On the grid, draw the graph of y+2x=6 for values of x from -2 to 4

Let x be an even number. Then, x = 2k for some integer k. The negative of x, -x, is equal to -2k, which is also an even number. Thus, the additive inverse of an even number is an even number.

An even number is any number that can be divided by 2 without any remainder, meaning that it can be written in the form x = 2k for some integer k. The additive inverse, or negative, of an even number, x, is -x. By definition, this is equal to -2k. As -2k can still be divided by 2 without any remainder, it is also an even number.

This can also be understood by looking at the positive and negative sides of the number line. If x is an even number, then it is two units away from 0. Therefore, -x is also two units away from 0, which means it is an even number. This shows that the additive inverse of an even number is an even number.

To prove this, we can look at a specific example. Let x = 8. Then, 8 = 2x4. The negative of 8, -8, is equal to -2x4, which is still an even number. Thus, this proves that the additive inverse of an even number is an even number.

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Answer:

Step-by-step explanation:

The balance after 3 years can be calculated as follows:

I = P * r * t

Where:

I = interest

P = principal amount (2200)

r = interest rate (0.0295)

t = time in years (3)

So,

I = 2200 * 0.0295 * 3

I = 153.1

The final balance would be:

P + I = 2200 + 153.1

P + I = 2353.1

The final balance after 3 years is $2353.1, which is closest to option B ($2,329.80).

Answer: 101.6

Since we are trying to find the sides of both the triangles, we will need to use the Sin, Cos, & Tan trigonometry functions. There are 3 equations:

[tex]Sin (Angle) = \frac{Opposite}{Hypotenuse} \\Cos (Angle) = \frac{Adjacent}{Hypotenuse} \\Tan (Angle) = \frac{Opposite}{Adjacent}[/tex]

For this triangle shown in the picture, we can infer that the 88 is OPPOSITE to the 60° and 30° angles. So we already have the opposite, and since we are trying to find the adjacent, we will use the formula that consists both opposite and adjacent, which is the following:

[tex]Tan(Angle) = \frac{Opposite}{Adjacent}[/tex]

Since [tex]x[/tex] is only a part of the long triangle, we will subtract the small triangle's side from the big one, which will give us [tex]x\\[/tex].

We can input our values to solve each triangle's side lengths.

(You have to use the calculator for these)

Small one:

[tex]Tan(60) = \frac{88}{Adjacent}\\Adjacent = \frac{88}{Tan(60)}\\Adjacent = \frac{88\sqrt{3} }{3} = 50.807 (3 d.p)[/tex]

Big one:

[tex]Tan(30) = \frac{88}{Adjacent} \\Adjacent = \frac{88}{Tan(30)} \\Adjacent = 88\sqrt{3} = 152.420 (3d.p)[/tex]

Now, to calculate [tex]x[/tex] , we will subtracat the small one from the big one like this: (it is better to input the values with the surds and not the real numbers for accurate marks and calculations)

[tex]88\sqrt{3} - \frac{88\sqrt{3} }{3} = 101.6 (1 d.p)[/tex]

That is the answer. If you did not understand it completely, please reach me back and I will help you :)

3±2√5 is the solution of the equation x²−6x=11

A quadratic equation is a second-order polynomial equation in a single variable x , ax²+bx+c=0. with a ≠ 0 .

The given equation is s x²−6x=11

By completing the square, then rearrange the equation as x²−6x=11

add 9 to each side.

To find the solution of equation by quadratic formula, substitute 11 on both sides

x²−6x-11=0

a=1, b=-6 and c=-11

x=-b±√b²-4ac/2a

=6±√36+44/2

=6±√80/2

=3±2√5

Hence, 3±2√5 is the solution of the solution of the equation x²−6x=11

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The shaded region in the graph represents the possible solution sets to the inequality.

Given is the inequality -

x² + 15 ≥ 23

The given inequality is -

x² + 15 ≥ 23

Refer to the graph attached.

The shaded region represents the possible solution sets to the inequality above.

Therefore, the shaded region in the graph represents the possible solution sets to the inequality.

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The other endpoint of the line segment is (13.8, 6).

The midpoint of a line segment is the point that lies exactly halfway between the two endpoints.

In this case, we have one endpoint, (6.9), and the midpoint (0,-6). Here is how we find the other endpoint:

To find the other endpoint, we need to subtract the midpoint from the given endpoint and then multiply by 2. The midpoint formula is given by:

M = (x1 + x2) / 2 and (y1 + y2) / 2

Where M is the midpoint, (x1, y1) and (x2, y2) are the coordinates of the two endpoints.

