8x-2(x+1)=2(3x-1)A.0
B.2
C.no solution <-- that's what I think it is.
D.identity.

Can someone check my answer

Answer:

Therefore, the cost of purchasing 5 lip glosses, as represented by the function C(5), is 41.

Step-by-step explanation:

To find the cost of purchasing 5 lip glosses, we need to use the given function C(1) = 31 + 2, which represents the cost of ordering one lip gloss including the flat rate shipping charge. To find the cost of purchasing 5 lip glosses, we can substitute 5 for the variable in the function: C(5) = 31 + 2 * 5 C(5) = 31 + 10 C(5) = 41

Final answer:

The cost of purchasing 5 lip glosses represented in the function C(1)=31+2 is evaluated as C(5)=31+2*5, which equals 41 units.

Explanation:

This question involves the mathematical concept of functions, specifically, simple linear functions. In this example, we have the function C(1)=31+2, which informs us that the cost to order one lip gloss, denoted as 'L', is '31 plus twice the number of lip glosses ordered'

To answer the question 'What represents the cost of purchasing 5 lip glosses?', we substitute the number of lip glosses we want to buy (5) into our function. So instead of evaluating C(1), we evaluate C(5)=31+2*5, following the same structure of '31 plus twice the number of lip glosses ordered'. The solution to this would be C(5)=41, meaning it would cost 41 units (the currency isn't stated) for 5 lip glosses.

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Answer: 12y

Step-by-step explanation:

Solving the system we can see that the sum of the y-values of the two solutions is 139.

How to get the sum of y₁ and y₂?

Let's solve the system of equations.

y = 10 + 16x − x²

y = 3x + 50

We can write this as a single quadratic equation:

10 + 16x - x² = 3x + 50

10 + 16x - x² - 3x - 50 = 0

-x² + 13x - 40 = 0

Using the quadratic formula we will get the two solutions for x:

So the two solutions are:

x = (-13 + 3)/-2 = 5

x = (-13 - 3)/-2 = 8

Evaluating the linear equation in these two values we will get y1 and y2.

if x = 5

y₁ = 3*5 + 50 = 65

if x= 8

y₂ = 3*8 + 50 = 74

The sum is:

65 + 74  =139

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Final answer:

The distinct solutions to the system of equations are (5, 65) and (8, 74), and the sum of the y-values is 139.

Explanation:

To find the sum of y-values of the distinct solutions to this system of equations, first, you need to set the two equations equal to each other to find the x-values of the solutions:

10 + 16x − x^2 = 3x + 50.

Then, solve the resulting equation for x:

x^2 - 13x + 40 = 0.

This is a quadratic equation, and it can be solved either by factoring or using the quadratic formula. The solutions for x result in:

x = 5 and x = 8.

These are the two distinct x-values for the intersections of the graphs of the two equations. To find the corresponding y-values, plug these x-values into either of the original equations. We'll use the simpler equation, y = 3x + 50:

For x = 5, y = 65 and for x = 8, y = 74.

Therefore, the distinct solutions to the system of equations are (5, 65) and (8, 74). Finally, the sum of y1 and y2 is 65 + 74 = 139.

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