Please help I would be very greatful. On a coordinate plane, a solid straight line has a positive slope and goes through (0, 0.2
) and (3, 2.2). Everything to the right of the line is shaded. Which linear inequality is represented by the graph? y > Two-thirdsx – One-fifth y ≥ Three-halvesx + One-fifth y ≤ Two-thirdsx + One-fifth y < Three-halvesx – One-fifth
1 answer:
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Answer:
x ∈ [-2, 7]
Step-by-step explanation:
The given equation ...
x^2 -5x -4 ≤ 10
can be rewritten as ...
x^2 -5x -14 ≤ 0
and factored as ...
(x +2)(x -7) ≤ 0
Clearly, the "or equal to" condition will be met when x=-2 and x=7. For values of x between these numbers, one factor is negative and the other is positive. Hence the product will be negative. So, numbers in that interval are the solution set.
x ∈ [-2, 7]
<h3><u>Explanation</u></h3>
- Given the system of equations.
- Solve the system of equations by eliminating either x-term or y-term. We will eliminate the y-term as it is faster to solve the equation.
To eliminate the y-term, we have to multiply the negative in either the first or second equation so we can get rid of the y-term. I will multiply negative in the second equation.
There as we can get rid of the y-term by adding both equations.
Hence, the value of x is 3. But we are not finished yet because we need to find the value of y as well. Therefore, we substitute the value of x in any given equations. I will substitute the value of x in the second equation.
Hence, the value of y is 4. Therefore, we can say that when x = 3, y = 4.
- Answer Check by substituting both x and y values in both equations.
<u>First</u><u> </u><u>Equation</u>
<u>Second</u><u> </u><u>Equation</u>
Hence, both equations are true for x = 3 and y = 4. Therefore, the solution is (3,4)
<h3><u>Answer</u></h3>