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Margarita [4]
2 years ago
9

Find the volume of a rectangular box whose length is a-2 inches, width is ‘ a ‘ inches and its height is a+3 inches.

Mathematics
1 answer:
SVEN [57.7K]2 years ago
6 0
The volume of a rectangular prism, in this case the box, is just length x width x height.

We know all three:
L = a-2
W = a
H = a+3

Therefore the volume is:
(a - 2) \times (a) \times (a + 3)
Work out the left two terms first:
(a-2)x(a) =
{a}^{2}  - 2a
Then multiply the height:
({a}^{2}  - 2a) \times (a + 3)
= {a}^{3}  - 2 {a}^{2}  + 3 {a}^{2}  - 6a
Collect like terms:
=  {a}^{3}  +  {a}^{2}  - 6a
Then factorise (if needed)
= a( {a}^{2}  + a - 6)
= a(a  + 3)(a  - 2)
See how the final answer is the same as the length, witdh and height? That's a good way to check your work.
So the volume is:

{a}^{3}  +  {a}^{2}  - 6a
cubic inches
or a(a+3)(a-2) cubic inches

Hope this helped



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Billy is incorrect. There are  3 apples and  1 pepper in the picture. The ratio of the number of apples to the number of peppers is  3:1

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Cuánto es 6321 dividido 694?
Maksim231197 [3]

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Find the distance between xequals[Start 2 By 1 Matrix 1st Row 1st Column 8 2nd Row 1st Column negative 5 EndMatrix ]and yequals[
kherson [118]

Answer:

Distance =√(x₁ - y₁)²+ (x₂ - y₂)² = √97 = 9.85

Step-by-step explanation:

The Matrix X and Y could also be referred to as vectors in Rⁿ dimensions.

if Vector X = ( x₁ , x₂)   and  Vector  Y = (y₁ , y₂)

then, Distance (X-Y) = ||X-Y|| = √(x₁ - y₁)²+ (x₂ - y₂)²

where, x₁ = 8, x₂ = -5   and  y₁ = -1 , y₂ = -9

Distance = √(8 - (-1))²+ (-5 - (-9))² = √9² + 4² =√97 = 9.85

4 0
3 years ago
Find the perimeter and area of the polygon shown below. The polygon is a trapezoid made up of a rectangle and a right triangle.
algol13

Since, the polygon is a trapezoid made up of a rectangle and a right triangle. Therefore, according to the question, the figure of the polygon is attached.


Since, perimeter is the total length of the outer boundary of the figure. Therefore,

Perimeter of the polygon is=AB+BE+ED+DC+CA

                                             =18+17+8+18+15

                                             =76 \ ft


Area of the polygon = Area of Rectangle + Area of Triangle

                                  =[(18) \times (15)] + [(\frac{1}{2}) \times (8) \times (15)]

                                  =270 + [(\frac{8}{2}) \times (15)]

                                  =270 + [4 \times (15)]

                                  =270 + 60

                                  =330 \ {ft}^{2}

7 0
2 years ago
Read 2 more answers
The frequency table below shows the antenna careers among the incoming class of first-year college students. Every student is ch
neonofarm [45]

To solve this you must use a proportion like so...

\frac{part}{whole} = \frac{part}{whole}

The total number of students that can be chosen are 4,663. This number will represent the whole of one fraction in the proportion. We want to know what percent probability out of these students are engineer, medical doctor/surgeon. This would be considered the part of this fraction. Sum the number of engineering students (615) with medical doctors/surgeons (723) to find this number

723 + 615 = 1,338 students that want to be an engineer or medical doctor/surgeon

Percent's are always taken out of the 100. This means that the other fraction in the proportion will have 100 as the whole and x (the unknown) as the part.

Here is your proportion:

\frac{1,338}{4,663} =\frac{x}{100}

Now you must cross multiply

1,338*100 = 4,663*x

133,800 = 4,663x

To isolate x divide 4,663 to both sides

133,800/4,663 = 4,663x/4,663

28.7 = x

This means that there is a 28.7% of a student with the intent of becoming an engineer or a medical doctor/surgeon to be chosen at random

Hope this helped!

~Just a girl in love with Shawn Mendes

8 0
2 years ago
Read 2 more answers
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