There are 82 people in a restaurant. Four groups of 3 leave and then five groups of 2 enter. Evaluate the expression 82 - 4(3) + 5(2) Find how many people are in the restaurant.

Answer:

The answer should be:

[tex]=\frac{8x^3-18x}{3x+2}[/tex]

The closest answer is A, so I'll go with that.

Step-by-step explanation:

So we have the rational expression:

[tex]\frac{4x^3-9x}{2x-7}\div\frac{3x^2+2x^2}{4x^2-14x}[/tex]

First, remove the division sign. To do so, turn the division into multiplication and flip the second term:

[tex]\frac{4x^3-9x}{2x-7}\cdot \frac{4x^2-14x}{3x^2+2x}[/tex]

Now, simplify. From the first term, in the numerator, factor out a x. On the second term, factor out a 2x in the numerator and a x in the denominator:

[tex]\frac{x(4x^2-9)}{2x-7}\cdot\frac{2x(2x-7)}{x(3x+2)}[/tex]

Multiply straight across:

[tex]\frac{x(4x^2-9)(2x)(2x-7)}{(2x-7)(x)(3x+2)}[/tex]

Cancel out the (2x-7):

[tex]\frac{x(4x^2-9)(2x)}{x(3x+2)}[/tex]

Cancel out the x:

[tex]\frac{(2x)(4x^2-9)}{(3x+2)}[/tex]

At this point, we can factor the (4x^2-9) term, but we won't be able to cancel it out. Thus, this is the simplest it can get.

To get the answer, expand the numerator:

[tex]=\frac{8x^3-18x}{3x+2}[/tex]

Thus, the answer is...

A?

Answer:

The right solution is option a : [tex]\frac{8x^2 - 18}{3x+2}[/tex]

Step-by-step explanation:

We have to simplify the following rational expression,

[tex]\frac{4x^3-9x}{2x-7}[/tex] ÷ [tex]\frac{3x^3+2x^2}{4x^2-14x}[/tex]

Take into account the rule (a / b) / (c / d) = ad / bc. This simplifies the expression a bit further --- (1)

[tex]\left(4x^3-9x\right)\left(4x^2-14x\right)[/tex] ÷ [tex]\left(2x-7\right)\left(3x^3+2x^2\right)[/tex]

Let's now factor each individual expression as demonstrated below. Afterwards we can substitute back into the expression above --- (2)

Goal - Factor : (4x³ - 9x)(4x² - 14x),

4x³ - 9x ⇒ x(4x² - 9)

4x² - 14x ⇒ 2x(2x - 7)

[tex]x\left(4x^2-9\right)\cdot \:2x\left(2x-7\right) = 2x^2\left(4x^2-9\right)\left(2x-7\right)[/tex]

That leaves us with the following expression,

[tex]2x^2\left(4x^2-9\right)\left(2x-7\right)[/tex] ÷ [tex]\left(2x-7\right)\left(3x^3+2x^2\right)[/tex]

As you can see the " 2x - 7 " cancel out, and the " x² " cancel as well, leaving us with a further simplified expression,

[tex]2\left(4x^2-9\right)[/tex] ÷ [tex]3x+2[/tex]

Which can also be rewritten as [tex]8x^2 - 18[/tex] ÷ [tex]3x + 2[/tex] = [tex]\frac{8x^2 - 18}{3x+2}[/tex], in other words the first option.

Answer:

x^2 -9

Step-by-step explanation:

Let x be the number

x^2 -9

Answer:

[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{8 + 8i}}}}}[/tex]

Option D is the correct option.

Step-by-step explanation:

[tex] \sf{(3 + i) + (5 + 7i)}[/tex]

When there is a ( + ) in front of an expression in parentheses , there is no need to change the sign.

That means, the expression remains the same.

Just remove the unnecessary parentheses

⇒[tex] \sf{3 + i + 5 + 7i}[/tex]

Collect like terms and simplify

⇒[tex] \sf{3 + 5 + i + 7i}[/tex]

⇒[tex] \sf{8 + 8i}[/tex]

Hope I helped!

Best regards!!