So, in our case, the other endpoint will be given by:

(x2, y2) = 2 * (6.9, 0) - (0, -6)

Expanding the expression, we get:

x2 = 2 * 6.9 - 0 = 13.8

y2 = 2 * 0 - (-6) = 6

Therefore, the other endpoint of the line segment is (13.8, 6).

Complete question:

Find the other end point of the line segment with the given endpoint and midpoint endpoint: (6.9), midpoint (0,-6)

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There are seven kids tickets and 4 adult tickets.

We know that we have to solve the simultaneous equation here;

Let cost of one kids ticket be x and the cost of one adult ticket be y

3x + 9y = 75 ---- (1)

8x + 6y = 67 ----- (2)

We then have that multiplying (1) by 8 and (2) by 3

24x + 72 y = 600 ---- (3)

24x + 18 y = 201 --- (4)

Subtract (4) from (3)

54 y = 399

y = 7

Then;

3x + 9(7) = 75

x = 4

We are going to end up having that there are seven kids tickets and 4 adult tickets.

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The equation expressing the statement is A = k/r, where k is the constant of proportionality. Given that r = 3 and A = 7, the constant of proportionality can be found by rearranging the equation to k = A × r and substituting the given values to calculate: k = 7 × 3 = 21.

The statement "A varies inversely as r" can be expressed mathematically as an equation: A = k/r, where k is the constant of proportionality. This equation states that A is proportional to 1/r, meaning that as r increases, A decreases, and as r decreases, A increases. To find k, we can rearrange the equation to k = A × r and substitute the given values. In this case, if r = 3 and A = 7, then k = 7 × 3 = 21. Therefore, the constant of proportionality is 21. This equation can be used to determine the values of A, given a value of r, or the values of r, given a value of A. For example, if r = 4, then A = k/4 = 21/4 = 5.25. Conversely, if A = 10, then r = k/A = 21/10 = 2.1. This equation can be used to determine the values of A and r for any given situation.

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The Proof of ( x + h)² +( y + h)²  =  (a + b)² is shown below.

In geometry, two similar forms are those whose dimensions are identical or have a same ratio but the size or length of their sides differ. Examples include similar triangles, similar rectangles, and similar squares. The scale factor is another name for the common ratio. Additionally, the equivalent angles have the same magnitude.

Given:

BHC and BCA are similar

HC / BC = CA / BA    

so, h / a  =  b / ( x + y) ........... (1)

Working with your expansion

x² + h²  = a²  and

y² + h²  = b²

So, subtracting out the equal parts we are left with

2xh  + 2yh   =  2ab ..........(3)    divide through by 2

xh + yh  = ab    

h( x + y) = ab  which we can rearrange as

h / a   =  b / ( x+ y)..............(2)

Since this is equal to (1) and it's just a rearrangement of (3) adding all the other equal parts of the expansion shows that

(x² + h²) + (y² + h²) + ( 2xh + 2yh) =  a²+ b²+ 2ab

( x² + 2xh + h²) + ( y² + 2yh + h²)  =  ( a + b)²

( x + h)²   +  ( y + h)²  =  (a + b)²      

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Answer:

3

28

Step-by-step explanation:

The expression (f/g) (4) is equal to f(4) / g(4).

f(4) = 4^2 + 2*4 - 3 = 16 + 8 - 3 = 21

g(4) = 4^2 - 9 = 16 - 9 = 7

So, (f/g) (4) = 21 / 7 = 3.

The expression (f + g) (4) is equal to f(4) + g(4).

f(4) = 4^2 + 2*4 - 3 = 16 + 8 - 3 = 21

g(4) = 4^2 - 9 = 16 - 9 = 7

So, (f + g) (4) = 21 + 7 = 28.

The sum of all the positive numbers from 1 to 116, inclusive, is 6350.

The sum of the first n positive integers can be found using the formula n(n+1)/2. In this case, n=116, so the sum of all the positive numbers from 1 to 116, inclusive, is 116 * 117 / 2 = 6350. This formula can be useful in a variety of mathematical and real-world applications, such as finding the total number of objects in a sequence or the total distance traveled by an object moving at a constant speed.

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Answer:

Step-by-step explanation:

A function is the inverse of another function if it "undoes" the original function. In other words, if you apply the original function to an input and then apply the inverse function to the result, you get the original input.

To find the inverse of a function, you can swap the input and output values of the original function, and then solve for the new input variable. For example, if the original function is f(x) = y, the inverse function would be f^-1(y) = x.

