Which Expression Represents The Volume, In Cubic Units, Of The Composite Figure?

WILL GIVE BRAINLIEST Which expression represents the volume, in cubic units, of the composite figure? A. (8)(6)(6) + (8)(6)(4)B. (8)(6)(10) + (8)(6)(4)C. (8)(6)(4) – (8)(6)(6)D. (8)(6)(4) – (8)(6)(10)

Solution:

The figure is splitted into two shapes.

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One is rectangular pyramid and the other is rectangular prism.

Rectangular pyramid:

Length = 8

Width = 6

Height = 10 – 4 = 6

Volume of rectangular pyramid =

*

Volume of rectangular pyramid

*

Rectangular prism:

Length = 8

Width = 6

Height = 4

Volume of rectangular prism = length × width × height

= 8 × 6 × 4

Volume of rectangular prism = (8)(6)(4)

Volume of figure = Volume of pyramid + volume of prism

*

The volume of the composite figure is cubic units.

“Let”s see if it works with the two consecutive integers 5 and 6:

let x = 5

so x + 1 = 6

5 + 6 = 11, so:

2x + 1 = 11

2x = 10 (subtracted 1 from both sides)

x = 5 (divided both sides by 2)

it works!”

represent the sequence 16,24,32,40…

Step-by-step explanation:

The sequence given is

16,24,32,40.

And the options given are

an=4n+1

an=8n+8

an=8n+16

We will check for all so as to find the correct expression.

In the given sequence the first term is 16,

i.e a1 = 16

1). We will check for an = 4n+1 whether the first term is 16 or not.

We will put the value of n as 1;

*

With this option we get the first term as 5 but in the given sequence first term is 16.

Hence this option is Incorrect.

2). We will check for an = 8n+8 whether the first term is 16 or not.

We will put the value of n as 1;

*

With this option we get the first term as 16 and in the given sequence also first term is 16.

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Hence this option is correct.

3). We will check for an = 8n+16 whether the first term is 16 or not.

We will put the value of n as 1;

*

With this option we get the first term as 24 but in the given sequence first term is 16.

Hence this option is Incorrect.

Hence we can say that an = 8n+8 represent the sequence 16,24,32,40…

D. 6x³ + 5x² – 3x – 2

Step-by-step explanation:

First assign each variable with its number.

l = 2x + 1

w = x + 1

h = 3x – 2

Now, plug in.

v = (2x + 1)(x +1)(3x – 2)

Now combine the first two pairs following the FOIL method. (First Outer Inner Last)

(2x² + 3x + 1)(3x – 2)

Now you would multiply the 3x on to each term and the -2 on to each term.

6x³ + 9x² + 3x – 4x² – 6x – 2

Now combine like terms.

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6x³ + 5x² – 3x – 2

p:20

p:25

Step-by-step explanation:

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