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Given:

The set of data points on the graph.

To find:

The equation of line that connects the set of data points.

Solution:

From the given graph it is clear that the data points are (20,40), (35,50), (50,60), (65,70).

If a line passes through two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex], then the equation of line is

[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]

Let as consider the line passes through (20,40) and (50,60), then the equation of line is

[tex]y-40=\dfrac{60-40}{50-20}(x-20)[/tex]

[tex]y-40=\dfrac{20}{30}(x-20)[/tex]

[tex]y-40=\dfrac{2}{3}(x-20)[/tex]

Multiply both sides by 3.

[tex]3(y-40)=2(x-20)[/tex]

[tex]3y-120=2x-40[/tex]

Isolate variable terms.

[tex]-2x+3y=120-40[/tex]

[tex]-2x+3y=80[/tex]

Therefore, the standard form of the required line is [tex]-2x+3y=80[/tex].

Answer:

41.3° and 48.7°

Step-by-step explanation:

Complementary angles are angles with the sum of 90°

if one of the angle is 7.4° less than other

(90 - 7.4) ÷ 2 = 41.3° is the measure of smaller angle and

41.3 + 7.4 = 48.7° is the measure of bigger angle

Step-by-step explanation:

When the sum of two angles is equal to 90 degrees, they are called complementary angles.

So

x + x + 50° = 90°

2x = 90° - 50°

2x = 40°

x = 40°/2

x = 20°

x + 50 = 20 + 50 = 70°

Hope it helps :)

Answer:

let 1st angle be x

and another angle be x+50°

two angles are said to be complementary,if the some of their measures is 90°

so,

x+x+50=90

2x+50 =90

2x=90-50

x=40/2

:-x= 20 ....... 1st angle

another angle (x+50)=20+50=70°

Answer:

I think i would be 2hours and 30 mins. Srry if it's wrong

Step-by-step explanation:

Answer:

141 coins

Step-by-step explanation:

Given that Mark has a total of 380 coins(assumed to be shared amongst Albert,Casey, Lily and Logan)

Albert= x

Casey= 2x

Lily= 2x+5

Logan=3x

There's a total of 380 coins

x+2x+2x+5+3x= 380

8x+5=380

8x=380-5

x=375/8

x= 46.9

Therefore Logan's coins = 3x= 3×46.9= 140.61 coins

Approximately Logan's coins =141 coins

Answer:

17/24

Step-by-step explanation:

1. This is an addition problem. Remember, when adding fractions, you first need to find a common denominator.

2. To find the numerator, multiply the current numerators by the number of times the original denominators divide into 24.

3. Now that the denominators are the same, add the numerators and keep the denominator for now.

4. Usually, you would have to reduce the fraction, but since 17/24 is already reduced to its simplest form, 17/24 is your answer.

Answer:

Rest of the team= 20 goals

Step-by-step explanation:

Giving the following information:

Joshua= (2/7)

His team scored 28 goals this past season.

First, we determine hoy many goals Joshua score:

Joshua= (2/7)*28

Joshua= 8 goals

Now, the rest of the team:

Rest of the team= 28 - 8

Rest of the team= 20 goals

Answer:

y=6x+1

Step-by-step explanation:

count from your first point (0,-5) then count up to positive 1 on the y-axis, then go over 1 and you are at your other point. when you count up that is your slope. when you count over that is your b

Answer:

i dont know if this is to answer buying 2

$75.74 for 2

Step-by-step explanation:

50.25*1.5=75.735

Answer:

25%

Step-by-step explanation:

because whats 50%-50%=0% so there's 25% left.

Answer:

-31

Step-by-step explanation:

hope this helped! <3

Answer:

The equation in the point-slope form for the line that passes through point (-1, -4) and has a slope of -3 is y+4=-3(x+1).

Step-by-step explanation:

Given that:

Line passes through the point = (-1, -4)

Slope of the line = -3

Point slope form of a line is given by;

[tex]y-y_1=m(x-x_1)[/tex]

Here,

x1 = -1 , y1 = -4 and m = -3

Putting the values in the point-slope form of the equation,

y-(-4) = -3(x-(-1))

y+4= -3(x+1)

Hence,

The equation in the point-slope form for the line that passes through point (-1, -4) and has a slope of -3 is y+4=-3(x+1).

Answer:

the solution is in the figure

the number is -5

Answer:

h=√p^2+b^2

13 = √x^2+(x+7)^2 now you can solve

Answer:

x = 5

Step-by-step explanation:

Using Pythagoras' identity in the right triangle.