Given the function f(x) = -2, 3, 8, 13, it is not possible to find a simple algebraic inverse function for the given values of x = -1, 0, 1, 2. The inverse of a function is only well-defined if the function is one-to-one, meaning that for every output value, there is only one input value that maps to it. In this case, the function does not appear to be one-to-one, so it does not have an inverse function.

On solving the provided question we can say that The inequality we have here is  -5(x-3) ≥ 3[4-(x+4)] => 15/17 ≥ x

An inequality in mathematics is a relationship between two expressions or values that is not equal. Thus, imbalance leads to inequality. An inequality creates the link between two values that are not equal in mathematics. Egality is distinct from inequality. When two values are not equal, most commonly use the not equal sign (). Different inequalities are used to contrast values, no matter how little or large. Many simple inequalities may be resolved by modifying the two sides until the variables are all that remain. But a number of things contribute to inequality: Negative values on both sides are divided or added. Trade off the left and right.

The inequality we have here is

-5(x-3) ≥ 3[4-(x+4)]

-5x + 15 ≥ 12x

15 ≥ 17x

15/17 ≥ x

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Answer:

x * 2.54 = centimeters

Step-by-step explanation:

The equation to convert inches to centimeters is as follows:

x inches * 2.54 cm/inch = y centimeters

Where x is the number of inches and y is the equivalent length in centimeters.

To elaborate, the conversion factor between inches and centimeters is 2.54 cm/inch, meaning that for every inch there are 2.54 centimeters. To convert from inches to centimeters, we simply multiply the number of inches by the conversion factor. This gives us the equivalent length in centimeters.

Answer:

$400

Step-by-step explanation:

Here is my crack at it:

To find Heather's weekly salary, we can set up an equation using the information given. Let's call Heather's weekly salary "x".

According to the problem, $20 is 5% of her salary, so we can write this as an equation:

$20 = 0.05x

Now we can solve for x by dividing both sides by 0.05:

x = 400$

So Heather's weekly salary was $400.

Heather’s weekly salary would be 400$.  

If heather saved $20 a week. This was 5% of her salary. Heather’s weekly salary would be

Given, $20 = 5%

As we know, the total salary will be 100 %

If 5% = $20

then, 100% = $400 (multiplying both the sides by 20)

Thus, Heather’s weekly salary was 400$.

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The Maurya Empire was founded in 322 B.C. by Chandragupta Maurya, after overthrowing Dhana, the king of the Nanda dynasty. Chandragupta initiated battles to defeat and conquer the kingdoms left by Alexander the Great and gained additional lands west of the Indus River by force. He enlarged his power westward across central and western India, and by 320 B.C., the empire had fully occupied Northwestern India. Chandragupta Maurya became the first emperor to unite India into one state, under a central government.

Chandragupta Maurya was the creator of the Maurya Empire in ancient India. He established one of the largest empires on the Indian subcontinent.

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Step-by-step explanation:

So basically To find the mean you have to add all the numbers and divide by how many numbers you have, but to do that you have to make sure the numbers are lined up correctly so

157,158,161,162,172 ( Correct Order ) Smallest to biggest now add these up

157 + 158 + 161 + 162 + 172 = 810 / 5 = 162

The mean height is 162 cm

The new mean height

Again we're going to do the same thing

157 + 158 + 161 + 162 + 169 + 172 = 979/6 = 163.16666 = 163 cm

Hence the first mean height is 162 cm and the new mean height is 162 cm

The value for x vector is [tex]v=\left[\begin{array}{ccc}-25\\-22\end{array}\right][/tex].

What is a vector?

A vector in mathematics is a quantity that not only expresses magnitude but also motion or position of an object in relation to another point or object. Euclidean vector, geometric vector, and spatial vector are other names for it.

Given a vector v ∈ R² let (x, y) be its standard coordinates, i.e., coordinates with respect to the standard basis [tex]e_1=\left[\begin{array}{ccc}5\\-1\end{array}\right][/tex] and [tex]e_1=\left[\begin{array}{ccc}-7\\-4\end{array}\right][/tex].

The desired coordinates x, y satisfy -

v = xe1 + ye1

So, the vector v is -

[tex]v=2\left[\begin{array}{ccc}5\\-1\end{array}\right] +5\left[\begin{array}{ccc}-7\\-4\end{array}\right][/tex]

[tex]v=\left[\begin{array}{ccc}10\\-2\end{array}\right] +\left[\begin{array}{ccc}-35\\-20\end{array}\right][/tex]

[tex]v=\left[\begin{array}{ccc}-25\\-22\end{array}\right][/tex]

Therefore, the matrix is [tex]v=\left[\begin{array}{ccc}-25\\-22\end{array}\right][/tex].

