simplify the following expression

Answer:

y=3x+15

Step-by-step explanation:

she can make 3 a day so 3x and she already has 15 so the line crosses the y-axis  at 15

For given angle of elevation equals to 66 degree and distance to kite is 303feet and hand is 4 feet above the ground then kite is 280.8feet high.

As given,

Shown in diagram attached,

Angle of elevation ∠AEB=66°

Distance to the kite AE=303 feet

Hand above the ground DE=4feet

DE=BC

BC=4feet

Let 'h' be height of AB

Height of the kite=(h +4)feet

In ΔABE,

sin66°=h/303

⇒h=sin66° ×303

     =0.9135 ×303

      =276.7905

      ≈276.8 feet

Height of kite=(h +4) feet

                             =276.8 +4

                             =280.8 feet

Therefore, for given angle of elevation equals to 66 degree and distance to kite is 303feet and hand is 4 feet above the ground then kite is 280.8feet high.

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To find the percent of happy people, we just have to divide the number of happy participants by the total number of them.

Then, we multiply it by 10 to express it as a percentage.

A function is defined as a relation between a set of inputs having one output each.

The value of y when x = 48 is 96.

A function is defined as a relation between a set of inputs having one output each.

The inputs are called the domain of the function.

The outputs are called the range of the function.

We have,

The value of y varies directly with x.

y = 8, when x = 4.

Domain = input = 4

Range = output = 8

Now,

We can say that y is a function.

i.e y = 2x.

Where x = input = domain and y = range = output.

The value of y when x = 48:

y = 2x

y = 2 x 48

y = 96

Thus,

The value of y when x = 48 is 96.

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Carly needs to perform 33 additional sales to earn 100 this week.

Firstly forming the expression as per the weekly earning and individual payment on extra sale. Writing the expression -

Amount earned = 35 + 2×number of sales

Keep the value of amount earned in mentioned formula to find the number of sales.

100 = 35 + 2×number of sales

2×Number of sales = 100 - 35

Performing subtraction on Right Hand Side of the equation

2×Number of sales = 65

Shifting 2 to Right Hand Side of the equation

Number of sales = 65/2

Performing division on Right Hand Side of the equation

Number of sales = 32.5

Round off the number

Number of sales = 33

Therefore, she needs to make 33 additional sales.

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A solution set exists the set of values that satisfy a given set of equations or inequalities.

Its position must be 1600 then It takes 10s to get to the ground.

A solution set exists the set of values that satisfy a given set of equations or inequalities. For instance, for a set of polynomials over a ring , the solution set exists the subset of on which the polynomials all vanish (evaluate to 0), formally.

The formula,

h = 16t²

where h is height and t is time.

You want to see how long it will take an object to fall 1600 feet down to the ground. These means its position must be 1600.

By setting the equation equal to this value,

we get:

1600 = 16t²

To estimate the value of t.  

First, divide both side by 16, getting:

100 = t²  

Now taking the square root of both sides, we get:

√(100) = 10 seconds.

It takes 10s to get to the ground.

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Answer:

y = 3

Step-by-step explanation:

y = -5(-4) - 17
multiply first

y = (-5*-4) - 17

y = +20 -17

y = 3

Inequality is 32.50x + $10.50 ≤ $160 and 4 people can go to the amusement park.

inequality, A declaration of an order relationship between two numbers or algebraic expressions, such as greater than, greater than or equal to, less than, or less than or equal to.

Given that,

$160 = Amount of money they have

$10.50 = Parking Cost

$32.50 = Cost of tickets per person

Because they only have $160, they can't spend more than that amount.

Therefore, the inequality would be the ticket cost per person, times the amount of people being payed for (x) plus the parking cost is less than or equal to the amount of money they have to spend. Hence the inequality:

32.50x + $10.50 ≤ $160

Solve the equation

$160 - $10.50 = $149.50 (149.50 is how much is left for tickets after subtracting the parking cost)

$32.50 x 4 = $130 (4 tickets can be bought for the price of $32.50)

$149.50 - $130 = $19.50 (19.50 isn't enough for another person)

So, the solution to the inequality is 4 people can go to the amusement park.
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The mass of two bodies are attracted with a force of 745N.if their distance of separation is 70.3m, then the mass of one the bodies is

[tex]m_{1} = 1.88(10)^{-7}[/tex]

The amount of matter that makes up every object or body is the greatest way to understand mass. Everything that we can see has mass. Examples of objects with mass include a table, a chair, your bed, a football, a glass, and even air. The mass of a thing determines whether it is light or heavy.

