Answer:
(5 - y) ^3 = 125 - 75y + 15y^2 - y^3
Step-by-step explanation:
Binomial expression
1
1. 1
1. 2. 1
1. 3. 3. 1 --------power of 3
( 5 - y) ^3
( 5 - y) (5 - y) (5 - y)
( a + b) ^3 = a^3 + 3a^2b + 3ab^2 + b^3
a = 5
b = -y
( 5 - y) ^2 = ( 5 - y) (5 - y)
= 5( 5 - y) - y(5 - y)
= 25 - 5y - 5y + y^2
=(25-10y+y^2)
( 25 - 10y + y^2)( 5 - y)
= 5(25 - 10y + y^2) - y( 25 - 10y + y^2)
= 125 - 50y + 5y^2 - 25y + 10y^2 - y^3
Collect the like terms
= 125 - 50y - 25y + 5y^2 + 10y^2 - y^3
= 125 - 75y + 15y^2 - y^3
Answer:
29-12 is a 17 difference
52-29 is a 23 difference (adding 6 to the number 17)
81-52 is a 29 difference (adding 6 to the number 23)
116-81 is a 35 difference (adding 6 to the number 29)
Step-by-step explanation:
<h3>
Answer: 864</h3>
=======================================================
Work Shown:
There are,
- 3 sizes of coffee
- 4 types of coffee
- 2 choices for cream (you pick it or you leave it out)
- 2 choices for sugar (same idea as the cream)
This means there are 3*4*2*2 = 12*4 = 48 different coffees. We'll use this value later, so let A = 48.
There are 6 bagel options. Also, there are 3 choices in terms of if you order the bagel plain, with butter, or with cream cheese. This leads to 6*3 = 18 different ways to order a bagel. Let B = 18.
Multiply the values of A and B to get the final answer
A*B = 48*18 = 864
There are 864 ways to order a coffee and bagel at this restaurant.
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If you're curious why you multiply the values out, consider this smaller example.
Let's say you had 3 choices of coffee and 2 choices for a bagel. Form a table with 3 rows and 2 columns. Place the different coffee choices along the left to form each row. Along the top, we'll have the two different bagel choices (one for each column).
This 3 by 2 table leads to 3*2 = 6 individual table cells inside. Each cell in the table represents a coffee+bagel combo. This idea is applied to the section above, but we have a lot more options.
97.356
<span>ninety seven and three hundred fifty six <span>thousandths</span></span>
Answer:
10. 7n - 1 < -8
Isolate the variable, n. Do the opposite of PEMDAS. Treat the < as equal sign, what you do to one side, you do to the other. First, add 1 to both sides:
7n - 1 (+1) < - 8 (+1)
7n < - 8 + 1
7n < - 7
Isolate the variable, n. Divide 7 from both sides:
(7n)/7 < (-7)/7
n < -7/7
n < -1
n < -1 is your answer.
11. 3 > -7v + 4v
Combine like terms, then isolate the variable, v. First, add -7v and 4v together.
3 > (-7v + 4v)
3 > (4v - 7v)
3 > (-3v)
Isolate the variable, v. Divide -3 from both sides. Note that since you are dividing a negative number, you must flip the sign:
(3)/-3 > (-3v)/-3
3/-3 > v
-1 < v
v > -1 is your answer.
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