Estimate: 25.73 – 2.19

The given equation translated 4 units to the left is  x - 1.

It is required to write the given equation translated 4 units to the left.

Coordinate geometry is defined as the study of geometry using the coordinate points. Coordinate geometry is required to provide a link between algebra and geometry through the use of line and curve graphs.

Given that:

Replace x in f(x) with x + 4 to translate 4 units to the left.

Replace x in f(x) with x - 4 to translate 4 units to the right.

Since you want to go left,

f(x) → f(x + 4)

f(x)  = (x + 4) - 5

∴f(x)  = x - 1

Therefore, the given equation translated 4 units to the left is  x - 1.

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In equation (a), x=30 is the solution. In equation (b), it has an infinite number of solutions. In equation (c), it has no solution.

(a) To solve the equation 6x+4x-6=24+9x, we need to simplify both sides of the equation and isolate the variable x. Start by combining like terms on both sides of the equation:

10x-6=24+9x

Next, move all the terms with x to one side of the equation by subtracting 9x from both sides:

10x-9x-6=24

Simplify further:

x-6=24

Now, isolate x by adding 6 to both sides:

x-6+6=24+6

x=30

Therefore, the equation has one solution, x=30.

(b) To solve the equation 25-4x=15-3x+10-x, we need to simplify both sides of the equation and isolate the variable x. Start by combining like terms on both sides of the equation:

25-4x=15-3x+10-x

Combine like terms:

25-4x=25-4x

Notice that both sides of the equation are identical. This means that the equation is an identity, and it has an infinite number of solutions.

(c) To solve the equation 4x+8=2x+7+2x-20, we need to simplify both sides of the equation and isolate the variable x. Start by combining like terms on both sides of the equation:

4x+8=2x+7+2x-20

Combine like terms:

4x+8=4x-13

Notice that both sides of the equation are not equal. This means that the equation is a contradiction, and it has no solution.

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Final Answer:

The revenue function is R(x) = 150x.
The profit function is P(x) = -0.1x² + 141x - 3200.
To make a profit, Gymnast Clothing should manufacture between approximately 23.07 and 1386.93 pairs of cleats. Because they cannot manufacture a fraction of a cleat, they should manufacture at least 24 pairs and no more than 1386 pairs.

Explanation:

Let's start by defining the revenue and profit functions for Gymnast Clothing.
**Revenue Function:**
The revenue function, R(x), is calculated by multiplying the number of cleats sold, x, by the selling price per pair of cleats. Since Gymnast Clothing sells cleats at $150 per pair, the revenue function is:
R(x) = 150x

**Cost Function:**
The cost function, C(x), is given as:
C(x) = 3200 + 9x + 0.1x²

**Profit Function:**
The profit function, P(x), represents the money made after subtracting costs from the revenue. It's defined as the difference between the revenue function and the cost function:
P(x) = R(x) - C(x)

Substitute R(x) with the revenue function and C(x) with the cost function to get:
P(x) = 150x - (3200 + 9x + 0.1x²)

Simplify the profit function by combining like terms:
P(x) = -0.1x² + 141x - 3200

This is the profit function, which tells us how the profit varies with the number of x pairs of cleats manufactured and sold.

**Determining the Number of Cleats to Manufacture for Profit:**
To figure out how many cleats Gymnast Clothing should manufacture to make a profit, we need to determine when the profit P(x) is greater than zero:
P(x) > 0

In other words, we want to find the values of x for which:
-0.1x² + 141x - 3200 > 0

Solving this inequality for x gives us the interval within which manufacturing the cleats will be profitable. Based on the solution to the inequality, the number of pairs of cleats that Gymnast Clothing should manufacture to make a profit is between approximately 23.07 and 1386.93 pairs.

Summary:
- The revenue function is R(x) = 150x.
- The profit function is P(x) = -0.1x² + 141x - 3200.
- To make a profit, Gymnast Clothing should manufacture between approximately 23.07 and 1386.93 pairs of cleats. Because they cannot manufacture a fraction of a cleat, they should manufacture at least 24 pairs and no more than 1386 pairs.

Revenue: [tex]\( R(x) = 150x \)[/tex]. Profit: [tex]\( P(x) = -0.1x^2 + 141x - 3200 \).[/tex] Solve [tex]\(-0.1x^2 + 141x - 3200 > 0\)[/tex] for profit.

To find the exact values for the revenue and profit functions, we'll use the given cost function and selling price.

1. Revenue Function [tex](\(R(x)\))[/tex]: The revenue is given by the product of the number of units sold [tex](\(x\))[/tex] and the selling price per unit[tex](\$150):[/tex] [tex]\[ R(x) = 150x \][/tex]

2. Profit Function [tex](\(P(x)\)):[/tex] The profit is the difference between revenue and cost: [tex]\[ P(x) = R(x) - C(x) \][/tex]

Given that the cost function is [tex]\(C(x) = 3200 + 9x + 0.1x^2\),[/tex] we substitute this into the profit function: [tex]\[ P(x) = 150x - (3200 + 9x + 0.1x^2) \][/tex]

Simplify the expression:

[tex]\[ P(x) = -0.1x^2 + 141x - 3200 \][/tex]

So, the exact functions are:

1. Revenue Function:  [tex]\[ R(x) = 150x \][/tex]

2. Profit Function: [tex]\[ P(x) = -0.1x^2 + 141x - 3200 \][/tex]

To find how many cleats Gymnast Clothing should manufacture to make a profit, we set the profit function greater than zero and solve for x: [tex]\[ -0.1x^2 + 141x - 3200 > 0 \][/tex]

Solving this inequality will provide the exact values of x for which the company makes a profit within the given range [tex]\(0 \leq x \leq 500\)[/tex]. This involves factoring, using the quadratic formula, or graphing to determine the valid range of x values for profit.

