140 is the solution of the inequality
Step-by-step explanation:
The inequalities are used just like equations.
Given
Total amount to be raised = $950
Price of one ticket = $2.50
The inequality that represents the situation is:
2.50x≥950
Dividing both sides by 2.50
![\frac{2.50x}{2.50} \geq \frac{950}{2.50}\\x\geq 140](https://tex.z-dn.net/?f=%5Cfrac%7B2.50x%7D%7B2.50%7D%20%5Cgeq%20%5Cfrac%7B950%7D%7B2.50%7D%5C%5Cx%5Cgeq%20140)
140 is the solution of the inequality
Keywords: Inequality, cost
Learn more about inequalities at:
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Answer:
The standard equation of the parabola is:
![y=-\frac{3}{2}x^2+12x-18](https://tex.z-dn.net/?f=y%3D-%5Cfrac%7B3%7D%7B2%7Dx%5E2%2B12x-18)
Step-by-step explanation:
An x intercept of 2 means that the point (2, 0) is in the graph of the parabola.
We can also write the general expression for the parabola in vertex form, since we can use the information on the coordinates of the vertex: (4, 6) - recall that the axis of symmetry of the parabola goes through the parabola's vertex, so the x-value of the vertex must be x=4.
![y-y_{vertex}=a\,(x-x_{vertex})^2\\y-6=a\,(x-4)^2](https://tex.z-dn.net/?f=y-y_%7Bvertex%7D%3Da%5C%2C%28x-x_%7Bvertex%7D%29%5E2%5C%5Cy-6%3Da%5C%2C%28x-4%29%5E2)
Now we can find the value of the parameter "a" by using the extra information about the point (2, 0) at which the parabola intercepts the x-axis:
![y-6=a\,(x-4)^2\\0-6=a\,(2-4)^2\\-6=a\,4\\a=-\frac{6}{4} =-\frac{3}{2}](https://tex.z-dn.net/?f=y-6%3Da%5C%2C%28x-4%29%5E2%5C%5C0-6%3Da%5C%2C%282-4%29%5E2%5C%5C-6%3Da%5C%2C4%5C%5Ca%3D-%5Cfrac%7B6%7D%7B4%7D%20%3D-%5Cfrac%7B3%7D%7B2%7D)
Then the equation of the parabola becomes:
![y-6=-\frac{3}{2} \,(x-4)^2\\y-6=-\frac{3}{2} (x^2-8x+16)\\y-6=-\frac{3}{2}x^2+12x-24\\y=-\frac{3}{2}x^2+12x-18](https://tex.z-dn.net/?f=y-6%3D-%5Cfrac%7B3%7D%7B2%7D%20%5C%2C%28x-4%29%5E2%5C%5Cy-6%3D-%5Cfrac%7B3%7D%7B2%7D%20%28x%5E2-8x%2B16%29%5C%5Cy-6%3D-%5Cfrac%7B3%7D%7B2%7Dx%5E2%2B12x-24%5C%5Cy%3D-%5Cfrac%7B3%7D%7B2%7Dx%5E2%2B12x-18)
D
1/8 = 0.125
0.125*5=0.625
0.625+1=1 5/8
Answer:
They are NOT equivalent
Step-by-step explanation:
4x-x+5 and 8-3x-3
<u>simplify</u>
3x+5 and 5x-3