Answer: 20 hours
Step-by-step explanation:
Since, One watch is slow and loses two minutes every hour
⇒ 1 hour of slow watch = 62 minutes
And, the other one is fast and gains one minute every hour.
⇒ 1 hour of fast watch = 59 minutes,
Hence, in 1 hour, the difference between slow and fast watch in 1 hour = 62 - 59 = 3 minutes.
⇒ The between slow and fast watch in 20 hours = 20 × 3 = 60 minutes or 1 hour.
Hence, after 20 hours the difference between the watches will be 1 hours.
(2, 36) → x = 2, y = 36
Substitute the value of x and y to the equations of the functions:
A. y = 2x^2
36 = 2(2)^2 → 36 = 8 FALSE
B. y = (3x)^2
36 = (3 · 2)^2 → 36 = 6^2 → 36 = 36 CORRECT
C. y = 7x^2 + 2
36 = 7(2)^2 + 2 → 36 = 7 · 4 + 2 → 36 = 30 FALSE
D. y = (x + 4)^2
36 = (2 + 4)^2 → 36 = 6^2 → 36 = 36 CORRECT
Answer: B. y = (3x)^2 and D. (x + 4)^2
Answer:
x = -2 or -9
Step-by-step explanation:
You want the values of x such that the line defined by the two points (2x+3, x+2) and (0, 2) is perpendicular to the line defined by the two points (x+2, -3-3x) and (8, -1).
<h3>Slope</h3>
The slope of a line is given by the slope formula:
m = (y2 -y1)/(x2 -x1)
Using the formula, the slopes of the two lines are ...
m1 = (2 -(x+2))/(0 -(2x+3)) = (-x)/(-2x-3) = x/(2x +3)
and
m2 = (-1 -(-3-3x))/(8 -(x+2)) = (2+3x)/(6 -x)
<h3>Perpendicular lines</h3>
The slopes of perpendicular lines have product of -1:
![\dfrac{x}{2x+3}\cdot\dfrac{2+3x}{6-x}=-1\\\\x(3x+2)=(2x+3)(x-6)\qquad\text{multiply by $(2x+3)(6-x)$}\\\\3x^2+2x=2x^2-9x-18\qquad\text{eliminate parentheses}\\\\x^2+11x+18=0\qquad\text{put in standard form}\\\\(x+2)(x+9)=0\qquad\text{factor}](https://tex.z-dn.net/?f=%5Cdfrac%7Bx%7D%7B2x%2B3%7D%5Ccdot%5Cdfrac%7B2%2B3x%7D%7B6-x%7D%3D-1%5C%5C%5C%5Cx%283x%2B2%29%3D%282x%2B3%29%28x-6%29%5Cqquad%5Ctext%7Bmultiply%20by%20%24%282x%2B3%29%286-x%29%24%7D%5C%5C%5C%5C3x%5E2%2B2x%3D2x%5E2-9x-18%5Cqquad%5Ctext%7Beliminate%20parentheses%7D%5C%5C%5C%5Cx%5E2%2B11x%2B18%3D0%5Cqquad%5Ctext%7Bput%20in%20standard%20form%7D%5C%5C%5C%5C%28x%2B2%29%28x%2B9%29%3D0%5Cqquad%5Ctext%7Bfactor%7D)
<h3>Solutions</h3>
The values of x that satisfy this equation are x = -2 and x = -9. The attached graphs show the lines for each of these cases.
Answer:
the answer is 6x^2
Step-by-step explanation:
goodluck
Answer:
The C is right
Step-by-step explanation:
5x – y = 8 ( multiple both sides by 4)
20 x – 4y = 24
we have
20x –4 y = 32
20 x – 4y = 24
----------------------------------( sustract side by side)
0 = 32-24
or 0 = 8
Impossible
There is so solution.
The C is right.