Mathematics High School

Find the length of the third side. If necessary, write in simplest radical form.

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Answer 1

Answer:

2√6

using pythagoras theorem:

a² + b² = c²

5² + b² = 7²25 + b² = 49b² = 49 - 25b² = 24b = √24b = 2√6

Answer 2

Answer:

2√6 units

Step-by-step explanation:

The length of the third side can be determined using pythogoras theorem. Keep in mind that pythogoras theorem can only be used when finding the missing side length of a right triangle.

[tex]\text{Pythagoras theorem: (Longest side})^{2} = (\text{Leg of right triangle}_{1} ) ^{2} + (\text{Leg of right triangle}_{2} )^{2}[/tex]

In this triangle, we are given that:

The longest side of the triangle is measuring 7 units. A leg of the triangle is measuring 5 units

Substitute the measures into the pythogoras theorem:

[tex](7})^{2} = (5 ) ^{2} + (\text{Leg of right triangle}_{2} )^{2}[/tex]

Simplify both sides of the equation:

[tex]\rightarrowtail (7 \times 7}) = (5 \times 5) + (\text{Leg of right triangle}_{2} )^{2}[/tex]

[tex]\rightarrowtail49 = 25 + (\text{Leg of right triangle}_{2} )^{2}[/tex]

Subtract 25 both sides:

[tex]\rightarrowtail49 - 25 = 25 - 25 +(\text{Leg of right triangle}_{2} )^{2}[/tex]

[tex]\rightarrowtail24 = (\text{Leg of right triangle}_{2} )^{2}[/tex]

Square root both sides and simplify:

[tex]\rightarrowtail\sqrt{24} = \sqrt{(\text{Leg of right triangle}_{2} )^{2}}[/tex]

[tex]\rightarrowtail\sqrt{3 \times 2\times 2 \times 2} = \sqrt{(\text{Leg of right triangle}_{2} )^{2}}[/tex]

[tex]\rightarrowtail2\sqrt{3 \tim \times 2} = \text{Leg of right triangle}_{2}[/tex]

[tex]\rightarrowtail\boxed{2\sqrt{6} \ \text{units} = \text{Leg of right triangle}_{2}}[/tex]

Related Questions

Mike invests $4000 in an account that earns 3% annual interest. How much money will there be in the account after 3 years if the interest is compounded semi-annually?

Answers

Answer:

$4786.72

Step-by-step explanation:

4000(1+0.03/6)^12(3)

Use this formula to find the compounded interest after each 6 months, which would have an interest rate used to increase the amount of money.

What additional information could be used to prove that the triangles are congruent using AAS?
Select two options

Answers

Answer:

Step-by-step explanation:

We have two congruent angles, so we need a pair of congruent sides. This is satisfied by options 2 and 3.

You are a chef and you are tasked to prepare a lunch menu proposal for an upcoming
symposium of different youth organizations to be catered by the restaurant your
restaurant. You need to do the following:
1. Come up with 5 sets of lunch menus with a unique title for each. Consider the
different food preferences (according to the age group, culture, and others). (You
may include descriptions and appetizing pictures.)
2. Out of these menus, how many ways can the event organizer choose 3 out of the
five lunch menus you prepared for their initial selection? (Show your solution)
a. With repetition
b. Without repetition
3. Give at least 3 of these ways.
a. With repetition
b. Without repetition
Your output will be rated according to the following criteria:
Presentation of the Lunch Menus (which may include pictures). Accuracy of the use of
Mathematical Concepts (Combination and/or Probability of Simple Events), and
Feasibility of the Proposed Lunch Menus.

Answers

The lunch menu is an illustration of permutation and combination

There are 125 ways to select three lunch menus with repititionThere are 10 ways to select three lunch menus without repitition

The lunch menu

To answer this question, the following set of lunch menu would be used:

Fish and chips.Ham sandwich.Superfood salad.Cheese sandwich.Jacket potato with filling.

How to select 3 lunch menu with repitition?

Since the event organizers can repeat lunch menu, then each of the 5 lunch menus can be selected each of the 3 times.