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is

x² + (x + 7)² = 13² ← expand and simplify left side

x² + x² + 14x + 49 = 169 ( subtract 169 from both sides )

2x² + 14x - 120 = 0 ( divide through by 2 )

x² + 7x - 60 = 0 ← in standard form

(x + 12)(x - 5) = 0 ← in factored form

Equate each factor to zero and solve for x

x + 12 = 0 ⇒ x = - 12

x - 5 = 0 ⇒ x = 5

But x > 0 , thus x = 5

Answer:

x=22

Step-by-step explanation:

(x-2)^1 =5                  Anything to the 1st power is 1 Multiply both sides by 4                                                            

x-2=20                      Move the constant (20) to the right and change its

x=20+2                      sign

x=22

Answer:

Area = 56mm²

Step-by-step explanation:

Area of a trapezium/trapezoid

[tex] = \frac{1}{2} \times h \times (a + b)[/tex]

[tex] = \frac{1}{ 2} \times 7 \times (4 + 12)[/tex]

[tex] = \frac{7}{2} \times16[/tex]

[tex] = 7 \times 8[/tex]

[tex] = 56[/tex]

Answer:

7,560 words were typed in 3 hours.

Answer:

The solution is x=-6 and y=7

Step-by-step explanation:

Given equations are:

[tex]4x+4y =4\\3x+4y = 10[/tex]

In elimination method, the co-efficient of one of the variables are equated so that one variable can be eliminated by adding or subtracting the equations

In the given system of equations, the co-efficient of y is already same i.e. 4 so we only have to subtract the equations

Subtracting equation 2 from equation 1

[tex]4x+4y-(3x+4y) = 4-10\\4x+4y-3x-4y = -6\\4x-3x = -6\\x = -6[/tex]

Putting x = -6 in equation 1

[tex]4(-6)+4y = 4\\-24+4y = 4\\4y = 4+24\\4y = 28\\\frac{4y}{4} = \frac{28}{4}\\y = 7[/tex]

Hence

The solution is x=-6 and y=7

Answer:

$115.43

Step-by-step explanation:

From the above question:

1 hour of work = $8.55

13.5 hours of work = x

Cross Multiply

x = 13.5 × $8.55

x = $115.425

Approximately to the nearest hundredth = $115.43

If John works 13.5 hours, the amount of money he makes = $115.43

Answer:

1) 4    2)1/5   X=10

Step-by-step explanation:

Small to large is a fraction

Large to small is a whole number

Answer:

Scale Factor (Dilation) The scale factor in the dilation of a mathematical object determines how much larger or smaller the image will be (compared to the original object). When the absolute value of the scale factor is greater than one, an expansion occurs.

Step-by-step explanation:

Step-by-step explanation:

First we find the slope of f(x):

When x increases by 1, f(x) increases by 8. Slope of f(x) = 8/1 = 8.

Slope of g(x) = Coefficient of x = 3.

Therefore the slope of f(x) is greater than the slope of g(x).

When x = 0, f(x) = -1 (given ii the table) Therefore the y-intercept of f(x) is -1.

Y-intercept of g(x) = Constant term = -2.

Since -1 > -2, f(x) have a greater y-intercept.

Step-by-step explanation:

There are 12 white tiles surrounding 3 green tiles, and 16 white tiles surrounding 5 green tiles.

Common difference = (16-12)/(5-3) = 2.

Hence number of white tiles = 2n + 6.

Answer:

um sorry i wish i could help but mabye post a specfic

question Step-by-step explanation:

Answer:

London

Step-by-step explanation:

Euro= 1.14 x 5

5.70

Answer:11/29

Step-by-step explanation:

The numerator is alredy given as 11 students play both an instrument and a sport. Denominator is how many students in the class which is 29.

Answer:

x = 15 ounces

Step-by-step explanation:

A mixture is made with two types of solutions.

Solution A - 45 ounces of 10% saline solution

Solution B - x ounces of 70% saline solution

Resulting mixture - (x + 45) ounces of 25% saline solution

To get the value of x, equation will be,

(45 × 0.10) + (x × 0.70) = (x + 45) × 0.25

4.5 + 0.70x = 0.25x + 11.25

0.25x - 0.70x  = 4.5 - 11.25

-0.45x = -6.75

x = [tex]\frac{6.75}{0.45}[/tex]

x = 15 ounces