Answer:
the correct answer is 2,432
In a proportional relationship, x and y will increase at the same rate. In order to find the value of x when y=4, we first have to find the ratio of x:y. We can do this by creating a fraction. After we know the ratio, simply replace the y value with 4 and solve for x. Here's the math:
y=15 when x=3 given values
y/x = 15/3 = 5 ratio of y to x
y=5x equation representing the proportional relationship
4=5x replace y with 4
4/5=x divide both sides by 5 to isolate x
Answer: The value of x=4/5 when y=4.
Hope this helps!
The vertex of f
(
x
) is at x = −
8/
2
= −
4
Colfax:
Add the ratio numbers together:
5 + 4 = 9
Divide total students by that:
270 / 9 = 30
Multiply each ratio by 30:
Boys = 30 *5 = 150
Girls = 30 * 4 = 120
Do the same for Winthrop:
4 +5 = 9
180 /9 = 20
Boys = 20 * 4 = 80
Girls = 20 * 5 = 100
Total students = 270 + 180 = 450
Total Girls = 120 + 100 = 220
Fraction that are girls = 220 / 450 which reduces to 22/45
Answer:
Points -2 and -6 on the number line are the two solutions.
Step-by-step explanation:
Use the definition of absolute value as a starting point
![|x|=x\,\,\mbox{for}\,\,x\geq 0\\|x|=-x\,\,\mbox{for}\,\,x](https://tex.z-dn.net/?f=%7Cx%7C%3Dx%5C%2C%5C%2C%5Cmbox%7Bfor%7D%5C%2C%5C%2Cx%5Cgeq%200%5C%5C%7Cx%7C%3D-x%5C%2C%5C%2C%5Cmbox%7Bfor%7D%5C%2C%5C%2Cx%3C0)
To solve the equation, you need to treat the two cases as above:
![|x+4|=x+4=2\,\,\,\mbox{for}\,\,x+4\geq 0\implies x\geq -4\\x+4=2\implies x=-2](https://tex.z-dn.net/?f=%7Cx%2B4%7C%3Dx%2B4%3D2%5C%2C%5C%2C%5C%2C%5Cmbox%7Bfor%7D%5C%2C%5C%2Cx%2B4%5Cgeq%200%5Cimplies%20x%5Cgeq%20-4%5C%5Cx%2B4%3D2%5Cimplies%20x%3D-2)
The solution x=-2 is consistent with the condition x>=-4, so it is the first and valid solution. Now the second case of the absolute value:
![|x+4|=-(x+4)=2\,\,\,\mbox{for}\,\,x+4< 0\implies x](https://tex.z-dn.net/?f=%7Cx%2B4%7C%3D-%28x%2B4%29%3D2%5C%2C%5C%2C%5C%2C%5Cmbox%7Bfor%7D%5C%2C%5C%2Cx%2B4%3C%200%5Cimplies%20x%3C-4%5C%5C-%28x%2B4%29%3D-x-4%3D2%5Cimplies%20x%20%3D%20-6)
Again, the second solution -6 complies with the requirement that x<-4, so it is valid.