The answer to this is 244
Answer:
72
Step-by-step explanation:
Find the Rule :
2-1=1
3-1.5=1.5= constant
Verification :
1x1.5=1.5
2x1.5=3
9x1.5=13.5
48x1.5=72
What is the rule for input-output table?
An input-output table, like the one shown below, can be used to represent a function. Each pair of numbers in the table is related by the same function rule. That rule is: multiply each input number (x-value) by 1.5 to find each output number (y-value)
Dividing by a fraction is equivalent to multiply by its reciprocal, then:
Now, we need to express the quadratic polynomials using their roots, as follows:
where y1 and y2 are the roots.
Applying the quadratic formula to the first polynomial:
![\begin{gathered} y_{1,2}=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ y_{1,2}=\frac{7\pm\sqrt[]{(-7)^2-4\cdot3\cdot(-6)}}{2\cdot3} \\ y_{1,2}=\frac{7\pm\sqrt[]{121}}{6} \\ y_1=\frac{7+11}{6}=3 \\ y_2=\frac{7-11}{6}=-\frac{2}{3} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20y_%7B1%2C2%7D%3D%5Cfrac%7B-b%5Cpm%5Csqrt%5B%5D%7Bb%5E2-4ac%7D%7D%7B2a%7D%20%5C%5C%20y_%7B1%2C2%7D%3D%5Cfrac%7B7%5Cpm%5Csqrt%5B%5D%7B%28-7%29%5E2-4%5Ccdot3%5Ccdot%28-6%29%7D%7D%7B2%5Ccdot3%7D%20%5C%5C%20y_%7B1%2C2%7D%3D%5Cfrac%7B7%5Cpm%5Csqrt%5B%5D%7B121%7D%7D%7B6%7D%20%5C%5C%20y_1%3D%5Cfrac%7B7%2B11%7D%7B6%7D%3D3%20%5C%5C%20y_2%3D%5Cfrac%7B7-11%7D%7B6%7D%3D-%5Cfrac%7B2%7D%7B3%7D%20%5Cend%7Bgathered%7D)
Applying the quadratic formula to the second polynomial:
![\begin{gathered} y_{1,2}=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ y_{1,2}=\frac{-1\pm\sqrt[]{1^2-4\cdot2\cdot(-3)}}{2\cdot2} \\ y_{1,2}=\frac{-1\pm\sqrt[]{25}}{4} \\ y_1=\frac{-1+5}{4}=1 \\ y_2=\frac{-1-5}{4}=-\frac{3}{2} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20y_%7B1%2C2%7D%3D%5Cfrac%7B-b%5Cpm%5Csqrt%5B%5D%7Bb%5E2-4ac%7D%7D%7B2a%7D%20%5C%5C%20y_%7B1%2C2%7D%3D%5Cfrac%7B-1%5Cpm%5Csqrt%5B%5D%7B1%5E2-4%5Ccdot2%5Ccdot%28-3%29%7D%7D%7B2%5Ccdot2%7D%20%5C%5C%20y_%7B1%2C2%7D%3D%5Cfrac%7B-1%5Cpm%5Csqrt%5B%5D%7B25%7D%7D%7B4%7D%20%5C%5C%20y_1%3D%5Cfrac%7B-1%2B5%7D%7B4%7D%3D1%20%5C%5C%20y_2%3D%5Cfrac%7B-1-5%7D%7B4%7D%3D-%5Cfrac%7B3%7D%7B2%7D%20%5Cend%7Bgathered%7D)
Applying the quadratic formula to the third polynomial:
![\begin{gathered} y_{1,2}=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ y_{1,2}=\frac{3\pm\sqrt[]{(-3)^2-4\cdot2\cdot(-9)}}{2\cdot2} \\ y_{1,2}=\frac{3\pm\sqrt[]{81}}{4} \\ y_1=\frac{3+9}{4}=3 \\ y_2=\frac{3-9}{4}=-\frac{3}{2} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20y_%7B1%2C2%7D%3D%5Cfrac%7B-b%5Cpm%5Csqrt%5B%5D%7Bb%5E2-4ac%7D%7D%7B2a%7D%20%5C%5C%20y_%7B1%2C2%7D%3D%5Cfrac%7B3%5Cpm%5Csqrt%5B%5D%7B%28-3%29%5E2-4%5Ccdot2%5Ccdot%28-9%29%7D%7D%7B2%5Ccdot2%7D%20%5C%5C%20y_%7B1%2C2%7D%3D%5Cfrac%7B3%5Cpm%5Csqrt%5B%5D%7B81%7D%7D%7B4%7D%20%5C%5C%20y_1%3D%5Cfrac%7B3%2B9%7D%7B4%7D%3D3%20%5C%5C%20y_2%3D%5Cfrac%7B3-9%7D%7B4%7D%3D-%5Cfrac%7B3%7D%7B2%7D%20%5Cend%7Bgathered%7D)
Applying the quadratic formula to the fourth polynomial:
![\begin{gathered} y_{1,2}=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ y_{1,2}=\frac{-1\pm\sqrt[]{1^2-4\cdot1\cdot(-2)}}{2\cdot1} \\ y_{1,2}=\frac{-1\pm\sqrt[]{9}}{2} \\ y_1=\frac{-1+3}{2}=1 \\ y_2=\frac{-1-3}{2}=-2 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20y_%7B1%2C2%7D%3D%5Cfrac%7B-b%5Cpm%5Csqrt%5B%5D%7Bb%5E2-4ac%7D%7D%7B2a%7D%20%5C%5C%20y_%7B1%2C2%7D%3D%5Cfrac%7B-1%5Cpm%5Csqrt%5B%5D%7B1%5E2-4%5Ccdot1%5Ccdot%28-2%29%7D%7D%7B2%5Ccdot1%7D%20%5C%5C%20y_%7B1%2C2%7D%3D%5Cfrac%7B-1%5Cpm%5Csqrt%5B%5D%7B9%7D%7D%7B2%7D%20%5C%5C%20y_1%3D%5Cfrac%7B-1%2B3%7D%7B2%7D%3D1%20%5C%5C%20y_2%3D%5Cfrac%7B-1-3%7D%7B2%7D%3D-2%20%5Cend%7Bgathered%7D)
Substituting into the rational expression and simplifying:
Answer:
-10w -20
Step-by-step explanation:
5(-2w-4)
Distribute the 5
5*-2w -5*4
-10w -20
V=(pi)r 2 h. ( volume is equal to pi times radius squared times height). V= pi 2^2 x8
Pi times 4times8= pi times 32. Put in a calculator pi times 32 and you get 100.5 cubic inches ( I haven’t done this in awhile but I think this is correct)
