Solve the equation, justify
each step with an algebraic
property
-(x - 6) = 4

The solution to the system of equations is A. (-2, 2)

The system of equation was:

2x + 3y = 2 ..... i

y = 1/2x + 3 ...... ii

Substitute equation ii into i

2x + 3/2x + 9 = 2

Multiply through by 2.

7x + 18 = 4

7x = -14

Divide

x = 14/7

x = -2

Also, y = 1/2x + 3

y = 1/2(-2) + 3

y = -1 + 3

y = 2

Therefore, the solution to the system of equations is (-2, 2).

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Lukas graphed the system of equations shown. 2x + 3y = 2 y = A system of equations. 2 x plus 3 y equals 2. y equals StartFraction one-half EndFraction x plus 3.x + 3 A coordinate grid with 2 lines. The first line passes through the points labeled (negative 2, 2), (0, 0.67) and (1, 0). The second line passes through the points labeled (negative 2, 2) and (0, 3). What is the solution to the system of equations? (–2, 2) (0, 0.67) (0, 3) (1, 0)

Answer:

Table (1)

Step-by-step explanation:

We have to find the table representing a linear function with slope = 5 and y-intercept = 20.

We know y-intercept means value of the function at x = 0,

From all the tables given in picture,

Table (1) shows the value of the function is 20 at x = 0,

So the table (1) should be the answer.

Now we will recheck the answer for the slope = 5

Since slope of a line passing through the two points \((x_1,y_1)\) and \((x_2,y_2)\) is calculated by the formula,

m = \(\frac{y_2-y_1}{x_2-x_1}\)

Therefore, slope of the line passing through (-4, 0) and (0, 20) will be,

m = \(\frac{20-0}{0-(-4)}\)

    = 5

Now we are sure that Table (1) is the answer.

Answer:

24/35

Step-by-step explanation:

Turn 1 1/7 into an improper fraction which would be 8/7 because 1 times 7 is 7 and 7 plus 1 is 8.

Then multiply that by 3/5 and get 8 times 3 which is 24 and 7 times 5 which is 35.

Answer:

2x+25/12

Step-by-step explanation:

Hope this helps and have a great day!!!!!

The "Wrap and complete the order" step at the sandwich shop is the bottleneck due to its total throughput time of 125 seconds. To improve production time and efficiency, the bottleneck needs to be improved by increasing the capacity of the wrapping area or reducing the time required for this step.

The bottleneck in this scenario is the "Wrap and complete the order" step at the sandwich shop. Let's see why it is the bottleneck?Given that the total throughput time is 125 seconds, the time it takes to produce a single sandwich is the sum of all the individual steps. Therefore, 30 + 15 + 20 + 20 + 40 = 125 seconds.As a result, there is no idle time in the sandwich-making process; each step is completed one after the other

. Since each sandwich spends the same amount of time at each stage, each sandwich should be finished at the same time. This implies that the "Wrap and complete the order" step is the bottleneck because it is the last step in the process. If two employees split the wrap up and order completion steps, the bottleneck shifts to the previous stage (Toast sandwich) since the sandwich production is completed before wrapping and order completion.

Hence, to improve the production time and efficiency, the bottleneck (wrap-up and order completion) needs to be improved by increasing the capacity of the wrapping area or by reducing the time required for this step.

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The length of the rectangle is 7.875 meters and the width of the rectangle is 5.625 meters.

Perimeter of a rectangle = 2(length + width)

27 = 2(1.4x + x)

27 = 2(2.4x)

27 = 4.8x

x = 27/4.8

x = 5.625

Therefore,

Length of the rectangle = 1.4x

= 1.4(5.625)

= 7.875 meters

Width of the rectangle = x

= 5.625 meters

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Answer:

  42, 38, 34, 30

Step-by-step explanation:

You want the first 4 terms of the sequence described by ...

  an = 42 -4(n -1), n ∈ ℕ

You can write the first 4 terms of the sequence by evaluating the 'an' expression for n = 1, 2, 3, 4.

Or, you can recognize the expression describes a sequence with a first term of 42 and a common difference of -4. That is, each term is 4 less than the one before.

The terms you want are ...

