Answer:
see explanation
Step-by-step explanation:
(a)
Given
2k - 6k² + 4k³ ← factor out 2k from each term
= 2k(1 - 3k + 2k²)
To factor the quadratic
Consider the factors of the product of the constant term ( 1) and the coefficient of the k² term (+ 2) which sum to give the coefficient of the k- term (- 3)
The factors are - 1 and - 2
Use these factors to split the k- term
1 - k - 2k + 2k² ( factor the first/second and third/fourth terms )
1(1 - k) - 2k(1 - k) ← factor out (1 - k) from each term
= (1 - k)(1 - 2k)
1 - 3k + 2k² = (1 - k)(1 - 2k) and
2k - 6k² + 4k³ = 2k(1 - k)(1 - 2k)
(b)
Given
2ax - 4ay + 3bx - 6by ( factor the first/second and third/fourth terms )
= 2a(x - 2y) + 3b(x - 2y) ← factor out (x - 2y) from each term
= (x - 2y)(2a + 3b)
Answer:
$24,960
Step-by-step explanation:
1. Find daily salary (12*8 hours = 96/day)
2. find weekly salary (96*5 days = 480/week)
3. find annual salary (480*52 weeks = 24,960/year)
Answer: 79
Step-by-step explanation:
Given the following :
Graduation Rates:
Grade:82
Weight: 50%
Passing Rates:
Grade: 75
Weight: 30%
Enrollment Numbers:
Grade: 60
Weight: 10%
Career readiness:
Grade: 95
Weight: 10%
Overall score : Σ(grade × weight)
(82 × 50%) + (75 × 30%) + (60 × 10%) + (95 × 10%)
= (41 + 22.5 + 6 + 9.5)
= 79
Hence, overall score is 79
" 100% " means "the whole thing",
and "is" can be replaced by "is equal to".
You have said "The whole thing of a number is equal to 61."
or
"61 is equal to the whole thing of a number."
The only number that 61 can be equal to is 61.
To get the extrema, derive the function.
You get y' = 2x^-1/3 - 2.
Set this equal to zero, and you get x=0 as the location of a critical point.
Since you are on a closed interval [-1, 1], those points can also have an extrema.
Your min is right, but the max isn't at (1,1). At x=-1, you get y=5 (y = 3(-1)^2/3 -2(-1); (-1)^2/3 = 1, not -1).
Thus, the maximum is at (-1, 5).
