Answer:
20(x+15)(x+10)
Step-by-step explanation:
Hi there!
As your question states, we need to fully factor the polynomial: 20x²+500x+3000
These are pretty big numbers; let's pull out the GCF, as that will make it easier to factor
the GCF is 20
so factoring 20 out of the polynomial will get:
20(x²+25x+150)
As you can see, the polynomial inside the parenthesis is a lot easier to factor than the original with really big numbers.
Now use FOIL to factor x²+25x+150 into 2 binomials
25 is the sum of the last terms
150 is the product of the last terms
think: which two numbers add up to 25 but multiply to get 150?
those two numbers are 15 and 10
x²+25x+150 factored is (x+15)(x+10)
but remember we have the 20 in front of x²+25x+150 (or now, (x+15)(x+10))
therefore the fully factored binomial is 20(x+15)(x+10)
Hope this helps! :)
The first option 3 miles, 15480 feet
To solve an absolute inequality first step is to isolate absolute value expression.
Hence remove -4 from the left side. So, add 4 to each sides of the inequality.
2|x + 7|−4 ≥ 0
2|x + 7|−4 +4≥ 0 +4
2|x + 7| ≥ 4 Combine the like terms.
Divide each sides by 2.
|x + 7| ≥2
Next step is to remove the absolute value sign. So,
x + 7≥2 and x+7≤-2.
x≥2-7 and x≤-2-7
x≥-5 and x≤-9
So, the correct choice is C. {x | x ≤ -9 or x ≥ -5}.
Answer:
see explanation
Step-by-step explanation:
Given
(x + 2)(x - 7) = 0 ← in standard form
Equate each factor to zero and solve for x
x + 2 = 0 ⇒ x = - 2
x - 7 = 0 ⇒ x = 7
Thus the zeros are x = - 2 and x = 7
Answer:
- {-3.2, -1.4, 0.4 2.2, 4.0, 5.8}
- common difference: 1.8
Step-by-step explanation:
The difference between the two numbers is ...
5.8 -(-3.2) = 9
The four "means" divide this interval into 5 parts, so each part has a length of ...
9/5 = 1.8 . . . . the common difference
The values of the "means" can be found by adding 1.8 successively:
-3.2 +1.8 = -1.4
-1.4 +1.8 = 0.4
0.4 +1.8 = 2.2
2.2 +1.8 = 4.0
Including the given numbers, the arithmetic sequence is ...
-3.2, -1.4, 0.4, 2.2, 4.0, 5.8 . . . . . common difference of 1.8