The construction of copying is started below. The next step is to set the width of the compass to the length of . How does this step ensure that the new angle will be congruent to the original angle?

The value of the given functions are:

(a) (f + g)(x) = (x -8 + 14) = x + 6

(b) (f-g)(x) = (x -8 - 14) = x - 22

(c) (f • g)(x) = (x - 8 (14)) = 14x - 112

(d) (f/g)(x) = (x - 8)/ 14

An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

We have the functions are as follows:

f(x)=x - 8,

g(x)=5 + 9

To solve :

a. (f + g)(x),

b. (f-g)(x),

c. (f • g)(x), and

d. (f/g)(x)

Now,

(a) (f + g)(x) = (x -8 + 14) = x + 6

(b) (f-g)(x) = (x -8 - 14) = x - 22

(c) (f • g)(x) = (x - 8 (14)) = 14x - 112

(d) (f/g)(x) = (x - 8)/ 14

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The given question is incomplete, complete question is:

For the functions f and g find a. (f+ g)(x), b. (f-g)(x), c. (f• g)(x), and d. (f/g)(x) f(x)=x - 8, g(x)=5 + 9

The solution of the inequality given is b < 64

the graph is attached

In the equation, let us replace b with x

To solve the inequality x/8 < 8 for x, we need to isolate x on one side of the inequality.

We can do this by multiplying both sides of the inequality by 8, which will cancel out the 8 in the denominator on the left side:

Therefore, the solution to the inequality x/8 < 8 is x < 64.

This means that any value of x that is less than 64 will make the inequality true.

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Valid row operations are:

Invalid row operations are:

0R₁ → R₁ (this is equivalent to multiplying a row by zero, which is not a valid row operation)

R₃ ÷ 0 → R₃ (division by zero is undefined)

-2 ÷ R₁ → R₁ (division by a variable is not a valid row operation)

2R₁ + R₂ → R₂ (the row operation should be adding multiples of one row to another row, not a combination of multiple rows)

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The value of p in the expression is 45

Additive inverse simply means changing the sign of the number and adding it to the original number to get an answer equal to 0.

For example a+5 = 2 , by solving this we add the additive inverse of 5 to both sides. The additive inverse of 5 is -5

this means,

a+5-5 = 2-5

a = 2-5

a = -3

Similarly, p-42 = 3 is solved in the same way. we add the additive inverse of -42 which is +42 to both sides,

p-42+42 = 3+42

p = 3+42

p = 45

therefore the value of p is 45

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Answer:

x = -2

Step-by-step explanation:

-4x + 3 = 11

Subtract 3 from both sides:

-4x = 8

Divide both sides by -4:

x = -2

The result of adding -3 (row 1) to row 2 is determined as (0  10) |-14.

The resultant of the row multiplication in the Matrice is calculated by applying the following method;

row 1 in the given matrices = [1  -4] | 8

To multiply row1 by -3, we will multiply each entity by 3 as shown below;

= -3(1  -4) | 8

= (-3  12) | -24

To add the result to 3;

(-3  12) | -24  +  (3   -2)|10

= (0  10) |-14

Thus, the result of the row multiplication is determined by multiplying each entry in row 1, by - 3.

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The sum expression [tex][2(4 + \frac9n)^4](\frac9n) + ... + [2(4 + \frac{9n}n)^4](\frac9n)[/tex] using the sigma notation is [tex]\sum\limits^{n}_{i=1} [2(4 + \frac{9i}n)^4](\frac9n)[/tex]

From the question, we have the following parameters that can be used in our computation:

[tex][2(4 + \frac9n)^4](\frac9n) + ... + [2(4 + \frac{9n}n)^4](\frac9n)[/tex]

From the above expression, we can see that the different expression in each term is

9/n

So, we introduce a variable

Assuming the variable is i, the i-th term of the expression would be[tex]t(i) = [2(4 + \frac{9i}n)^4](\frac9n)[/tex]

When represented using the sigma notation, we have

[tex]\sum\limits^{n}_{i=1} [2(4 + \frac{9i}n)^4](\frac9n)[/tex]

Hence, the sum expression using the sigma notation is [tex]\sum\limits^{n}_{i=1} [2(4 + \frac{9i}n)^4](\frac9n)[/tex]

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The answer choice which correctly represents the value of cos B as required is;  Cosine B = StartFraction 40 Over 41 EndFraction.

Therefore Choice B is correct

The law of cosines relates the lengths of the sides of a triangle to the cosine of one of its angles and it states that the square of the length of any side of a given triangle is equal to the sum of the squares of the length of the other sides minus twice the product of the other two sides multiplied by the cosine of angle included between them.

we know that from the trigonometric ratios that the cosine of an angle is the ratio of its opposite and hypothenuse.

Hence, we can say that:

cos B = 80 / 82

cos B = 40 / 41.

Inn conclusion, the cosine of angle B following from trigonometric ratios as requested is; cos B = 40 / 41.

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#complete question:

Evaluate the function requested. Write your answer as a fraction in lowest terms.

Triangle A B C. Angle C is 90 degrees. Hypotenuse A B is 82, adjacent B C is 18, opposite A C is 80.

Find cos B.

a.

Cosine B = StartFraction 9 Over 41 EndFraction

c.

Cosine B = StartFraction 9 Over 40 EndFraction

b.

Cosine B = StartFraction 40 Over 41 EndFraction

d.

Cosine B = StartFraction 41 Over 40 EndFraction

Hence Option A. 22 is correct.

Of the students in the maths club , 67% are not in the literature club.

So the number of students in Maths club =

[ ( Number of students in maths club but not in the literature club) / 67 ] * 100 % = [ 16 / 67 ] * 100% = 24 (Rounded)

Hence, Number of students in maths club and in the literature club =

x = Total Number of students in Maths club - Number of students in maths club but not in the literature club

x = 24 - 16 = 8

Of the students not in the maths club , 78% are not in the in the literature club.

So, Of the students not in the maths club , 100% - 78% = 22% are in the literature club.

So the number of students not in the Maths club =

[ ( Number of students not in the maths club and in the literature club) / 22 ] * 100 %

= [ 4 / 22 ] * 100% = 18.18 = 18 (Rounded)

Hence, Number of students not in the maths club and not in the literature club =

y = Total Number of students not in the Maths club - Number of students not in the maths club and in the literature club

y = 18 - 4 = 14

So, x + y = 8 + 14 = 22.

Hence Option A. 22 is correct.

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Answer:

35

Step-by-step explanation:

Simply plug in the value of your 'x' and 'y':

x = 4.5

y = 5.2

[tex]2(4.5)+5(5.2)=9+26=35[/tex]

The surface area of the shape will be 46 yards².

Surface area refers to the total area that the surface of a three-dimensional object covers. It is measured in square units, such as square meters (m²), square centimeters (cm²), square feet (ft²), etc.

The formula for the surface area of the 2 bases is just b*h

12*8=96 yd²

Finding the lateral area:

(10*10)+(10*10)+(12*10)=

100+100+120=

320 yd²

Add the lateral surface area and the surface area of the 2 bases for the total surface area:

320+96=416 yd²

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Answer:

It can't be factor

Step-by-step explanation:

n^4 − 4n^3 − 17n^2 − 36n + 108

The GCF of this is 1, so the equation can't be factor.

An equation that models the eggs used by LaNiyah is 2b + 6s = 144.

An equation is a mathematical statement that shows that two or more mathematical expressions are equal or equivalent.

Equations contain the equal symbol (=), unlike mathematical expressions that combine variables with numbers, and constants using mathematical operands only.

The number of eggs used to make brownies per unit = 2

The number of eggs used to make cakes per unit = 3

The number of eggs used to make soufflés per unit = 6

The total number of eggs used = 144

Let the total number of brownies made = b

Let the total number of soufflés made = s

2b + 6s = 144

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Answer: I did not do the math, I just tell people how to do it

Hope I helped.

Step-by-step explanation:

Multiply the number of triangles you created by 180.

The product of the two external segments and the sum of the lengths of each segment in the circle are equal if two secants are drawn to the circle from a single shared exterior point. The x has a value of 2 units.

If two secant segments are drawn to a circle from an exterior point, the product of the measurements of one secant segment and its external secant segment is equal to the product of the measurements of the second secant segment and its external secant segment.

So, we know that:

BE * AE = CE * DE

Now, insert the values as follows:

(x+1) * (x+12) = (x+4) * (x+5)

x² + x + 12x + 12 = x² + 4x + 5x + 20

13x + 12 = 9x + 20

4x = 8x

x= 2

Then: x = 2 units

Therefore, the product of the two external segments and the sum of the lengths of each segment in the circle are equal if two secants are drawn to the circle from a single shared exterior point. The x has a value of 2 units.

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The solution is:  the following probabilities for a normal distribution is:

a. 0.5434

b. 0.5746

c. 0.2957

d. 0.0902

Here, we have,

Explanation:

To find each probability we need to use the normal distribution table that is accumulated to the left, so each probability is equal to

P(-1.80 < z < 0.20) = P( z < 0.20) - P( z < -1.80)

P(-1.80 < z < 0.20) = 0.5793 - 0.0359

P(-1.80 < z < 0.20) = 0.5434

P(-0.40 < z < 1.40) = P( z < 1.40) - P( z < -0.40)

P(-0.40 < z < 1.40) = 0.9192 - 0.3446

P(-0.40 < z < 1.40) = 0.5746

P(0.25 < z < 1.25) = P(z < 1.25) - P(z < 0.25)

P(0.25 < z < 1.25) = 0.8944 - 0.5987

P(0.25 < z < 1.25) = 0.2957

P(-0.90 < z < -0.60) = P(z < -0.60) - P(z < -0.90)

P(-0.90 < z < -0.60) = 0.2743 - 0.1841

P(-0.90 < z < -0.60) = 0.0902

Therefore, the answers are,  the following probabilities for a normal distribution is:

a. 0.5434

b. 0.5746

c. 0.2957

d. 0.0902

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If the side AB=12 and side A'B'=9, then the scale factor of the dilation is 3/4.

The "Scale-Factor" of a dilation is the ratio of the corresponding side lengths of the two similar figures.

In this case, we can find the scale factor by dividing the length of side A'B' by the length of the corresponding side AB:

So, scale factor = A'B'/AB,

Substituting the values,

We get,

Scale factor = 9/12,

Scale Factor = 3/4,

Therefore, the scale factor of the dilation is 3/4. This means that all corresponding side lengths of the dilated triangle A'B'C' are 3/4 of the length of the corresponding side lengths of the original triangle ABC.

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Answer:

We can calculate the slope by taking 2 points on the line. I took A(4,4) and B(-4,0), so we get m=1/2.

2. y-intercept is the point where a line crosses the y-axis which is (0,2)

3. We have f(x)=1/2x +b

By taking a particular point on the line,we get :

2=1/2(0)+b

==》 b=2

So the slope intercept form is

y=1/2x+2

To move Point A(-5, -2) to Quadrant IV, we need to apply one or more transformations that result in a reflection about the x-axis and/or a rotation of 180 degrees. The following transformations would move Point A to Quadrant IV:

Reflection about the x-axis: This transformation would change the sign of the y-coordinate, making it positive. So, the image of A after this transformation would be (−5, 2).

Rotation of 180 degrees about the origin: This transformation would change the sign of both the x and y-coordinates, making them positive. So, the image of A after this transformation would be (5, 2).

Therefore, either a reflection about the x-axis or a rotation of 180 degrees would move Point A to Quadrant IV.

Based on the data displayed in the dot plot, it can be concluded there are 25 students in this class.

