Write the equation of the line in slope-intercept form. Explain how you found the slope and the y-intercept.

Answer:

D. y = -5^x – 27

Step-by-step explanation:

Find the negative reciprocal of the slope of the original line and use the point-slope formula  y − y 1 = m ( x − x 1 )  to find the line perpendicular to  − x + 5 y = 14 .

y = − 5 x − 27                         PERPENDICULAAR

...................................................................................................................................................

Find the slope of the original line and use the point-slope formula  y − y 1 = m ( x − x 1 )  to find the line parallel to  − x + 5 y = 14 .

y = 1 /5 x − 1                             PARALLEL

A salary slip for the month of March 2023 with information given below.

Salary Slip - March 2023

Employee Details:

Name: [Employee Name]

Employee ID: [Employee ID]

Designation: [Employee Designation]

Earnings:

Basic Salary: [Basic Salary]

House Rent Allowance (HRA): [HRA]

Dearness Allowance (DA): [DA]

Incentive: [Incentive]

Total Earnings: [Total Earnings]

Deductions:

Provident Fund (PF): [PF]

Insurance: [Insurance]

Loss of Pay (LOP): [LOP]

Total Deductions: [Total Deductions]

Net Pay: [Net Pay]

Breakdown:

Basic Salary: 50% of CTC (18L) = [Basic Salary]

HRA: 20% of Basic Salary = [HRA]

DA: 12% of Basic Salary = [DA]

Incentive: 75% of target completion = [Incentive]

Total Earnings = Basic Salary + HRA + DA + Incentive = [Total Earnings]

PF: 12% of Basic Salary = [PF]

Insurance: Rs. 2500 = [Insurance]

LOP: [LOP]

Total Deductions = PF + Insurance + LOP = [Total Deductions]

Net Pay = Total Earnings - Total Deductions = [Net Pay]

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The Area of Square is 81 cm².

let the side of the square which is length for both rectangles be a.

let the width of rectangle be x and y.

So, x+ y= a

sum of perimeters= 54

2 (a +x ) + 2 (a+ y) = 54

2a+ 2x + 2a+ 2y = 54

2a + 2a + 2(x+ y) = 54

4a + 2 (a) = 54

4a + 2a = 54

6a = 54

a= 54/6

a= 9

So, area of square

= 9 x 9

= 81 cm²

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The teacher can thus use social sciences as a vehicle to develop mathematical skills by facilitating the development of skills such as data interpretation and analysis.

As an instructor, I would use social sciences to develop mathematical skills in the following manner:Consider a social science topic like demography. In this case, a teacher could use mathematics to assist students in interpreting population statistics.

Teachers might guide students to gather information about population size, growth rate, and geographical distribution from various countries and then use statistics to analyze the data.

For example, a teacher could give students graphs or charts to help them understand population growth rates. They can be asked to make comparisons and identify trends.

In this way, students' understanding of the population is improved, as is their mathematical reasoning.Aside from using mathematics to interpret population statistics,

the teacher can also incorporate mathematical skills development in social sciences by using methods that involve understanding and analysis of data. In other words, students learn how to use data to reach conclusions and make decisions.

They learn how to interpret data and how to extract information from it.This method of teaching creates opportunities for the use of the same skills in different contexts and areas of learning.

It enables students to see connections between subjects and fosters an integrated approach to learning.

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The expression of the given statement is 2y - 3  = -1

Expressions are mathematical statements that comprise either numbers, variables, or both and at least two terms associated by an operator. The operations of mathematics include multiplication, division, addition, and subtraction.

A phrase is considered a mathematical expression if it contains at least two numbers or variables and one or more mathematical operations. Let's look at how expressions are written.

The expression of the given statement is 2y - 3  = 4.

Here, let the unknown number = y

Now, product of y and 2 =  2 times  y   =   2y

Also, three less than the product   =  Product - 3

So, three less than the product  of 3 and y =  2 y - 3

Now, this above expression is equivalent to -1.

⇒2 y - 3  = -1

Hence the expression of the given statement is 2y - 3  = -1

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The sentence "Three less than the product of 2 and a number is 4" can be translated into the equation: 2x - 3 = 4

A mathematical statement that demonstrates the equivalence of two expressions is known as an equation.