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Cost of direct materials per equivalent unit = $0.45.

Conversion cost per equivalent unit = $0.12.

The FIFO method is the First In First Out method. It is an accounting method used for cost flow assumption purposes in the cost of goods sold calculation.

In the Bottling Department,

The cost of direct materials transferred = $27,225.

The conversion cost = $7,596.

The total equivalent units for,

Direct materials = 60,500 liters.

conversion = 63,300 liters.

By using FIFO method,

The cost  of Direct materials per equivalent unit = [tex]\frac{27,225}{60,500}[/tex]

                                                                                =$0.45

Conversion cost per equivalent unit = [tex]\frac{7596}{63,300}[/tex]

                                                            = $0.12

Hence, the cost of direct materials and conversion cost per equivalent unit is $0.45 and $0.12 respectively.

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Therefore , the solution of the given problem of expression comes out to be 2x[(x-9)²] is the simplified factor.

There is a need for mathematical variable operations such addition, multiplication, multiplication, and division. When combined, they produce the following: A mathematical operator, some data, and an equation A statement of fact is composed of values, parameters, plus operations like additions, subtractions, multiplications, and divisions. It is possible to contrast and compare various sentences and words.

Here,

Given :

=> 2x³ - 36x² + 162x

=> 2x(x²-18x+81)

=>  2x[ x² - 2 (9)x + (9)²]

=> 2x[(x-9)²]

Thus ,

factor comes out to be 2x[(x-9)²].

Therefore , the solution of the given problem of expression comes out to be 2x[(x-9)²] is the simplified factor.

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The values of the trigonometric functions for the angle theta in Figure 1 are:

sin (theta) = 0.6 ,cos (theta) = 0.8, tan (theta) = 0.75.

A right triangle with sides of 3, 4, and 5 units is shown in Figure 1. The definitions of sine, cosine, and tangent allow us to evaluate the trigonometric properties of the triangle's angles as follows:

Theta = opposite / adjacent = 3 / 4 = 0.75 Tan = opposite / adjacent = 3 / 5 = 0.6 Cos = adjacent / hypotenuse = 4 / 5 = 0.8

As a result, the trigonometric functions' values for the angle theta in Figure 1 are as follows:

Tan(theta) = 0.75, sin(theta) = 0.6, cos(theta), and 0.8.

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The sum of 45 terms of the arithmetic progression whose sum of 18 th and 28 th terms is 36 is given by 810.

Let the first term of the arithmetic progression be A and the common difference for the same be D.

So 18th term of the progression is = A + (18 - 1) D = A + 17D

28th term of the progression is = A + (28 - 1) D = A + 27D

Given that the sum of the 18th and 18th terms of the progression is 36.

So, A + 17D + A + 27D = 36

2A + 44D = 26

So now the sum of 45 terms of the arithmetic progression is given by,

= 45/2 [2A + (45 - 1)D]

= 45/2 [2A + 44D]

= (45/2) * 36

= 45 * 18

= 810

Hence the sum of 45 terms of the arithmetic progression whose sum of 18 th and 28 th terms is 36 is given by 810.

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To reach a temperature of 100 degrees the pizza would take 750 minutes.

A line's steepness and direction are measured by the line's slope. Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all.

Any two different points on a line can be used to calculate the slope of any line. The ratio of "vertical change" to "horizontal change" between two different locations on a line is calculated using the slope of a line formula.

Since the pizza was heated at a constant rate, we can model the experiment as a line, where the slope represents how fast the pizza was heated.

The slope is given as:

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

Let

(x1,y1) = (6, 40)

(x2,y2) = (8, 55)

m = (55 - 40) / ( 8 - 6 )

m = 7.5 degrees per minute.

The pizza heats up an average of 7.50 degrees per minute

To reach a temperature of 100 degrees the pizza would take:

(100)(7.50) = 750 minutes.

Hence, to reach a temperature of 100 degrees the pizza would take:

(100)(7.50) = 750 minutes.

