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Blizzard [7]
3 years ago
9

Prove that there are no solutions in integers x and y to the equation 2x^2 + 5y^2 = 14

Mathematics
1 answer:
iren [92.7K]3 years ago
5 0
Solve the equation for y using the formula for slope: y + mx + b

2x^2 + 5y^2 = 14
5y^2 = -2x^2 + 14
y^2 = -2/5x^2 + 14/5
y = the sq root of -2x^2/5 + 14/5

There is no integer solution to the square root of a negative number.
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2 years ago
What is the solution to the system of equations? Use the substitution method.
BabaBlast [244]
The answer is:
4x+2y=11}  4x+2y=11} x=2-2y
x-2=-2y    }  x+2y=2    } x=2-2(-3/6)
                                      x=2-(-6/6)
4(2-2y)+2y=11              x=2-(-1)
8-8y+2y=11                   x=3
8-6y=11
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4 0
2 years ago
Given f ( x ) = 1 x + 10 , find the average rate of change of f ( x ) on the interval [ 8 , 8 + h ] . Your answer will be an exp
son4ous [18]

Answer: 1

Step-by-step explanation:

f(8+h)=8+h+10=18+h\\\\f(8)=8+10=18

So, the average rate of change is:

\frac{(18+h)-18}{(8+h)-8}=\frac{h}{h}=\boxed{1}

The question is wrong, the expression will not be in terms of h since it is a linear function.

6 0
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kondor19780726 [428]

Answer:

2 2/3

Step-by-step explanation:

8 0
3 years ago
A plot of land is valued at $18,000.Land tax is charged at the rate of 0.70 per $100. What is the total amount of tax paid for t
Vladimir [108]

Answer:

<em>The total amount of tax paid for the land was $126</em>

Step-by-step explanation:

<u>Proportions</u>

The land tax charged is 0.7 per each $100 of the land value. For easy calculations, we find the ratio or proportion to be applied to the value of the land as:

0.7 / 100 =0.007

This factor can be used to obtain the tax charged for a given value of the land.

The plot of land of the question is valued at $18,000.

The tax charged is, then:

0.007*18,000 = 126

The total amount of tax paid for the land was $126

8 0
3 years ago
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