Answer:
<em>8 more men are needed to complete the job</em>
Step-by-step explanation:
<u>Proportions</u>
This problem can be solved by step-by-step reasoning applying proportions:
- 16 men working 9 hrs a day complete the job in 14 days
- 16 men working 1 hr a day complete the job in 14*9 days
The above statement stands because the fewer hours of work, the more time the job needs to be completed. Let's continue.
- 1 man working 1 hr a day complete the job in 14*9*16 days
The same reasoning applies here, fewer men=more days.
Now for the second condition. Increase the hours/day:
- 1 man working 7 hrs a day complete the job in 14*9*16/7 days
More hours/day=less days to complete the job
- x men working 7 hrs a day complete the job in 14*9*16/(7*x) days
We know this last time is 12 days, thus:
Solving for x:
24 men are needed now, this is an increase of 24-16=8 more men
8 more men are needed to complete the job
A) 13 degrees because it would be 90-77
If two angles are complementary, then the two angles add up to 90 degrees.
If angle A is 77, then the complement would be 90-77 or 13 degrees.
b) The complement of the complement of the angle is the angle itself.
Say the angle A is 30 degrees. It's complement is 90-30 or 60 degrees.
The complement of the 60 degrees is 30 degrees.
So the complement of the complement of the angle would be the angle itself.
Hope this helps :)
(a) Length of the height is 2.732 m
(b) Length of the base is 5.466 m
<u>Explanation:</u>
An image is attached for reference.
(a)
In ΔAOB,
In ΔBGD,
According to the figure, BG = OE = 1.732 m
Height of the tent, AE = AO + OE
= 1 m + 1.732 m
= 2.732 m
(b)
DF = ?
In ΔAOB,
According to the figure, OB = GE = 1.733 m
In ΔBGD,
According to the figure, DE = DG + GE
DE = 1 m + 1.733 m
DE = 2.733 m
Length of the base, DF = 2 X DE
DF = 2 X 2.733 m
DF = 5.466 m
1. 36 = 6·6 and 42 = 6·7 have a common factor of 6.
... x⁴ and x² have a common factor of x²
The GCF is 6x².
The factorization is 36x⁴ -42x² = 6x²(6x² -7)
2. All coefficients are multiples of 4. All variable factors are multiples of x³.
The GCF is 4x³.
The factorization is 4x⁵ -8x⁴ -4x³ = 4x³(x² -2x -1)
3. The GCF of coefficients 6 and 15 is (15 mod 6) = 3, which is also a factor of the other coefficients. The lowest power of m, which is m² is also a factor of the other terms.
The GCF is 3m².
The factorization is 6m⁵ -15m⁴ -21m³ +27m² = 3m²(2m³ -5m² -7m +9)