Given that : The mass of two bodies are attracted with a force of 745N.if their distance of separation is 70.3m

F=[tex]G\frac{m_{1} .m_{2} }{r^{2} }[/tex]

[tex]m_{1} =\frac{F.r^{2} }{Gm_{2} }\\ m_{1} =\frac{745.(70.3)^{2} }{6.7(10)^{-11}.2050 }\\\\[/tex]

[tex]m_{1} =\frac{26881.3(10^{7} )}{13735}[/tex]

[tex]m_{1} = 1.88(10)^{-7}[/tex]

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Skydiver should wait 23.04 sec before pulling the cord, after freefall.

what is freefall?

Height of jump = 13500ft

Height from which cord will be pulled = 5000ft

Freefall, d=13500-5000 =8500ft

Distance traveled during freefall, d=16t²

substituting values, we get,

8500=16t²

t=23.04 sec

Skydiver should wait 23.04 sec before pulling the cord, after freefall.

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Answer:

How about:

0, 1, 2, 3, 4..............

lol jk here:

0, 66, 132, 198, 264

Step-by-step explanation:

Guess what it is! ;p

The answers to all the subparts are:

So, the reason for rational or irrational numbers:

(A) 0.21

It is a rational number as it can be represented in fractions.

(B) 3/12

It is a rational number as it is in fractions.

(C) 4.125

It is a rational number as it can be represented in fractions.

(D) 8⅒

It is a rational number as it can be represented in fractions.

(E) π/3.14/(22/7)

It is a rational number as it can be represented in fractions.

Therefore, the answers to all the subparts are:

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Step-by-step explanation:

it is a bit difficult to read the handwriting (and even the printed original texts) in this diffuse picture.

let's go through the 3 problems as I could decipher them.

1)

from what I can see you made a calculation mistake for y.

but you were right with your approaches.

12x - 8 = 15x - 23

15 = 3x

x = 5

therefore,

12x - 8 = 12×5 - 8 = 60 - 8 = 52°

and the large angle up there is

52 + 70 = 122°

and now

6y + 96 = (12x - 8) + 70 = 122

6y = 26

y = 26/6 = 13/3

by the way, x and y are not angles (and degrees). they are just factors in the expressions to calculate some angles.

12, 15 and 6 are not ° either. all are calculation factors or terms, that then together define the ° of angles.

2)

you made a mistake with the identification of what angles the linear pair is.

3x = 5x - 20

20 = 2x

x = 10 (again, not °, just a number)

3x = 3×10 = 30° (this is then an angle)

= 5x - 20

for y we could then use 2 different approaches

a) your linear pair approach.

4y is one angle, true, but the other is (2y + 3x) !

so,

4y + 2y + 30 = 180

6y = 150

y = 25 (again, not °, just a number)

2y = 50°

4y = 100°

3)

I hope you are right with (11x + 19) and (12y - 24). I would have read this in the picture as (11x + 18). and it could be (12y + 24).

assuming you are right :

11x + 19 = 7x + 47

4x = 28

x = 7 (again, not °, just a number)

11x + 19 = 7x + 47 = 96°

7z + 17 = 87

7z = 70

z = 10 (again, not °, just a number)

and yes, for y we are using the linear pair again. the two combining angles are (12y - 24) and (11x + 19).

(12y - 24) + (11x + 19) = 12y - 24 + 96 = 180

12y + 72 = 180

12y = 108

y = 9 (again, not °, just a number)

12y - 24 = 12×9 - 24 = 108 - 24 = 84°

Answer:

y=2(x−3)

Step-by-step explanation:

In the given relations , the relation (B) represents a function, others are not function. To become a function each input should have only one output. Since others does not satisfy this criteria they are not functions.

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Answer:

530 x

Step-by-step explanation:

Answer:

b = [tex]\frac{g}{(d^{2}+4) }[/tex]

Step-by-step explanation:

([tex]d^{2}[/tex] + 4)b = g  Divide both sides by ([tex]d^{2}[/tex] + 4)

b = [tex]\frac{g}{(d^{2}+4) }[/tex]

The length is 780 feet and the width is 430 feet.

Distance is measured in length.

The dimension of distance is a property of length in the International System of Quantities.

Let the length be x

Width = x - 350

Perimeter = 2260 feet

Now : 2(x + x +350) = 2260

or, 2 x + 700 = 2260

or, 2x = 1560

or, x = 780 feet

So length is 780 feet

Width = 780 -350 = 430 feet

Therefore the length is 780 feet and the width is 430 feet.

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Answer:

wait, its r + 0.5

Step-by-step explanation:

In the year 2006, the number of free throws is 100, number of 2 point field goals 128 and the number of 3 point field goals 90.

