Answer:
### What is the general equation of a Straight line inequality?

The** equation** of **line** passing through points **(-4, 1)** and **(2, 3) **will be

**3y = x + 7**

An** inequality** in mathematics compares **two values** or **expressions, **showing if one is less than, greater than, or simply not equal to another value. The **general equation** of a straight line **inequality** is -

**[y] < [m]x + [c]**

**[y] > [m]x + [c]**

**[y] ≥ [m]x + [c]**

**[y] ≤ [m]x + [c]**

where -

**[m] → **is** slope** of line which tells the **unit rate** of change of [y] with respect to [x].

**[c] **→ is the **y - intercept** i.e. the point where the graph cuts the **[y] axis.**

The** equation **of a **straight line****inequality **can be also written as -

Ax + By + C > 0

By > - Ax - C

**y > (- A/B)x - (C/A)**

Given is **inequality's solution** graphed [Refer to graph attached].

The **inequality **whose** solution** is graphed is -

5x + 3 > 3

On solving -

5x + 3 > 3

5x + 3 - 3 > 3 - 3

5x > 0

x > 0

Therefore, the** inequality **whose** solution** is graphed is

**5x + 3 > 3**

(Refer the image attached, for reference)

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Answer:
Here is the graph

The Answer is C) 5x + 3 > 3

The Answer is C) 5x + 3 > 3

Pls help me with these equations 2x-7/3 = 54 (x - 5) = 3 (x - 7) + x + 15x + 2x - 9 = 7x + 116x - 12 + 4 (x - 7) = 5 (2x - 4) - 15x - 1/3 = 8

Determine if the sequence below is arithmetic or geometric and determine thecommon difference / ratio in simplest form.100, 20, 4, ...

1) Refer back to Lesson 2, Part A. Assume that the average shoulder width of the people in the line was 1.325 feet. How long would the line be if it contained 10 million people? Express your answer in feet.

Evaluate the expression 3.14(a2 + ab) when a = 3 and b = 4.

Suppose the labor force is 189 million of a possible 244 million working-age adults. The total number of unemployed is 15 million. Whatis the standard unemployment rate?

Determine if the sequence below is arithmetic or geometric and determine thecommon difference / ratio in simplest form.100, 20, 4, ...

1) Refer back to Lesson 2, Part A. Assume that the average shoulder width of the people in the line was 1.325 feet. How long would the line be if it contained 10 million people? Express your answer in feet.

Evaluate the expression 3.14(a2 + ab) when a = 3 and b = 4.

Suppose the labor force is 189 million of a possible 244 million working-age adults. The total number of unemployed is 15 million. Whatis the standard unemployment rate?

The **common difference** of the given **A.P.** is **-2**.

A mathematical expression is made up of **terms (constants and variables) **separated by mathematical operators. A mathematical equation is used to **equate two expressions**. Equation modelling is the process of writing a **mathematical verbal expression** in the form of a mathematical expression for **correct analysis, observations **and **results** of the given problem. An **arithmetic sequence** is a sequence of numbers where the differences between every **two consecutive terms** is the **same**. The **nth term** of an A.P. is given by -

**a[n] = a + (n - 1)d**

We have the following **sequence **10, 8, 6, 4, ... .

We have -

10, 8, 6, 4, ...

The **common difference** of the given **A.P.** is -

d = 8 - 10 = 6 - 8 = 4 - 6

d = - 2

Therefore, the **common difference** of the given **A.P.** is **-2**.

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**Answer:**

-2

**Step-by-step explanation:**

10-8=2

8-6=2

6-4=2

4-2=2

b. Write down the fixed-step-size gradient algorithm for solving this optimization problem.

c. Suppose that Find the largest range of values for α such that the algorithm in part b converges to the solution of the problem.

**Answer:**

Answer for the question :

Consider the optimization problem where A m × n , m ≥ n , and b m .

a. Show that the objective function for this problem is a quadratic function, and write down the gradient and Hessian of this quadratic.

b. Write down the fixed-step-size gradient algorithm for solving this optimization problem.

c. Suppose that Find the largest range of values for α such that the algorithm in part b converges to the solution of the problem.

is explained din the attachment.

**Step-by-step explanation:**

**Answer:**

a) y= 2x +3

b) y= ¼x +1

**Step-by-step explanation:**

Please see the attached picture for the full solution.

Further explanation:

b) y-intercept of A= 5

y-intercept of line= 5 -4= 1

Since the gradient of the line is equal to the gradient of line A, gradient of line= ¼.

**Answer:**

**Step-by-step explanation:**

168000*28%=47,040

a. Calculate the contribution to profit from the special order.

**Answer:**

**The contribution to profit from the special order us $38,000.**

**Step-by-step explanation:**

Consider the provided information.

We need to calculate the contribution on to profit from the special order.

Wolff Construction Company, which operates outside Packer’s normal sales territory, asks Packer to pour 40 slabs for Wolff’s new development of homes. Packer has the capacity to build 300 slabs and is presently working on 250 of them. Wolff is willing to pay only $2,750 per slab.

Sale = 40 × $2,750 = $110,000

To find the profit subtract the materials and labor cost from sale amount.

Particulars Amount

Sale (40 × $2,750) $110,000

Less: Variable expense

Unit level materials (40× $1,200) $48,000

Unit level labor(40× $600) $24,000

Contribution margin $38,000

The overhead cost will not be considered while determine the contribution to profit from accepting the order of 40 slab.

**Hence, the contribution to profit from the special order us $38,000.**

Answer:

Null hypothesis: The average sales per salesperson of Carpetland is $8000 per week

Alternate hypothesis: The average sali per salesperson of Carpetland is greater than $8000 per week

Step-by-step explanation:

The null hypothesis is a statement deduced from a population parameter which is subject to testing

The alternate hypothesis is a statement that negates the alternate hypothesis which is accepted if the null hypothesis is tested to be false