Show that y = 11x + 5 is a tangent to the curve
y = 3x² + 5x + 8
1 answer:
Answer:
There is only 1 solution for x.
Step-by-step explanation:
Hi there!
![y = 11x + 5](https://tex.z-dn.net/?f=y%20%3D%2011x%20%2B%205)
![y = 3x^2 + 5x + 8](https://tex.z-dn.net/?f=y%20%3D%203x%5E2%20%2B%205x%20%2B%208)
This is a linear-quadratic system. If the line is tangent to the parabola, it means that it would only have 1 solution.
Set y equal:
![3x^2 + 5x + 8= 11x + 5](https://tex.z-dn.net/?f=3x%5E2%20%2B%205x%20%2B%208%3D%2011x%20%2B%205)
Move everything to the left side:
![3x^2 + 5x + 8-11x-5=0\\3x^2 -6x + 3=0](https://tex.z-dn.net/?f=3x%5E2%20%2B%205x%20%2B%208-11x-5%3D0%5C%5C3x%5E2%20-6x%20%2B%203%3D0)
Divide both sides by 3:
![x^2 -2x + 1=0](https://tex.z-dn.net/?f=x%5E2%20-2x%20%2B%201%3D0)
Factor:
![(x-1)^2=0](https://tex.z-dn.net/?f=%28x-1%29%5E2%3D0)
Solve for <em>x</em>:
![x-1=0\\x=1](https://tex.z-dn.net/?f=x-1%3D0%5C%5Cx%3D1)
Therefore, the only solution for x when y is set equal for both functions is 1. There is only 1 solution for x, so
is tangent to the curve
.
I hope this helps!
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Step-by-step explanation:
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Answer:
A
Step-by-step explanation:
To find the number of games they will win out of 162 using the ratio 6 to 8, you will create equivalent ratios and solve the proportion.
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8 162 Use cross products.
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