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bekas [8.4K]
4 years ago
7

Santana wants to cover a gift box shaped like a rectangular prism the foil costs $0.03 per square inch. santana has a choice bet

ween box a which is 8 inches long, 3 inches wide, and 6 inches high. box b is 10 inches long, 3 inches wide, and 4 inches wide. which box will be less expensive to cover with foil, and by how much?
Mathematics
1 answer:
lapo4ka [179]4 years ago
3 0
The answer is box b, by $0.48

Calculate the surface area of rectangular prism is A = 2 (wl + hl + wh)
w - width, l - length, h - height
The cost is $0.03 per square inch: C = .0.03 * A

Box a:
l = 8 in
w = 3 in
h = 6 in
A = 2 (wl + hl + wh) = 2(3 * 8 + 6 * 8 + 3 * 6) = 2(24 + 48 + 18) = 2 * 90 = 180 in²
C = 0.03 * A = 0.03 * 180 = $5.40

Box b:
l = 10 in
w = 3 in
h = 4 in
A = 2 (wl + hl + wh) = 2(3 * 10 + 4 * 10 + 3 * 4) = 2(30 + 40 + 12) = 2 * 82 = 164 in²
C = 0.03 * A = 0.03 * 164 = $4.92

Thus, it is less expensive to cover box b with foil by $5.40 - $4.92 = $0.48
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Answer:

Step-by-step explanation:

Base of triangle = b = 8 cm

Height of triangle = h = 6 cm

Length of rectangle = l = 6 cm

Sides of the triangle :  S1 = 6 cm ;  S2 = 8 cm and S3 = 10 cm

Surface area of triangular prism= bh + l *(s1+ S2 + S3)

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                                                     = 48 + 144

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3 years ago
Parallelogram ABCD has the coordinates shown. A(-3,2) B(0,4) C(3,4) Find the coordinates of point D. A) (0, 1) B) (1, 2) C) (2,
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In a parallelogram opposite sides are equal and parallel;
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The line BC is equal to line AD and the two lines are parallel to y-axis; 
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Find the focus of the parabola whose equation is y=1/8 x^2
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Answer:

The focus is: (0,2)

Step-by-step explanation:

Given

y = \frac{1}{8}x^2

Required

Determine the focus

The focus of a parabola

(x- h)^2 = 4p(y - k)

is:

(h,k+p)

So, we have:

y = \frac{1}{8}x^2

Cross multiply

8y = x^2

Rewrite as:

x^2 = 8y

Rewrite as:

(x - 0)^2 = 8(y - 0)

Express 8 as 4 * 2

(x - 0)^2 = 4 * 2(y - 0)

By comparison with: (x- h)^2 = 4p(y - k)

h = 0    p =2     k = 0

So, the focus (h,k+p) is:

(h,k+p) = (0,0+2)

(h,k+p) = (0,2)

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3 years ago
Which of the following represent(s) an equation of the line passing through the points A(5, 6) and B(4, 8). Select all that appl
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Answer:

The equations that represent the equation of the line are:

y = -2x + 16 ⇒ A

2x + y = 16 ⇒ D

y - 6 = -2(x - 5) ⇒ E

Step-by-step explanation:

The slope intercept form of the linear equation is y = m x + b, where

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The formula of the slope is m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}

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∴ x_{1} = 5 and  x_{2} = 4

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∴ m = -2

- Substitute it in the form of the equation

∴ y = -2 x + b

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∵ x = 5 and y = 6

∴ 6 = -2(5) + b

∴ 6 = -10 + b

- Add 10 to both sides

∴ 16 = b

∴ y = -2 x + 16

∴ The equation of the line is y = -2x + 16

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∴ D represents the equation of the line

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∴ y - 6 = -2x + 10

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∴ y = -2x + 16

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y = -2x + 16 ⇒ A

2x + y = 16 ⇒ D

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