1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Kaylis [27]
3 years ago
10

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
1 answer:
frutty [35]3 years ago
3 0

Answer:

V = 10a^3+91a^2+54a-792

Step-by-step explanation:

V = (2a+11) (5a-12) (a+6)

V = (10a^2-24a+55a-132)(a+6)

V = (10a^2+31a-132)(a+6)

V = (10a^3+60a^2+31a^2+186a-132a-792)

V = 10a^3+91a^2+54a-792

You might be interested in
6x – 2y = 10 2x + 3y = 51 Solving the first equation above for y gives: y = x – 5
Virty [35]

Answer:

<h2>x =6</h2><h2>y =13</h2>

Step-by-step explanation:

This is  the method I am familiar with.

I Hope It helps :)

METHOD- 1 : Elimination\\6x - 2y=10------(1)\\2x+3y =51------(2)\\Multiply -eq-(1)- by -the-coefficient-of-x-in-equation (2)\\Multiply-eq-(2) -by -the-coefficient-of-x-in-equation (1)\\6x - 2y=10------(1) *2\\2x+3y =51------(2)*6\\\\12x-4y=20 ------(3)\\12x+18y=306 ------(4)\\Subtract -eq- (4)- from- eq -(3)\\-22y =-286\\\frac{-22y}{-22} =\frac{-286}{-22} \\y =13\\

Substitute- 13- for y -in-equation -(1)-or-(2)\\6x - 2y=10------(1)\\6x -2(13)=10\\6x -26=10\\6x =10+26\\6x =36\\\frac{6x}{6} =\frac{36}{6} \\x =6

6 0
3 years ago
Read 2 more answers
Write words to match the expression. <br><br> 5. 3+(4*12)
lana [24]
Five plus 4 multiplied by 12
5 0
3 years ago
Read 2 more answers
cookies for a school fundraiser cost $3.75 per box. The total amount recieved from the cookie sale is $2718.75. How many boxes o
Cloud [144]

Answer:

725

Step-by-step explanation:

5 0
2 years ago
100,000 less than five hundred sixty thousand,three hundred thirteen is __________.​
Vlad1618 [11]

Answer:

100,000>56,313 56, 56,313<100,000

8 0
3 years ago
Help with b please. thank you<br>​
erastovalidia [21]

Answer:

See explanation.

General Formulas and Concepts:

<u>Algebra I</u>

  • Terms/Coefficients
  • Factoring

<u>Algebra II</u>

  • Polynomial Long Division

<u>Pre-Calculus</u>

  • Parametrics

<u>Calculus</u>

Differentiation

  • Derivatives
  • Derivative Notation

Derivative Property [Multiplied Constant]:                                                           \displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)

Derivative Property [Addition/Subtraction]:                                                         \displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)]

Basic Power Rule:

  1. f(x) = cxⁿ
  2. f’(x) = c·nxⁿ⁻¹

Derivative Rule [Quotient Rule]:                                                                           \displaystyle \frac{d}{dx} [\frac{f(x)}{g(x)} ]=\frac{g(x)f'(x)-g'(x)f(x)}{g^2(x)}

Parametric Differentiation:                                                                                     \displaystyle \frac{dy}{dx} = \frac{\frac{dy}{dt}}{\frac{dx}{dt}}

Step-by-step explanation:

<u>Step 1: Define</u>

<em>Identify</em>

\displaystyle x = 2t - \frac{1}{t}

\displaystyle y = t + \frac{4}{t}

<u>Step 2: Find Derivative</u>

  1. [<em>x</em>] Differentiate [Basic Power Rule and Quotient Rule]:                             \displaystyle \frac{dx}{dt} = 2 + \frac{1}{t^2}
  2. [<em>y</em>] Differentiate [Basic Power Rule and Quotient Rule]:                             \displaystyle \frac{dy}{dt} = 1 - \frac{4}{t^2}
  3. Substitute in variables [Parametric Derivative]:                                           \displaystyle \frac{dy}{dx} = \frac{1 - \frac{4}{t^2}}{2 + \frac{1}{t^2}}
  4. [Parametric Derivative] Simplify:                                                                   \displaystyle \frac{dy}{dx} = \frac{t^2 - 4}{2t^2 + 1}
  5. [Parametric Derivative] Polynomial Long Division:                                     \displaystyle \frac{dy}{dx} = \frac{1}{2} - \frac{7}{2(2t^2 - 1)}
  6. [Parametric Derivative] Factor:                                                                   \displaystyle \frac{dy}{dx} = \frac{1}{2} \bigg( 1 - \frac{9}{2t^2 + 1} \bigg)

Here we see that if we increase our values for <em>t</em>, our derivative would get closer and closer to 0.5 but never actually reaching it. Another way to approach it is to take the limit of the derivative as t approaches to infinity. Hence  \displaystyle \frac{dy}{dx} < \frac{1}{2}.

Topic: AP Calculus BC (Calculus I + II)

Unit: Parametrics

Book: College Calculus 10e

7 0
3 years ago
Other questions:
  • Joan sells 21muffins and 32 bagels evaluate the expression to find the total number of muffins and bagels Joan sells in 5 days
    8·1 answer
  • A rectangle has a length of 23 inches and a perimeter of 74 inches. what is the width of the rectangle?
    8·2 answers
  • Which of the following lines is perpendicular to the line Y = 3x -4
    6·1 answer
  • Sal has 8 comic books and 4 detective books his sister says 2/3 of his books are comic books sal says that 8/12 of his books are
    12·1 answer
  • What is the sum of the geometric sequence 1,4,16 if there are 8 terms
    6·1 answer
  • Solve the simultaneous equations 4x-3y=19 and 2x+3y=23​
    9·2 answers
  • William just got hired for a new job and will make \$78,000 in his first year. William was told that he can expect to get raises
    11·1 answer
  • Find the next four numbers in the pattern. (What is the pattern?)Explain. 1,2,5,10,13, 26, 29,___,____,____,______
    15·1 answer
  • Adela has 12 red apples and 24 yellow apples.If she has nine baskets,how many apples will she able to portion into each basket?
    8·1 answer
  • The dimensions of a right triangle are shown in the diagram.
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!