A television set is 36 inches wide and has a diagonal length of 42 inches. To the nearest inch, how tall is the set?

9

13

22

55​

Answer:

x = 15

y = 12

m < AED = 83°

m < DEC = 97°

Step-by-step explanation:

According to the given problem:

< AED = (6x - 7)°

< BEC = (4x + 23)°

< AEB = (8y + 1)°

< DEC = (5y + 37)°

Two angles are vertical angles if they are opposite angles formed by the intersection of two lines. Vertical angles are congruent.

Given that < AED and < BEC are vertical angles, then it means that they have the same measure.

The same goes with < AEB and <DEC, they are also considered as vertical angles.

To solve for x:

< AED = < BEC

(6x - 7)° = (4x + 23)°

Subtract 4x from both sides:

6x - 4x - 7 = 4x - 4x + 23

2x - 7 = 23

Add 7 to both sides:

2x - 7 + 7 = 23 + 7

2x = 30

Divide both sides by 2 to solve for x:

2x/2 = 30/2

x = 15

To solve for y:

< AEB = <DEC

(8y + 1)° = (5y + 37)°

Subtract 5y from both sides:

8y - 5y + 1 = 5y - 5y + 37

3y + 1 = 37

Subtract 1 from both sides:

3y + 1 - 1 = 37 - 1

3y = 36

Divide both sides by 3 to solve for y:

3y/3 = 36/3

y = 12

To double check whether our values of x and y are correct, substitute these values into the established equality statements:

< AED = < BEC

(6x - 7)° = (4x + 23)°

[6(15) - 7]° = [4(15) + 23]°

(90 - 7)° = (60 + 23)°

83° = 83° (True statement. Therefore, x = 15 is the correct answer, and m < AED = 83°).

< AEB = <DEC

(8y + 1)° = (5y + 37)°

[8(12) + 1)° = [5(12) + 37]°

(96 + 1)° = (60 + 37)°

97° = 97° (True statement. Therefore, y = 12 is the correct answer, and m < DEC = 97°).

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Answer: The new scale factor needs to be 10/3

Explanation:

Consider a line segment that is 10 units long. Apply the scale factor 3/10 to it, and now it's 3 units long because (3/10)*10 = 3.

To get it back to 10 units, we multiply by the scale factor 10/3 which is the reciprocal of the original scale factor. Note that (3/10)*(10/3) = 1. Those two scale factors multiply to 1 to indicate no change has been made overall.

Payton will make money after 14 weeks is $378.

Income is the money your business takes in and expenses are what it spends money on. Your net income is generally your revenue, or all the money coming into your business, minus all of your expenses.

For the given situation,

Item Expenses Revenue after 1 week

Number of Cups = $5

Number of Lemonade = $6

Number of Ice = $7

Total revenue, Income = $45

Formula to find the net income,

Net Income = Total Revenue - Total Expenses

⇒ Net Income = [tex]45 - ( 5+6+7 )[/tex]

⇒ Net Income = [tex]27[/tex]

Thus net income for 14 weeks = [tex]14[/tex] × [tex]27[/tex]

⇒ [tex]378[/tex]

Hence we can conclude that Payton will make money after 14 weeks is $378.

Learn more about income and expenses here

https://brainly.com/question/26313056

#SPJ2

Answer:

57,600

Step-by-step explanation:

720 * 80 = 57,600

Answer:

9

Step-by-step explanation:

You divide the answer with the first number and you'll get the answer, 9.

Answer:

C) 3,192 Canadian dollars

Step-by-step explanation:

$2,400 x 1.33 = $3,192

Answer:

I think the first one is x < 2 and the second is x > 3

Using a system of equations, it is found that 595 students picked Science as their favorite subject.

For our system, we suppose that x is the number of students that picked science, and y is the number of students that picked math.