Let x = number of free throws

y = number of 2 point field goals

z =  number of 3 point field goals

However given that Rebecca has a total of 806 points,

Thus x + 2y + 3z = 806 ---------- equation 1

Number of 2 point field goals that Rebecca made was 52 less than double the number of​ three-point field goals she made ;

thus y = 2z - 52 ---------------- equation 2

Number of 3 point field goals that Rebecca made was 28 less than the number of​ two-point field goals she made ;

thus x = y - 28 ------------------ equation 3

Thus on solving these three above mentioned equations :

we get x = 2z - 52 -28 [ substituting values in eq 3 from eq 2]

x = 2z - 80 ------------- equation 5

So equation 1 becomes ; 2z - 80 + 2y + 3z = 806

5z + 2y = 886 -------------- equation 4

Thus on solving equation 4 and 2 we get

2 X equation 2 = 4z - 2y = 104

                            5z + 2y = 886

                      = 11 z = 990

thus z = 90 and so y = 4 × 90 - 104 = 2y

y= 360 - 104 / 2

= 256/2 = 128

thus y = 128 .

And x= 2z -80 from equation 5 ; x = 180 - 80 = 100 .

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Step 1:

First count the number of stickers on a page

There are 12 stickers in a page

Step 2

There are 30 pages,

Hence, the number of stickers in 30 pages = 30 x 12 = 360

Final answer

Dana has 360 stickers in all

Answer:

1) 4, 1.25, 2
2) 12, 5, 3

3) 2, 18, 5

4)5, 8, 12

Step-by-step explanation:

1) You had to either multiply/divide by 4

2)You had to either multiply/divide by 3

3)You had to either multiply/divide by 6

4)You had to either multiply/divide by 5

Answer:

x = 5

Step-by-step explanation:

The equation is 15 + 0.5x = 25 + 0.25x and number of miles is 40.

While writing the equation for green and blue cars, one time fee will be added with cost of driving for miles. Let us assume the number of miles to be x.

Firstly writing the equation for green car -

Cost = 15 + 0.5×x

Now writing the equation for blue car -

Cost = 25 + 0.25×x

The number of miles for same cost will be calculated by equating the expressions.

15 + 0.5x = 25 + 0.25x

0.5x - 0.25x = 25 - 15

Performing subtraction on Left Hand Side and Right Hand Side of the equation

0.25x = 10

Shifting 0.25 to Right Hand Side of the equation

x = 10 ÷ 0.25

Performing division on Right Hand Side of the equation

x = 40

So, if both the cars travel 40 miles, the rental cost will be same. The correct equation for calculation is 15 + 0.5x = 25 + 0.25x.

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Answer:

2, 9, 12

Step-by-step explanation:

We know that the first number is ten less than the third number and that the third number is one more than the first number and second number combined. Because of this, our third number has to be one away than the combination of the first two numbers. Now, we just have to see the numbers of the first two values and the first number is 10 less than the third number. You can mostly guess the numbers once you understand. I hope that this didn't confuse you more. Hope this helps!

Answer:

x + 7y = 34

Step-by-step explanation:

the altitude through C meets the opposite side AB at right angles

calculate the slope of AB using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = A (2, - 4 ) and (x₂, y₂ ) = B (3, 3 )

[tex]m_{AB}[/tex] = [tex]\frac{3-(-4)}{3-2}[/tex] = [tex]\frac{3+4}{1}[/tex] = [tex]\frac{7}{1}[/tex] = 7

given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{7}[/tex] , then

y = - [tex]\frac{1}{7}[/tex] x + c ← partial equation of the altitude

to find c substitute C (- 1, 5 ) into the partial equation

5 = [tex]\frac{1}{7}[/tex] + c ⇒ c = 5 - [tex]\frac{1}{7}[/tex] = [tex]\frac{35}{7}[/tex] - [tex]\frac{1}{7}[/tex] = [tex]\frac{34}{7}[/tex]

y = - [tex]\frac{1}{7}[/tex] x + [tex]\frac{34}{7}[/tex] ( multiply through by 7 )

7y = - x + 34 ( add x to both sides )

x + 7y = 34 ← equation of altitude in standard form

Answer:

a = [tex]\frac{1}{2}[/tex]

Step-by-step explanation:

since (2, - 3 ) lies on the graph then it makes the equation true.

substitute x = 2 and y = - 3 into the equation and solve for a

2(- 3) = a(2) - 7 , that is

- 6 = 2a - 7 ( add 7 to both sides )

1 = 2a ( divide both sides by 2 )

[tex]\frac{1}{2}[/tex] = a

Answer:

x = [tex]\frac{d - f}{f}[/tex]

Step-by-step explanation:

d = f + fx

Subtract f from both sides

d - f = fx

Divide both sides by f

[tex]\frac{d - f}{f}[/tex] = x

Answer:

Find the slope by putting your rise over your run. Make sure to label your points.

Step-by-step explanation: