Complete the equations below.

Answer:

EZ Excavation: y = 24.5x

Happy Hauling Service: y = 25x

Step-by-step explanation:

✔️Equation for EZ Excavation:

This can be written in slope-intercept form, y = kx

Where k is the unit rate/slope/constant of proportionality

y = cost

x = dirt

Thus,

k = y/x

Using any given pair of values from the table, say, (8, 196),

k = 196/8

k = 24.5

To write the equation, substitute k = 24.5 into y = kx

Thus:

y = 24.5x

✔️Equation for Happy Hauling Service:

This can be written in slope-intercept form, y = kx

Where k is the unit rate/slope/constant of proportionality

y = cost

x = dirt

Thus,

k = y/x

Using the coordinate of any point on the line, say (1, 25),

k = 25/1

k = 25

To write the equation, substitute k = 25 into y = kx

Thus:

y = 25x

Step-by-step explanation:

1)90-50= 40°

2)90-25= 65°

3)90-80=10°

Answer: 8 units

Step-by-step explanation:

This can be solved using the Pythagorean Theorem:

c² = a² + b²

c is the hypotenuse

a and b are the sides

Solving for the length:

10² = 6² + b²

100 = 36 + b²

b² = 100 - 36

b² = 64

b = √64

b = 8 units

The missing side is 8 units.

Answer:

y=3x+1

Step-by-step explanation:

Slope-intercept form is y=mx+b, where m is the slope and b is the y intercept

the formula for slope (m) is given as (y2-y1)/(x2-x1)

we can pick any 2 points to use to find the slope. For example, let's use (2,7) and (3,10)

label the points:

x1=2

y1=7

x2=3

y2=10

now substitute into the formula:

m=(y2-y1)/(x2-x1)

m=(10-7)/(3-2)

m=3/1

m=3

the slope of the line is 3

here's our equation so far:

y=3x+b

now we need to find b (y intercept)

because the line will pass through any of the points given on the table, we can use any one of the given points to solve for b

Let's take (2,7) though since it's the first point

substitute 2 as x and 7 as y in the equation

7=3(2)+b

7=6+b

1=b

so our equation is y=3x+1

Hope this helps! :)

Step-by-step explanation:

3x+12=2x+2x

3x+12=4x

3x-4x=-12

-x=-12

x=12

Answer:

no, the answer is x = 12

Step-by-step explanation:

3(x + 4)= 2x - (-2x)

3(x + 4)= 2x + 2x

3x + 12 - 12 = 4x - 12

3x - 4x = 4x - 12 - 4x

-x = -12

x = 12

Answer:

8

Step-by-step explanation:

Given data

Volume of large box= 1000cm^3

Dimension of small box

L=5cm

W=5cm

H=5cm

Volume of small box= 5^3

V=125cm^3

Hence the number of small box that can fill the large box is

=1000/125

=8

Answer:

26²

Step-by-step explanation:

26 x 26 = 676

Answer:

62 feet

Step-by-step explanation:

During a football game, the ball is placed 20 yards 2 feet from the goal line. How many feet from the goal line is the football?

Step 1

We convert 20 yards to feet

1 yard = 3 feet

20 yards = x feet

Cross Multiply

1 yard × x feet = 20 yards × 3 feet

x feet = 20 yards × 3 feet/1 yard

x feet = 60 feet

Step 2

How many feet from the goal line is the football?

This is calculated as:

20 yards 2 feet =

60 feet + 2 feet = 62 feet

Therefore, the football is 62 feet from the goal line

Answer:

13.9

Step-by-step explanation:

7² x 12² = 49 + 144 = 193

√193= 13.89

Answer:

229.2

Step-by-step explanation:

Remark

There's a lot in this question. The x is not just any x. It is defined and limited by its relationship with the sine function.

The Sin is defined as Opposite over Hypotenuse in a right triangle. The 670 is the Hypotenuse. You know that by the definition of Sine.

So one thing you should always keep in mind: the x because of where it is in the definition, will always be smaller than the Hypotenuse. So you should get a value less than 670.

Formula

Just as you have it

Sin(20) = x / 670

Solution

Multiply both sides by 570

670 * sin(20) = x

sin(20) = 0.3420

x = 670 * 0.3420

x = 229.2

Answer:

180-130=50

Step-by-step explanation:

done hope you like it

i use the 180 because its a straight line from the x to the 130

Answer:

20% of students picked the vanilla cake.

Step-by-step explanation:

Total number of students: 16 + 64 = 80

Proportion that chose vanilla cake: 16/80 (simplify by dividing by 16) = 1/5 = 0.2 * 100 = 20%

Answer:

A

Step-by-step explanation:

Simplify both sides x+38.18=82.06

subtract 38.18 from both sides

x+38.18-38.18=82.06-38.08

x=43.88

Answer:

-2x - 9

Step-by-step explanation:

Answer:

−2x−9

I hope this helps

Answer:

x=3

Step-by-step explanation:

10x - 15 = 15

10x = 15 + 15

10x = 30 (divide both sides by 10 to get x)

10x/10 = 30/10

x = 3

Answer:

heres your answer

Step-by-step explanation:

Answer:

y = 12 + 2x

Step-by-step explanation:

Given that :

Let number of butterflies = y

Number of moths = x

y = 12 more than twice the number of moths

y = 12 + 2x

Hence, the expression which relates the number of butterflies he has is :

y = 12 + 2x

Answer:

Nope. Does not satisfy pythagoras theorem

Step-by-step explanation:

72 squared does nit equal 45 squared plus 56 squared

Answer is in the file below

tinyurl.com/wtjfavyw

Answer:

d

Step-by-step explanation:

Answer:

Slope is 1/5

Step-by-step explanation:

m = (y2 - y1)/ (x2 - x1)

m = (3-4)/(-2-3)

m = (-1)/(-5)

m = 1/5

Answer:

14 units

Step-by-step explanation:

Step-by-step explanation:

A: n(n+1) = 72

B

n^2 + n = 72

n^2 + n -72 =0

(n+9)(n-8) = 0

Answer:

See Explanation

Step-by-step explanation:

Given

[tex]\frac{4}{5} = \frac{9}{10}[/tex] --- Jack's thought

Because:

[tex]\frac{4+5}{5+5} = \frac{9}{10}[/tex]

Jack's thought is incorrect.

This is so because, to get an equivalent fraction; you don't add common terms to the numerator and the denominator but instead you multiply the numerator and the denominator by a common term.

Take for instance, the common term is: 2

The fraction becomes:

[tex]\frac{4 * 2}{5 * 2} = \frac{8}{10}[/tex]