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:
12 sales
Step-by-step explanation:
Let x represent the number of sales each man had.
For Salesman A, he earns $65 per sale; this is 65x.
For Salesman B, he earns $40 per sale; this is 40x. We also add to this his weekly salary of $300; this gives us 40x+300.
Since their pay was equal, set the two expressions equal:
65x = 40x+300
Subtract 40x from each side:
65x-40x = 40x+300-40x
25x = 300
Divide both sides by 25:
25x/25 = 300/25
x = 12
$1500 divided by 12 months = $125 per month. 0.75% x 120 (10 years x 12 months in each) = 90%. $125 x 120 = $15,000 + ($125 x 90%= $11,250) = $26,250. $26,250 + $2500 = $28,750 overall in the account after 10 years
Answer:
4095
Step-by-step explanation:
This Is for the 4.07 K-12 Quiz! <3
