Answer:
4(k - 3)(3k + 5)
Step-by-step explanation:
Given
12k² - 16k - 60 ← factor out 4 from each term
= 4(3k² - 4k - 15) ← factor the quadratic
Consider the factors of the product of the coefficient of the k² term and the constant term which sum to give the coefficient of the k term
product = 3 × - 15 = - 45 , sum = - 4
Factors are - 9 and + 5
Use these factors to split the middle term
3k² - 9k + 5k - 15 → ( factor the first/second and third/fourth terms
= 3k(k - 3) + 5(k - 3) ← factor out (k - 3)
= (k - 3)(3k + 5)
Hence
12k² - 16k - 60 = 4(k - 3)(3k + 5) ← in factored form
Answer:
X = 21/4 - 7/4 = 14/4 = 7/2 = 3 and 1/2
Step-by-step explanation:
X + (2 and 1/2) - 3/4 = 5 and 1/4
X + 2 and 2/4 - 3/4 = 5 and 1/4 <--- common denominator
X + 10/4 - 3/4 = 21/4
X + 7/4 = 21/4
X = 21/4 - 7/4 = 14/4 = 7/2 = 3 and 1/2
Y – y1 = m(x – x1)
y-(-1)=-5(x-2)
Y+1=-5(x-2)
1-1/4 feet is the base side length.
<span>(A) Find the approximate length of the plank. Round to the nearest tenth of a foot.
Given that the distance of the ground is 3ft.
In order to get the length of the plank,
we can use the this one.
cos 49 = ground / plank
cos 49 = 3 / plank
plank = cos 49 / 3
plank = 0.10 ft
</span><span>(b) Find the height above the ground where the plank touches the wall. Round to the nearest tenth of a foot.
</span><span>
The remaining angle is equal to
angle = 180 - (90+49)
angle = 41
Finding the height.
tan 41 = height / ground
tan 41 = height / 3
height = tan 41 / 3
height = 0.05 ft.
(A) 0.10 feet
(B) 0.05 feet</span>