Ratio of science to math of 3:5, thus:

[tex]\frac{x}{y} = \frac{3}{5}[/tex]

Then

[tex]5x = 3y[/tex]

[tex]x = \frac{3y}{5}[/tex]

238  more students picked Math as their favorite subject, thus:

[tex]y = 238 + x[/tex]

[tex]y - \frac{3y}{5} = 238[/tex]

[tex]\frac{2y}{5} = 238[/tex]

[tex]y = \frac{238(5)}{2}[/tex]

[tex]y = 595[/tex]

595 students picked Science as their favorite subject.

A similar problem is given at https://brainly.com/question/21244414

Answer:

Step-by-step explanation:

The formed triangles are similar and the ratio of corresponding sides is equal:

The light source should be at 3 m height

Both triangles are congruent so

[tex]\\ \bull\sf\longmapsto \dfrac{x}{4}=\dfrac{9}{12}[/tex]

[tex]\\ \bull\sf\longmapsto 12x=36[/tex]

[tex]\\ \bull\sf\longmapsto x=3[/tex]

Light source should be at 3m

Let missing side be x

[tex]\\ \sf\longmapsto \dfrac{2}{5}=\dfrac{x}{10}[/tex]

Now

[tex]\\ \sf\longmapsto 5x=20[/tex]

[tex]\\ \sf\longmapsto x=\dfrac{20}{5}[/tex]

[tex]\\ \sf\longmapsto x=4[/tex]

The constant of variation is 1/3 and when x = 3/4, y = 1/4

Two variables are proportional to each other if as one variable increase or decrease, the other variable does the same.

Given that y and x have a constant variation, hence:

y ∝ x

y = kx;

where k is the constant of variation

y=2 when x=6;

2 = 6k

k = 1/3

y = (1/3)x

When x = 3/4;

y = (1/3)(3/4)

y = 1/4

Hence the constant of variation is 1/3 and when x = 3/4, y = 1/4

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Answer:

The answer is 24

Step-by-step explanation:

Answer:

The answer is 24 or D

Step-by-step explanation:

Well, first you need to figure out the equation in these [ ].

[-5 (2-4) ÷ 2]

[-5 (-2) ÷ 2] ---> -5(-2) = -5 x -2

[10 ÷ 2]

[5]

Then, you need to complete the equation in these { }

{3+[5]} OR {3+5}

{8}

Then, you need to finish the equation!

{8} · 3 OR 8 x 3

__________________________

Hope this helped!

Answer:

Each of the congruent angles is 34

Step-by-step explanation:

A = 112                               A is the given angle

A + x + x = 180                   A + x + x = 180 All triangles have 180 degrees  

112 + x + x = 180                 Combine

112 + 2x = 180                     Subtract 112 from both sides

112-112 + 2x = 180 - 112       Combine

2x = 68                                Divide both sides by 2

2x/2 = 68/2

x = 34

Let the numbers be x, x+1 and x+2 .

Equation :-

=> x+(x+1)+(x+2)=78

=> x+x+1+x+2=78

=> 3x+3=78

Subtract 3 from both sides..

3x=75

Divide both sides by 3 .

x=25

The three consecutive integers are

x , x+1 and x+2..In the place of x replace 25

∴ 25 , 26 and 27 are the three consecutive integers.

Given : Three consecutive integers have a sum of 78. Find the integers

Solution : Let's assume that the variable be x

The first one be x itself. Now, as it's consecutive the number should be increased by 1. So, let the second one be x + 1. As we know again it will be increased by 1. Hence, the third one be x + 1 + 1 i.e. x + 2

So, we got all the three now let's proceed

The result is 78

Taking 3 as common on the RHS of the equation

1st number = x = 25

2nd number = x + 1 = 26

3rd number = x + 2 = 27

Answer:

x = (180 - 68) / 2

Step-by-step explanation:

x = 56°

Answer:

56°

Step-by-step explanation:

(180° - 68°) ÷ 2 = 112° ÷ 2

= 56°

your welcome :)

Answer:

Step-by-step explanation:

(6 + 1, 3 + 1) = (7, 4)

Answer:

60

Step-by-step explanation:

Interior and exterior angle from a linear pair.

