Answer:
(x, y) = (-2, 3)
Step-by-step explanation:
In this form, it is easy to determine the x- and y-intercepts of each equation. That makes it easy to graph the first one, but not so easy to graph the second one on the given form.
The x-intercept is found by solving for x when y=0. In the two equations, the x-intercepts are ...
x = 4
x = -8 . . . . . . not shown on the given grid
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The y-intercepts are found by solving for y when x=0. In the two equations, the y-intercepts are ...
y = 4/2 = 2
y = -8/-2 = 4
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For the second equation, you can solve for y to put it in slope-intercept form.
x -2y = -8
x +8 = 2y . . . . . add 2y+8
y = 1/2x +4 . . . . . . . slope = 1/2, y-intercept = 4 (which we already knew)
This means the graph of the second equation will have a rise of 1 for each run of 2 units to the right. Working to the left from the y-intercept, we find another point to be (-2, 3), a point 2 left and 1 down from the y-intercept. This point is also on the line produced by the first equation, so (-2, 3) is the solution to the system.
Answer:
12 L of the 20% solution should be used with 18 L of the 70% alcohol solution
Step-by-step explanation:
assuming that the concentration given is in terms of mass/volume , then doing an mass balance
C₁*V₁ + C₂*V₂ =C₃*V₃
where C= concentration , V= volume , 1,2,3 denotes first , second and final solution respectively.
and since we are mixing the same substance, the total volume V₃ will be the sum of the solutions mixed
V₁ + V₂ = V₃ → V₂=V₃-V₁
thus
C₁*V₁ + C₂*(V₃-V₁) =C₃*V₃
(C₁-C₂)*V₁ + C₂*V₃ = C₃*V₃
(C₁-C₂)*V₁ = (C₃- C₂) *V₃
V₁ = V₃ * (C₃- C₂)/(C₁-C₂)
replacing values
V₁ = V₃ * (C₃- C₂)/(C₁-C₂) = 30 L * (50%-70%)/(20%- 70%) = 12 L
then
V₂=V₃-V₁=30 L - 12 L = 18 L
therefore 12 L of the 20% solution should be used with 18 L of the 70% alcohol solution
Answer:
239.556
Step-by-step explanation:
Difference of ratio=9-5=4
Sum of ratio=9+5=14
we know that Eric got $56 more
which means
4/14=56
1/14=56/4
1/14=14
1=14*14
=196
now we need to find
9/14=(196*14)/9
= 239.556
Answer:
Part A: Carie is not correct
Part B: D(2 ,1)
Step-by-step explanation:
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