Remark
If the lines are parallel, there are no solutions to the system of equations. Start with the equation you know the most about.
x + 6y = 7 Subtract x from both sides
x - x + 6y = 7 - x Combine
6y = - x + 7 Switch and divide by 6
y = -x / 6 + 7/6
The general equation for a line is y = mx + b where m is the slope of the line.
m = - 1/6
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Now look at the second equation
10ay - 5x = 32 Add 5x to both sides
10ay = 5x + 32 Divide by 10a
y = (5/10a)x + 32/(10a)
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Now you must make
5/10a = - 1/6 Cross Multiply
5* 6 = - 10a * 1
30 = - 10a Divide by - 10
a = 30 / - 10
a = - 3
So these two equations will have no solution when a = - 3
Answer:
The anser is 2:5 or 2/5.
Step-by-step explanation:
Answer:
Graph A
Step-by-step explanation
The problem: y=2x^2+8x+3
1) You will need to determine the direction of the parabola, If a > 0 then the parabola opens upward, if a < 0 then the parabola opens downward.
2) If when doing this you get an imaginary solution, you would have no x intercepts. The first thing you need to do is find the x intercepts, you can do this by plugging in 0 for y, so this would give you 0=2x^2+8x+3. Once you have this you start by subtracting 3 from both sides, dividing 8 from both side, etc. (If you would like me to elaborate don't hesitate to ask!)
3) To find the graphs y intercept you plug in 0 for x, which gives you y=2(0)^2+8(0)+3, you do the same thing you did during the previous step for y. (Once again, I am willing to elaborate further if you need!)
4) You then need to find the vertex (h,k)
To find h: h= -b/2a
To find k: k = a(h)2 + b(h) + c
5) Once you've worked through this you can graph the point!
Hope this helped!
Answer: 40
Step-by-step explanation: 65/1.6= around 40
