Which graph represents a linear function?

Answer:

(a) The number of units that will give the maximum profit is 2,000 units.

(b) The maximum possible profit is $274,000.

Step-by-step explanation:

(a) How many units will give the maximum profit?

From the attached photo in the question, we are given;

R(x) = 324x - 0.0495x^2 ………………....................................……….. (1)

C(x) = 8000 + 162x - 0.099x^2 + 0.00003x^3 …………………….. (2)

In economics, profit function, P(x), is obtained as follows:

P(x) = R(x) - C(x) ………………………. (3)

Substituting the equations (1) and (2) for R(x) and C(x) respectively into equation (3) and then simplify, we have:

P = 324x - 0.0495x^2 - (8000 + 162x - 0.099x^2 + 0.00003x^3)

P = 324x - 0.0495x^2 - 8000 - 162x + 0.099x^2 - 0.00003x^3

P = -8000 + 162x + 0.0495x^2 - 0.00003x^3 ………………….. (4)

Taking a derivative of equation (4) with respect to x and equating to 0, we have:

162 + 0.099x - 0.00009x^2 = 0 .................... (5)

Using the almighty formula as follows:

x = (-b +/- (b^2 - 4ac)^0.5) / 2a ………………. (6)

Where, from equation (5);

a = - 0.00009

b = 0.099

c = 162

Substituting the values into equation (6), we have:

x = (-0.099 +/- (0.099^2 - (4 * (- 0.00009) * 162))^0.5) / (2 * - 0.00009)

x = (-0.099 +/- 0.261) / -0.00018

x = (-0.099 + 0.261) / -0.00018, or x = (-0.099 - 0.261) / -0.00018

x = -900, or x = 2000

Since negative number does not have economic value in economics, the number of units that will give the maximum profit is therefore 2,000 units.

(b) What is the maximum possible profit?

From part a, x = 2000

Substituting x = 2000 into equation (4) and then solve, we have:

P(x) = -8000 + (162 * 2000) + (0.0495 * 2000^2) - (0.00003 * 2000^3)

P(x) = 274,000

Therefore, the maximum possible profit is $274,000.

Answer:

You must turn the variables, or the "x" into a number to make the numbers on the left equal the numbers on the right.

Step-by-step explanation:

In order to solve these problems, you must replace the variable with a number to have the equation on the left equal what is on the right.

Equation 1:

x - 4y = -12 <----- This is the original problem.

-8 - 4y = -12 <----- Replace the variable.

-12y = -12 <----- This is a true statement.

Equation 2:

  5x=20y+60 <----- This is the original problem.

5(16) =20y+60 <----- Replace the variable/Do the addition.

80 = 80y <------ This is a true statement.

Hope this helps! :D

The expressions are simplified to 2x and [tex]\frac{2}{(x+ 1)(x - 1)}[/tex]

1.

Given the expression;

[tex]\frac{8x^2 - 4x}{4x - 2}[/tex]

Let's factorize the numerator;

[tex]\frac{2x( 4x - 2)}{4x - 2}[/tex]

Factor the common terms, we have;

2x

2. [tex]\frac{1}{x-1} - \frac{2}{x} + \frac{1}{x + 1}[/tex]

Find the Lowest common multiple

[tex]\frac{x(x+ 1) - 2 (x+ 1)(x - 1) + x(x-1)}{x(x-1)(x+ 1)}[/tex]

expand the brackets

[tex]\frac{x^2 + x -2(x^2 -x + x -1) + x^2 -x}{x(x-1)(x+ 1)}[/tex]

[tex]\frac{x^2+x - 2x^2 -2 + 2x + 2 + x^2 - x}{x(x+1) (x -1)}[/tex]

collect like terms

[tex]\frac{2x}{x(x+ 1) (x-1)}[/tex]

Divide common terms

[tex]\frac{2}{(x+ 1)(x - 1)}[/tex]

Thus, the expressions are simplified to 2x and [tex]\frac{2}{(x+ 1)(x - 1)}[/tex]

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Answer:

NO

Step-by-step explanation:

no, 9/31 is not an irrational number. ... So we have shown that the square root of any non-square cannot be rational; hence, it is irrational.

The square root of 9/31 rational is not a rational number.

We have given that  9/31.

We have to determine is the square root of 9/31 rational

A rational number is a number that can be expressed as the quotient of two integers, with the denominator not equal to zero.

9/31 is not an irrational number.

So we have shown that the square root of any non-square cannot be rational.

hence, it is irrational.

Therefore it is not a rational number.

To learn more about the rational number visit:

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Answer: C=50.24 ft, A=200.96 ft^2

Step-by-step explanation:

Area:

A=(pi)*r^2

A=(3.14)*8^2

A=200.96 ft^2

Circumference:

C=2*(pi)*r

C=2*(3.14)*8

C=50.24 ft

Answer:

The father is 67 and the son is 38

Step-by-step explanation:

TRUST ME Bois and Girls

Answer:

Prime Number

Step-by-step explanation:

Answer:

The answer is D

Step-by-step explanation:

Answer:

2(p - 10)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Step-by-step explanation:

Step 1: Translate

"Twice" is multiplied by 2.

"Difference" is subtraction.

"p" is p.

"10" is 10.

Step 2: Write expression

2(p - 10)

2p - 20

In one week he's made $1,500

Answer:

1,500 fffffffffffffffffffffffffffffffff

Answer: Its 1

Step-by-step explanation:

Answer:

x = infinite amount of solutions

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Step-by-step explanation:

Step 1: Define Equation

8 + 2(x - 6) = -2 + 2x - 2

Step 2: Solve for x

Here we see that x does indeed equal x.

∴ x = infinite amount of solutions.

Answer:

Step-by-step explanation:

1 and 2.

slope is m = ( y2-y1) / (x2-x1)

slope of BC = 5-3 /6-1 = 2/5

slope of AD = 1 +1 / 7-2 = 2/5

3 and 4

use the distance formula d= √(x2-x1)² +(y2-y1)²

BC = √( 6-1)²+(5-3)² = √5²+2²= √29

AD = √(7-2)²+(1+1)² = √5²+2² = √29

5.

since BC and AD have the same slope then they are parallel

since BC and AD are same length the segments are ≅

so ABCD is a rectangle

Answer:

b

Step-by-step explanation:

Answer:

b he is your answer dear friend

Answer:

.5

Step-by-step explanation:

22

23

=

22

23

=

2*2

2*2*2

=

1

2

(Decimal: 0.5)

Answer:

1-positive

2-negitive

3-zero

4-undefined

Answer:

1 ) positive 2) negative 3) undefined 4) undefined

Step-by-step explanation:

Answer:

-1/4

Step-by-step explanation:

But in reality, it is going from positive to negative, so the answer is -1/4.

Answer:

-1/4

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

-20 + 15 = -35

a negative + a positive = a negative

Hope this helps!

The linear function f(x) = 4/5x - 9

Given,

f(-20) = -25

Slope, m = 4/5

We have to find the linear function f(x)

We know the slope-intercept form, y = mx + b

Here,

f(-20) = -25

x = -20 and y = -25

slope, m = 4/5

So, lets solve for b.

y = mx + b

-25 = 4/5 (-20) + b

-25 = 4 × (-4) + b

-25 = -16 + b

Add 16 to both sides

16 - 25 = -16 + 16 + b

We get,

-9 = b

Now, find f(x)

f(x) = 4/5x - 9

That is, the linear function f(x) = 4/5x - 9

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Answer:

e) 0.842

Step-by-step explanation:

Answer:

B) 4/15

Step-by-step explanation:

green marbles: 4

total marbles: 15

probability

4/15

Answer:

answer is 14   and it is a example of derivative

Step-by-step explanation:

Answer:

Triangle sum of equation: x° + 109° = 180°

value of x = 71°

Answer:

She would expect to find about 282 fish in the lake.

Step-by-step explanation:

Answer:

Step-by-step explanation:a

Answer:

[tex]6d \: is \: same \: as \: 4d + 2d[/tex]

Step-by-step explanation:

[tex]4d + 2d = 6d \\ pls \: mark \: as \: brainliest[/tex]