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Felix worked at a music shop during the summer. The table below shows some of Felix’s hours and earnings. The amount of money he earned is proportional to the number of hours he worked.


2. Let x represent the number of hours he worked, y represents the amount of money he earned.Write an equation that represents this relationship.



3. If Felix worked 180 hours, then how much money did he earn?

Answer:

Activity 1:-

1) Pi (π) is the ratio of circumference and the diameter of the circle which is 22/7. So

[tex]\frac{c}{d} =\pi = \frac{22}{7}[/tex]

[tex]=> c = \frac{22}{7} d[/tex] where circumference is directly proportional to diameter (d).

2) Area of a parallelogram = Altitude × Base

Base = 10 cm. So ,

[tex]A = 10a[/tex] where area (A) is directly proportional to altitude (a).

3) Let the fare of 1 unit distance be f

So, for distance d , total fare (F) will be [tex]F = fd[/tex] where total fare (F) is directly proportional to distance (d).

4) Let the distance be 'D' , speed be 's' & time be 't' .

We know that [tex]s = \frac{D}{t}[/tex] where speed (s) is directly proportional to distance (D) & inversely proportional to time (t).

5) We know that area of a square (A) = side² (s²)

[tex]=> A = s^{2}[/tex] where area(A) is directly proportional to side(s).

Activity 2:-

1) p is directly proportional to sum of u & w.

⇒ p ∝ u + w

⇒ p = k (u + w)

Putting the values of p , u & w

⇒ 14 = k(4 + 3)

⇒ 7k = 14

⇒ k = 14/7 = 2

2) r is directly proportional to square of t.

⇒ r ∝ t²

⇒ r = k × t²

Putting the values of r & t

⇒ 16 = k × 16²

⇒ k = 16² ÷ 16 = 16

3) y is directly proportional to cube root of x.

⇒ y ∝ ∛x

⇒ y = k × ∛x

Putting the values of x & y ,

⇒ 2 = k × ∛27

⇒ 3k = 2

⇒ k = 2/3

4) z is directly proportional to cube of d.

⇒ z ∝ d³

⇒ z = k × d³

Putting the values of d & z ,

⇒ 5 = k × 2³

⇒ 8k = 5

⇒ k = 5/8

5) Total Surface Area (SA) is directly proportional to square of the sides (s).

⇒ SA ∝ s²

⇒ SA = k × s²

Putting the values of SA & s ,

⇒ 96 = k × 4²

⇒ 16k = 96

⇒ k = 96/16 = 6

Answer:

Step-by-step explanation:

85-x=100

85 represents sarah's hw

x represent Emily's hw

100 represents total completion

Answer:

85 + x

C is the answer

Step-by-step explanation:

Answer:

$33

Step-by-step explanation:

Hope this helps!

Answer:

The line graph is also attached below.

Step-by-step explanation:

Given

[tex]8m-6<10[/tex]

Add 6 to both sides

[tex]8m-6+6<10+6[/tex]

Simplify

[tex]8m<16[/tex]

Divide both sides by 8

[tex]\frac{8m}{8}<\frac{16}{8}[/tex]

Simplify

[tex]m<2[/tex]

Therefore, m = 3 NOT a solution of the inequality because 'm' must be less than 2.

Hence,

VERIFICATION:

Given

[tex]8m-6<10[/tex]

substitute m = 3

8(3) - 6 < 10

24 - 6 < 10

18 < 10

FALSE

Answer: 3

Step-by-step explanation: 9/3=3

Answer:

C.{(-3,10),(-2,5),(1,2),(-2,-4)}

Answer:

1/2^3

Step-by-step explanation:

When an exponent is negative you flip the fraction, in this case from numerator to denominator.

1/2^3

Step-by-step explanation:

Answer: nope

Step-by-step explanation:

Answer: 14s - 7s/2 = 84

Step-by-step explanation:

Given that s is the length of the unknown side:

Area of the shaded region = 84

Area of rectangle - Area of triangle = 84

Area of rectangle = L * W

= 14 * s

= 14s

Area of triangle = ¹/₂ * base * height

= ¹/₂ * 14 * s/2

= 7s/2

Area of shaded region:

14s - 7s/2 = 84

Solving for s:

14s - 7s/2 = 84

28s - 7s = 168

21s = 168

s = 168/21

s = 8 inches

Answer:

14/27 feet

Step-by-step explanation:

2 1/3 feet : 4 1/2 feet

= 7/3 : 9/2

= 7/3 ÷ 9/2

= 7/3 × 2/9

= (7*2)/(3*9)

= 14/27 feet

2 1/3 feet : 4 1/2 feet = 14/27 feet

Answer:

2

Step-by-step explanation:

5 and 7 are the coefficients if you need them

Answer:

The answer is B

Hope this helps

Answer:

The first answer

Explanation:

Ok I added an explanation lol-

So B is incorrect. It gets confused. 332/4 simplified isn't 1/83, but it's 83/1 (aka 83)

C doesn't even make sense 6-6

And D isn't 5 2/5 it's 7 2/5

Answer:

-3

Step-by-step explanation:

[tex]log_{\frac{1}{2} }8=-log_{2}8=-log_{2} (2^{3})=-3[/tex]

Answer:

-3

Step-by-step explanation:

i forgot how to do the log thingy but the guy on top is also correct

Answer:

x+5>-7

Step-by-step explanation:

The sum of a number and five translates to x+5. It then states that this expression is more than negative seven, therefore you use a greater than sign to get x+5>-7

Answer:

yo

Step-by-step explanation:

yo

Answer:

thanks dude

Step-by-step explanation:

:)

Answer:

I think it is 3^8

Step-by-step explanation:

(3^5)^2

÷

3^-2

3^10

÷

3^-2

=3^8

Answer:

I believe the output is f(6) is -1, the output of f(2) is -4, and f(x)=-4 has the outputs of  2, 4, 8, and 10.

I think.

Answer:

I believe it is yes because he is correct

Answer:

-1/2

Step-by-step explanation:

Formula to find slope is y2-y1/x2-x1

Chose one ordered pair to be the 2 and the other one to be the 1

I chose the 2nd one to be 2.

Plug in the y-value from the 2nd ordered pair to y2 because its the 2.

Plug in the x-value from the 2nd ordered pair to x2 because its the 2.

Now you have 0-y1/5-x1

Do the same thing but for the 1.

Plug in the y-value from the 1st ordered pair to y1 because its the 1.

Plug in the x-value from the 1st ordered pair to x1 because its the 1.

Now you have 0-5/5--5

In this situation, you have 2 minus signs.

2 minus = 1 positive.

Now you have 0-5/5+5

Simplify.

Now you have -5/10.

Simplify.

-1/2.

Hope this helps!

19/16 or 1 3/16 :D I hope this helped u

Answer:

1500%

Step-by-step explanation:

The formula for Percentage increase is

Increase/ Initial Amount × 100

Increase = Current Amount - Initial Amount

Increase = $320,000 - $20,000

Increase = $300,000

Percentage Increase =

$300,000/$20,000 × 100

= 1500%

The percent increase in home value in those 50 years is 1500%

Answer:

3/4

Step-by-step explanation:

6/8 divided by 2 is 3/4

Answer: =17x

Step-by-step explanation: hope this help, hope you understand it too.

Let's simplify step-by-step.

2x+5x+10x

Combine Like Terms:

=2x+5x+10x

=(2x+5x+10x)

=17x

Answer:

b = 4

Step-by-step explanation:

Try setting up the equation of the pythagorean theorem.

hypotenuse^2 = leg(a)^2 + leg(b)^2

c^2 = a^2+b^2

Now substitute what you know and solve for the unknown.

5^2 = 3^2+b^2

25 = 9 + b^2

b^2 = 25-9 = 16

b = 4.

Answer:

(C) 48 ft^3

Step-by-step explanation:

Volume=L*W*H=6*4*2=24*2=48, making the correct choice (C) 48 ft^3

Answer:

25

Step-by-step explanation:

because 25 is %25 of 100

Answer:

25

Step-by-step explanation:

25% is 25 pieces out of 100 (cent). This means 25 corresponds to 25%. Another answer could be .25, but that is not there.

Answer:

30° , 170°

Step-by-step explanation:

Let the remaining two angles be 3x & 17x. As it is a quadrilateral , the sum of all the angles of quadrilateral is 360°. So,

[tex]3x + 17x + 60 + 100 = 360[/tex]

[tex] = > 20x + 160 = 360[/tex]

[tex] = > 20x = 360 - 160 = 200[/tex]

[tex] = > x = \frac{200}{20} = 10[/tex]

Putting the value of x , remaining angles are

(3×10 = 30°) & (17×10 = 170°)

Step-by-step explanation:

Answer:

( D )Each sandwich has 2 pounds of ham.

Answer:

1/2 of ham

Step-by-step explanation: