what is the quotient of the rational expressions shown below? make sure your answer is in reduced form x^2-16/x+5 divided by x^2-8x+16/2x+10

What is needed to be congruent to show that ABC=AXYZ is AC ≅ XZ. option D

Given that in ΔABC and ΔXYZ, ∠X ≅ ∠A and ∠Z ≅ ∠C.

We are to select the correct condition that we will need to show that the triangles ABC and XYZ are congruent to each other by ASA rule..

ASA Congruence Theorem: Two triangles are said to be congruent if two angles and the side lying between them of one triangle are congruent to the corresponding two angles and the side between them of the second triangle.

In ΔABC, side between ∠A and ∠C is AC,

in ΔXYZ, side between ∠X and ∠Z is XZ.

Therefore, for the triangles to be congruent by ASA rule, we must have AC ≅ XZ.

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The equation of the ellipse with foci (7, 17) and (7, -13), and a major axis of length 34 is[tex](x^2/289) + (y^2/225) = 1.[/tex]

To determine the equation of an ellipse given its foci and the length of its major axis, we need to use the standard form equation for an ellipse. The standard form equation for an ellipse centered at the origin is:

[tex](x^2/a^2) + (y^2/b^2) = 1[/tex]

where 'a' represents the semi-major axis and 'b' represents the semi-minor axis.

In this case, we know that the distance between the foci is equal to 2a, which means a = 34/2 = 17. The foci of the ellipse are given as (7, 17) and (7, -13). The foci lie on the major axis of the ellipse, and since their y-coordinates differ by 30 (17 - (-13) = 30), the length of the major axis is equal to 2b, which means b = 30/2 = 15.

Now we have the values of a and b, so we can substitute them into the standard form equation:

[tex](x^2/17^2) + (y^2/15^2) = 1[/tex]

Simplifying further, we have:

[tex](x^2/289) + (y^2/225) = 1[/tex]

Therefore, the equation of the ellipse with foci (7, 17) and (7, -13), and a major axis of length 34 is:

[tex](x^2/289) + (y^2/225) = 1.[/tex]

This equation represents an ellipse centered at the point (0, 0) with a semi-major axis of length 17 and a semi-minor axis of length 15.

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Answer:

The equation of the ellipse with foci (7, 17) and (7, -13), and a major axis of length 34 is

To determine the equation of an ellipse given its foci and the length of its major axis, we need to use the standard form equation for an ellipse. The standard form equation for an ellipse centered at the origin is:

where 'a' represents the semi-major axis and 'b' represents the semi-minor axis.

In this case, we know that the distance between the foci is equal to 2a, which means a = 34/2 = 17. The foci of the ellipse are given as (7, 17) and (7, -13). The foci lie on the major axis of the ellipse, and since their y-coordinates differ by 30 (17 - (-13) = 30), the length of the major axis is equal to 2b, which means b = 30/2 = 15.

Now we have the values of a and b, so we can substitute them into the standard form equation:

Simplifying further, we have:

Therefore, the equation of the ellipse with foci (7, 17) and (7, -13), and a major axis of length 34 is:

This equation represents an ellipse centered at the point (0, 0) with a semi-major axis of length 17 and a semi-minor axis of length 15.

Answer:A

Step-by-step explanation:the graph shows the values that are greater than 2

We can solve for the missing elements as follows:

1. Radius - 10 inches

Diameter - 20

Circumference -  62.8

Area - 314

2.  Radius  - 6ft

Diameter - 12

Circumference - 37.68

Area - 113.04

3.  Radius - 18

Diameter - 36 yards

Circumference - 113.04

Area - 1017.36

4.  Radius 15

Diameter - 30 cm

Circumference 94.2

Area - 706.5

5.  Radius - 5 mm

Diameter 10

Circumference 31.4

Area -78.5

6. Radius 20

Diameter - 40 inches

Circumference  125.6

Area -1256

To solve for the given values, we will use the formulas for area, circumference. Also, we can obtain the radius by dividing the diameter by 2 and the diameter is 2r. So we will solve for the values this way:

1. radius = 10 inches

diameter = 20

circumference = 2pie*r 2 *3.14*10 = 62.8

Area = 314

2. radius = 6ft

diameter = 12

circumference = 37.68

Area = 113.04

3. radius = 18

diameter = 36 yards

circumference = 113.04

Area = 1017.36

4. radius = 15

diameter = 30 cm

circumference = 94.2

Area = 706.5

5. radius = 5 mm

diameter = 10

circumference = 31.4

Area = 78.5

6. radius = 20 inches

diameter = 40 inches

circumference = 125.6

area = 1256

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Answer: the answer is (3,-2)

Step-by-step explanation: when you rotate a point about the origin 180 degrees clockwise, (x,y) turns into (-x,-y)

therefore

(-3,2) becomes (3,-2)

I'm pretty sure

Answer:

BC = 24 (D)

Step-by-step explanation:

Special Right Triangles (30-60-90 triangle)

Answer:

arc LKF = 208°

Step-by-step explanation:

the angle FLX between the tangent and the secant is half the measure of the intercepted arc LKF , then intercepted arc is twice angle FLX , so

arc LKF = 2 × 104° = 208°

The product of the given fractions is 224/61.

To calculate the product of the given fractions, let's simplify and cancel out any common factors.

We have:

(4/5) x (5/7) x (7/9) x (9/11) x (11/13) x (13/15) x (15/17) x (17/19) x (19/21) x (21/23) x (23/25) x (25/27) x (27/28) x (29/37) x (31/35) x (33/33) x (35/31) x (37/29)

Starting from the numerator and denominator of the first fraction, we observe the following cancellations:

5 in the numerator and denominator cancel out.

7 in the numerator and denominator cancel out.

9 in the numerator and denominator cancel out.

11 in the numerator and denominator cancel out.

13 in the numerator and denominator cancel out.

15 in the numerator and denominator cancel out.

17 in the numerator and denominator cancel out.

19 in the numerator and denominator cancel out.

21 in the numerator and denominator cancel out.

23 in the numerator and denominator cancel out.

25 in the numerator and denominator cancel out.

27 in the numerator and denominator cancel out.

Now, let's multiply the remaining fractions:

(4/1) x (1/28) x (29/37) x (31/1) x (1/35) x (37/29)

This simplifies to:

(4 x 1 x 29 x 31 x 37) / (1 x 28 x 37 x 29 x 35)

Simplifying further:

(4 x 29 x 31) / (28 x 35)

We can calculate this to get the final result:

(4 x 29 x 31) / (28 x 35) = 3584 / 980 = 224 / 61.

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Julio bought clothes for $5000 with a 20% down payment, which amounts to $1000. Hence, he ends up paying $4000 for the clothes.

Julio's clothing purchase involved a total cost of $5000. To secure the purchase, he made a down payment of 20% of the total cost. To calculate the down payment, we multiply the total cost by the down payment percentage:

Down payment = 20% * $5000

Down payment = 0.20 * $5000

Down payment = $1000

The down payment amount is $1000. To determine the final amount that Julio ends up paying for the clothes, we need to subtract the down payment from the total cost:

Total cost - Down payment = $5000 - $1000

Total cost - Down payment = $4000

Therefore, Julio ends up paying $4000 for the clothes.

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The question probable may be:

Julio bought clothes for a cost of $5000, for which he left a 20% down payment. How much money does he end up paying for the clothes?

The total number of times the digit "9" would have been written to number the entire photo album is 12 + 9 = 21 times.

To determine how many times the digit "9" would have been written to number all the pages of the photo album, we need to analyze the numbering pattern.

Since the album has 108 pages, we can observe that the numbers 1 to 9 are repeated 12 times (1-9, 10-19, 20-29, ..., 90-99) to cover the first 99 pages. Each repetition consists of ten numbers, and the digit "9" appears once in each repetition.

So, the digit "9" would have been written 12 times for the numbers 9, 19, 29, ..., 89 and 99.

However, we have an additional 9 pages to consider, which are 100, 101, 102, ..., 108. Each of these pages contains a single "9" in its numbering.

Therefore, the total number of times the digit "9" would have been written to number the entire photo album is 12 + 9 = 21 times.

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Answer:

the first 2

Step-by-step explanation:

let me know if it is wrong

(a) 58 = 2(w + 5 + w)

(b)  I. The width of the rectangle is 12 cm.

II. The length of the rectangle is 17 cm.

III. The area of the rectangle is 204 cm².

Let's solve the problem step by step:

(a) To write an equation for the perimeter of the rectangle, we know that the perimeter is the sum of all four sides. Let's denote the width of the rectangle as "w" (in cm). Given that the length is 5 cm more than the width, the length would be "w + 5" (in cm). The formula for the perimeter is:

Perimeter = 2(length + width)

Substituting the values, we have:

58 = 2(w + 5 + w)

Simplifying the equation, we get:

58 = 2(2w + 5)

(b) Now let's solve for the width and length of the rectangle:

I. To find the width, we solve the equation:

58 = 2(2w + 5)

Dividing both sides by 2, we get:

29 = 2w + 5

Subtracting 5 from both sides, we have:

24 = 2w

Dividing both sides by 2, we find:

w = 12 cm

Therefore, the width of the rectangle is 12 cm.

II. To find the length, we substitute the value of the width into the equation:

Length = w + 5 = 12 + 5 = 17 cm

Therefore, the length of the rectangle is 17 cm.

III. The area of the rectangle can be calculated using the formula:

Area = length × width

Substituting the values, we have:

Area = 17 cm × 12 cm = 204 cm²

Therefore, the area of the rectangle is 204 cm².

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The total cost for 24 copper hearts would be $21.41.

To calculate the total cost for 24 copper hearts, we need to determine the total amount of copper used and then multiply it by the cost of copper per pound.

First, let's find out the total amount of copper used for 24 copper hearts. Each heart uses 0.75 square inches of copper, so for 24 hearts, the total amount of copper used would be:

0.75 square inches/heart [tex]\times 24[/tex]hearts = 18 square inches.

Next, we need to convert the square inches into cubic inches. Since we don't have information about the thickness of the hearts, we'll assume they are flat hearts with a thickness of 1 inch. Therefore, the volume of copper used for the 24 hearts would be:

18 square inches [tex]\times 1[/tex] inch = 18 cubic inches.

Now, we can calculate the total weight of copper used. Given that there is 0.323 pounds of copper per cubic inch, the total weight of copper for the 24 hearts would be:

18 cubic inches [tex]\times 0.323[/tex] pounds/cubic inch = 5.814 pounds.

Finally, we multiply the total weight of copper by the cost of copper per pound to find the total cost:

5.814 pounds [tex]\times[/tex] $3.68/pound = $21.41.

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Answer:

The slope of the graphed line is A. -5

Step-by-step explanation:

Since when we move one step in x direction, we move 5 steps downwards in y direction, so, the slope is,

m = y/x

m = -5/1

m = -5

The shape is represented as below

The figure is of three shapes, the firs two are whole numbers then the last is a fraction.

Adding them results to

shape 1 + shape 2 + shape 3

1 + 1 + 1/4

As one fraction

= 9/4

as a mixed number

= 2 1/4

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The second table with x and y values (1, 2, 3, 4, 5) and (11, 13, 15, 17, 19) shows a positive correlation.

To determine which table shows a positive correlation, we need to examine the relationship between the values in the x and y columns. Positive correlation means that as the values in one column increase, the values in the other column also tend to increase.

Let's analyze each table:

Table 1:

x: 1, 2, 3, 4, 5

y: 15, 12, 14, 11, 18

In this table, as the values in the x column increase, the values in the y column are not consistently increasing or decreasing. For example, when x increases from 1 to 2, y decreases from 15 to 12. Therefore, this table does not show a positive correlation.

Table 2:

x: 1, 2, 3, 4, 5

y: 11, 13, 15, 17, 19

In this table, as the values in the x column increase, the values in the y column also consistently increase. For example, when x increases from 1 to 2, y increases from 11 to 13. This pattern continues for all the rows. Therefore, this table shows a positive correlation.

Table 3:

x: 1, 2, 3, 4, 5

y: 18, 16, 14, 12, 11

In this table, as the values in the x column increase, the values in the y column consistently decrease. For example, when x increases from 1 to 2, y decreases from 18 to 16. This pattern continues for all the rows. Therefore, this table does not show a positive correlation.

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The calculated length of the arc JK is 7π

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

Central angle = 140 degrees

Radius, IJ = 9 inches

Using the above as a guide, we have the following:

JK = Central angle/360 * 2 * π * Radius

Substitute the known values in the above equation, so, we have the following representation

JK = 140/360 * 2 * π * 9

Evaluate

JK = 7π

Hence, the length of the arc is 7π

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Answer:

5.9

Step-by-step explanation:

sin Θ = opp/hyp

sin 36° = x/10

x = 10 × sin 36°

x = 5.88

Answer: 5.9

Answer:

a. To fill in the missing data in the table, we can use the information given in the table along with the fact that the total number of employees is 186.

For value A: Since the total number of employees with no college credit is 28, and the total number of men is 79, we can subtract the number of men with some college (C) and college graduates (15) from the total number of men to find the missing value A. So A = 79 - C - 15.

For value B: Since the total number of women is 186, we can subtract the number of women with some college (D) and college graduates (22) from the total number of women to find the missing value B. So B = 186 - D - 22.

For value C: Since the total number of employees with some college is 81, and we have already determined the values A and D, we can subtract A and D from the total number of employees with some college to find the missing value C. So C = 81 - A - D.

For value D: Similarly, we can subtract B and E from the total number of women to find the missing value D. So D = 186 - B - E.

For value E: Since the total number of college graduates is 37 (15 men + 22 women), we can subtract the number of college graduates among men (15) from the total to find the missing value E. So E = 37 - 15.

For value F: Since the total number of employees is 186, we can subtract the total number of men (79) from the total to find the missing value F. So F = 186 - 79.

b. Joint relative frequency refers to the proportion of individuals that fall into a particular combination of categories. For example, the joint relative frequency of men with no college credit is the number of men with no college credit divided by the total number of employees (28/186). These data are joint and relative because they represent the proportion of individuals in a specific category combination relative to the total population.

c. To summarize the data using conditional relative frequency, we can calculate the proportion of individuals in each category given a specific condition. For example, we can calculate the conditional relative frequency of women who are college graduates by dividing the number of women who are college graduates (22) by the total number of women (186). Similarly, we can calculate the conditional relative frequency of men with some college by dividing the number of men with some college (C) by the total number of men (79).

To summarize the data using marginal relative frequency, we can calculate the proportion of individuals in each category by dividing the number of individuals in that category by the total number of individuals. For example, we can calculate the marginal relative frequency of men by dividing the total number of men (79) by the total number of employees (186). Similarly, we can calculate the marginal relative frequency of college graduates by dividing the total number of college graduates (37) by the total number of employees (186).

d. The data in the table can be analyzed to determine if there is an association or relationship between the variables. If the values in the table change depending on the categories of the other variable, then the variables are dependent. In this case, the data is dependent because the number of individuals with certain educational levels (no college credit, some college, college graduate) varies based on their gender. For example, there are different proportions of men and women in each educational category, indicating a relationship between gender and education level.

Step-by-step explanation:

The missing values in the two-way frequency table are filled based on the given values and the composition of the table. The table represents joint relative frequency, which is the proportion of specific groups in the total population. We can summarize the data using marginal and conditional relative frequencies, and the data are considered dependent because an employee's education level depends on their gender.

To fill in the missing values of the two-way frequency table, we need to use the given numbers and the rules of the two-way frequency table. Here are the strategies used for filling in the values for A through F:

The table will also represent joint relative frequency because each cell represents the joint occurrence of two categories (gender and education level). For example, the number of male employees with no college credit (28) divided by the total number of employees (186) is a joint relative frequency.

We may summarize the table data using conditional relative frequency and marginal relative frequency. The marginal relative frequency is the total of each row or column divided by the grand total. The conditional relative frequency would be, for example, the proportion of women among those with no college credit.

The data are dependent because the education level depends on whether the employee is a man or a woman.

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1. the linear equation 5(x + 7) - 3(x - 4) = 7x + 2, x = 9

2. In linear equation 4(3x + 5) - 3 = 9x - 7, x = -8

3. the linear equation 1/3(5x - 9) = 2(1/3x + 6), x = 15

A linear equation is an equation in only on variable.

1. To solve the linear equation 5(x + 7) - 3(x - 4) = 7x + 2, we proceed as follows

5(x + 7) - 3(x - 4) = 7x + 2

Expanding the brackets, we have

5x + 35 - 3x + 12 = 7x + 2

Collecting like terms in the expression, we have

5x + 35 - 3x + 12 = 7x + 2

5x - 3x - 7x = 2 - 35 - 12

-5x = -45

x = -45/-5

x = 9

2. To solve linear equation 4(3x + 5) - 3 = 9x - 7, we proceed as follows

4(3x + 5) - 3 = 9x - 7

Expanding the brackets, we have

12x + 20 - 3 = 9x - 7

Collecting like terms in the expression, we have

12x - 9x = - 7 + 3 - 20

3x = -24

x = -24/3

x = -8

3. To solve  the linear equation 1/3(5x - 9) = 2(1/3x + 6), we proceed as follows

1/3(5x - 9) = 2(1/3x + 6)

Expanding the brackets, we have

5x/3 - 3 = 2/3x + 12

Collecting like terms, we have

5x/3 - 2x/3 = 12 + 3

3x/3 = 15

x = 15

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An estimate for the mean is 47.6 kg.

In Mathematics and Geometry, the mean for this set of data can be calculated by using the following formula:

Mean = [F(x)]/n

Cumulative frequency = 10 + 7 + 2 + 8 + 3

Cumulative frequency = 30

For the total number of data based on the frequency, we have;

Total weight, F(x) = 10(40) + 7(52.5) + 2(65) + 8(77.5) + 3(90)

Total weight, F(x) = 40 + 367.5 + 130 + 620 + 270

Total weight, F(x) = 1427.5

Now, we can calculate the mean weight as follows;

Mean = 1427.5/30

Mean = 47.6 kg.

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Answer: D. 145°

Step-by-step explanation:

Since it is a parallelogram given by the symbol, then angle B is equal to angle D which is 145°.

Answer:

l

Step-by-step explanation:

Answer:

113.1 is the answer. I used the arbitory height of 4 so the volume of both are now 314.16 and 201.06

314.16-201.06=113.1

Answer:

a. Y(t) = At³ + Be^t + Ct² + Dt + E

b. Y(t) = At + B + Ce^t + Dsin(t) + Ecos(t)

c. Y(t) = Aet + Bte^t + Csin(t) + Dcos(t)

d. Y(t) = At³ + Bt² + Ct + D + Ecos(2t) + Fsin(2t)

e. Y(t) = At² + Bt + C + Dsin(t) + Ecos(t) + Fsin(t) + Gcos(t)

f. Y(t) = Aet + Bte^-t + Ccos(t) + Dsin(t) + E + Ft + G

Answer:

It's A and B: Opposite sides are parallel and Corresponding parts of congruent triangles are congruent.

Step-by-step explanation:

Answer:

first, arrange the numbers from least to greatest order. (Actually this is a longer step, if you also want to find the median. But since you are only asking for range and standard deviation, I won't do that here.) So, just find the lowest number and the highest number. Subtract the lowest from the highest. That is your range.

Your problem:

lowest: 98.6

highest: 131.9

subtract: 131.9 - 98.6 = 33.3  ← this is your range

Now, standard deviation.

Standard deviation is the amount of variety you have in your data sample.

Step 1: Find the mean

Add up all your numbers and divide by how many numbers you have.

You have 10 numbers in your sample.

115.6 + 109.3 + 126 + 104.9 + 131.9 + 113.7 + 119.8 + 98.6 + 131.9 + 131.9 

total = 1,183.6

now divide this by 10.  (n is the variable used here, so n = 10. This is because you have ten numbers. )

so n = 10

and 1,183.6/10 = 118.3

Now subtract each number by 118.3.

115.6 - 118.3 = -2.7

109.3 - 118.3 = -9

126 - 118.3 = 7.7

104.9 - 118.3 = -13.4

131.9 -118.3 = 13.6

113.7 - 118.3 = -4.6

119.8 - 118.3 = 1.5

98.6 - 118.3 = -19.7

131.9 - 118.3 = 13.6

131.9 - 118.3 = 13.6

now square all these numbers

7.29

81

59.29

179.56

184.96

21.16

0.75

388.09

184.96

184.96

Find the sum of these squares now. (We're almost done!)

sum = 1,292.02

remember our n?

it was n=10

now the formula for this is,

sum of squares ÷ n-1

substitute all this in.

1,292.02 ÷ 9 = 143.55

Remember. This is the VARIANCE. NOT the standard deviation.

The last step to find the standard deviation is, to find the square root of what we got. (143.55)

√143.55

= 11.9812353286 this is the number, but rounded two more decimal places is..

11.98 is the standard deviation.

Hope this helped!