They are intersecting lines if they are not parallel so the other option is that they are intersecting.<span />
Answer:
x=-3.5 or -7/2 (same thing)
y=21/5
Step-by-step explanation:
x intercept is when y=0
y intercept is when x=0
so
x intercept is
-6x=21
x=21/-6
x=-3.5
y intercept is
5y=21
y=21/5
Keeping in mind that for a cost C(x) and profit P(x) and revenue R(x), the marginal cost, marginal profit and marginal revenue are respectively dC/dx, dP/dx and dR/dx, then
![\bf P(x)=0.03x^2-3x+3x^{0.8}-4400 \\\\\\ \stackrel{marginal~profit}{\cfrac{dP}{dx}}=0.06x-3+2.4x^{-0.2} \\\\\\ \cfrac{dP}{dx}=0.06x-3+2.4\cdot \cfrac{1}{x^{0.2}}\implies \cfrac{dP}{dx}=0.06x-3+2.4\cdot \cfrac{1}{x^{\frac{1}{5}}} \\\\\\ \cfrac{dP}{dx}=0.06x-3+\cfrac{2.4}{\sqrt[5]{x}}](https://tex.z-dn.net/?f=%5Cbf%20P%28x%29%3D0.03x%5E2-3x%2B3x%5E%7B0.8%7D-4400%0A%5C%5C%5C%5C%5C%5C%0A%5Cstackrel%7Bmarginal~profit%7D%7B%5Ccfrac%7BdP%7D%7Bdx%7D%7D%3D0.06x-3%2B2.4x%5E%7B-0.2%7D%0A%5C%5C%5C%5C%5C%5C%0A%5Ccfrac%7BdP%7D%7Bdx%7D%3D0.06x-3%2B2.4%5Ccdot%20%5Ccfrac%7B1%7D%7Bx%5E%7B0.2%7D%7D%5Cimplies%20%5Ccfrac%7BdP%7D%7Bdx%7D%3D0.06x-3%2B2.4%5Ccdot%20%5Ccfrac%7B1%7D%7Bx%5E%7B%5Cfrac%7B1%7D%7B5%7D%7D%7D%0A%5C%5C%5C%5C%5C%5C%0A%5Ccfrac%7BdP%7D%7Bdx%7D%3D0.06x-3%2B%5Ccfrac%7B2.4%7D%7B%5Csqrt%5B5%5D%7Bx%7D%7D)
![\bf a)\qquad \cfrac{dP}{dx}=0.06(200)-3+ \cfrac{2.4}{\sqrt[5]{200}} \\\\\\ b)\qquad \cfrac{dP}{dx}=0.06(2000)-3+\cfrac{2.4}{\sqrt[5]{2000}} \\\\\\ c)\qquad \cfrac{dP}{dx}=0.06(5000)-3+\cfrac{2.4}{\sqrt[5]{5000}} \\\\\\ d)\qquad \cfrac{dP}{dx}=0.06(10000)-3+\cfrac{2.4}{\sqrt[5]{10000}}](https://tex.z-dn.net/?f=%5Cbf%20a%29%5Cqquad%20%0A%5Ccfrac%7BdP%7D%7Bdx%7D%3D0.06%28200%29-3%2B%20%5Ccfrac%7B2.4%7D%7B%5Csqrt%5B5%5D%7B200%7D%7D%0A%5C%5C%5C%5C%5C%5C%0Ab%29%5Cqquad%20%5Ccfrac%7BdP%7D%7Bdx%7D%3D0.06%282000%29-3%2B%5Ccfrac%7B2.4%7D%7B%5Csqrt%5B5%5D%7B2000%7D%7D%0A%5C%5C%5C%5C%5C%5C%0Ac%29%5Cqquad%20%5Ccfrac%7BdP%7D%7Bdx%7D%3D0.06%285000%29-3%2B%5Ccfrac%7B2.4%7D%7B%5Csqrt%5B5%5D%7B5000%7D%7D%0A%5C%5C%5C%5C%5C%5C%0Ad%29%5Cqquad%20%5Ccfrac%7BdP%7D%7Bdx%7D%3D0.06%2810000%29-3%2B%5Ccfrac%7B2.4%7D%7B%5Csqrt%5B5%5D%7B10000%7D%7D)
Answer: The cost of each pound of jellybean is $2.5
The cost for each pound of trail mix is $1.5
Step-by-step explanation:
Let the cost for each pound of jellybeans be x.
Let the cost of each pound of trail mix be y.
Based on the information given, we can form an equation which will be:
For 2 pounds of jellybeans and 12 pounds of trail mix, the total cost is $23. This will be:
2x + 12y = 23 ...... i
For 5 pounds of jellybeans and 3 pounds of trail mix, the total cost is $17. This will be:
5x + 3y = 17...... ii
2x + 12y = 23 ...... i
5x + 3y = 17...... ii
Multiply equation i by 5
Multiply equation ii by 2
10x + 60y = 115 ...... iii
10x + 6y = 34 ..... iv
Subtract iv from iii
54y = 81
y = 81/54
y = 1.5
The cost for each pound of trail mix is $1.5
From equation i
2x + 12y = 23
2x + 12(1.5) = 23
2x + 18 = 23
2x = 23 - 18
2x = 5
x = 5/2 = 2.5
The cost of each pound of jellybean is $2.5
