Answer:
x = 3 ± 2
Step-by-step explanation:
given
x² - 6x + 1 = 0 ( subtract 1 from both sides )
x² - 6x = - 1
To complete the square
add (half the coefficient of the x- term)² to both sides
x² - 6x + (- 3)² = - 1 + (- 3)²
x² - 6x + 9 = - 1 + 9
(x - 3)² = 8 ( take the square root of both sides )
x - 3 = ± 
= ± 2 ( add 3 to both sides )
x = 3 ± 2
Answer:
The correct anser is option
B. 2x + 2 = 18
Step-by-step explanation:
Let the number of hot dogs eaten by the runner up be represented by x
If Dave ate 2 more than twice x, this means that the number eaten by him = 2x + 2
Since the total number of hot dogs eaten by Dave is 18
Therefore, the equation will be
2x + 2 = 18
So the number of hot dogs eaten by the runner-up is determined by solving for x
2x= 18-2
2× = 16
x = 16/2
x = 8
The runner up are 8
While Dave are
2×8 + 2 = 18.
Answer:
Step-by-step explanation:
pyramid has a height of 5 inches and a volume of 60 cubic inches. Select all figures that could be the base for this pyramid.
A:
a square with side length 6 inches
B:
a 3 inch by 4 inch rectangle
C:
a 4 inch by 9 inch rectangle
D:
a circle with radius 4 inches
E:
a right triangle with one side 5 inches and the hypotenuse 13 inches
F:
a hexagon with an area of 36 square inches
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 solution to this system is (4, 1/6).
Step-by-step explanation:
Please separate these two equations for clarity. I like to write them in column format:
2.5y + 3x = 27
5x – 2.5y = 5
---------------------
8x = 32, and x = 4.
Subbing 4 for x in the second equation yields 5(4) - 2.5y = 5.
Then 20 - 2.5y = 5, or 15 = 2.5y. Solving for y, we get y = 1/6.
The solution to this system is thus (4, 1/6).
