Amanda purchased n notebooks. They were 4 dollars each. Write an equation to represent the total cost c that Amanda paid.
1 answer:
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Answer:
The insect's combined body length is shorter than 4/10
Step-by-step explanation:
To get the combined length of the insect's body, we add the length of the head of the insect to the length of the body of the insect.
The body of the insect is 1/10 inch long and the head of the insect is 3/100 inch long. Hence, its combined body length is:
Finding the Lowest Common Multiple of the denominators and simply, we have:
The combined body length of the insect is 13/100 inches.
13/100 is smaller than 4/10 (4/10 is equivalent to 40/100).
Hence, the insect's combined body length is shorter than 4/10.
Note: if we are to pay attention to units, we would not be able to compare 13/100 inches to 4/10 because 4/10 is unitless.
Answer:
x = 6, 9
Step 1:
To solve this equation, we need to subtract 3 from both sides like this:
Step 2:
We square both sides (multiply using FOIL) to get rid of the radical.
If you did not understand how these were done, here is an example:
(x + 1)(x + 2)
First terms: x * x = <u><em>x^2</em></u>
Outer terms: x * 2 = 2x
Inner terms: 1 * x = x
2x - x = <u><em>x</em></u>
Last terms: 1 * 2 =<em> </em><u><em>2</em></u>
x^2 + x + 2
Step 3:
Solve for x:
9x - 45 = x^2 - 6x + 9
x^2 - 6x + 9 (+45) = 9x - 45 (+45)
x^2 - 6x + 54 (-9x) = 9x (-9x)
x^2 - 15x + 54 = 0
Factor:
(x^2 - 6x) + (- 9x + 54)
x(x - 6) - 9(x - 6)
Factor out (x - 6):
(x - 6)(x - 9) = 0
x - 6 = 0; 6 - 6 = 0
x - 9 = 0; 9 - 9 = 0
Our anwer: x = 6, 9