Answer:

L=18cm

W=4cm

Step-by-step explanation:

P=2l+2w

44=2[3x+6]+2x

44=6x+12+2x

44=8x+12

8x=44-12

8x=32

x=4

l=3x+6

l=3 x 4=12 + 6=18

Answer:

(-3,-4)

Step-by-step explanation:

The vertex is where the parabola curves.

Answer:

(A)-3 (B)-4

Step-by-step explanation:

♥☺

Answer:

Step-by-step explanation:

18+7*2+11x+4

18+14+11x+4

32+11x+4

11x+36

I'm not sure what some of the ordered pairs are in what you wrote, but a function is when each input has one output. So, for every x there is one y. The x values can not repeat. So, remove one of two ordered pairs where the x value is repeating.

Answer:

7

Step-by-step explanation:

The value of x in the equation -3-(-8)-(-2) = x is 7.

The correct option is 07.

When resolving expressions containing several operations, the procedure to follow is denoted by the acronym PEMDAS. "Parenthesis," "exponents," "multiplication," "division," "addition," and "subtraction" are all represented by the letters P through E.

Given information:

The given equation is described as -3-(-8)-(-2) = x.

To solve the equation as per the PEMDAS rule:

First, we need to simplify the terms within the parentheses: -(-8) is the same as +8, and -(-2) is the same as +2. Therefore, the equation becomes:

-3 + 8 + 2 = x

Next, we can simplify the addition and subtraction from left to right:

-3 + 8 = 5

5 + 2 = 7

Therefore, the value of x is 7.

To learn more about the PEMDAS;

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Answer:

Interest earned in two years is approximately $1,837

Step-by-step explanation:

A= P( 1+r/n)^nt

Where,

A= principal + interest

P= principal= $10,000

r= interest rate = 8.5%

t= Time = 2years

n = periods = 4

A= P( 1+r/n)^nt

= 10,000(1+0.085/4)^4*2

= 10,000( 1 + 0.0213)^8

= 10,000(1.0213)^8

= 10,000(1.1837)

=11,837

A= $11,837

The interest earned in two years is

A = p + I

A - P = I

$11,837 - $10,000 = I

$1,837 = I

I= $1,837

Interest earned in two years is approximately $1,837

Answer:

See below.

Step-by-step explanation:

The set of all real numbers except for 100 in set builder notation (assuming the variable is x) is:

[tex]\{x|x\in\mathbb{R},x\neq100\}[/tex]

The very first x represents the variable.

The second with the R represents the number. Here, we want all real numbers.

And the third is the constraint. We want all real numbers except for 100.

Answer:rises slowly floats steadily loses altitude rises auickly

Step-by-step explanation:

I did the question it's not that hard

Answer:

Rise slowly

Floats steadily

Loses altitude

Rises quickly

Step-by-step explanation:

I hope I helped

Answer:

n=-20

Step-by-step explanation:

[tex]0 = 4 + \frac{n}{5} \\ ⟶ 0 - 4 = \frac{n}{5} \\ ⟶ - 4 \times 5 = n \\ ⟶ - 20 = n[/tex]

Answer:

-20

Step-by-step explanation:

Zero equals four plus n over 5

Solving for n:

Answer:

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

Since T is the midpoint of PQ, we know that PT = TQ, therefore:

3x + 1 = 5x - 5

-2x = -6

x = 3

Since PT = 3x + 1, the answer is PT = 3 * 3 + 1 = 10.

Answer:

$29.16.

Step-by-step explanation:

Each gallon of gas is $2.16.

13.5 gallons of gas is 2.16 (13.5) = $29.16.

Answer:

he payed 29.16 dollars for gas

Step-by-step explanation:

“Neurons are building blocks of nervous system. They process and transmit signals.”  

“In a neuron, the nucleus is found inside cell body”.  

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Since, We know that;

The neurons are the structural and functional system of nervous system. It is composed of parts such as:

Dendrites – Branched structure located at the terminal of the cell body.

Cell body – It contains nucleus.

Nucleus – It is the controlling center of the cell.

Axon – Transports the signals from cell body to synapses.

Synapses – Sends the signal from one neuron to another neuron.

Thus, “Neurons are building blocks of nervous system. They process and transmit signals.”  

“In a neuron, the nucleus is found inside cell body”.  