  42, 38, 34, 30

__

Additional comment

The equation for the n-th term of an arithmetic sequence is ...

  an = a1 +d(n -1)

where a1 is the first term, and d is the common difference. Comparing this to the given equation, we see a1 = 42, d = -4.

<95141404393>

a. The number of graks after 1.5 years are given as follows: 707.

b. The same amount of graks and of sprogs is after 18 years.

The definition of an exponential function is presented as follows:

\(y = a(b)^{\frac{x}{n}}\)

In which the terms of the function are listed as follows:

Then the functions are given as follows for this problem:

After 1.5 years, the number of graks is given as follows:

y = 500 x 2^(0.5) = 707 graks.

The amounts will be the same when:

\(4000(2)^{\frac{x}{6}} = 500(2)^{\frac{x}{3}}\)

\(\frac{(2)^{\frac{x}{3}}}{(2)^{\frac{x}{6}}} = \frac{4000}{500}\)

\(2^{\left(\frac{x}{3} - \frac{x}{6}\right)} = 8\)

\(2^{\left(\frac{x}{3} - \frac{x}{6}\right)} = 2^3\)

Hence:

x/3 - x/6 = 3

x/6 = 3.

x = 18 years.

In the first question, it is after 1.5 years.

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The equilibrium price and quantity for each pair of demand and supply functions are as follows:

a. Q = 10 - 2P

To find the equilibrium, we set the quantity demanded equal to the quantity supplied:

10 - 2P = P

By solving this equation, we can determine the equilibrium price and quantity. Simplifying the equation, we get:

10 = 3P

P = 10/3 ≈ 3.33

Substituting the equilibrium price back into the demand or supply function, we can find the equilibrium quantity:

Q = 10 - 2(10/3) = 10/3 ≈ 3.33

Therefore, the equilibrium price is approximately $3.33, and the equilibrium quantity is also approximately 3.33 units.

b. Q = 1640 - 30P

Setting the quantity demanded equal to the quantity supplied:

1640 - 30P = P

Simplifying the equation, we have:

1640 = 31P

P = 1640/31 ≈ 52.90

Substituting the equilibrium price back into the demand or supply function:

Q = 1640 - 30(1640/31) ≈ 51.61

Hence, the equilibrium price is approximately $52.90, and the equilibrium quantity is approximately 51.61 units.

In summary, for the demand and supply functions given:

a. The equilibrium price is approximately $3.33, and the equilibrium quantity is approximately 3.33 units.

b. The equilibrium price is approximately $52.90, and the equilibrium quantity is approximately 51.61 units.

In the first paragraph, we summarize the steps taken to determine the equilibrium price and quantity for each pair of demand and supply functions. We set the quantity demanded equal to the quantity supplied and solve the resulting equations to find the equilibrium price. Substituting the equilibrium price back into either the demand or supply function allows us to calculate the equilibrium quantity.

In the second paragraph, we provide the specific calculations for each pair of functions. For example, in case a, we set Q = 10 - 2P equal to P and solve for P, which gives us P ≈ 3.33. Substituting this value into the demand or supply function, we find the equilibrium quantity to be approximately 3.33 units. We follow a similar process for case b, setting Q = 1640 - 30P equal to P, solving for P to find P ≈ 52.90, and substituting this value back into the function to determine the equilibrium quantity of approximately 51.61 units.

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Answer:

200 cans

Step-by-step explanation:

8 cans x 5 cans = 40 cans on the base

5 layers of 40 cans=5 x 40 = 200 cans total

Answer:

exchange 9 with 12

simplyfy both til 1/2*4/3

2/3 finally

The  Smallest numbers is 3.068 and 3.6

Check the whole number portion of each decimal number before placing them in ascending order. Since 4 is the smallest whole number, the smallest decimal number is 4.926. The remaining decimal digits all contain the same whole number, or 18.

The least number among those given is 1.

The smallest three-digit number in the number system is 100, which becomes a two-digit number, which is 99, when one is deducted from the number (a two-digit number). Therefore, in the number system, 100 is the smallest three-digit number. The smallest three-digit number is 100, which is so proven.

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The elimination of the equations 18x-6y=-20 and -9x+3y=15 is 0 = 10, which is a contradiction. This means that there is no solution to the system of equations.

What is an elimination?

