Part A: Explain why the x-coordinates of the points where the graphs of the equations y = 4−x and y = 2x + 3 intersect are the s
olutions of the equation 4−x = 2x + 3. (4 points) Part B: Make tables to find the solution to 4−x = 2x + 3. Take the integer values of x between −3 and 3. (4 points) Part C: How can you solve the equation 4−x = 2x + 3 graphically? (2 points)
1 answer:
Try this explanation:
A: The property of intersection point is: on the graphs it belongs to the first line and to the second line, in another word, it belongs to the <u>both</u> lines. 'To the both lines; means, for the both equations, this value of 'x' converts the left side and the right side to the same value (one value 'x' ⇒ one value on the left part and the same value on the right part of the equation 4-x=2x+3).
B: see the attachment, based on 4 steps.
C: see the attached graph. The intersection point is marked with green colour.
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Answer:
a) 504
b) 56
c) 0.111
Step-by-step explanation:
Data provided in the question:
There are nine golf balls numbered from 1 to 9 in a bag
Three balls are randomly selected without replacement
a) 3-digit numbers that can be formed
=
n = 9
r = 3
= ⁹P₃
=
= 9 × 8 × 7
= 504
b) 3-digit numbers start with the digit 1
= _ _ _
in the above 3 blanks first digit is fixed i.e 1
we and we have 8 choices left for the last 2 digits
Thus,
n = 8
r = 2
Therefore,
= 1 × ⁸P₂
= 1 ×
= 1 × 8 × 7
= 56
c) Probability that the 3-digit number formed is less than 200
Now,
The number of 3-digit number formed is less than 200 will be the 3-digit numbers start with the digit 1 i.e part b)
and total 3-digit numbers that can be formed is part a)
therefore,
Probability that the 3-digit number formed is less than 200
= 56 ÷ 504
= 0.111