Answer:
40) w = 32/3
41) x = 23/4
42) w = 1/12
Step-by-step explanation:
40) Real world problem:
If Lisa takes 
of the pie from a total of 
slices, then the remaining pie is 
. Find w.
So, the equation would become:
This can be written as:
This is equivalent to 
Since, the denominator is the same, the numerators can be added now.
Hence, the answer is 32/3.
41) The given equation is: 
and
So, 
The answer is 23/4.
42) The given equation is 
The answer is 1/12.
I’m not sure if I’m right but I think you might have to divide the 78% by 7. There’s a website that I like to use as a calculator called Calculator Soup and it help with stuff like fractions, percentages, decimals, ect. Good luck on your homework :)
9514 1404 393
Answer:
- x+y=70; 8.50x+12.50y=10.56(70)
- 36 pounds Antigua
- 34 pounds Rift
Step-by-step explanation:
At the insistence of the problem author, we will let x represent pounds of Antigua coffee and y represent pounds of Rift coffee. Then we have ...
x + y = 70
8.50x +12.50y = 10.56(70) . . . . . total cost of the mix
__
We like to use the variable to represent the high-cost contributor. Here, that is y, so we'll substitute for x:
x = 70-y
8.50(70 -y) +12.50y = 10.56(70)
__
595 +4y = 739.2 . . . . . . . . . . . . . . simplify
4y = 144.2 . . . . . . . . . . . subtract 595
y = 36.05 . . . . . . . divide by 4
x = 70 -36.05 = 33.95
About 36 pounds of Rift Valley coffee and 34 pounds of Gualtemala Antigua coffee must be mixed.
_____
<em>Additional comment</em>
By letting the variable in our equation 8.50(70 -y) +12.50y = 10.56(70) represent the high-cost coffee, we ensure that the simplified equation will have a positive coefficient for the variable. This means we don't have to mess with negative numbers, so eliminating a common source of math errors.
The problem requirement that we use x for the low-cost contributor meant we introduced an extra equation that would not have been needed.
Answer:
-3
Step-by-step explanation:
Remember the general equation for a line, y= mx+b. The slope is always the m value, and in this case your slope is -3
Let
T = theta
Use the Law of Cosines to get
c^2 = a^2+b^2 - 2ab*cos(T)
<span>7^2 = 10^2+8^2 - 2*10*8*cos(T)
</span><span>49 = 164 - 160*cos(T)
-160cos(T) = 49-164
</span><span>-160cos(T) = -115
</span>cos(T) = -115/(-160)
cos(T) = 23/32
cos(T) = 0.71875 which rounds to 0.72
The final answer is C) 0.72
