The point (-2, 5) is not included in the solution area
<h3>The graph of the inequalities</h3>
The system of inequalities is given as:
y > 5x + 5
y > -2x+1
See attachment for the graph.
Since the inequalities use the greater than symbol, then the lines of the inequalities would be a dotted line and the upper part would be shaded
<h3>The solution area</h3>
The point is given as:
(-2, 5)
The point (-2, 5) is not in the shaded area of the system of inequalities
Hence, the point is not included in the solution area
Mathematically, we have:
5 > 5 * -2 + 5 ⇒ 5 > -5 --- true
5 > -2 * -2 +1 ⇒ 5 > 5 --- false
Since both inequalities are not true, then the point is justified
Read more about system of inequalities at:
brainly.com/question/19526736
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1.53
2.115
3.122
4.106
5.49
6.110
left to right
Note how all four answer choices begin with "x=-2(." This tells us that we have the graph of a horizontal parabola that opens to the left, because of the "-" symbol.
Given that the vertex is located at (-1,-3), we know that the (y-c) term must be (y-[-3]), or (y+3). Thus,we can immediately eliminate answer choices b and d
The only answer choice that fits this situation is (a): x = -2(y+3) - 1.
I'm assuming you want the total surface area.
This is a trapezoidal prism. The bases are the parallel faces running horizontal (parallel to the ground) and they are congruent trapezoids. The lateral sides are rectangles.
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Lateral Faces:
The back face (hidden from view) is a rectangle that is 12 inches by 3 inches, so it has an area of 12*3 = 36 sq inches
The front slant faces on the left and right are each 3*5 = 15 sq inches in area
The front center lateral face has area of 6*3 = 18 sq inches
The total lateral surface area is 15+18+15+36 = 84 sq inches
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The bases are each the same trapezoid. The trapezoid has two parallel sides of 12 and 6 inches. Call this b1 and b2. The height of the trapezoid is h = 4. Imagine the trapezoid is laid flat in a 2D perspective instead of a 3D one.
The area of one trapezoid is...
A = h*(b1+b2)/2
A = 4*(12+6)/2
A = 4*(18)/2
A = 72/2
A = 36
So the area of both base faces combined is 2*36 = 72
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The total surface area is then found by adding the total lateral surface area (84) and the total base area (72) to get 84+72 = 156
Final Answer: 156 square inches
Both the vertical and horizontal cross-section would be a square. The cross-sections are the same because all of a cube's dimensions are the same. A cube is made up of 6 congruent square faces.