So, the number of selection is:

n = 5³

Evaluate

n = 125

Possible selections are:

Fish and chips, Jacket potato with filling and Jacket potato with filling.Ham sandwich, Ham sandwich and Ham sandwichHam sandwich, Superfood salad and Cheese sandwich

How to select 3 lunch menu with repitition?

Since the event organizers cannot repeat lunch menu, then each of the 5 lunch menus can be selected once of the 3 times.

So, the number of selection is:

n = ⁵C₃

Evaluate

n = 10

Possible selections are:

Fish and chips, Jacket potato with filling and Ham sandwichHam sandwich, Superfood salad and Cheese sandwichFish and chips, Ham sandwich and Superfood salad.

Answers

Answer:

43690

Step-by-step explanation:

hope u understand it

For the data set 1, 7, 7, 7, 8, the mean is 6

Answers

Answer:

Yes

Step-by-step explanation:

1+7+7+7+8=30

30/5= 6

Can the sides of a triangle have lengths 7, 15, and 18?

Answers

Answer:

Yes it can!

Step-by-step explanation:

The 2 shortest sides how to be bigger than the longest sides when combined

7 + 15 = 22 and 22 is bigger than 18. So yes you can make a triangle with those side lengths.

Answer:

Step-by-step explanation:

If this is a right angle triangle then no, it is impossible since this set of lengths is NOT a pythagorean triple.

If this is a non-right angle triangle then yes.

PLEASE HELP !!!!! I HAVE TO TURN THIS IN BY TOMORROW

Answers

Answer:

Step-by-step explanation:

Given the equation: y = 8 * 2ˣ, substitute the x-values in the table for x in your equation, to find the y-values.

For x = -1

[tex]y = 8 * 2^x\\y=8*2^{-3}\\y=8*\frac{1}{2^3} < ==negative\ exponent\ property: x^{-n}=\frac{1}{x^n}\\y=8*\frac{1}{8}\\y=8*0.125\\y=1\\\\(-1,1)[/tex]

For -2:

[tex]y = 8 * 2^x\\y=8*2^{-2}\\y=8*\frac{1}{2^2} < ==negative\ exponent\ property: x^{-n}=\frac{1}{x^n}\\y=8*\frac{1}{4}\\y=8*0.25\\y=2\\\\(-2,2)[/tex]

For -1:

[tex]y = 8 * 2^x\\y=8*2^{-1}\\y=8*\frac{1}{2^1} < ==negative\ exponent\ property: x^{-n}=\frac{1}{x^n}\\y=8*\frac{1}{2}\\y=8*0.5\\y=4\\\\(-1,4)[/tex]

For 0:

[tex]y = 8 * 2^x\\y=8*2^0\\y=8*\frac{1}{2^2} < ==zero\ exponent\ property: x^0=1\\y=8*1\\y=8\\\\(0,8)[/tex]

For 1:

[tex]y = 8 * 2^x\\y=8*2^1\\y=8*2\\y=16\\\\(1,16)[/tex]

For 2:

[tex]y = 8 * 2^x\\y=8*2^2\\y=8*4\\y=32\\\\(2,32)[/tex]

For 3:

[tex]y = 8 * 2^x\\y=8*2^3\\y=8*8\\y=64\\\\(3,64)[/tex]

Hope this helps!

What is the solution to this system of equations?

Answers

Answer:

Replace the y, z, and x values with real numbers .

0 - 3 = -3

5 + 4 = 9

3 + 4 = 7

Destiny worked her 40 regular hours last week plus 5 overtime hours at the time-and-a-half rate. Her gross pay was $926.25. What is her regular hourly rate?

Answers

Answer: $19.50

Step-by-step explanation:

What’s the distance between the points (-3,10)and(6,-2)

Answers

Answer:

i think its 20

Step-by-step explanation:

Answer number 11 please. Thank you.

Answers

Answer:

A po 232.5n mm²

Step-by-step explanation:

#carryonlearning

and right triangle sin (40 - x)° equals cos(3x)° degrees what is the value of x.

