MATHEMATICS MIDDLE SCHOOL

A manufacturer wants to make a box with a volume of 24 cubic feet.a. Sketch two possible designs for the box.

b. If the box is to be made out of wood that costs $4 per square foot, which of your designs would be less expensive to produce? Explain.

Answers

Answer 1
Answer: First: You should know the formulas for volume and surface area of a rectangular prism.
V=whl
SA=2wl+2wh+2hl

Now, if our volume is 24 ft³, then the 3 dimensions of the box must multiply to make 24. We want to make two designs, so let's think of some possible dimensions.
Let's say...2 × 2 × 6 and 2 × 3 × 4.
You should be able to sketch boxes and label the sides. Just draw two rectangles and draw lines between all of the points. (see attached for reference)

Now all we have to do is find the surface area. Plug in our width, length, and height and solve.
First box
SA = 2wl + 2wh + 2hl
SA = 2×2×2 + 2×2×6 + 2×2×6
SA = 8 + 24 + 24
SA = 56
Second box
SA = 2wl + 2wh + 2hl
SA = 2×2×3 + 2×2×4 + 2×3×4
SA = 12 + 16 + 24
SA = 52

At $4 / ft²...
56 ft² = $224
52 ft² = $208

The second box is less expensive to produce because it has less surface area and therefore less wood needed to build the sides of the box.

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Helen's house is located on a rectangular lot that is 1 1/8 miles by 9/10. Estimate the distance around the lot.

Answers

You round 1 1/8 to 1 and 9/10 to 1 (since you are estimating) and then you add 1+1+1+1, which is 4 because to find perimeter you add the lengths and the widths together.

Answer:You round 1 1/8 to 1 and 9/10 to 1 (since you are estimating) and then you add 1+1+1+1, which is 4 because to find perimeter you add the lengths and the widths.

Joanne buys a rectangle rug with an area of 34/4 square meters the length of the rug was 7/2

Answers

Answer:

5/2

Step-by-step explanation:

area formula = l*w=A

in this case l=7/2, and A=35/4

7/2*w=35/4

divide  7/2 with 35/4 to get the value of "w"

35/4*2/7=5/2

hope this helps, if it does plz vote my answer the brainiest, thanks!

Solve the following: -3x + 7(x + 5) = 5x + 38

please explain!

Answers

Answer: -3

Step-by-step explanation:

-3x+ 7x+ 35= 5x + 38

You solve the distributive property on the left side and set it equal to the right

4x+35= 5x+38

-4x -4x

35= x+38

-38 -38

X=-3

What is the exponent on 10 when you write 5.3 in scientific notation

Answers


It's 1. Because 5.3 can't be simplified to any other scientific notation. It's 5.3 x 10^1

Please help i have know idea what to do please help and show work so i can understand thank you!1.) k+3/4k-2 * (12k^2-3)
2.) x^2-16/6x * 7x/x+5
3.) q+5/2 * 4q/q+4
4.)y^2-9/-2y * -5y/y+3
5.)(8x^2-20x+15) divided by (2x-3)
6.)(8x^3-30+21) divided by (4x-6)
7.)(-10m^9-4m-12m^6) divided by 2m^4

Answers

1.(k + 3)/(4k - 2)(12k^(2) - 3})
   (k + 3)/(2(2k) - 2(1))(3(4k^(2)) - 3(1))
   (k + 3)/(2(2k - 1))(3(4k^(2) - 1))
   (k + 2)/(2(2k - 1))(3(4k^(2) + 2k - 2k - 1))
   (k + 3)/(2(2k - 1))(3(2k(2k) + 2k(1) - 1(2k) - 1(1))
   (k + 3)/(2(2k - 1))(3(2k + 1) - 1(2k + 1))
   (k + 3)/(2(2k - 1))(3(2k - 1)(2k + 1))
   (3(k + 3)(2k + 1))/(2)

2.((x^(2) - 16)/(6x))((7x)/(x + 5))
   ((x^(2) + 4x - 4x - 16)/(6))((7)/(x + 5))
   ((x(x) + x(4) - 4(x) - 4(4))/(6))((7)/(x + 5))
   ((x(x + 4) - 4(x + 4))/(6))((7)/(x + 5))
   (((x - 4)(x + 4))/(6))((7)/(x + 5))
   (7(x - 4)(x + 4))/(6(x + 5))

3.((q + 5)/(2))((4q)/(q + 4))
   ((q + 5)/(1))((2q)/(q + 4))
   (2q(q + 5))/(q + 4)

4.((y^(2) - 9)/(-2y))((-5y)/(y + 3))
   ((y^(2) + 3y - 3y - 9)/(2))((5)/(y + 3))
   ((y(y) + y(3) - 3(y) - 3(3))/(2))((5)/(y + 3))
   ((y(y + 3) - 3(y + 3))/(2))((5)/(y + 3))
   (((y - 3)(y + 3))/(2))((5)/(y + 3))
   ((y - 3)/(2))((5)/(1))
   (5(y - 3))/(2)

5.(8x^(2) - 20x + 15)/(2x - 3)

6.(8x^(3) - 30 + 21)/(4x - 6)
   (8x^(3) - 9)/(2(2x) - 2(3))
   (8x^(3) - 9)/(2(2x - 3))

7.(-10m^(9) - 12m^(6) - 4m)/(2m^(4))
   (-10m^(9))/(2m^(4)) - (12m^(6))/(2m^(4)) - (4m)/(2m^(4))
   -5m^(5) - 6m^(2) - (2)/(m^(3))

HELP PLEASE Sam and George both worked hard over the summer. Together they earned a total of $525. George earned$75 more than Sam.
a. Write a system of equations for the situation. Use s for the amount Sam earned and g for the
amount George earned.
b. Graph the equations in the system. Be sure to label all axes and show your scale.
c. Use your graph to determine how much each person earned.

Answers

Answer:


Step-by-step explanation:


g = s + 75


g + s = 525


That's just the answer for (a). You'll have to graph it yourself.


Guide to the methodology:


You need to plot 2 points for each equation and draw a line between the points. Where the two lines intersect gives you the values that solve the equations.


To get your co-ords,


Let g = 0


s = -75


Create a graph with g as one axis and s as the other. Plot a point of (0,-75)


Let s = 0


g = 75


Plot another point (0,75)


Draw a line between the two points. This is your line for g = s +75


You then need to plot a line for the second equation.


Let g = 0. S = 525. First co-ordinate is (0,525)


Let s = 0. G = 525. Second co-ordinate is (525,0)
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I need help fast will give brainiest!!!!