It has two sides that are divided by the equals sign (=).

Variables, constants, coefficients, operators, and functions can all be used in the expressions on either side of the equation.

Here, x represents the unknown number that we are trying to solve for. The expression "the product of 2 and a number" is represented by 2x, and "three less than" is represented by the subtraction of 3 from that product. This expression is set equal to 4, which is the result given in the original sentence.

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Answer:

27

Step-by-step explanation:

b/c the formula of premeter of hexagon is P = 6s

s means sides then halved is 4.5

6*4.5=27

Answer:

this equation cannot be solved by completing the square

Step-by-step explanation:

Answer:

5 x 5 x 5 x 5 x 5

Step-by-step explanation:

Answer:

20

Step-by-step explanation:

5 times 4 = 20

A second-degree polynomial takes the form

\(f(x) = ax^2 + bx + c\)

for some constants a, b, and c. Such a function is continuous and differentiable everywhere in its domain.

Differentiating f(x) with respect to x gives

\(\dfrac{df}{dx} = 2ax + b\)

We're told that

• f(x) is increasing on [0, 8]

• f(x) is decreasing on ]-10, 0]

and since df/dx is continuous, this tells us that df/dx = 0 when x = 0. It follows that b = 0, and we can write

\(f(x) = ax^2 + c\)

We're also given that the curve passes through the point (-8, 4), which gives rise to the constraint

\(f(-8) = 64a - 8b + c = 4 \implies 64a + c = 4\)

Since f(x) is decreasing on ]-10, 0], we have df/dx < 0 when x = -8, so

\(2ax+b < 0 \implies -16a < 0 \implies a > 0\)

This means f(x) is minimized when x = 0, with min{f(x)} = c, so the co-domain of f(x) is the set {f(x) ∈ ℝ : f(x) ≥ c}.

Without another condition, that's all we can say about the co-domain. There are infinitely many choices for the constants a and c that satisfy the given conditions. For example,

a = 1, c = -60   ⇒   f(x) = x² - 60   ⇒   f(-8) = 4

⇒   co-domain = {f(x) ∈ ℝ : f(x) ≥ -60}

a = 2, c = -124   ⇒   f(x) = 2x² - 124   ⇒   f(-8) = 4

⇒   co-domain = {f(x) ∈ ℝ : f(x) ≥ -124}

etc.

Length of rectangle         Width of rectangle         Area of rectangle  

A. a + 5                                     3                                    3(a + 5) = 3a + 15

B. 6 + x                                     1/3                                  1/3(6 + x) = 2 + 1/3x

C. 3                                             r                                   r(1+1+1) = 3r

What is a rectangle?

An example of a quadrilateral with equal and parallel opposite sides is a rectangle. It is a polygon with four sides and four angles that are each 90 degrees. A rectangle is a shape with only two dimensions.

A.

There are 2 rectangles with side a and 5.

Therefore the length of the rectangle is (a + 5).

The width the rectangle is 3.

The area of rectangle is product of length and width.

The area of the rectangle is 3(a + 5)

Applying distributive property:

= 3a + 15

B.

There are 2 rectangles with side 6 and x.

Therefore the length of the rectangle is (6 + x).

The width the rectangle is 1/3.

The area of rectangle is product of length and width.

The area of the rectangle is 1/3(6 + x)

Applying distributive property:

= 2 + 1/3 x

C.

There are 3 rectangles with side 1, 1, and 1.

Therefore the length of the rectangle is (1 + 1 + 1).

The width the rectangle is r.

The area of rectangle is product of length and width.

The area of the rectangle is r(1 + 1 + 1)

Applying distributive property:

= r + r + r

= 3r

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Answer:

Step-by-step explanation:

She must write an email to the new employees explaining how to access documents that need editing and what to do with new versions of the documents.

Answer: 20 ways

Step-by-step explanation: I believe that you would need to use permutation, so:

5P2 = 20

Answer:

angle xdq= 90-49= 41

angle uxd= 180-41= 139

Step-by-step explanation:

A right angle equals 90 degrees.

