Answer:
The statement is true for every n between 0 and 77 and it is false for 
Step-by-step explanation:
First, observe that, for n=0 and n=1 the statement is true:
For n=0: 
For n=1: 
From this point we will assume that 
As we can see,
and
. Then,

Now, we will use the formula for the sum of the first 4th powers:

Therefore:

and, because
,

Observe that, because
and is an integer,

In concusion, the statement is true if and only if n is a non negative integer such that 
So, 78 is the smallest value of n that does not satisfy the inequality.
Note: If you compute
for 77 and 78 you will obtain:
Answer:
Step-by-step explanation:
5, -4
5-4=1
5(-4)=-20
Answer:
a) 4 people ordered streak dinner
b) 3 people ordered chicken dinner
Step-by-step explanation:
Let the number of people that ordered steak dinner be x
and the number of people that ordered chicken dinner be y
From the question,
There are 7 people in your family
Hence, we can write that
x + y = 7 ...... (1)
Also from the question
Some order the chicken dinner for $13 and some order the steak dinner for $18 and the total bill was $111.
We can then write that
13y + 18x = 111 ...... (2)
From equation (1)
x + y = 7
Then,
x = 7 - y ...... (3)
Put this into equation (2)
13y + 18x = 111
13y + 18(7 - y) = 111
13y + 126 - 18y = 111
-5y = -15
5y = 15
y = 15 / 5
y = 3
Put the value of y into equation (3) to get x
x = 7 - y
Then
x = 7 - 3
x = 4
Hence, 4 people ordered streak dinner
and 3 people ordered chicken dinner
a) 4 people ordered streak dinner
b) 3 people ordered chicken dinner
Answer: 4,536
Step-by-step explanation: Multiply your two 9's to get 81. Multiply your 8 and 7 to get 56. Multiply 81 and 56 together to get your answer of 4,536.
9 x 9 = 81
8 x 7 = 56
81 x 56 = 4,536
Use long multiplication to evaluate this equation.
I hope this helps you out! ♥
Answer:
c = -a - b + 180
Step-by-step explanation:
Isolate the c. Note the equal sign, what you do to one side, you do to the other. Subtract a and b from both sides
a (-a) + b (-b) + c = 180 (-a) (-b)
c = 180 - a - b
c = -a - b + 180 is your answer
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