The coat would cost $0.60 more in Delaware County than in Fairfield County.

To determine how much more the coat would cost in Delaware County compared to Fairfield County, we need to calculate the total cost of the coat in both counties, including their respective sales tax rates, and then find the difference between these two amounts.

First, let's calculate the total cost of the coat in Delaware County:

1. Original price of the coat: $80

2. Sales tax rate in Delaware County: 7.25%

The sales tax amount in Delaware County is calculated as:

[tex]\[\text{Sales tax} = \text{Original price} \times \left(\frac{\text{Sales tax rate}}{100}\right) = 80 \times \left(\frac{7.25}{100}\right) = 80 \times 0.0725 = 5.80\][/tex]

So, the total cost in Delaware County is:[tex]\[\text{Total cost} = \text{Original price} + \text{Sales tax} = 80 + 5.80 = 85.80\][/tex]

The sales tax amount in Fairfield County is calculated as:

[tex]\[\text{Sales tax} = \text{Original price} \times \left(\frac{\text{Sales tax rate}}{100}\right) = 80 \times \left(\frac{6.5}{100}\right) = 80 \times 0.065 = 5.20\][/tex]

So, the total cost in Fairfield County is:

[tex]\[\text{Total cost} = \text{Original price} + \text{Sales tax} = 80 + 5.20 = 85.20\][/tex]

Now, let's find the difference in total costs between Delaware County and Fairfield County:

[tex]\[\text{Difference} = \text{Total cost in Delaware County} - \text{Total cost in Fairfield County} = 85.80 - 85.20 = 0.60\][/tex]

Using the concept of similar triangles to calculate the scale factor, the height of the streetlight is 3 times the height of the person.

Length of shadow cast = 10 feets

Height of person = 6 feets

Distance of person from streetlight light = 20 feets

Since the triangles are similar :

Comparing the length of both triangles :

The scale factor is :

Using the scale factor ; the height of the streetlight will be :

Height of streetlight = 18 feets

Height of person = 6 feets

Therefore, the streetlight is (18/6 = 3) 3 times the height of the person.

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0.7x-1.4 =-3.5

 add 1.4 to each side

0.7x = -2.1

 x = -2.1 / 0.7

x = -3

 Answer is B -3

[tex]-3[/tex] is the value of x in the equation [tex]0.7x -1.4 = -3.5[/tex]

What is equation?

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

According to question, we have to find the value of  x in the equation [tex]0.7x -1.4 = -3.5[/tex]

Now,[tex]0.7x -1.4 = -3.5[/tex]

⇒[tex]x=\frac{-2.1}{0.7} \\[/tex]

⇒[tex]x=-3[/tex]

So,-[tex]3[/tex] is the  value of x in the equation [tex]0.7x -1.4 = -3.5[/tex]

Hence, Option(B) is correct.

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We have that   1.888 as a mixed number is

[tex]\frac{9}{5}=1\frac{4}{5}[/tex]

From the Question we are told that

1.888 is given

Generally

[tex]1.8888 \approx\frac{9}{5}[/tex]

Therefore

the Mixed number is given as

[tex]\frac{9}{5}=1\frac{4}{5}[/tex]

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Answer:

  No.

Step-by-step explanation:

Zero does not have a reciprocal. 1/0 is undefined.

Answer:

y=7x or the answer is 7

Step-by-step explanation:

i took the test in (k12)

112-88 = 24

 they save $24 per month

so 650/24 = 27.083

so it will pay for itself in 27.083 months, round up to 28 months

9514 1404 393

Answer:

  -7.2, -0.8

Step-by-step explanation:

Those numbers are ...

  -4 ± 3.2 = {-4 -3.2, -4 +3.2} = {-7.2, -0.8}

The numbers -7.2 and -0.8 are a distance of 3.2 from -4 on the number line.

Except for pair (6, 2), all pairs  (4, 6), (10, 2), and (2, 24) have the greatest common factor of 2.

Given that,
Which pair of numbers have the greatest common factor of 2 from the options is to be determined.

The greatest common factor is defined as a group of the set of numbers that is the most considerable and greatest factor that all the numbers includes.

Here,

The greatest common factor of 4 and 6 is 2.
The greatest common factor of 10 and 2 is 2.
The greatest common factor of 6 and 12 is  6.
The greatest common factor of 2 and 24 is 2.

Thus, except pairs 6 and 12 all pairs  (4, 6), (10, 2), and (2, 24) has greatest common factor of 2.

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first number is x , second number is y

 y = x-6

 so answer is B 22-6 = 16

B (22,16)

The freezer's temperature decreased by 30 degrees Celsius from its original temperature of 18 degrees Celsius to reach -12 degrees Celsius.

The temperature change in the freezer is calculated by finding the difference between the final temperature and the initial temperature.

In this case, the freezer started at 18 degrees Celsius and cooled down to -12 degrees Celsius.

To determine the difference, subtract the initial temperature from the final temperature:

-12 degrees Celsius (final temperature) - 18 degrees Celsius (initial temperature) = -30 degrees Celsius.

The negative sign indicates a decrease in temperature.

Therefore, the temperature of the freezer decreased by 30 degrees Celsius.

This temperature change represents the amount by which the freezer's internal temperature dropped during the cooling process.

It's crucial to note that the negative value signifies a colder temperature than the initial state.

The cooling process might be influenced by factors such as the freezer's capacity, insulation, and cooling mechanism.

Temperature changes is essential for various applications, including food preservation and scientific experiments where precise temperature control is crucial.

The freezer experienced a temperature decrease of 30 degrees Celsius, resulting in a colder temperature of -12 degrees Celsius from its initial state of 18 degrees Celsius.