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4 years ago

Which could be the dimensions of a rectangular prism to service area is less than 160 ft.² check all that apply

Mathematics

2 answers:

Dovator [93]4 years ago

6 0

Area of a rectangular prism: 2(wl+hl+hw), given w=width, l=length, and h=height.

Plug the answer choices into this formula to find which one(s) are less than 160 sq. feet.

A. 136 sq. feet

B. 188 sq. feet

C. 202 sq. feet

D. 162 sq. feet

E. 142 sq. feet

So, the only ones that are less than 160 sq. feet are A (8 feet by 4 feet by 3 feet) and E (3 feet by 5 feet by 7 feet).

Your answers are A and E.

I hope this helps :)

raketka [301]4 years ago

3 0

Area of rectangular prism is given by:

A=2(wl+hl+lw)

where w=width h=height, l=length

checking for given options

1. 8 ft, by 4ft by 3ft

Area = 136 square feet

5. 3 feet by 5 feet by 7 feet

Area =142 square feet

so our first and last option matches the requirement of area less than 160 square feet.

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serg [7]

The answer should be hid

6 0

3 years ago

Jean and Sarah are buying tubs of ice cream. 2 scoops of ice cream are twice the price of 1 scoop of ice cream. Jean buys 4 tubs

liberstina [14]

Answer:

The answer is below

Step-by-step explanation:

Let x represent the cost of 1 scoop of ice cream. Since the cost of 2 scoops of ice cream are twice the price of 1 scoop of ice cream, therefore the cost of 2 scoops of ice cream = 2x

Jean buys 4 tubs with 2 scoops in them and 2 tubs with 1 scoop each. Therefore the money spent by Jean is:

Money spent by Jean = 4(2x) + 2(x) = 8x + 2x = 10x

Sarah buys 2 tubs of 2 scoops and 4 tubs of 1 scoop. The money spent by Sarah is:

Money spent by Sarah = 2(2x) + 4(x) = 4x + 4x = 8x

Sarah spends 2.50 € less than Jean. Therefore:

Money spent by Sarah = Money spent by Jean - 2.5

8x = 10x - 2.5

2x = 2.5

x = €1.25

Therefore the cost of 1 scoop of ice cream is €1.25, the cost of 2 scoops of ice cream is €2.50.

Money spent by Jean = 10x = 10(1.25) = €12.5

Money spent by Sarah = 8x = 8(1.25) = €10

3 0

3 years ago

Please walk me through how to do this so I can di the other questions

Naddik [55]

Answer:

Axis is a vertical line at x = 2

Vertex is (2, -1)

y-intercept is (0, 3)

Solutions are x = 1 and x = 3

Step-by-step explanation:

To draw the graph of the quadratic equation you must find at least 5 points lie on the graph by choose values of x and find their values of y

Let us do that

Use x = -1, 0, 1, 2, 3, 4, 5

∵ y = x² - 4x + 3

∵ x = -1

∴ y = (-1)² - 4(-1) + 3 = 1 + 4 + 3 = 8

→ Plot point (-1, 8)

∵ x = 0

∴ y = (0)² - 4(0) + 3 = 0 + 0 + 3 = 3

→ Plot point (0, 3)

∵ x = 1

∴ y = (1)² - 4(1) + 3 = 1 - 4 + 3 = 0

→ Plot point (1, 0)

∵ x = 2

∴ y = (2)² - 4(2) + 3 = 4 - 8 + 3 = -1

→ Plot point (2, -1)

∵ x = 3

∴ y = (3)² - 4(3) + 3 = 9 - 12 + 3 = 0

→ Plot point (3, 0)

∵ x = 4

∴ y = (4)² - 4(4) + 3 = 16 - 16 + 3 = 3

→ Plot point (4, 3)

∵ x = 5

∴ y = (5)² - 4(5) + 3 = 25 - 20 + 3 = 8

→ Plot point (5, 8)

→ Join all the points to form the parabola

From the graph

∵ The axis of symmetry is the vertical line passes through the vertex point

∵ x-coordinate of the vertex point is 2

∴ Axis is a vertical line at x = 2

∵ The coordinates of the vertex point of the parabola are (2, -1)

∴ Vertex is (2, -1)

∵ The parabola intersects the y-axis at point (0, 3)

∴ y-intercept is (0, 3)

∵ x² - 4x + 3 = 0

∵ The solutions of the equation are the values of x at y = 0

→ That means the intersection points of the parabola and the x-axis

∵ The parabola intersects the x-axis at points (1, 0) and (3, 0)

∴ Solutions are x = 1 and x = 3

3 0

3 years ago

please help i will mark brainliest, no spam answers i will report.

vovikov84 [41]

9514 1404 393

Answer:

Step-by-step explanation:

Point E partitions both the x-distance and the y-distance in the ratio 2 : 1. That is, for either the x-coordinates or the y-coordinates, ...

CE : ED = 2 : 1

Try the answers with the x-coordinates.

CE : ED = (1 -(-1)) : (5 - 1) = 2 : 4 . . . . incorrect

CE : ED = (-3 -(-1)) : (5 -(-3)) = -2 : 8 . . . . incorrect

CE : ED = (3 -(-1)) : (5 -3) = 4 : 2 = 2 : 1 . . . . correct

CE : ED = (-1 -(-1)) : (5 -(-1)) = 0 : 6 . . . . incorrect

The only viable choice is (3, 3).

_____

Alternate solution

For a partitioning of m : n, the desired point is ...

E = (n×C +m×D)/(m+n)

For partitioning of 2 : 1, the desired point is ...

E = (1×(-1, -3) + 2×(5, 6))/(2+1) = (-1+10, -3 +12)/3

E = (3, 3)

3 0

3 years ago

2 Construct a rational function that will help solve the problem. Then, use a calculator to answer the question.

vaieri [72.5K]

Answer:

Dimension of box:-

Side of square base = 10 in

Height of box = 5 in

Minimum Surface area, S = 300 in²

Step-by-step explanation:

An open box with a square base is to have a volume of 500 cubic inches.

Let side of the base be x and height of the box is y

Volume of box = area of base × height

$500=x^2y$

Therefore, $y=\dfrac{500}{x^2}$

It is open box. The surface area of box, S .

$S=x^2+4xy$

Put $y=\dfrac{500}{x^2}$

$S(x)=x^2+\dfrac{2000}{x}$

This would be rational function of surface area.

For maximum/minimum to differentiate S(x)

$S'(x)=2x-\dfrac{2000}{x^2}$

For critical point, S'(x)=0

$2x-\dfrac{2000}{x^2}=0$

$x^3=1000$

$x=10$

Put x = 10 into $y=\dfrac{500}{x^2}$

y = 5

Double derivative of S(x)

$S''(x)=2+\dfrac{4000}{x^3}$ at x = 10

$S''(10) > 0$

Therefore, Surface is minimum at x = 10 inches

Minimum Surface area, S = 300 in²

7 0

4 years ago