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The statistics interpreted from the given data is:

a. Median = 26.5

b. Q1 = 22.5

c. Q3 = 60

d. IQR = 37.5

e. Range = 95

The given data sample of this year’s grants(given in thousands of dollars) in ascending order is :

5 22 23 25 26 27 50 70 90 100

The median of a data set is the middle value when the data is arranged in ascending or descending order. When number of values is even, there are two values in the middle, so we take the average of the two. So the median is

= (26 + 27)/ 2

= 26.5

The first quarter or the lower quartile (Q1), is the value under which 25%, that is first quarter of the data points are found when they are arranged in increasing order. Here Q1 is  0.25*10,  that is 2.5th value, but its not possible. So we should interpolate

Q1 = 22.5

Similarly third quartile, Q3 is the value under which 75% of the data points are found when they are arranged in increasing order. So

Q3 = (70 + 50)/2

= 60

And inter quartile range (IQR)

= Q3 - Q1

= 60 - 22.5

= 37.5

Range is

= 100 - 5

= 95

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The break-even point refers to the amount of revenue necessary to cover the total fixed and variable expenses incurred by a company.

In business accounting, the break-even point refers to the amount of revenue necessary to cover the total fixed and variable expenses incurred by a company within a specified time period.

To calculate the break-even point in units use the formula:

Break-Even point (units) = Fixed Costs ÷ (Sales price per unit – Variable costs per unit) or in sales dollars using the formula: Break-Even point (sales dollars) = Fixed Costs ÷ Contribution Margin.

Insurance Requirements the part of a commercial contract in which the types and minimum amounts of insurance the parties agree to provide in connection with their performance of the contract are specified.

A break even point is used in multiple areas of business and finance. In accounting terms, it refers to the production level at which total production revenue equals total production costs. In investing, the break even point is the point at which the original cost equals the market price.

Therefore, the break-even point refers to the amount of revenue necessary to cover the total fixed and variable expenses incurred by a company.

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95% CI for the true posttreatment self-esteem score is:

(24.47, 28.73)

The formula for calculating a 95% confidence interval for the mean self-esteem score is as follows:

(standard deviation/square root of sample size) * (mean (critical value)

The standard deviation of a set of data is a measure of its spread or dispersion. It denotes the average deviation of individual values in a data set from the data set's mean.

A low standard deviation indicates that the data points are close to the mean, whereas a high standard deviation indicates that the data points are scattered across a wide range.

For a normal distribution and a 95% confidence level, the critical value is 1.96.

As a result, the 95% confidence interval for the mean posttreatment self-esteem score is as follows:

26.6 ± 1.96 * (7.4/sqrt(21)) = 26.6 ± 2.13

As a result, the 95% CI for the true posttreatment self-esteem score is:

(24.47, 28.73)

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The sample that have the greatest mean is sample {4, 5, 2, 4, 3, 6}

The correct option is D.

A sample space is a set of potential results from a random experiment. The letter "S" is used to denote the sample space. Events are the subset of potential experiment results. Depending on the experiment, a sample area could contain a variety of results.

Given:

Peter wants to estimate the mean value rolled on a fair number cube.

He has generated four samples containing five rolls of the number cube, as shown in the table below.

The mean of the data sample 1:

(1 + 4 + 5 + 2 + 4 + 3)/6 = 3.167

The mean of the data sample 2 = 3.83

The mean of the data sample 3 = 3.67

The mean of the data sample 4 = 24/6 = 4

Therefore, the mean of the data sample 4 has greatest mean.

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The complete question:

Peter wants to estimate the mean value rolled on a fair number cube. He has generated four samples containing five rolls of the number cube, as shown in the table below. Which sample will result in the greatest mean? Sample Data Sample 1 4 5 2 4 3 Sample 2 2 2 6 5 6 Sample 3 4 6 3 4 2 Sample 4 5 2 4 3 6

The answer options that are quadratic functions include the following:

B. y = (5x - 3x^2)/4 + 1.

C. y = 2x^2 - 3x + 7.

In Mathematics, a quadratic function can be defined as a mathematical expression which defines and represent the relationship that exists between two (2) or more variable on a graph, with a maximum exponent of two.

Generally speaking, the standard form of a quadratic function is given by this mathematical expression;

ax² + bx + c = 0

Where:

In this context, we can reasonably infer and logically deduce that the expressions that are quadratic functions include both y = (5x - 3x²)/4 + 1 and y = 2x² - 3x + 7 because they have a maximum exponent of two.

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Answer: Brand A: 24 ounces for $2.25

Brand B: 40 ounces for $3.75

Price per ounce for Brand A = $2.25 / 24 ounces = $0.09375

Price per ounce for Brand B = $3.75 / 40 ounces = $0.09375

Both brands have the same price per ounce.

Step-by-step explanation: