Using the side lengths of PQR and STU, which angle has a cosine ratio of 15/17

20c2 + 10c = {c | c ≠ 0}

The sets for these two rational expressions are as follows:


22x + 11 x2 – 3x – 10 = {x | x ≠ 1/2}


1 – 2c = {c | c ≠ 1/2}


20c2 + 10c = {c | c ≠ 0}


To simplify the expressions, use the following steps:


1. Factor out the greatest common factor (GCF) if one exists.


2. Simplify the numerator and denominator separately.


3. Combine the numerator and denominator.

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The probability of the sum of the two numbers being even can be calculated using the formula for the probability of independent events.
The formula for the probability of independent events is: P(A and B) = P(A) x P(B
In this case, A represents the first die and B represents the second die.

To calculate the probability of the sum being even, we need to consider the possible outcomes for each die that would result in an even sum.
For the first die, there are three possible outcomes that would result in an even sum: 1, 3, and 5. The probability of any of these outcomes occurring is 3/6, or 1/2.
For the second die, there are also three possible outcomes that would result in an even sum: 2, 4, and 6. The probability of any of these outcomes occurring is also 3/6, or 1/2.
Using the formula for the probability of independent events, we can calculate the probability of the sum being even:
P(A and B) = P(A) x P(B) = (1/2) x (1/2) = 1/4

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x≤8 is the inequality of the number line.

A number system is defined as a system of writing to express numbers.

A number line is a picture of a graduated straight line that serves as visual representation of the real numbers.

In the given number line the shaded dot is at 8 at the arrow is to the left side of the number line which means the value of x is decreasing from point 8.

x≤8 is the inequality

Hence, x≤8 is the inequality of the number line.

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All of the functions have a constant rate of change since they are linear functions with a slope (rate of change) that is equal to the coefficient of the independent variable. Therefore, all functions have a constant rate of change of their slope.

Option A: y = 6(2) = 12 has a slope of 6, which means it increases by 6 for every unit increase in x.

Option B: y = 2(3) = 6 has a slope of 2, which means it increases by 2 for every unit increase in x.

Option C: y = 3(4) = 12 has a slope of 3, which means it increases by 3 for every unit increase in x.

Option D: y = 4(2) = 8 has a slope of 4, which means it increases by 4 for every unit increase in x.

Therefore, option A has the most rapid rate of change with a slope of 6.

Answer:

the ans the last person gave is very correct

The next term in the sequence would be -31.

What is Sequence ?

A sequence is a list of numbers or objects that follow a specific pattern or rule. Each number in the sequence is called a term, and the terms can be finite or infinite.

A. {31, 26, 21, 16, 11,...}

To find the common difference (d) between consecutive terms in the arithmetic sequence, we can subtract any term from the term that comes after it. For example, we can subtract 26 from 31 to get:

31 - 26 = 5

Similarly, we can subtract 21 from 26, 16 from 21, and so on:

26 - 21 = 5

21 - 16 = 5

16 - 11 = 5

Since the differences between consecutive terms are all the same, we can conclude that the common difference is d = 5.

To find the next term in the sequence, we can add the common difference (d = 5) to the last term (11):

11 + 5 = 16

Therefore, the next term in the sequence would be 16.

B. {-45, -38, -31, -24, . . .}

To find the common difference (d) between consecutive terms in the arithmetic sequence, we can subtract any term from the term that comes after it. For example, we can subtract -38 from -45 to get:

-45 - (-38) = -7

Similarly, we can subtract -31 from -38, -24 from -31, and so on:

-38 - (-31) = -7

-31 - (-24) = -7

Since the differences between consecutive terms are all the same, we can conclude that the common difference is d = -7.

To find the next term in the sequence, we can add the common difference (d = -7) to the last term (-24):

-24 - 7 = -31

Therefore, the next term in the sequence would be -31.

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Answer: surface area is _______ square centimeters.

To answer this question, I would need to know the dimensions of the rectangular prism, as both the total surface area and the lateral surface area depend on the dimensions of the prism.

Assuming the rectangular prism has length (l), width (w), and height (h), the formulas for the total surface area and the lateral surface area are:

Total surface area = 2lw + 2lh + 2wh

Lateral surface area = 2lh + 2wh

Therefore, to find the total surface area and lateral surface area of a specific rectangular prism, I would need to know its dimensions (length, width, and height) and plug them into these formulas.

