Answer: 4
Step-by-step explanation:
The true statement about the graph's slope is (c) Its slope is zero.
<h3>How to determine the true statement?</h3>
From the question, we have:
A horizontal line is at y = 2.5.
The horizontal line implies that the cost of lunch do not change
Horizontal lines have a slope of 0
Hence, the true statement about the graph's slope is (c) Its slope is zero.
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Which two ratios represent quantities that are proportional?
Answer:
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20:24 is My Answer
Step-by-step explanation:
y = kx, where k is the constant of proportionality. In other words, these quantities always maintain the same ratio
proportion is an equation with a ratio on each side. It is a statement that two ratios are equal.
For example 2/5 is Equal to 4/10 this Would be A Example Of a Proportional relationship!
Answer:
the dimensions of the box that minimizes the cost are 5 in x 40 in x 40 in
Step-by-step explanation:
since the box has a volume V
V= x*y*z = b=8000 in³
since y=z (square face)
V= x*y² = b=8000 in³
and the cost function is
cost = cost of the square faces * area of square faces + cost of top and bottom * top and bottom areas + cost of the rectangular sides * area of the rectangular sides
C = a* 2*y² + a* 2*x*y + 15*a* 2*x*y = 2*a* y² + 32*a*x*y
to find the optimum we can use Lagrange multipliers , then we have 3 simultaneous equations:
x*y*z = b
Cx - λ*Vx = 0 → 32*a*y - λ*y² = 0 → y*( 32*a-λ*y) = 0 → y=32*a/λ
Cy - λ*Vy = 0 → (4*a*y + 32*a*x) - λ*2*x*y = 0
4*a*32/λ + 32*a*x - λ*2*x*32*a/λ = 0
128*a² /λ + 32*a*x - 64*a*x = 0
32*a*x = 128*a² /λ
x = 4*a/λ
x*y² = b
4*a/λ * (32*a/λ)² = b
(a/λ)³ *4096 = 8000 m³
(a/λ) = ∛ ( 8000 m³/4096 ) = 5/4 in
then
x = 4*a/λ = 4*5/4 in = 5 in
y=32*a/λ = 32*5/4 in = 40 in
then the box has dimensions 5 in x 40 in x 40 in
Axis of symmerty from form
ax²+bx+c is -b/2a
the axis of symetry is the x value of the vertex so just put the axis of symetry for x an evaluate
4x²-8x-3
-b/2a=-(-8)/(2*4)=8/8=1
input for x
4(1)²-8(1)-3=4-8-3=-7
(1,-7) is vertex
A is answer