Learn more about the mathematical expression visit:

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Answer:

[tex] \frac{1}{2} [/tex]

Step-by-step explanation:

Given line is passing through the points (8, 0) & (0, - 4)

[tex]slope \: of \: line = \frac{ - 4 - 0}{0 - 8} = \frac{ - 4}{ - 8} = \frac{1}{2} \\ [/tex]

Answer:

14-1=13 range= 13

Step-by-step explanation:

The range of a set of data is the difference between the highest and lowest values in the set. To find the range, first order the data from least to greatest. Then subtract the smallest value from the largest value in the set.

Answer:

No, but (13,52) is

Step-by-step explanation:

To find this you need to understand what (13,51) means.

13 = x coordinate

51 = y coordinate

If you plug 13 into the equation given (P = 4s) you get 52. Therefore, (13,51) is not a solution but instead (13,52) is.

This means each of the four sides has a length of 13 units.

I hope this helps!

-TheBusinessMan

Answer:

P = 52

Step-by-step explanation:

51 = 13(4)     13x4=52

51 does not equal 52 there fore those values are immensely incorrect.  However you may state  52 as the perimeter therefore allowing 52 1to equal 13(4).

New solution 52 =13(4)

Answer:

33

Step-by-step explanation:

On bottom left add 3 and 4 getting 7  then add 4 and 5 getting 9 then 5 and 3 getting 8

Then on the second row there is 7 + 9 = 16 then 9 + 8 = 17

Last of all the top is 16 + 17 = 33

Answer: 33

Step-by-step explanation: You add the two numbers underneath and on top is the answer

Answer:

p(1/2)= 0 , p(-1/2)= -2

Step-by-step explanation:

p(1/2)= 2(1/2)-1

= 1-1

= 0

p(-1/2) = 2(-1/2)-1

= -1-1

= -2

Answer:

x = 17

Step-by-step explanation:

To solve this equation, we can illustrate the algebraic concepts being employed and solve for the variable.

3(x - 4) = 2x + 5 Distribute the 3 into the parentheses.

3x - 12 = 2x + 5 Subtract 2x from both sides of the equation to combine like terms.

x - 12 = 5 Add 12 to both sides of the equation.

x = 17

Answer:

[tex] \displaystyle \rm \longmapsto \:3(x - 4) = 2x + 5[/tex]

[tex] \displaystyle \rm \longmapsto \:3x - 12 = 2x + 5[/tex]

[tex] \displaystyle \rm \longmapsto 3x - 2x - 12 = 2x - 2x + 5[/tex]

[tex]\displaystyle \rm \longmapsto x - 12 = 5[/tex]

[tex]\displaystyle \rm \longmapsto x - 12 + 12 = 5 + 12[/tex]

[tex]\displaystyle \rm \longmapsto x = 15[/tex]

Answer:

integers

integers are both whole and real numbers as well as they can be negative and/or positive

Answer:

Step-by-step explanation:

The center of dilation is at the point of intersection of the lines through an image point and the corresponding pre-image point.

Here, A and A' are both on the line x=5. C and C' are both on the line y=2, so the center of dilation is (x, y) = (5, 2).

__

The point A' is half as far from (5, 2) as the point A is, so the scale factor of the dilation is 1/2. (A' is 3 units down; A is 6 units down from the center of dilation.)

Answer: 5

Step-by-step explanation: -4×5=-20

Answer:

121, 64, and 16

Step-by-step explanation:

A perfect square is the product of a rational number multiplied by itself. So 11*11=121, 8*8=64, and 4*4=16

Answer:

Step-by-step explanation:

24: the domain is the set of all values of x, and the range are the input y

{(–5, 8), (–5, 2), (–3, 3), (–3, 1), (0, 4), (0, 5), (–5, 7), (–3, 6)}

Answer:

[tex] \frac{51}{17} [/tex]is a rational number.

Step-by-step explanation:

As, [tex] \frac{51}{17} [/tex]

can be written in the form p/q where p is a integer and q is not equally to 0.

Answer:

yes it is a rational because ia in the form of p\q

Answer:

-5

Step-by-step explanation:

First do whats in the parentheses

so it will look like this

3x+3=2x-2 now subract 2x from 3x you get x

x+3=-2

now minus 3 from -2 and you get -5

x= -5