Let the exterior angle = x

x + 120 = 180

        x = 180 - 120

x = 60

Answer:

f(-3) = (-3)^2 + (-3) = 9 - 3 = 6

Answer:

I believe the answer is 6

Step-by-step explanation:

1) If f(-3), x is equal to -3 ( I think )

2) f(x) = -3^2 + (-3)

3) f(x) = 9 - 3

4) f(x) = 6

The answer is f(x) = 6

Hey there!

- 9 • (-7/3)

= - 9 × -7/3

= 63/3

= 21.

For better understanding :-

[tex] \tt- 9 \: \cdot \: ( \frac{ - 7}{3} ) \\ = \tt\frac{ - 9 \times - 7}{3} \\ = \tt\frac{63}{3} \\ = \boxed{ \tt \: 21}[/tex]

Note :-

Hope it helps ya!

Answer:

ninety eight thousand two hundred forty eight

Answer:

Ninety-eight-thousand-and-two-hundred-and-forty-eight

Step-by-step explanation:

Answer:

0.42484

Step-by-step explanation:

place them on top of each other but the bottom one has to leave a space and put a zero in that space also go by the order of the decimal do not do 8.17 0.052 it will not give you the correct answer so they put it in a way to give you an answer. you should write it like this     0.052

                                                                  x 8.170

                                                                    _____

I hope this helps! If you can, can I have brainlest? I really want to level up.

Answer:

-18/10

Step-by-step explanation:

I think that is correct

Answer:

1 17/20

Step-by-step explanation:

if you × 8/10 it by 2 = 16/10

Answer:

Move the decimal point in 407.26 three places to the left = 0.407283

Step-by-step explanation:

Answer:

3, left

Step-by-step explanation:

When you're dividing a number by any power of 10 that is a whole number (10, 100, 1000, etc.), you move the decimal point to the left as many times as there are zeroes in the digit.

Examples:

30.22 ÷ 100 = 0.3022

There are two zeroes in 100, so move the decimal point two spaces to the left.

568.9 ÷ 10000 = 0.05689

There are four zeroes in 10000, so move the decimal point four spaces to the left.

The given equation in the problem is 407.26 ÷ 1000, so you move the decimal point 3 spaces to the left to find the correct answer.

Answer:

25×2.50=62.5

62.5+12=74.5

hope that helps

Answer:

$74.50

Step-by-step explanation:

M = 2.50(f) + 12

M = 2.50(25) + 12

M = 74.5

20/32

5/8

0.625

62.5

62.5%

x% x 32= 20; x%=20÷32: x%=.625:; x= 62.5%

Domain:

Range:

Function:

Domain:

Range:

Function:

Domain:

Range:

Function:

(a) $200 today is equivalent to having $208 in one year with 4% interest rate.

(b) $192.31 today would be equivalent to $200 in one year with 4% interest rate.

(c) true

Explanation:

(a) since simple interest is given as:

I = p x r x t/100

Where p = the principal amount

r = interest rate

t = number of years

Now, from the question our principal is $200 since we are to calculate the interest on it, and our rate is 4% as obvious from the question and as well as our time is 1year. Substituting these to the interest formula we get:

I = 200 x 4 x 1/100

And that gives $8 as the interest, therefore in one year the amount we shall have will be: $200 + $8 = $208

(b) assuming we have 200 as the amount, we have now, we can get the principal we had last year at 4% interest with the following

A = p(1 + rt/100)

Now our amount is assumed to be $200 for 1year at 4% interest rate, therefore we have:

200 = p(1+4 x 1/100)

This gives

200 = p x 1.04

which gives

200/1.04 = p

p = $192.31(to the nearest cents)

(c) The statement is obviously true, because the amount we buy things today are more expensive than the amount we bought them in previous years, so having $200 today is preferable because the interest on it is just so small and would be a waste of resources.    

I have no idea to be honest with you

Answer:

Step-by-step explanation:

Cuz I'm smart :)

Hope this helps :]  

pls make brainliest :3  

and have an amazing day <3