9514 1404 393
Answer:
4) (4, 0)
Step-by-step explanation:
I find it useful to graph the inequalities and the points.
The point on the dashed line is not in the solution set. The only point in the doubly-shaded area is (4, 0), choice (4).
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Another method of choosing the points is to try them in the inequalities. I find it easier to do the math if the inequalities are written in standard form:
2y < x +8 . . . . . multiply the first by 2
x -2y > -8 . . . . . add -8-2y and swap sides. This is the first inequality.
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y ≥ -x +1
x + y ≥ 1 . . . . . add x. This is the second inequality
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For the four points in the first inequality, we have ...
1) -5 -2(3) = -11 . . . not greater than -8
2) 0 -2(4) = -8 . . . not greater than -8
3) 3 -2(-5) = 13 . . . greater than -8, satisfies the first inequality
4) 4 -2(0) = 4 . . . greater than -8, satisfies the first inequality
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So, the two points that might possibly work are (3, -5) and (4, 0). Here, we try these in the second inequality.
3) 3 -5 = -2 . . . less than 1
4) 4 + 0 = 4 . . . greater than 1, satisfies the second inequality
The only point listed that is a solution to the system is (4, 0), point 4.
Check the picture below, that one in the picture is just an example of the correspondence of sine and cosine in a right-triangle, in this case, we're in the 0° < x < 90°, so in the I Quadrant, and thus we have a right-triangle.
to make it short, sin(90° - 19°) = cos(19°), or that is sin(71°), thus x = 71.
<em>The question doesn't show any graph, but I have included it to help you with the problem.</em>
Answer:
<em>The new graph will be shifted up by 3 units</em>
Step-by-step explanation:
<u>Graph of a Real Function</u>
The total cost of belonging to the book club depends on one fixed cost, the initial joining fee, and a variable cost, depending on the number of books purchased. Call C the total cost and x the number of purchased books, then
By giving x some values, we get the corresponding values of C and then we can plot the graph as a blue line, in the image provided below.
If the joining fee goes up by $3, the new function is
The graph is also shown in the image, but with a red line. We can see the graph is shifted up by 3 units in the y-axis, but the slope remains the same, as the cost per book hasn't changed
