Question

Ever wonder what Albert Einstein’s formula E = MC2 means? Don’t worry, your teacher doesn’t really understand that one either, but what the heck is a “formula” anyway?

What’s a formula?
It’s a way to show how things are related. It may be a mathematical pattern. In math class, we use an equation such as y = 20x. What do the variables x & y stand for? It could be anything related in that pattern.
Example: You earn $20 per hour babysitting your friend’s baby T-Rex (watch those baby teeth). The equation or “formula” for your money earned: Money = 20 X Hours
We could also use letters such as M = 20H or y = 20x
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Definition for formula, with example:

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Can you think of any two things related in a pattern?
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Basic steps for using a formula:
1. Write the formula. Example: volume = length X width X height
2. Find out what you know. Example: length = 2, width = 3, height = 1
3. Plug in the numbers and solve. Volume = 2 X 3 X 1 = 6
4. Double check your “units”, like if the length is inches and the width is feet, you need to change something.
Note: it makes things easier to understand if you use letters or symbols, like V = LWH
(we can show multiplication different ways, like above is multiplying, or use * instead of x)

Changing the subject: We can use simple math to solve for anything we don’t know in a formula or equation.
Example from above: V = L W H
If I know the volume of a box is 20, length is 2 and width is 5. What is the H or height?
20 = 2 X 5 X H or 20 = 10 times H or 20 = 10H
Solve for H: It must be 2! You can also do the reverse operation, like 20 divided by 10 equals 2, our answer.
It helps to think of simple math, like we know 12 = 6 x 2 or 6 = 12/2 or 2 = 12/6
Make sure you check “units”, like volume could be cubic inches, so the length, width and height all need to be in inches for it to work.
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Please answer the questions below. Thank you.








1. Arlene Arva has five times as many diamonds as she has rubies.
a. Write a formula to describe this pattern, using D = number of diamonds and R = number of rubies.
Using words: Number of diamonds =
Or using letters: D =
b. If she has 4 rubies, how many diamonds does she have?
c. If she has 10 rubies, how many diamonds does she have?
d. How many rubies would she have if she has 15 diamonds?
e. Write a formula for the number of rubies, R =


2. Answer the questions below using this formula: A = B + C
a. If B = 5 and C = 2, the A =
b. If A = 10 and C = 2, then B =
c. Name any two values for B & C so that the A = 7: B = ___ & C = _____
d. Write a formula for B: B =

3. Formulas (equations): A = 3x and B = 5x + 1
a. As x increases, does A or B go up faster?
b. If x=0, then A =
c. If x=1 then B =

4. Formulas (equations): A = 2x and B = x2
Note: x2 means x squared, or x times x. Example: 32 = 3 * 3 = 9
a. If x = 1, then A =___ and B = _____
b. If x = 3, then A =___ and B = _____


5. The diameter of a circle is twice the radius.

The “formula” for this: Diameter = 2 (radius) or D = 2R
a. If a circle radius is 8, then the diameter is ____
b. If R = 3, then D =
c. If D = 20, then R =
d. If D = 100, then R =
e. Write a formula for a circle radius: R =



6. A cool thing about ALL circles is that the ratio of circumference divided by diameter equals π (pi).


So, we can write a “formula” for pi: π = C / D
We can also write it as C = π D (circumference equals pi times diameter)
a. Use 3.14 for π and if D = 20 centimeters, then C =
b. Use 3.14 for π and if D = 10 inches, then C =
c. If we round π to 3.14, and a string 18 inches long goes around the circle, what is the diameter? D =
Tip: think of simple numbers, like 10 = 2 * 5 so we know that 10/2 = 5

7. Formula: Speed = distance / time or S = D/T
Example: you travel 50 miles in 1 hour, so your average speed is 50 miles/hour. Or, you go 100 miles in 2 hours, so your average speed is 100/2 = 50 miles per hour (mph).
a. If your paper airplane travels 12 feet in 3 seconds, what is its average speed?
b. If Superman travels 100 miles in 5 seconds, what is his average speed?
c. Name any values for distance (D) and time (T) to get 4 feet per second speed.
D =___ and T =____
subject is Science i just cant find it

Answer 1

Answers are mentioned along with explanations/

Step-by-step explanation:

1. We are given D = 5R

where D = no. of diamonds and R = no. of rubies

a. In words, Number of diamonds = 5 times no. of rubies

In letters D = 5R

b. Given R = 4, so D = 5 x R = 5x 4

D = 20

c. Given R = 10 , so D = 5 x R = 5x 10

D = 50

d. Given D = 15 , D = 5R so , R = D/5 = 15/5 = 3

R = 3

e. R =
`(D)/(5)` because D = 5R

2. Given A = B + C

a. B = 5 , C = 2 => A= 5+2 => A= 7

b. B = A - C from above equation and given A = 10 , C = 2 , B= 10 - 2

B = 8

c. two values of B and C for A to be 7

B = 4 C = 3 and vice versa as 4+3 = 7

d. B = A - C by moving C on the RHS thus changing its prefix sign.

3. Given A = 3x and B = 5x+1

a. B goes up faster because it is 5 times x plus 1 where A is just 3 times x

b. if x = 0, A = 3x = 3x0 = > A = 0

c. if x =1 , B = 5x+1 = 5x1 +1 = 5+1 => B = 6

4. Given A = 2x and B = x2 where x2 means x*x so,

a. if x=1 , A = 2*1 = 2 and B = 1*1 = 1

b. if x = 3, A = 3*1 = 3 and B = 3*3 = 9

5. Given D =2R

a. given R = 8 , D = 2*8 => D=16

b. given R =3 then D = 2*3 => D = 6

c. D= 20 given, R = D/2 = 20/2 => R = 10

d. D = 100 so R = D/2 = 100/2 => R =50

e. R =
`(D)/(2)` or D/2

6. Given C = π D and π = 3.14

a. if D = 20, C = 3.14*20 => C = 62.8 centimeters

b. if D = 10, C = 3.14*10 => C = 31.4 inches

c. Given C = 18, D = C/31.4 = 18/3.14 => D = 5.732 inches

7. Given S = D/T

a. S = 12/3 = 4 feet/seconds

b. S = 100/5 = 20 miles/seconds

c. For S = 4feet per second , D = 8 ft and T = 2 seconds as S = D/T