Answer:
Quotient = x - 7
Step-by-step explanation:
We are dividing x^2 - 5x +8 by x + 2
x + 2√x^2 - 5x + 8
Starting with dividing by x
x - 7
x + 2√ x^2 - 5x + 8
Multiplying x by x + 2
x
x + 2√ x^2 - 5x + 8
-
x^2 + 2x
= -7x + 8
Step ii, pick -7 for division
-7x + 8
-
-7x - 14
= +8 -(-14)
= 8+14
= 22
The answer is
( x - 7) remainder 22
(x - 7) is the quointent
22 is the remainder
Answer: The slope of the line is 15 and y-intercept is 12.
Step-by-step explanation: We are given to find the slope and y-intercept of the straight line defined by the points (3, 57) and (5, 87).
We know that
the slope of a line passing through the points (3, 57) and (5, 87) is given by

Since the straight line passes through the point (3, 57), so its equation will be

So, the required equation of the straight line is 
Thus, the slope of the line is 15 and y-intercept is 12.
There are infinitely many irrational numbers between 8 and 8.1, if I'm not mistaken.
Answer:
x > 36 in
Step-by-step explanation:
Let x = the width of the picture frame.
Then x + 6 = the length of the frame.
The formula for the perimeter P of a rectangle is'
P = 2l + 2w.
So, the condition is
2l + 2w > 156
2(x + 6) + 2x > 156 Distribute the 2
2x + 12 + 2x > 156 Combine like terms
4x + 12 > 156 Subtract 12 from each side
4x > 144 Divide each side by 4
x > 36
The perimeter of the picture frame will be greater than 156 in if x > 36 in.