To eliminate one of the variables, we need to manipulate one or both of the equations so that when we add them together, one of the variables is eliminated.

Let's start with the given equations:

18x - 6y = -20

-9x + 3y = 15

We can see that the coefficients of y in both equations are opposite, which means we can eliminate y by adding the two equations together. However, we need to make sure the coefficients of y have the same absolute value, so we'll multiply the second equation by 2:

18x - 6y = -20

-18x + 6y = 30

Now we can add the two equations together:

0x + 0y = 10

This equation simplifies to 0 = 10, which is a contradiction. This means that there is no solution to the system of equations. In other words, the two equations represent two parallel lines that never intersect.

Alternatively, we can recognize that the two equations represent the same line when simplified, since the second equation is simply half of the first equation. In this case, there are infinitely many solutions, since any point on the line satisfies both equations.

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Complete question is: The elimination of the equations 18x-6y=-20 and -9x+3y=15 is 0 = 10.

Answer:

sorry I'm not the best with math and sorry if I just waisted your time... :)

The probability that the line is a line of symmetry for the square is given as follows:

C. 2/5.

A probability is calculated as the division of the number of desired outcomes by the number of total outcomes.

Point P is the first point to be chosen in this problem, meaning that for the second point, there will be a total of 80 options left.

From the second image given at the end of the answer, of the remaining 80 points, 32 are going to belong to one of the possible symmetry lines to the square, hence the probability is calculated as follows:

p = 32/80 = 4/10 = 2/5.

Which means that the correct option is given by option C.

The problem is given by the first image shown at the end of the answer.

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Answer:

He will earn $140, my bad miss calculated...

Step-by-step explanation:

Its 140....

Answer:

-35

Step-by-step explanation:

-|35|

-35

Answer:

-35

Step-by-step explanation:

−|−5⋅(−7)|

Multiply inside the absolute values

−|35|

Take the non negative value inside the absolute value

- 35

465 is the cost of the cash price will she pay overall for the car.

What is cost ?

25 % of cash price 4500 ×  25%  = 1125

12 monthly    320 ×  12  = 3840

All 1125 + 3840  =  4965

more than  4965  -  4500  = 465

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To find the total number of minutes used, divide $175 by the $.25 per minute charge. This equals 650 minutes, meaning the user had used 650 minutes throughout the month.

$50 initial fee + $.25 per minute = $225

$225 - $50 = $175

$175 / $.25 = 650 minutes

The initial fee for the phone plan was $50, and for every minute used, an additional $.25 was charged. Last month's bill was $225, so subtracting the $50 initial fee from the total cost of the bill leaves $175, which is the cost of the minutes used. To find the total number of minutes used, divide $175 by the $.25 per minute charge. This equals 650 minutes.

The phone plan charges an initial fee of $50 for the month, as well as an additional $.25 for every minute used. Last month's bill was $225, so to find the total number of minutes used, subtract the $50 initial fee from the total cost of the bill. This results in $175, which is the cost of the minutes used. To find the total number of minutes used, divide $175 by the $.25 per minute charge. This equals 650 minutes, meaning the user had used 650 minutes throughout the month.

A user's phone plan last month costed $225, which included an initial fee of $50 plus $.25 for every minute used. After subtracting the initial fee from the total bill cost, $175 was left which was the cost of the minutes used. Dividing this number by the $.25 per minute charge reveals that the user had used 650 minutes.

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The measure of angle Q in the triangle QMN is 52.83°

An equation is an expression that shows the relationship between two or more variables and numbers.

For a triangle with sides a, b, c and respective opposite angles A, B, C, cosine rule is:

a² = b² + c² - 2bc * cos(A)

In triangle QMN, QM = 18, MN = 17, QN = 20, hence:

17² = 18² + 20² - 2(18)(20) * cos(Q)

Q = 52.83°

The measure of angle Q in the triangle QMN is 52.83°

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Answer:

53

Step-by-step explanation:

its rounded

Answer:

c or a

Step-by-step explanation:

Answer:

A(-3,-1)-----A'(-1,2)

B(2,1)------B'(4,4)

here

x is increased by -1--3=2

and

y is increased by2--1= 3

so

A.(x',y')=(x+2,y+3)

The maximum value of the objective function will be:50(100) + 50(20) = 5000 + 1000 = 6000

The given linear programming is:Max 50A + 50Bs.t.10A ≤ 100010B ≤ 80020A + 40B ≤ 4000A, B ≥ 0 To solve the linear programming using the solver follow these steps:Step 1: Open the Excel spreadsheet and go to Data, choose the solver and enable it.

