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BARSIC [14]
2 years ago
13

The volume of a rectangular prism is given by the formula V = lwh, where l is the length of the prism, w is the width, and h is

the height. Suppose a box in the shape of a rectangular prism has length (2a + 11), width (5a – 12), and height (a + 6). Which expression represents the volume of the box?
Mathematics
2 answers:
DaniilM [7]2 years ago
6 0

Answer:

Volume = 10a³ + 91a² + 54a - 792

Step-by-step explanation:

In the absence of answer choices, let's find the expression for the volume.

Given: Volume = length×width×height

V = lwh

length =(2a + 11)

width =(5a – 12)

height= (a + 6)

V =  (2a + 11)(5a – 12) (a + 6)

Expand the first two brackets using distributive property

V = (10a² -24a +55a - 132)(a + 6)

Collect like terms

V = (10a² + 31a -132)(a + 6)

Expand the two brackets using distributive property

V = 10a³ + 31a² - 132a + 60a² + 186a - 792

Collect like terms

V = 10a³ + 91a² + 54a - 792

The expression that represents the volume of the box = 10a³ + 91a² + 54a - 792

astra-53 [7]2 years ago
3 0

Answer:

Volume = 10a³ + 91a² + 54a - 792

Step-by-step explanation:

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A company manufactures penny number 2 nails that are 1 inch in length. The actual length is allowed to vary by up to \displaysty
Diano4ka-milaya [45]

The absolute value equation representing the length of the nail is :

  • \frac{31}{32}  \leqslant x \leqslant 1 \frac{1}{32}

A nail of length 1.05 inches is unacceptable

Actual Length of nail = 1 inch

Allowable variation = 1/32 inches

The minimum allowable length :

actual length - allowable variation

  • 1 -  \frac{1}{32}  =  \frac{31}{32}

The maximum allowable length :

Actual length + allowable variation

  • 1 +  \frac{1}{32}  = 1 \frac{1}{32}

The length of X, of the nail must be follow the equation :

Minimum ≤ X ≤ maximum

\frac{31}{32}  \leqslant x \leqslant 1 \frac{1}{32}

A nail of length 1.05 inches

Maximum nail length = 1 1/32 = 1.031

1.05 > 1.031 ; hence, it is greater than the maximum allowable length and hence, Unacceptabe

Learn more : brainly.com/question/24656203

7 0
2 years ago
Which is the equation for the line perpendicular to y = –5/3 x + 11 1/3 and containing P(–2, 3)?
kati45 [8]
Okay, to answer this question, 
<span>Perpendicular lines have slopes that are inverse of one another and with opposite signs so, 
If a line has a slope of m= -2 than a perpendicular line will have slope m=1/2
If a line has a slope of m= -3/4 than a perpendicular line will have slope m=4/3 If a line has a slope of m= 6 than a perpendicular line will have slope m=-1/6

So, just find the slope of your line, using it, get the slope of the line that will be perpendicular and then just get the equation for a line that has that slope and passes through point (-2,3) using: y - y1 = m(x - x1)
I hope I helped you with my answer</span>
7 0
3 years ago
The length of the path of the first swing of the bob of a pendulum is 0.6 in. Each
ycow [4]

Answer:

0.3188646

Step-by-step explanation:

an=a×r^n-1

a6=0.6×0.9^5

=0.354294

1st swing: 0.6

2nd swing: 0.9×0.6=0.54

3rd swing: 0.9×0.54= 0.486

4th 0.9×0.486= 0.4374

5th 0.9×0.4374= 0.39366

6th 0.9×0.39366=0.354294

Brainliest please~

8 0
3 years ago
In ΔQRS, the measure of ∠S=90°, the measure of ∠R=29°, and SQ = 5.8 feet. Find the length of RS to the nearest tenth of a foot.
taurus [48]

Answer:

10.5 ft

Step-by-step explanation:

In ΔQRS,

  • m∠S=90°
  • m∠R=29°,
  • SQ = 5.8 feet.

See the diagram below.

The triangle is a Right Triangle,

Using trigonometric ratios,

Tan R=\dfrac{|SQ|}{|RS|} \\Tan 29^\circ=\dfrac{5.8}{|RS|}\\$Cross multiply$\\|RS|XTan 29^\circ=5.8\\|RS|=\dfrac{5.8}{Tan 29^\circ}\\$=10.5 ft (to the nearest tenth of a foot)

7 0
3 years ago
Shawna, Ryan, and Dominic ate a whole pizza. Shawna ate 1
mafiozo [28]

Answer:

\frac{1}{6}

Step-by-step explanation:

You need to add the amount Shawna & Ryan ate together, then subtract it from 1 to find the amount of pizza that was left for Dominic to eat.

\frac{1}{3} + \frac{1}{2} = ?

Make all the denominators the same to add fractions.

\frac{1}{3}  is \frac{2}{6}

\frac{1}{2}  is \frac{3}{6}

\frac{2}{6} +  \frac{3}{6} = \frac{5}{6}

1 -  \frac{5}{6} = \frac{1}{6}

4 0
2 years ago
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