Answer:
The number of liters of 50% antifreeze solution is 50 and the number of liters of 90% antifreeze solution is 150
Step-by-step explanation:
Let
x ----> number of liters of 50% antifreeze solution
y ----> number of liters of 90% antifreeze solution
we know that
50%=50/100=0.50
90%=90/100=0.90
80%=80/100=0.80
x+y=200
x=200-y ------> equation A
0.50x+0.90y=0.8(200) -----> equation B
substitute equation A in equation B and solve for y
0.50(200-y)+0.90y=160
100-0.50y+0.90y=160
0.40y=160-100
0.40y=60
y=150 liters
Find the value of x
x=200-y
x=200-150=50 liters
therefore
The number of liters of 50% antifreeze solution is 50
The number of liters of 90% antifreeze solution is 150
Solving <span>8x-5y=10 for y helps us to identify the y-intercept:
-5y = -8x + 10. Dividing both sides by -5, we get (8/5)x -2. Therefore, y = (8/5)x - 2; the y-intercept is (0,-2).
The equation </span><span>-6x-7y=-6 can be solved for its slope in the same manner.
7y = -6x + 6; then y = (-6/7)x + 6/7. Its slope is -7/6. A line perpendicular to this line has slope equal to the negative reciprocal of -7/6, which is 6/7.
So, using the slope-intercept form, y = mx + b becomes y = (6/7)x -2.</span>
Answer:
80 pages
Step-by-step explanation:
x = number of pages of articles
x = 110 - (23 + 14/2)
x = 110 - (23 + 7)
x = 110 - 30
x = 80
The angles inside a triangle add up to 180°
The 3rd angle is supplementary to (6x+1)°
Supplementary means they make a straight line (i.e 180°)
1st angle = 79°
2nd angle = (2x+10)°
3rd angle = 180° - (6x+1)°
180 = 79 + (2x+10) + 180 - (6x+1)
180 = 79 + 2x + 10 + 180 - 6x - 1
combine like terms
180 - 180 - 79 - 10 + 1 = 2x - 6x
-88 = -4x
-88/-4 = x
22 = x
