Answer:
Step-by-step explanation:
Prove: That the sum of the squares of 4 consecutive integers is an even integer.
An integer is a any directed number that has no decimal part or indivisible fractional part. Examples are: 4, 100, 0, -20,-100 etc.
Selecting 4 consecutive positive integers: 5, 6, 7, 8. Then;
= 25
= 36
= 49
= 64
The sum of the squares = 25 + 36 + 49 + 64
= 174
Also,
Selecting 4 consecutive negative integers: -10, -11, -12, -13. Then;
= 100
= 121
= 144
= 169
The sum of the squares = 100 + 121 + 144 + 169
= 534
Therefore, the sum of the squares of 4 consecutive integers is an even integer.
Answer:
T = 49
Step-by-step explanation:
T = w - ma
w = 85
m = 12
a = 3
Plug in the corresponding numbers to the corresponding variables:
T = (85) - (12) * (3)
Remember to follow PEMDAS. PEMDAS is the order of operations, and stands for:
Parenthesis
Exponents (& Roots)
Multiplications
Divisions
Additions
Subtractions
First, multiply, then subtract:
T = 85 - (12 * 3)
T = 85 - 36
T = 49
T = 49 is your answer.
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4x + 3 + x - 2 +4x +3 +x - 2
5x + 1 + 4x + 3 + x - 2
5x + 1 + 5x + 1
10x + 2
Let's use K for Kona and F for Fuji. The system of equations has to be a balanced system. For example, you can't mix the number of pounds of beans with the cost for each because pounds and dollars are different and you can only combine like terms...pounds with pounds and dollars with dollars. So let's start with the number of pounds. Since we don't know how much of each he bought we have the 2 unknowns, F and K, but we DO know that he bought 23 pounds total. So the first equation is
K + F = 23
Now let's see what we can do with the dollars. Again, we don't know how much he bought of each kind of coffee, but we do know that Kona beans cost $11 per pound and that Fuji beans cost $7.50 per pound, and we know that he spent a total of $197. So let's set that up:
11K + 7.50F = 197
Those are your 2 equations. It doesn't say you need to solve them, so you're done.
