Answer:
12 and 13
Step-by-step explanation:
(a)
To evaluate f(g(2)), evaluate g(2) then use the value obtained to evaluate f(x)
g(2) = 2(2) - 1 = 4 - 1 = 3, then
f(3) = 3² + 3 = 9 + 3 = 12
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(b)
To evaluate g(f(2)), evaluate f(2) the use the value obtained to evaluate g(x)
f(2) = 2² + 3 = 4 + 3 = 7, then
g(7) = 2(7) - 1 = 14 - 1 = 13
To plot these points on the number line, you should label the long lines on the number line as such starting from the left (-5-already there, -4,-3,-2,-1,0,1,2,3,4,5-already there).
Now take each number and convert the improper fraction into a mixed number. 9/2 = 4 1/2 and -7/2 = -3 1/2.
4 1/2 would plotted on the line exactly in between the 4 and 5.
-3 1/2 would be plotted on the line exactly halfway between -3 and -4.
You will draw a dot to show each of these positions on a number line.
Since the scale factor is smaller than one (the original), the resulting image is smaller than the original.
Hope this helped, and feel free to ask more questions if needed(:
Answer:
The number of boys who play tennis is 36.
Step-by-step explanation:
Let the number of boys who play tennis is x.
number of boys who play cricket = y
x = 3 y..... (1)
12 boys plays both cricket and tennis.
According to the question,
x - 12 = y + 1 2
3 y - 12 = y + 12
2 y = 24
y = 12
So, the number of boys who plays tennis is x = 3 x 12 = 36.
The complete proof statement and reason for the required proof is as follows:
Statement Reason
m<PNO = 45 Given
MO Given
<MNP and <PNO are a
linear pair of angles Definition of linear pairs of angles
<MNP and <PNO are
supplementary angles Linear Pair Postulate
m<MNP + m<PNO = 180° Definition of supplementary angles
m<MNP + 45° = 180° Substitution property of equality
m<MNP = 135° Subtraction property of equality
