Answer:
See Explanation Below
Step-by-step explanation:
Given
Required
Prove
To start with; we open the bracket on the left hand side
Reorder
From trigonometry;
So;
becomes
Also from trigonometry;
So,
becomes
Proved
A company has actual unit demand for four consecutive years of 100, 105, 135, and 150. The respective forecasts were 120 for all
1 answer:
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To begin with, the question is asking for the answer in days, so let's change 3 weeks to days. There are 7 days in 1 week; 3 weeks times 7 days = 21 days.
21 total days of vacation.
Max + Jared + Wesley = 21 days
(Let's use the first letter of their name to represent their vacation time)
M + J + W = 21 [This is the equation we'll be coming back to]
Now, we can use the clues given in the question to have an equation for each variable/boy.
Max was on vacation twice as long as Jared. We can interpret this as M= 2J Max was on vacation only half as long as Wesley. We can interpret this as M = (1/2)W.
So far we have these three equations: M + J + W = 21M = 2J M = (1/2)W
To have an equation for each individual boy, we must rearrange the last two equations in the list.
First, M = 2J.
Divide both sides by 2
M/2 = 2J/2
(1/2)M = J
Second, <span>M = (1/2)W
Multiply both sides by 2
2M = W
New equations:
</span><span>M + J + W = 21 [From the old list]
</span>J = (1/2)W
W = 2M
Now we can substitute the last two equations into the first one.
M + J + W = 21
M + (1/2)W + 2M = 21
[Combine Like Terms]
<span>(7/2)M = 21
</span>
Then, solve for M (Max's vacation days):
Multiply both sides by 2/7
M = 6
Now we know Max was on vacation for 6 days.
If Max was on vacation twice as long as Jared, that means Jared was on vacation HALF as long as Max.
So...
<span>J = (1/2)M
J = (1/2) * 6
J = 3
Jared was on vacation for 3 days
</span>
Wesley was on vacation twice as long as Max so... W = 2M
W= 2*6
W = 12
Wesley was on vacation for 12 days.
Let's double check our answer:
M + J + W = 21 days<span>6 + 3 + 12 = 21
The numbers work out so the math is correct. Hope this helps and makes sense!</span>
21 total days of vacation.
Max + Jared + Wesley = 21 days
(Let's use the first letter of their name to represent their vacation time)
M + J + W = 21 [This is the equation we'll be coming back to]
Now, we can use the clues given in the question to have an equation for each variable/boy.
Max was on vacation twice as long as Jared. We can interpret this as M= 2J Max was on vacation only half as long as Wesley. We can interpret this as M = (1/2)W.
So far we have these three equations: M + J + W = 21M = 2J M = (1/2)W
To have an equation for each individual boy, we must rearrange the last two equations in the list.
First, M = 2J.
Divide both sides by 2
M/2 = 2J/2
(1/2)M = J
Second, <span>M = (1/2)W
Multiply both sides by 2
2M = W
New equations:
</span><span>M + J + W = 21 [From the old list]
</span>J = (1/2)W
W = 2M
Now we can substitute the last two equations into the first one.
M + J + W = 21
M + (1/2)W + 2M = 21
[Combine Like Terms]
<span>(7/2)M = 21
</span>
Then, solve for M (Max's vacation days):
Multiply both sides by 2/7
M = 6
Now we know Max was on vacation for 6 days.
If Max was on vacation twice as long as Jared, that means Jared was on vacation HALF as long as Max.
So...
<span>J = (1/2)M
J = (1/2) * 6
J = 3
Jared was on vacation for 3 days
</span>
Wesley was on vacation twice as long as Max so... W = 2M
W= 2*6
W = 12
Wesley was on vacation for 12 days.
Let's double check our answer:
M + J + W = 21 days<span>6 + 3 + 12 = 21
The numbers work out so the math is correct. Hope this helps and makes sense!</span>
Answer:
C
Step-by-step explanation:
Answer:
Step-by-step explanation:
First, on the right-hand side of the equation, let's distribute the to each term in the parenthesis:
Now, let's move all the terms with an to the left-hand side, and everything else to the right-hand side of the equation:
Let's combine like terms:
Finally, let's divide each side by to get
by itself on the left-hand side of the equation: