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masya89 [10]
2 years ago
9

Vada places a box of toys and a box of books together. The box of toys has a length of 5 feet, a width of 3 feet, and a height o

f 2 feet. The box of books has a length of 6 feet, a width of 4 feet, and a height of 2 feet. What is the combined volume of the boxes?
Mathematics
2 answers:
Elena L [17]2 years ago
7 0

Answer:

78 ft³

Step-by-step explanation:

<u />

Volume of a rectangular prism = length × width × height

<u />

<u>Toy Box</u>

  • length = 5 ft
  • width = 3 ft
  • height = 2ft

⇒ volume = 5 × 3 × 2 = 30 ft³

<u>Book Box</u>

  • length = 6 ft
  • width = 4 ft
  • height = 2 ft

⇒ volume = 6 × 4 × 2 = 48 ft³

Total combined volume = 30 + 48 = 78 ft³

Mars2501 [29]2 years ago
7 0

Answer:

78 ft cubed

Step-by-step explanation:

First calculate the volume of the toys...

5 x 3 x 2 = 30

Now the book boxes...

6 x 4 x 2 = 48

30 + 48 = 78

The combined volume should be 78 feet cubed! hope this helps!!!

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4/7 divided by 1 3/4
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3 years ago
A rectangle has perimeter 28cm. Its area is 42sq.cm. Determine the dimensions of the rectangle. Include a diagram in your soluti
yawa3891 [41]

The dimensions of the rectangle are: b=9.65 cm and h=4.35 cm or b=4.35 cm and h= 9.65 cm.

<h3>Quadrilaterals</h3>

There are different types of quadrilaterals, for example, square, rectangle, rhombus, trapezoid, and parallelogram.  Each type is defined accordingly to its length of sides and angles. For example, in a rectangle,  the opposite sides are equal and parallel and their interior angles are equal to 90°.

The area of a rectangle is equal to base x height (A=bh). The perimeter of a geometric figure is the sum of its sides. Thus, for a rectangle, the perimeter is 2b+2h.

<h3>System of Linear Equations</h3>

System of linear equations is the given term math for two or more equations with the same variables. The solution of these equations represents the point at which the lines intersect.

The question gives:

Perimeter=28cm

Area= 42 cm²

If the perimeter is the sum of all sides of the rectangle, you have:

Perimeter= 2b+2h=28

If the area of the rectangle is 42cm², you have:

Area=bh=42 cm²

You can write a system of linear equations.

2b+2h=28 (1)

bh=42 (2)

From equation 2, you have  b=\frac{42}{h}. Then, you can replace it in equation 1.

2*\frac{42}{h}+2h=28 \\ \\ 84+2h^2=28h\\ \\ 2h^2-28h+84=0 \; dividing\; by\; 2\\ \\ h^2-14h+42=0

Now, you should solve the quadratic equation.

h_{1,\:2}=\frac{-\left(-14\right)\pm \sqrt{\left(-14\right)^2-4\cdot \:1\cdot \:42}}{2\cdot \:1}

h_{1,\:2}=\frac{-\left(-14\right)\pm \:2\sqrt{7}}{2\cdot \:1}

h_1=\frac{-\left(-14\right)+2\sqrt{7}}{2\cdot \:1}=7+\sqrt{7}=9.65 cm

h_2=\frac{-\left(-14\right)-2\sqrt{7}}{2\cdot \:1}=7-\sqrt{7}=4.35cm

If h1=9.65 cm, then b_1=\frac{42}{9.65} =4.35 cm, and if  h2=4.35 cm, then b_1=\frac{42}{4.35} =9.65 cm.

Read more about the quadratic function here:

brainly.com/question/1497716

#SPJ1

8 0
1 year ago
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