Answer:
Alan buys 12.05 ounces of sour patch kids candy in all.
Step-by-step explanation:
We are given that Alan buys 5.3 ounces of sour patch kids candy. After sharing with his friends he returns to buy an additional 6.75 ounces.
And we have to find the total ounces he buys in all.
As we know that for finding the total quantity or amount, we will use addition for calculating it.
Firstly, Alan buys = 5.3 ounces of sour patch kids candy
Additional ounces of sour patch kids candy Alan buys = 6.75
So, the total ounces of sour patch kids candy he buys in all = 5.3 + 6.75
= 12.05 ounces
Hence, he buys 12.05 ounces in all.
The two triangles we can see in the diagram are similar, which means that their measurements are proportional. Line MN on the larger triangle MNP is 71.5ft long, and its corresponding line, MA, on the smaller triangle is 71.5-22= 49.5ft long. This means that the scale factor from the bigger to the smaller triangle is 71.5/49.5=13/9.
If line MP on the bigger rectangle is 97.5ft long, then its corresponding line, MB, must be 97.5÷13/9=67.5 ft long.
Therefore, x=67.5 ft
Answer: A and B
Explanation: If you draw the graph out it crosses the points (1,2) and (-1,-2) and those are points A and B
Answer:
C
Step-by-step explanation:
Firstly, we know that the function must be negative due to its shape. This means that the answer cannot be B
Next we can use the equation
that is used in order to find the vertex of the parabola.
A)
![f(x)=-x^2+6x+7\\a=-1,b=6,c=7\\\\x=\frac{-6}{-2} \\x=3](https://tex.z-dn.net/?f=f%28x%29%3D-x%5E2%2B6x%2B7%5C%5Ca%3D-1%2Cb%3D6%2Cc%3D7%5C%5C%5C%5Cx%3D%5Cfrac%7B-6%7D%7B-2%7D%20%5C%5Cx%3D3)
As the vertex is at x=3 on the graph, this one could be a contender.
C)
![f(x)=-x^2+6x-7\\a=-1,b=6, c=-7\\\\x=\frac{-6}{-2} \\\\x=3](https://tex.z-dn.net/?f=f%28x%29%3D-x%5E2%2B6x-7%5C%5Ca%3D-1%2Cb%3D6%2C%20c%3D-7%5C%5C%5C%5Cx%3D%5Cfrac%7B-6%7D%7B-2%7D%20%5C%5C%5C%5Cx%3D3)
This also could be the equation
D)
![f(x)=-x^2-6x-7\\\\a=-1, b=-6, c=-7\\\\x=\frac{6}{-2} \\\\x=-3](https://tex.z-dn.net/?f=f%28x%29%3D-x%5E2-6x-7%5C%5C%5C%5Ca%3D-1%2C%20b%3D-6%2C%20c%3D-7%5C%5C%5C%5Cx%3D%5Cfrac%7B6%7D%7B-2%7D%20%5C%5C%5C%5Cx%3D-3)
This rules option D out.
For this last step, we can look at where the zeroes would be for each equation. (These values are irrational, so we cannot look at specific number)
A)
![f(x)=-(x^2-6x-7)](https://tex.z-dn.net/?f=f%28x%29%3D-%28x%5E2-6x-7%29)
As this equation has a negative value for c, this means that one zero must be positive and the other must be negative.
This means that option A can be ruled out
C)
![f(x)=-(x^2-6x+7)](https://tex.z-dn.net/?f=f%28x%29%3D-%28x%5E2-6x%2B7%29)
As this equation has a positive value for c, this means that both of the zeroes must be positive. This means that it is the only one that fits all of the criteria.