Answer: (x + 4)(x + 2)
Step-by-step explanation: In this problem, we're given a trinomial with an x² term, an x term, and a constant term so we can factor it as the product of two binomials.
The first term in each binomial will be a factor of x² and since x² factors as x time x, we use x as the first term in each binomial.
To fill the second position in each binomial, we use the factors of the last term that add together to equal the coefficient of the middle term.
So we're looking for factors of +8 that add to +6.
+8 factors as 8 x 1 or 4 x 2. Since 4 and 2 add together to equal +6, we put a +4 in our first binomial and a +2 in our second binomial and we have our answer (x + 4)(x + 2) which is a factored version of x² + 6x + 8.
Answer:
D
Step-by-step explanation:
Recall that a⟌b means b/a. So, we want to find the expression: 20⟌4 and 4 ÷ 20. By examining, we see that D has those two expressions.
So, the answer is and we're done!
the denominator yields no critical points, so is only that one, which IS within the range of [0, 4].
f(0) = 0 and f(4) is about 0.2222... whilst f(√2) is about 0.3536
now, doing a first-derivative test, the √2 points is a maximum, and and the 0 and 4 are both minima, from which the 0 is lowest than the 4, notice f(0) = 0 and f(4) is up above that.
so the absolute minimum is f(0), and the absolute maximum is f(√2).
Answer:
<em>The interest earned is $302.18</em>
Step-by-step explanation:
<u>Compound Interest
</u>
It occurs when the interest is reinvested rather than paying it out. Interest in the next compound period is earned on the principal sum plus previously accumulated interest.
The formula is:
Where:
A = final amount
P = initial principal balance
r = interest rate
n = number of times interest applied per time period
t = number of time periods elapsed
The investment described in the question is of P=$600 at a rate of r=6%=0.06 for t=7 years compounded annually. The compounding period coincides with the time of interest rate, thus n=1.
Applying the formula:
A = $902.18
The interest is:
I = A - P = $902.18 - $600 = $302.18
The interest earned is $302.18
Answer:
35
Step-by-step explanation:
We know the factors of Lena's age are 2 and 5. The least common multiple must have these factors and the factors of 14, so will at least have factors of 2, 5, and 7.
Apparently, the dad's age is 5·7 = 35.
___
The GCF is 5; the LCM is 70 = 5×14.
_____
Sometimes, I use a little 3-part diagram to think about LCM and GCF. Here, it would look like ...
(2 [5) 7]
where the numbers in curved brackets (2·5) and the numbers in square brackets [5·7] are factors of the two numbers of concern (Lena's age, her dad's age). The middle number in both brackets [5) is the greatest common factor, and the product of all three numbers is their least common multiple.
Here, the product of outside numbers, 2·7 = 14, represents the ratio of the LCM to the GCF. We know that Lena's age has factors of only 2 and 5, so the numbers in the diagram have to be (2[5)7], where 2 and 7 are on the ends and 5 is in the middle.