Dot plots represent data and trends but using dots. In these types of graphs, each individual is represented with a dot. For example, in the number 3, we can see there are 3 dots, which means three students have a first name made of three letters.

Therefore, you can get the total of students by counting all the dots. Based on this, there are 25 students in this class.

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Alan and his mom will each have completed 10 rows after 3 hours.

An expression is a combination of numbers, variables, and/or operations (such as addition, subtraction, multiplication, division, exponents, and roots) that are grouped together to represent a value.

Let x be the number of hours it takes for Alan and his mom to have planted the same number of rows.

Alan will have planted 4 + 2x rows of carrots, and his mom will have planted 7 + x rows of tomatoes.

Setting these two expressions equal to each other gives:

4 + 2x = 7 + x

Solving for x, we get:

x = 3

Thus, after 3 hours, Alan will have planted:

4 + 2(3) = 10 rows of carrots

And his mom will have planted:

7 + (3) = 10 rows of tomatoes

Therefore, they will each have completed 10 rows of vegetables after 3 hours.

To graph these equations, we can plot them on a coordinate plane, where the x-axis represents the number of hours and the y-axis represents the number of rows planted.

Alan's equation is y = 2x + 4, and his mom's equation is y = x + 7.

The graph of these two equations intersect at the point (3, 10), which represents the moment when they have each planted 10 rows.

Therefore, Alan and his mom will each have completed 10 rows after 3 hours

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Therefore, the solution to the equation -2 - 5/4x = 13 is x = -12.

A mathematical statement proving the equality of two expressions is known as an equation. Variables, numbers, and mathematical operations like addition, subtraction, multiplication, and division are frequently included. In addition to representing a connection between variables, an equation may also be used to find an unknown number. As they enable us to define and evaluate connections between things and make predictions about how they will behave under various circumstances, equations are a crucial tool in many domains, including mathematics, physics, engineering, and many more.

To solve for x in the equation -2 - 5/4x = 13, you can follow these steps:

Add 2 to both sides of the equation to isolate the fraction on the left side:

-2 - 5/4x + 2 = 13 + 2

-5/4x = 15

Multiply both sides of the equation by -4/5 to get x by itself:

(-4/5) * (-5/4x) = (-4/5) * 15

x = -12

Therefore, the solution to the equation -2 - 5/4x = 13 is x = -12.

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Answer:

To find the value of A, we can substitute g(-3) = 2 into the given equation and solve for A.

g(q) = (2q-4) / (q-A)

2 = (2(-3)-4) / (-3-A)

Multiplying both sides by (-3-A), we get:

2(-3-A) = -10 - 2A

Expanding the left side, we get:

-6 - 2A = -10 - 2A

Adding 2A to both sides, we get:

-6 = -10

This is a contradiction, which means that there is no value of A that satisfies the given conditions. Therefore, the answer to the question is:

There is no value of A that satisfies the given conditions.

The true statement is that the difference between the maximum profit earned by the sandwich shop and the smoothie stand is $2,700. (option d).

To determine the maximum profit earned by each business, we need to find the vertex of each quadratic function. The vertex of a quadratic function of the form ax² + bx + c is given by the formula (-b/2a, f(-b/2a)), where f(-b/2a) is the maximum value of the function.

The equations for the two functions are:

f(x) = -500x² + 9000x + 7500 g(x) = -500x² + 7500x + 4200

To find the vertex of f(x), we need to first rewrite the function in standard form:

f(x) = -500(x² - 18x - 15)

Completing the square, we get:

f(x) = -500(x - 9)² + 12000

So the vertex of f(x) is (9, 12000), which represents the maximum profit earned by the sandwich shop.

Similarly, to find the vertex of g(x), we rewrite the function in standard form:

g(x) = -500(x² - 15x - 8.4)

Completing the square, we get:

g(x) = -500(x - 7.5)² + 14100

So the vertex of g(x) is (7.5, 14100), which represents the maximum profit earned by the smoothie stand.

