex]Ladder = \frac{9}{4}\ m[/tex]

[tex]Ladder = 2\frac{1}{4}\ m[/tex]

Hence, the length of the ladder is: [tex]2\frac{1}{4}\ m[/tex] or 2.25m

How many solutions does the system have?
x = -6y + 3
5x + 30y = 15
one solution
two solutions
infinitely many solutions
no solution​

Answers

Answer:

infinitely many solutions

Step-by-step explanation:

we have: x+6y= 3

5x+30y=15

where a1/a2 = b1/b2 = c1/c2 (1/5 = 6/30 = 3/15)

Thus, the system has infinitely many solutions.

another approach:

convert to slope-intercept form

y= -1/6x + 1/2

y= -1/6x + 1/2

thus, the system has infinitely many solutions.

(explain: if two lines have a same slope (-1/6), they can be either parallel or coincided. But in this case, they also have a same y-intercept so they must be the latter case)

Estimate the value 118 to the nearest integer.​

Answers

Step-by-step explanation:

118 is already an integer

Raphael and his friends made cookies for the bake sale. Raphael made 60 cookies and his friends made 350 cookies. What percent of the total cookies did Raphael make? ​Round your answer to the nearest whole percent.

Answers

Answer: 16%

Step-by-step explanation:

The total amount of cookies is 410.

410 represents 100%

410/100=65/x

X represents the unknown percentage

Cross multiply: 410x=6500

Divide: x=15.85

Round up: 16%

In a group of 38 pupils, 14 play the flute only.
8 play the piano only.
11 play both instruments.
A student is chosen at random.
What is the probability the student plays neither instrument?



pLZZZZZ need help, will give brainlist if solved

Answers

Hey there!

The answer to your question is 5/38

We can find this answer by taking the total group and subtracting all the data to see how many are left who don't play either:

38 - 14 - 8 - 11

5

This means that 5 out of every 38 pupils do not play either instrument, so the probability would be 5/38.

Hope this helps! Have a great day and good luck on your assignment!

Special Right Triangles

Answers

Answer:

first option

Step-by-step explanation:

Using the sine/ cosine ratios in the right triangle and the exact values

sin30° = [tex]\frac{1}{2}[/tex] , cos30° = [tex]\frac{\sqrt{3} }{2}[/tex]

sin30° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{x}{32}[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )

2x = 32 ( divide both sides by 2 )

x = 16

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

cos30° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{y}{32}[/tex] = [tex]\frac{\sqrt{3} }{2}[/tex] ( cross- multiply )

2y = 32[tex]\sqrt{3}[/tex] ( divide both sides by 2 )

y = 16[tex]\sqrt{3}[/tex]

which numbers for b would make √b irrational​

mark as brilliant!

Answers

Answer:

All of the options when substituted for b will make the root of b irrational

Step-by-step explanation:

Mathematically, surds are roots of non-perfect squares and they are tagged as irrational numbers

For b to be irrational, all of the numbers given would fit. This is because all of these numbers are non-perfect squares meaning they do not have square root.

So what this mean is that these numbers when put under the root umbrella are irrational numbers as they are not perfect squares

The number of trees in a rainforest decreases each month by 0.5%. The forest currently has 2.5 billion trees. Which expression represents how many trees will be left in 10 years. Group of answer choices

Answers

Answer:

[tex]y=2.5*10^9(0.005^{12 0}) \\\\[/tex]

Step-by-step explanation:

The above question is in the form of an exponential decay. The equation for an exponential decay is given by:

[tex]y=ab^x[/tex]

where y and x are variables, b < 1, a is the initial value of y (that is the value of y when x = 0).

Let y represent the number of trees left and x represent the number of months. Given that there is currently 2.5 billion trees, therefore a = 2.5 * 10⁹, b = 0.5% = 0.005. The equations becomes:

[tex]y=2.5*10^9(0.005^x)\\\\After\ ten\ years(x=10*12\ months=120\ months):\\\\y=2.5*10^9(0.005^{12 0}) \\\\[/tex]

Sophia bought 24 chicken wings for $52.80. How much does each wing cost?​

Answers

Answer:

2.2$

Step-by-step explanation:

Because 52.80 divided b 24 equals 2.2$

have a nice day! :>

Please answer my question

Answers

Answer:

1 is 55

2 is 128

3 is 175

4 is no because the sell price is not 12 dollars, its 12 dollars extra

5 is A

Step-by-step explanation:

Suppose you anticipate needing to call the UK for a total of 250 minutes and France for 100 minutes. Will a $75 card cover the cost of this much calling? Explain your answer.

Answers

Complete question :

You have relatives living in the United Kingdom and in France. Suppose that you have purchased a prepaid phone card with a value of $75. Calls to the United Kingdom cost 23¢ per minute, while calls to France cost 21¢ per minute."Suppose you anticipate needing to call the UK for a total of 250 minutes and France for 100 minutes. Will a $75 card cover the cost of this much calling?

Answer:

cell phone card won't be enough.

Step-by-step explanation:

Cell phone card value = $75

United kingdom = 23cent per minute

France = 21 cent per minute

United Kingdom minutes = 250

France minutes = 100

Total cost :

23 cent = $0.23

21 cent = $0.21

Total :

United Kingdom = 0.23 * 250 = $57.5

France = 0.21 * 100 = $21

$21 + $57.5 = $78.5

$78.5 > $75

Then, it can be concluded that the cell phone card won't be enough.

Write an ordered pair for 3 glasses
and the amount of juice needed.
( PLEASE HURRYY !!)

Answers

Apples are amazing

Althea paid $5.00 each for two bracelets and later sold each for $15.00. She paid $8.00 each for three bracelets
and sold each of them for $9.00.
a. Write an expression that represents the profit Althea made.
b. Evaluate the expression. Name the property used in each step.

Answers

Answer:

I have the same question

Step-by-step explanation:

message me if anyone helps I need it too

help me pleaseee pleaseee

Answers

Answer:

x=3

PAW = 40

Step-by-step explanation:

-11x+173-x+43=180

-12x+ 216 = 180

12x = 36

what is 3 1/8 x 2 3/5

Answers

Answer:

[tex]8\frac{1}{8}[/tex]

Step-by-step explanation:

[tex]3\frac{1}{8} \times 2 \frac{3}{5}[/tex]

[tex]=\frac{25}{8} \times \frac{13}{5}[/tex]

[tex]=\frac{25\times13}{8\times5}[/tex]

[tex]=\frac{325}{40}[/tex]

[tex]=\frac{325/5}{40/5}[/tex]

[tex]=\frac{65}{8}[/tex]

[tex]=8\frac{1}{8}[/tex]

Hope this helps :)

Help it’s due now! Please

Answers

Answer:

44

Step-by-step explanation:

Substitute the values for the variables.

5(8) + 12/3

40 + 4 = 44

The answer is wat she or he said ^^ your welcome.! :)

Please help!!! thank you so so much!!! will give brainliest!

Answers

Answer:

A

HOPE THIS HELPS YOU

GIVE THANKS

MARK AS BRAINLIEST

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