Step 2: A Solver Parameters dialog box will appear. Input the necessary details as follows:Set Objective: 50A + 50BTo: Max Subject to constraints:

10A ≤ 100010B ≤ 80020A + 40B ≤ 4000

Select variables to change: A, BStep 3: Click Solve and the optimal value of A and B will be found.In this case, the optimal value of A is 100 and that of B is 20.

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Step-by-step explanation:

option A

3 IS CORRECT

HOPE IT HELPS

Answer:

3

Step-by-step explanation:

edge 2021

Answer:

x is greater than 3

Step-by-step explanation:

Answer:

2x + 5 < 5x - 4

5 + 4 < 5x -2x

9 < 3x

3 < x

Answer: −12f+6g

Step-by-step explanation:

a. y = 3x^4 - 10x^3 + 6x^2 + 1 has a local minimum at x = 0, a local maximum at x ≈ 0.44, and another local minimum at x ≈ 4.56.

b. y = 6 does not have any local maximum, local minimum, or point of inflection. Its graph is a horizontal line at y = 6.

To find the stationary values of a function, we need to first find the critical points, where the derivative is equal to zero or undefined. Let's consider each function separately.

a. y = 3x^4 - 10x^3 + 6x^2 + 1

To find the critical points, we need to find the derivative of the function and set it equal to zero.

First, let's find the derivative:

y' = 12x^3 - 30x^2 + 12x

Next, set the derivative equal to zero and solve for x:

12x^3 - 30x^2 + 12x = 0

Factoring out 6x from each term:

6x(x^2 - 5x + 2) = 0

Now, we have two possibilities:

1. 6x = 0, which gives us x = 0.
2. x^2 - 5x + 2 = 0, which can be solved using the quadratic formula.

Using the quadratic formula, we get two more values for x:

x ≈ 0.44 and x ≈ 4.56

Now, we have three critical points: x = 0, x ≈ 0.44, and x ≈ 4.56.

To determine whether these critical points yield a local maximum, local minimum, or point of inflection,

we need to examine the behavior of the function around these points using the first and second derivative.

Let's analyze the behavior of the function using the first and second derivative:

First, let's find the second derivative:

y'' = 36x^2 - 60x + 12

Now, let's substitute the critical points into the second derivative:

1. For x = 0, y'' = 12 > 0. This indicates a local minimum.

2. For x ≈ 0.44, y'' ≈ -0.43 < 0. This indicates a local maximum.

3. For x ≈ 4.56, y'' ≈ 188.2 > 0. This indicates a local minimum.

Therefore, the function has a local minimum at x = 0, a local maximum at x ≈ 0.44, and another local minimum at x ≈ 4.56.

Now, let's move on to the second function:

b. y = 6

This function is a constant function, meaning that its derivative is always zero.

Therefore, there are no critical points, and the function does not have any local maximum, local minimum, or point of inflection. The graph of this function would be a horizontal line at y = 6.

To summarize:
a. y = 3x^4 - 10x^3 + 6x^2 + 1 has a local minimum at x = 0, a local maximum at x ≈ 0.44, and another local minimum at x ≈ 4.56.

b. y = 6 does not have any local maximum, local minimum, or point of inflection. Its graph is a horizontal line at y = 6.

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Answer:

12.5

Step-by-step explanation:

Answer:

A line parallel to this one would have a slope of 3. where m is the slope and b is the y intercept. In this case, the equation y=3x+5 is already in slope intercept form, which means the slope is 3. Parellel lines have the same slope, so any other line with slope 3 is parallel to this line.

I think that's the answer

Answer: y = -3x - 3

Step-by-step explanation:

If you are looking for a line that is parallel, then it must have the same gradient

Therefore;

y= -3x +c

And because it passes through (0,3), substitute in the values to find c

3 = -3 x 0 + c

c = 3

So the equations would be y = -3x -3