In the accompanying diagram, right triangle ABC is similar to right triangle RST with ZA E ZR. If AB = 6. AC = 9. and RS = 4. find RT. T D 4

A circle has rotational symmetry, and  it in such a way that it looks different from its original position by rotating it with an angle that is not a multiple of 360 degrees.

A circle in such a way that it looks different. This is possible because a circle has rotational symmetry, meaning it looks the same from every angle of rotation around its center.

To make it look different, rotate the circle by any angle other than a multiple of 360 degrees (or 2π radians). For example, if you rotate the circle by 90 degrees, 180 degrees, 270 degrees, etc., it will still look the same as the original circle. However, if you rotate the circle by any other angle, it will change its appearance and look different from the original position.

For instance, consider rotating the circle by 45 degrees. After this rotation, the circle will appear rotated and look different from its initial orientation. The same applies to any non-multiple of 360 degrees rotation.

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Answer:

a) 10/3  

b) hyperbola

c) x = ± 6/5

Step-by-step explanation:

a) A conic section with a focus at the origin, a directrix of x = ±p where p is a positive real number and positive eccentricity (e) has a polar equation:

\(r=\frac{ep}{1\pm e*cos\theta}\)

Given the conic equation: \(r=\frac{12}{3-10cos\theta}\)

We have to make it to be in the form \(r=\frac{ep}{1\pm e*cos\theta}\):

\(r=\frac{12}{3-10cos\theta}\\\\multiply\ both\ sides\ by\ \frac{1}{3} \\\\r=\frac{12*\frac{1}{3}}{(3-10cos\theta)*\frac{1}{3}}\\\\r=\frac{12*\frac{1}{3}}{3*\frac{1}{3}-10cos\theta*\frac{1}{3}}\\\\r=\frac{4}{1-\frac{10}{3}cos\theta } \\\\r=\frac{\frac{10}{3}(\frac{6}{5} ) }{1-\frac{10}{3}cos\theta }\)

Comparing with  \(r=\frac{ep}{1\pm e*cos\theta}\)

e = 10/3 = 3.3333, p = 6/5

b) since the eccentricity = 3.33 > 1, it is a hyperbola

c) The equation of the directrix is x = ±p = ± 6/5

Explanation:

Segment AW bisects angle CAD.

This leads to the smaller pieces (angles CAW and DAW) to be equal to one another. Both are 20 degrees each. That totals to 20+20 = 40 degrees.

Therefore, angle CAD = 40 degrees.

The supplement of this is angle DAX

(angle CAD) + (angle DAX) = 180

angle DAX = 180 - (angle CAD)

angle DAX = 180 - 40

angle DAX = 140 degrees

The slope of the lined graph is 5 / 3

The formula for determining the slope of a line is expressed as;

Slope = y2 - y1/ x2 - x1

From the graph shown;

Now, let's substitute the values

Slope, m = 4 - (-1) / 3 - 0

Find the differences

Slope, m = 4 + 1/ 3

Slope, m = 5 / 3

Thus, the slope of the lined graph is 5 / 3

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Answer:

remaining amount of animals should be 35

Step-by-step explanation:

First add up all the pets in the store = 37

Then minus the 2 puppies = 35

then put it as 2:35

Answer:

3:7

Step-by-step explanation:

Answer:

Unknown

Step-by-step explanation:

Hi! so you didn't add the ordered pair options but I will do my best :) so if you see the ordered pair (0.7) that could definitely be a solution because using the slope intercept form equation you gave I know that's our y Intercept. the slope is 4/1 so moving up 4 and to the right 1 or down 4 and to the left 1 on a graph could show you more points! If you don't want to draw it you could use Desmos and just put this equation in or give me the ordered pairs and I will give you your answer!

hope this helps :)

Answer:

174°, 174°, 6°

Step-by-step explanation:

opposite angles in a parallelogram are congruent, so one of the other angles = 6°

parallelogram = 360°

the other angles in the parallelogram = x

x + x + 6° + 6° = 360°

2x = 348

x = 174°

Check Your Work:

174° + 174° + 6° + 6° = 360°

Let me know if you have any more doubts! :D

Answer:

325.2

Step-by-step explanation:

Percent decrease =

(difference in prices)/(original price) × 100

(2.85 - 2.78)/2.85 × 100

= (0.07)/2.85 ×100 ≈ 2.5%

Answer:

Step-by-step explanation:

x + x + 90 = 180

2x + 90 = 180

2x = 90

x = 45

The probability of randomly selecting two women from 884 subjects is 1.

The probability of randomly selecting two women from 884 subjects can be calculated using the following formula: P(A and B) = P(A) x P(B). In this case, A is the event of randomly selecting a woman from 884 subjects and B is the event of randomly selecting a second woman from the remaining 883 subjects.

Therefore, P(A) = 884/884 = 1 and P(B) = 883/883 = 1. Thus, P(A and B) = 1 x 1 = 1. Then, the probability of randomly selecting two women from 884 subjects is 1. To round to four decimal places, the probability is 0.0000.

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Answer:

3n + 5 = 23,

3n = 18

n = 6

since "n" = 6,

2n - 3

= 2×6 - 3

12 - 3

= 9

The missing number in Sequence 2 is 780.

To find the missing number in Sequence 2, let's analyze the pattern:

In Sequence 1, the numbers increase by 1 each time: 126, 127, 128, 129, ...

In Sequence 2, the numbers seem to follow a pattern where each number is obtained by multiplying the corresponding number in Sequence 1 by a certain factor:

2 x 126 = 252

3 x 127 = 381

4 x 128 = 512

5 x 129 = 645

...

Looking at this pattern, we can see that the missing number in Sequence 2 should be:

6 x 130 = 780

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Question isnt well formatted :

Answer:

1 : 6

Step-by-step explanation:

Given the question :

3x = 1/2y

3x = y/2

Multiply both sides by 2

3x * 2 = y/2 * 2

6x = y

This can be interpreted as :

y = 6 times the value of x

x = y/6

x : y

1 : 6

Answer:

QUESTION:

which experimental probability from coach nelson's experiment equals the theorectical probability? what is this probability?

ANSWER:

This will explain everything to you.

https://www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-probability-statistics/cc-7th-theoretical-and-experimental-probability/v/comparing-theoretical-to-experimental-probabilites

Step-by-step explanation:

Hope that this helps you out! :)          

If you have any questions please put them in the comment section below this answer.          

Have a great rest of your day/night!          

Please thank me on my profile if this answer has helped you.

\(\quad \huge \quad \quad \boxed{ \tt \:Answer }\)

\(\qquad \tt \rightarrow \: (3 {a}^{2} - 7xy)(3 {a}^{2} + 7xy) = 9 {a}^{ 4 } - 49 {x}^{2} {y}^{2} \)

____________________________________

\( \large \tt Solution \: : \)

\(\qquad \tt \rightarrow \: (3 {a}^{2} - 7xy)(3 {a}^{2} + 7xy)\)

\(\qquad \tt \rightarrow \:(3 {a}^{2} \sdot3 {a}^{2} ) + (3a {}^{2} \sdot7xy) - (7xy \sdot3 {a}^{2} ) - (7xy \sdot7xy)\)

\(\qquad \tt \rightarrow \:9 {a}^{4} + 21a {}^{2} xy- 21 {a}^{2} xy - 49 {x}^{2} {y}^{2} \)

\(\qquad \tt \rightarrow \: 9 {a}^{ 4 } - 49 {x}^{2} {y}^{2} \)

or

Apply property :

\(\qquad \tt \rightarrow \: (p + q)(p - q) = {p}^{2} - {q}^{2} \)

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

Answer:

x= 54°

Step-by-step explanation:

43 + x - 7 = 90°

36 + x = 90°

x= 90-36

x= 54°

Answer:

54

Step-by-step explanation:

90-43 = 47

x-7 = 47

x=47+7

x = 54

The functions f(x) and g(x) are different functions.

The function f(x) is a cubic function, while the function g(x) is a logarithmic function. The common feature of both functions is their range

The functions are given as:

f(x) = x³ + x² - 2x + 3 and g(x) = log(x) + 2

This means that the function f(x) is a cubic function, while the function g(x) is a logarithmic function.

From the attached graph, we have the following features:

Domain: -∞ < x < ∞

Range: -∞ < y < ∞

y-intercept = 3

x - intercepts = -2.37

Function g(x)

Domain: x > 0

Range: -∞ < y < ∞

y - intercept = None

x - intercepts = 0.01

By comparing the key features above, we can conclude that the common features in both functions are their range

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Given,

The expression is,

Substracting 4 from both sides then,

Substracting 6n from both sides then,

Multiplying both sides by 1/3 then,

Hence, the solution for n is n<= (-10/3).

Answer:

Question 1: The appropriate measures of center for this data set would be (1) Mean and (2) Median. There is no mode in this data set as there are no repeating values.

Question 2: To find the standard deviation, we first need to find the mean:

Mean = (513 + 490 + 496 + 380 + 490 + 513 + 503 + 513 + 500 + 492) / 10 = 494.0

Next, we find the difference between each data point and the mean:

(513 - 494.0), (490 - 494.0), (496 - 494.0), (380 - 494.0), (490 - 494.0), (513 - 494.0), (503 - 494.0), (513 - 494.0), (500 - 494.0), (492 - 494.0)

19, -4, 2, -114, -4, 19, 9, 19, 6, -2

Then we square each difference:

361, 16, 4, 12996, 16, 361, 81, 361, 36, 4

The sum of these squared differences is:

361 + 16 + 4 + 12996 + 16 + 361 + 81 + 361 + 36 + 4 = 14136

To find the variance, we divide the sum of squared differences by the number of data points minus one:

Variance = 14136 / 9 = 1570.7

Finally, we find the standard deviation by taking the square root of the variance:

Standard deviation = √1570.7 ≈ 39.6 (rounded to the tenths place)

Step-by-step explanation:

The requried population increased by approximately 60.53%.

To find the absolute increase, we subtract the initial population from the final population:

Absolute increase = Final population - Initial population

Absolute increase = 6100 - 3800

Absolute increase = 2300

Therefore, the population increased by 2300 people.

To find the relative increase, we first calculate the percent change:

Percent change = (New value - Old value) / Old value x 100%

Percent change = (6100 - 3800) / 3800 x 100%

Percent change = 2300 / 3800 x 100%

Percent change = 60.53%

Therefore, the population increased by approximately 60.53%.

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The value of cos ø, for the given coordinates (8, 6), is 4/5 in the lowest terms.

To find the value of cosine (cos) ø, we need the coordinates (8, 6) of a point on the unit circle.

The unit circle is a circle with a radius of 1, and the coordinates (8, 6) do not lie on the unit circle. However, we can use these coordinates to calculate the cosine value indirectly.

First, we need to find the hypotenuse (r) of the right triangle formed by the coordinates (8, 6). We can use the Pythagorean theorem:

r = √(8² + 6²) = √(64 + 36) = √100 = 10

Now, we can find the cosine value by dividing the adjacent side length (x-coordinate) by the hypotenuse:

cos ø = 8 / 10 = 4/5.

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Answer:

70%

Step-by-step explanation:

the ratio is 14 to 6 so if you have 14 small milkshakes you would also have 6 regular milkshakes

to find a percentage we can buff up the ratio to add up to 100

14 + 6 = 20

100 / 20 = 5

that means we must multiply each side by 5

14 * 5 = 70

6 * 5 = 30

the ratio is now 70 to 30

you would have 70% of milkshakes that are small

Answer:

D: Mittens

Step-by-step explanation:

We are given;

Population mean;

- Abyssinian: μ = 12

- Colorpoint shorthair: μ = 14

Population standard deviation;

- Abyssinian: σ = 1.5

- Colorpoint shorthair: σ = 1

Sample mean;

-Fluffy the Abyssinian: x¯ = 13

-Mittens the colorpoint shorthair; x¯ = 15

To find which cat had a longer lifespan, we need to find the z-score for both breeds and the one with the higher z-score is the one with longer lifespan.

Z-score formula is;

z = (x¯ - μ)/σ

For Fluffy the Abyssinian;

z = (13 - 12)/1.5

z = 0.667

For Mittens the colorpoint shorthair;

z = (15 - 14)/1

z = 1

Z-score of Mittens is higher and thus it has a longer lifespan.

Answer:

320

80

Step-by-step explanation:

Answer:

Step-by-step explanation:

Combination has to selection. When selecting 4 people out of a pool of  15 people, this can be done as thus according to combination formuka:

15C4 = 15!/(15-4)!4!

15C4 = 15!/11!4!

15C4 = 15*14*13*12*11!/11!*4*3*2

15C4 =  15*14*13*12/24

15C4 = 32760/24

15C4 = 1365 different ways.

Hence this can be done in 1365 different ways

The cost of renting skates is $3. It would cost $19 for 4 hours. The solution has been obtained by using linear equations.

What is a linear equation?

The greatest linear equation has a degree of one. In light of this, it can be seen that linear equations with exponents greater than one lack variables. A straight line results from such an equation on the graph.

We are given that an ice-skating rink charges $4 per hour to skate on the rink and the option to rent skates for an additional cost.

Marlo paid $13 to rent ice skates and to skate for two-and-a-half hours.

a. Let the cost of renting be 'x'.

So,

⇒x + 2.5(4) = 13

⇒x + 10 = 13

⇒x = 3

So, cost of renting is $3.

b. Cost to rent skates and be on the ice for 4 hours will be

⇒ 3 + 4(4) = $19

Hence, the cost of renting skates is $3 and it would cost $19 for 4 hours.

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Answer:

128 servings

Step-by-step explanation:

5/4 cups of milk for 10 servings is equal to 1/8 cup per 1 serving

there are 16 cups in a gallon

let 'n' = # servings in a gallon

so 1/8 : 1 is 16 : n

1/8n = 16

n = 16(8)

n = 128