Answer:
Fernando does not have enough clay to finish the structure since, the expressions for the volume left are not the same.
Step-by-step explanation:
Let w be the length of the longest slab. Since each slab is 2 inches less than the one beneath it, we have the width of the other 3 slabs as w - 2, w - 2 - 2 = w - 4 and w - 4 - 2 = w - 6 respectively.
Since the base of each slab is a square and has thickness 2 inches, the volume of each slab from largest to smallest is thus 2w², 2(w - 2)², 2(w - 4)² and 2(w - 6)² respectively.
We have that we have half of the container of clay left after forming the first two slabs(which are the bottom-most slabs). Let V be the volume of each clay container. Since we have half left, that is V/2, we have used 2V - V/2 = 3V/2 to make the two bottom-most slabs.
So, 3V/2 = 2w² + 2(w - 2)²
= 2w² + 2(w² - 4w + 4)
= 2w² + 2w² - 8w + 8
= 4w² - 8w + 8
= 4(w² - 2w + 2) (1)
Also we want to know if V/2 is equal to the volume of the two top-most slabs.
So, V/2 = 2(w - 4)² + 2(w - 6)²
= 2(w² - 8w + 16) + 2(w² - 12w + 36)
= 2w² - 16w + 32 + 2w² - 24w + 72
= 4w² - 40w + 104
= 4(w² - 10w + 26)
From (1) V/2 = 4(w² - 2w + 2)/3 ≠ 4(w² - 10w + 26)
<u>Since the expressions for the remaining volume are not the same, Fernando does not have enough clay to finish the structure.</u>
Answer:
5(11x-2) = 155
55x - 10 = 155
55x = 165
x = 165/55
x = 3
Step-by-step explanation:
hope it helps
Part A: x = -5/4, 3 || (-5/4, 0) (3, 0)
To find the x-intercepts, we need to know where y is equal to 0. So, we will set the function equal to 0 and solve for x.
4x^2 - 7x - 15 = 0
4 x 15 = 60 || -12 x 5 = 60 || -12 + 5 = -7
4x^2 - 12x + 5x - 15 = 0
4x(x - 3) + 5(x - 3) = 0
(4x + 5)(x - 3) = 0
4x + 5 = 0
x = -5/4
x - 3 = 0
x = 3
Part B: minimum, (7/8, -289/16)
The vertex of the graph will be a minimum. This is because the parabola is positive, meaning that it opens to the top.
To find the coordinates of the parabola, we start with the x-coordinate. The x-coordinate can be found using the equation -b/2a.
b = -7
a = 4
x = -(-7) / 2(4) = 7/8
Now that we know the x-value, we can plug it into the function and solve for the y-value.
y = 4(7/8)^2 - 7(7/8) - 15
y = 4(49/64) - 49/8 - 15
y = 196/64 - 392/64 - 960/64
y = -1156/64 = -289/16 = -18 1/16
Part C:
First, start by graphing the vertex. Then, use the x-intercepts and graph those. At this point we should have three points in a sort of triangle shape. If we did it right, each of the x-values will be an equal distance from the vertex. After we have those points graphed, it is time to draw in the parabola. Knowing that the parabola is positive, we draw in a U shape that passes through each of the three points and opens toward the top of the coordinate grid.
Hope this helps!
Given:$75
25 hours
Painting USA : Fixed cost: $75 ; Variable Cost: $25x
Total Cost = 75 + 25(25) = 75 + 625 = 700
Upscale Home Painting: No Fixed Cost ; Variable Cost : $40x
Total Cost = 40(25) = 1,000
The most cost effective company will be Painting USA whose charge will amount to $700.