90-49 = angle xdq = 41 degrees

49 + 90 + x = 180

angle x = 41

180-41 = angl uxd = 139

Answer:

A. 8

Step-by-step explanation:

Geometric mean= √(4×16) = √64 = 8

Answer:

Step-by-step explanation:

C. (-2, 2) and  (1, -1)

Since the point of intersection is the sole location where the two graphs come together, the coordinates of that location provide the answer to the equations involving the two variables. There are no solutions when the graphs are in parallel.

Given, the parabola Y = X² -2 and a line Y = -X. To find the intersection points of this graph we need to compare these equations.

Let's put the value of y in equation 1

- X = X²  - 2

X²  + X - 2 = 0

The factor of this quadratic equation is -2 and 1. Therefore the coordinate in which both graphs will intersect is (-2, 2) and  (1, -1). I am attaching an image for better understanding.

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Answer:

w-9≤12

I wrote it out.

Answer:

61 and -87

Step-by-step explanation:

If the numbers are x and x - 148, we can write the following equation:

x + x - 148 = -26

2x - 148 = -26

2x = 122

x = 61 so x - 148 = 61 - 148 = -87

Answer:

8( b - 4 )

Step-by-step explanation:

8 x ( b - 4 )

8( b - 4 )

I hope this helps!

Answer:

B, C, and E

Step-by-step explanation:

B; C = score + 25 percent of score

C; C = 125% of score (which equals 1 plus 25%)

E; t plus 25% of t score

The integers in the set s: {-2,-3,-4,-5} will make the inequality 4p-7 \(\geq\) 9p+8 true are : -3, -4, -5

Let's solve the inequality first

4p -7 \(\geq\)  9p  +8

Taking p's on the same side we will get :

-7 - 8 \(\geq\) 9p - 4p

-15 \(\geq\) 5p

Divide by 5 into both sides

-3 \(\geq\) p

i.e. p \(\leq\) -3

Therefore p must be less than or equal to -3

From the set, we have the numbers -3,-4,-5 which are less than or equal to -3

Hence the integers -3,-4,-5 will make the  inequality 4p-7 \(\geq\) 9p+8 true

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The man still owes R87,726 in taxes.

To calculate the tax amount the man still owes, we need to determine his taxable income first.

Gross income: R500,000

Less: PAYE deductions (17% of gross income): R500,000 * 0.17 = R85,000

Taxable income: R500,000 - R85,000 = R415,000

Next, we can use the tax table information provided to calculate the tax owed based on the taxable income.

Tax owed: R93,135 + 36% of (taxable income - R393,200)

Tax owed: R93,135 + 0.36 * (R415,000 - R393,200)

Tax owed: R93,135 + 0.36 * R21,800

Tax owed: R93,135 + R7,848

Tax owed: R100,983

Finally, we subtract the rebate amount of R13,257 from the tax owed to find the amount the man still owes.

Tax owed - Rebate: R100,983 - R13,257 = R87,726

Therefore, the man still owes R87,726 in taxes.

The correct option is not provided among the given answer choices.

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Answer:

it's a reduction because it's smaller than the original shape

Step-by-step explanation:

(a reduction means the new shape is smaller than the original, and an enlargement means the new shape is bigger than the original one)

Answer:

Step-by-step explanation:

reduction

Answer: The answer is 2289.06

Step-by-step explanation: I assume it’s a circle as it has a radius so simply multiply 3.14 by the radius 27^2

Answer:

the slope is −12

Step-by-step explanation:

The equation of a perpendicular line to y=−x2+5 y = - x 2 + 5 must have a slope that is the negative reciprocal of the original slope.

-1/2

That would be the answer

The correct statement regarding the angle measures is given as follows:

m < 1 + m < 4 > m < 3.

The given angle measure is as follows:

m < 3 = 119º.

Angles 3 and 4 form a linear pair, meaning that they are supplementary, that is, the sum of their measures is of 180º.

Hence the measure of angle 4 is given as follows:

m < 4 + m < 3 = 180º.

m < 4 = 180º - 119º

m < 4 = 61º.

Angles 1 and 4 are opposite by the same vertex, hence they are congruent, thus the measure of angle 1 is given as follows:

m < 1 = m < 4

m < 1 = 61º.

Hence:

m < 1 + m < 4 = 2 x 61

m < 1 + m < 4 = 122º

122º > 119º

m < 1 + m < 4 > m < 3.

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