Which set of dimensions is possible for a rectangular prism with volume 420 cm3? A. 4 cm by 8 cm by 12 cm B. 4 cm by 10 cm by 12
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Answer:
First number: -39
Second number: -37
Step-by-step explanation:
An odd number can be written as where n is a whole number.
Let's call our first number 2n+1.
Our second, consecutive number will be 2 more than our first number, since it has to be odd. All numbers go: odd -> even -> odd -> even. If we have an odd number, and add 2, we'll get the next odd number.
First number: 2n+1
Second number: 2n+1+2 = 2n+3
The sum of these two numbers, 2n+1 and 2n+3 will be -76.
(2n+1) + (2n+3) = -76
2n + 2n + 1 + 3 = -76
4n + 4 = -76
4n = -80
n = -20
Since our first number is 2n+1:
2 * (-20) + 1 = -40 + 1 = -39
First number: -39
Our second number is 2n+3, or 2 more than our first number.
-39 + 2 = -37
Second number: -37
We can double check this:
-39 + (-37) = -39 - 37 = -76
It's a linear function. We need only two points to sketch the graph.
f(x) = -5x + 4 → y = -5x + 4
for x = 0 → y = -5(0) + 4 = 0 + 4 = 4 → (0, 4)
for x = 1 → y= -5(1) + 4 = -5 + 4 = -1 → (1, -1)
The domain and the range is the set of all real numbers.
