Answer:
1) 2(t - 7)(t + 1)
2) $32,000
Step-by-step explanation:
v(t) = 2t² - 12t - 14
v(t) = 2(t² - 6t - 7) = 2(t - 7)(t + 1)
x = -b/2a = 6/2 = 3
y = 2(3)² - 12(3) - 14 = -32
(3, -32) means at 3 months, -32 thousand dollars
Answer:
£265
Step-by-step explanation:
Total fraction of money spent= 
= 
Actual money spent = * £636
= £371
Money he has left = £(636 - 371)
= £265
One way to solve the system is to <u>substitute</u> a variable.
<u>Explanation:</u>
One approach to solve an equation is by substitution of one variable. Right now, a condition for one factor, at that point substitute that arrangement in the other condition, and explain. All value(s) of the variable(s) that fulfills a condition, disparity, arrangement of conditions, or arrangement of imbalances.
The technique for tackling "by substitution" works by settling one of the conditions (you pick which one) for one of the factors (you pick which one), and afterward stopping this go into the other condition, "subbing" for the picked variable and fathoming for the other. At that point you back-explain for the principal variable.
Answer: 67.500 ft²
Explanation:
1) Name the dimensions using variables:
y: length of the rectangular field
x: widht of the rectangular field
2) Model the amount of fence used by the two equal pastures:
two sides and one internal fence: 2x + x = 3x
two lengths: 2y
⇒ 3x + 2y = 1800 ← linear feet of fence
y = 1800 / 2 - 3x/2 ← solving for y
y = 900 - 3x/2
3) Area of each pasture
A = x(y/2) ← half ot xy
A = x (900 - 3x/2) ← replacing y with 900 - 3x/2
A = 900x - 3x² / 2 ← using distributive property
4) Maximum area ⇒ A' = 0
A' = 900 - 3x ← derivative of the polynomial 900x - 3x² / 2
900 - 3x = 0
⇒ 3x = 900
⇒ x = 900/3
⇒ x = 300
4) Determine y
y = 900 - 3x/ 2 = 900 - 3(300)/2 = 900 - 450 = 450
5) Area of each pasture
A = xy/2 = 300 × 450 /2 = 67500 ← final answer
Answer:
20.19°
Step-by-step explanation:
Find the diagram to the question attached. We are to look for <CAB
Applying sine rule on ΔABC:
cross multiply
Hence the angle <CAB is 20.19°