Finally, we can calculate the difference between the maximum profits earned by both businesses as:

12000 - 14100 = -2700

Therefore, the correct answer is option (d).

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Answer:

r=1

Step-by-step explanation:

The Pearson correlation coefficient is used to measure the strength of a linear association between two variables, where the value r = 1 means a perfect positive correlation and the value r = -1 means a perfect negataive correlation. So, for example, you could use this test to find out whether people's height and weight are correlated (they will be - the taller people are, the heavier they're likely to be).

Answer:

(x-24/5)^2 + (y-21/5)^2 = (sqrt(481)/5)^2, or (x-24/5)^2 + (y-21/5)^2 = 481/25

Step-by-step explanation:

The equation of a circle can be written in the form (x-a)^2 + (y-b)^2 = r^2, where (a,b) is the center of the circle and r is its radius. Since the lines are tangent to the circle at points (0,5) and (6,5), we can use these points to find the center and radius of the circle.

First, let’s find the slope of each line. The slope of the line y = 3/4x+5 is 3/4. The slope of the line 3x + 4y = 38 can be found by rearranging it into slope-intercept form: y = (-3/4)x + 19/2. So the slope of this line is -3/4.

Since the lines are tangent to the circle, they are perpendicular to the radius at their point of tangency. This means that the center of the circle lies on the line that passes through (0,5) and has a slope of -4/3, and also on the line that passes through (6,5) and has a slope of 4/3.

Let’s find the equation of these two lines. The line passing through (0,5) with a slope of -4/3 has an equation y - 5 = (-4/3)(x - 0), or y = (-4/3)x + 5. The line passing through (6,5) with a slope of 4/3 has an equation y - 5 = (4/3)(x - 6), or y = (4/3)x - 3.

The center of the circle is at the intersection of these two lines. To find it, we can set their right-hand sides equal to each other and solve for x: (-4/3)x + 5 = (4/3)x - 3. Solving this equation gives us x = 24/5. Substituting this value into either equation for y gives us y = (4/3)(24/5) - 3 = 21/5.

So the center of the circle is at (24/5, 21/5). To find its radius, we can use either point of tangency. Let’s use (0,5). The distance between this point and the center is given by sqrt((0-24/5)^2 + (5-21/5)^2), which simplifies to sqrt(481)/5.

Therefore, the equation of the circle is (x-24/5)^2 + (y-21/5)^2 = (sqrt(481)/5)^2, or (x-24/5)^2 + (y-21/5)^2 = 481/25.

Answer:

  (x -2)(x -4)

Step-by-step explanation:

You want to factor x² - 4x -2x +8.

We recognize that the product of the coefficients of the two linear terms is equal to the contant, so this is more easily factored by not combining like terms prior to factoring.

Grouping the terms in pairs, we find we can factor each pair:

  (x² -4x) + (-2x +8)

  = x(x -4) -2(x -4) . . . . . these terms have a common factor of (x -4)

  = (x -2)(x -4) . . . . . . . factored form of the expression

b. f(x) = x + 5, which represents a vertical shift of 5 units upwards.  f(x-a) = (x-a)^2, where a is a constant.

9) The function f(x) = x represents a linear function with a slope of 1 and y-intercept of 0. To shift the graph vertically, we need to add or subtract a constant from the function. Thus, the function that represents a vertical shift of f(x) = x would be of the form f(x) = x + b, where b is a constant.

Out of the given options, the correct answer is b. f(x) = x + 5, which represents a vertical shift of 5 units upwards.

10) To shift the graph of f(x) = x^2 horizontally, we need to add or subtract a constant inside the function, affecting the position of the vertex of the parabola. Thus, the function that represents a horizontal shift of f(x) = x^2 would be of the form f(x-a) = (x-a)^2, where a is a constant.

Out of the given options, the correct answer is a. f(x) = (x+2)^2, which represents a horizontal shift of 2 units to the left.

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