Multiplying fractions by whole numbers:
1. You have to convert the whole number into an improper fraction.
2. You then multiply the fractions straight across.
Ex: 2/3 × 6 =2/3 × 6/1 = 2×6/3×1= 12/3= 4
Use Pythagorean Theorem:
a² + b² = c²
"a" is one side of the right triangle.
Its length is: radius of larger circle minus radius of smaller circle: (11 - 3 = 8)
The distance between the center of the circles creates the hypotenuse (17)
8² + b² = 17²
b² = 225
b = 15
Answer: the length of the common external tangent is 15.
Answer:
domain: 0 - 10 range: 0 - 32
Step-by-step explanation:
Take the lowest x and the highest x and put them in set values to get domain.
lowest x = 0 and highest x = 10.
Take the lowest y and the highest y and put them in set values to get range.
lowest y = 0 and highest y = 32
Answer:
The amount is $16718.7 and the interest is $4718.7.
Step-by-step explanation:
STEP 1: To find amount we use formula:
A=P(1+rn)n⋅t
A = total amount
P = principal or amount of money deposited,
r = annual interest rate
n = number of times compounded per year
t = time in years
In this example we have
P=$12000 , r=3.33% , n=4 and t=10 years
After plugging the given information we have
AAAA=12000(1+0.03334)4⋅10=12000⋅1.00832540=12000⋅1.393225=16718.7
STEP 2: To find interest we use formula A=P+I, since A=16718.7 and P = 12000 we have:
A16718.7II=P+I=12000+I=16718.7−12000=4718.7
Answer:
Orange = 12
Grape = 15
Cola = 23
Step-by-step explanation:
Turning this into equations you can give each soda a variable
Cola = C | Grape = G | Orange = R
Then you get:
8 + G = C
R + 3 = G
C + G + R = 50
We want to get a variable all by itself in an equation so first I'm going to put the second equation (R + 3 = G) in the first (8 + G = C) by replacing the G to get
8 + (R + 3) = C Combine the variables 11 + R = C and put that new equation into the last equation
(11 + R) + G + R = 50
Now plug our original second equation (R + 3 = G) into our third to get
(11 + R) + (R + 3) + R = 50
Combine and get
14 + 3R = 50 Subtract over the 14
3R = 36 Divide by 3
Orange Sodas = 12
Our new 3rd Equation is now: C + G + 12 = 50, subtract over 12 to get
C + G = 38
Plug either equation 1 or 2 into that one, I'll do 1
(8 + G) + G = 38
8 + 2G = 38
2G = 30
Grape Sodas = 15
Now our 3rd equation is C + 15 = 38, subtract over 15
Cola Sodas = 23
Orange = 12
Grape = 15
Cola = 23
12 + 15 + 23 = 50
