Answer:
Part 1) m∠EFG=94°
Part 2) m∠GFH=86°
Step-by-step explanation:
we know that
m∠EFG+m∠GFH=180° -----> by linear pair (given problem)
we have
m∠EFG=3n+22
m∠GFH=2n+38
substitute the values
(3n+22)°+(2n+38)°=180°
Solve for n
(5n+60)=180
5n=180-60
5n=120
n=24
<em>Find the measure of angle EFG</em>
m∠EFG=3n+22
substitute the value of n
m∠EFG=3(24)+22=94°
<em>Find the measure of angle GFH</em>
m∠GFH=2n+38
substitute the value of n
m∠GFH=2(24)+38=86°
4 of a 10 because there is 4 blue marbles and 6 yellow
It is 40.682414698, or about 40.7 feet of string.
Answer: Choice D
(a-e)/f
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Explanation:
Points D and B are at locations (e,f) and (a,0) respectively.
Find the slope of line DB to get
m = (y2-y1)/(x2-x1)
m = (0-f)/(a-e)
m = -f/(a-e)
This is the slope of line DB. We want the perpendicular slope to this line. So we'll flip the fraction to get -(a-e)/f and then flip the sign from negative to positive. That leads to the final answer (a-e)/f.
Another example would be an original slope of -2/5 has a perpendicular slope of 5/2. Notice how the two slopes -2/5 and 5/2 multiply to -1. This is true of any pair of perpendicular lines where neither line is vertical.
Answer:
<em>The baker bought 8 apples and 4 bananas</em>
Step-by-step explanation:
<u>System of Equations</u>
Let's call:
a = pounds of apples
b = pounds of bananas
The baker bought a total of 12 pounds of apples and bananas, thus:
a + b = 12 [1]
Apple cost $0.75 per pound and each pound of bananas cost $1.05 per pound. Thus the total cost is 0.75a + 1.05b. We know he spent a total of $10.20, thus
0.75a + 1.05b = 10.20 [2]
Solving [1] for a:
a = 12 - b [3]
Substituting in [2]:
0.75(12 - b) + 1.05b = 10.20
Operating
9 - 0.75b + 1.05b = 10.20
Simplifying:
0.30b = 10.20 - 9 = 1.20
Dividing by 0.30:
b = 1.20/0.30
b = 4
From [3]:
a = 12 - 4 = 8
a = 8
The baker bought 8 apples and 4 bananas