Answers

[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]

Let's solve ~

[tex]\qquad \sf \dashrightarrow \: \sin(40 - x) = \cos(3x) [/tex]

[tex]\qquad \sf \dashrightarrow \: \cos\{90 - (40 - x ) \} = \cos(3x) [/tex]

[tex]\qquad \sf \dashrightarrow \:90 - (40 - x) = 3x[/tex]

[tex]\qquad \sf \dashrightarrow \:90 - 40 + x = 3x[/tex]

[tex]\qquad \sf \dashrightarrow \:3x - x = 50[/tex]

[tex]\qquad \sf \dashrightarrow \:2x = 50[/tex]

[tex]\qquad \sf \dashrightarrow \:x = 25 \degree[/tex]

Suppose a city with population 300,000 has been growing at a rate of 8% per year. If this rate continues, find the population of this city in 10 years.

Answers

So the 8% of 100 is 8 & times it by 3 which is 24 then times it by 1000 which is 24000 so add it to the population, it will be 324000

HOW DO U DO THIS I LITERALLY TRIED EVERYTHING pls explain

Answers

Answer:

you just convert them into simple fractions the first one become -1159/9 and second one -790/3.

the difference in thier height is 1211/9.

Rectangle A, B, C, D is graphed in the coordinate plane. The following are the vertices of the rectangle: A(-1, -6),A(−1,−6),A, left parenthesis, minus, 1, comma, minus, 6, right parenthesis, comma B(-1,7)B(−1,7)B, left parenthesis, minus, 1, comma, 7, right parenthesis, C(1, 7)C(1,7)C, left parenthesis, 1, comma, 7, right parenthesis, and D(1, -6)D(1,−6)D, left parenthesis, 1, comma, minus, 6, right parenthesis.

Given these coordinates, what is the length of side ABABA, B of this rectangle?

Answers

Answer:

13 units

Step-by-step explanation:

Points A(-1, -6) and B(-1, 7) both lie on the vertical line x=-1. That means the distance between them is the difference of their y-coordinates:

By -Ay = 7 -(-6) = 13

Segment AB is 13 units long.

Pleas help. 5 Divided by 1/8

Answers

[tex]\dfrac{5}{\tfrac 18} = 5 \times \left(\dfrac 18 \right)^{-1}= 5\times 8 = 40[/tex]

Answer:

Step-by-step explanation:

[tex] \frac{5}{1} \div \frac{1}{8} [/tex]

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

[tex]40[/tex]

7. Mattie ran across a circular part. The
circumference of the park is 92.31 feet.
How far did Mattie run?

Answers

Answer:

29.39

Step-by-step explanation:

So, the formula for circumference is 2(3.14)r.

If the question is looking for the diameter,

You don't have to include the r, you can just do d(3.14)=92.31

You can divide 92.31 by 3.14 and you get 29.39

what are the exact volumes of x and y? (attached image)

Answers

Answer:

X is the value of y so work it out mothe

Answer:

Since already answered i need points so yea

Could someone explain each one of these questions (apart from a) step by step? Thanks!

Answers

part c:

100-3t = 64

100-64 = 3t

36 = 3t

t = 12

part d:

1/2 (x-5) = 9

x-5 = 9 / (1/2)

x-5 = 18

x = 23

When in algebra, you can do the same to both sides. Here is a simple example that will hopefully make things easier.

What is 100 x 96 x 44?

Answers

Answer:

Step-by-step explanation:

100×96×44=100×(100-4)×44

=100×[100×44-4×44]

=100×[4400-176]

=100×4224

=422400

Answer:

422400

Step-by-step explanation:

100

x96

-------

9600

x44

----------

38400

+384000

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

422400

Buses arrive at a stop every 18 min. Each bus waits 4 min before departing. What is the probability that a person arriving at the bus stop at a random time has to wait more than 8 min for a bus to leave?

Answers

Answer:

Socratic app

Step-by-step explanation:

it will help you

(0,3) and (5,13) what is the answer

Answers

Answer:

if you're asking for the slope the answer is 2

Step-by-step explanation:

i hope your asking for slope

How to find a surface are?

Answers

The surface area is found by finding the area of all shapes creating the surface, and then adding them together.

Example:

If we have a 5 x 5 x 5 cube, we will find all six sides. Since 5 x 5 is 25, and 25 x 6 = 150, the surface area of this example cube will be 150 units².

Why the x 6? Since it is a cube all the sides have the same area, and a cube has 6 sides.

what is the answer to two plus two divided by 3 times 6

Answers

Answer:

Step-by-step explanation:

2 + 2 = 4

4 / 3 = 1.3

1.3 x 6 = 8

Step 1: 2+2
Step 2: 4/3
Step 3: 1.3 x 6= 7.8

Fill in the missing values in the table. Scale Distance on map Distance in miles 1/4 inch = 1 mile) 2.5 inches 10 miles 1/2 inch = 1 mile 4.5 inches miles 1 inch = 1 mile 3.0 inches 3 miles 1 inch = 5 miles inches 30 miles 1 inch = 10 miles 3.0 inches miles 1 inch = 15 miles 2.0 inches miles

Answers

The missing values are 9 miles, 6 inches, 30 miles, and 30 miles, respectively.

Rule of Three

It's a math tool for solving problems about proportion. You can relate more than 2 variables and from the proportion, it's possible to find an unknown number.

The Line 02 of the Table

1/2 in= 1 mile, from the rule of three, you can find the distance in miles.

1/2 inch ------------- 1 mile

4.5 inches --------- x miles

Applying cross multiplication

1/2x=4.5

x=4.5 *2

x=9 miles

The Line 04 of the Table

1 in= 5 miles, from the rule of three, you can find the distance in miles.

1 inch ------------- 5 miles

x inches --------- 30 miles

Applying cross multiplication

5x=30

x=6 inches

The Line 05 of the Table

1 in= 10 miles, from the rule of three, you can find the distance in miles.

1 inch ------------- 10 miles

3 inches --------- x miles

Applying cross multiplication

x=3*10 miles

x=30 miles

The Line 06 of the Table

1 in= 15 miles, from the rule of three, you can find the distance in miles.

1 inch ------------- 15miles

2 inches --------- x miles

Applying cross multiplication

x=2*15 miles

x=30 miles

Read more about the rule of three here:

brainly.com/question/24514897

Answer:

9 miles, 6 inches, 30 miles, and 30 miles

Step-by-step explanation:

What he said. give him crown.

Find the value of x
Find the measures of the following angles

Answers

Answer:

Step-by-step explanation:

DOES ANYONE KNOW THIS ?? Its not 20 or 16 and the layers that can be put into the box is 4 number 2 thank u so much i will make u brainliest if its right

Answers

Answer:

4 layers

128 cm²

0.1 m

Step-by-step explanation:

Height of chocolate = 0.5 cmHeight of open box = 2 cm

Layers of chocolate

Height of box / Height of chocolate2 / 0.52 x 24 layers

Volume of box

8 x 8 x 264 x 2128 cm³

Length of river on map

x : 10,000 = 1 : 100,000x = 0.1 meters

Answer:

128

Step-by-step explanation:

Volume of an open box= 2(b x h) + 2(l x b) + 2(l x h)

now here the length and breadth are same, so both are 8, and there is no need to put 2 before (l x b) as it is an open box

(8 x 8) + 2(8 x 2) + (8 x 2)

Jessica has $32 to buy movie tickets that cost $5.25 each for her and her friends. the inequality 32≥5.25t represents the number of tickets t she could buy. what is the greatest number of tickets jessica can buy?

Answers

The greatest number of tickets she can buy is 6 tickets

help i need the awnser

Answers

Answer:

5 cm. Assuming the shape only has right angles.

Step-by-step explanation:

16-11=missing side

Do number 5 pleaseee

Answers

Answer:

Step-by-step explanation:

16 × 2 = 32

20 × 2 = 40

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￼￼ Find the length of the third side. If necessary, write in simplest radical form. IMAGE DOWN BELOW! SOMEONE PLEASE HELP ME!! ILL GIVE YOU BRAINLIST ANSWER

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Find the length of the third side. If necessary, write in simplest radical form.

IMAGE DOWN BELOW!

SOMEONE PLEASE HELP ME!! ILL GIVE YOU BRAINLIST ANSWER