Step-by-step explanation:

The probability distribution function of Y = |X| is given by:

P(Y ≤ y) = P(|X| ≤ y) = P(-y ≤ X ≤ y)

Since X ~ N(0, 2), we can use the standard normal distribution to find the probability;

P(Y ≤ y) = P(Z ≤ y/√2) - P(Z ≤ -y/√2)

where Z is a standard normal random variable.

To find E(|X|), we can use the formula:

E(|X|) = √(2/π) * σ

where σ is the standard deviation of X. Since X ~ N(0, 2), σ = √2, so:

E(|X|) = √(2/π) * √2 = √(4/π)

To find Var(|X|), we can use the formula:

Var(|X|) = E(X^2) - E(|X|)^2

Since X ~ N(0, 2), E(X^2) = σ^2 = 2. And we already found E(|X|) = √(4/π), so:

Var(|X|) = 2 - (4/π) = (2π - 4)/π

Therefore, the probability distribution function of Y = |X| is P(Y ≤ y) = P(Z ≤ y/√2) - P(Z ≤ -y/√2), the expected value of |X| is E(|X|) = √(4/π), and the variance of |X| is Var(|X|) = (2π - 4)/π.

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Answer:

136cm²

Step-by-step explanation:

explanation in the screenshot

The sum of angle in a triangle is 180°

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC.

The sum of angle A, B and C is 180 i.e A+B +C = 180°

Also a triangle is a 3 sided polygon. The sum of of angle in a polygon is( n-2)180

How do we prove that the sum of angle in a triangle is 180°?

Since triangle is 3 sided, n= 3, because n denote the number if sides

therefore the sum of angle = (n-2) 180 = (3-2)×180

= 180°

therefore the sum of angle In a triangle is 180°

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An increase in U.S. car production would be the most immediate effect of competition in car manufacturing.

As there will be an increase in the competition in car manufacturing the manufacturer will try to produce more and more cars of different types to attract customers. More market competition will provide consumers with more options to buy whatever products they desire, which will lead to a drop in the number of devoted customers for a given product line. Competitive markets have several advantages. Businesses that must constantly compete with one another for customers and market share are motivated to do so by offering products and services that are better than those of their rivals. In this market, businesses must constantly compete with one another by offering products and services that are more innovative, superior, and affordable.

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The linear equation y = 3x - 7 has a data that is correlated because it has a linear relationship and we cannot determine if there's a causation between x and y

A. y causes a. is not applicable in this case, as there is no variable named "a" in the equation.

B. The equation y = 3x - 7 represents a linear relationship between two variables, x and y. As the equation has a slope of 3, it indicates that as the value of x increases by 1, the value of y increases by 3. Therefore, the data are correlated positively.

C. This is incorrect. As mentioned in B, the equation represents a linear relationship between two variables, x and y, which are positively correlated.

D. This is correct. Although the equation represents a linear relationship between x and y, it does not imply causation. It is possible that x causes y, y causes x, or some other variable or variables may be influencing both x and y. Therefore, we cannot determine if there is causation between x and y based on the equation y = 3x - 7 alone

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Answer:

To find the coordinates of the root of the equation y = 3 + 2x - x^2, we need to find the values of x where y = 0 (because the root is the point where the function intersects the x-axis). So we can set y equal to 0 and solve for x:

0 = 3 + 2x - x^2

Rearranging, we get:

x^2 - 2x - 3 = 0

We can factor the quadratic equation by finding two numbers that add up to -2 and multiply to -3. These numbers are -3 and 1, so we can write:

(x - 3)(x + 1) = 0

This equation is true when either x - 3 = 0 or x + 1 = 0. So the roots of the equation are:

x = 3 or x = -1

Therefore, the coordinates of the roots of the equation y = 3 + 2x - x^2 are (3, 0) and (-1, 0).

The correct option representing possible sum for the long chain is B. 13 3 4 + 15 2 4 = 29 1 4.

Firstly let us convert the mixed fraction to fraction. So, the length of first chain = (13×4)+3/4

Length of first chain = 55/4 inches

Length of first chain = 13.75 inches

Length of second chain = (15×4)+2/4

Length of second chain = 62/4

Second chain length = 15.5 inches

So, total length = length of first chain + length of second chain

Total length = 13.75 + 15.5

Total length = 29.25 inches

Converting the decimal back to mixed fraction -

Total length = 29 1/4 inches

Thus, the correct answer B. 13 3 4 + 15 2 4 = 29 1 4.

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Step-by-step explanation:

so u could see that the yellow cab that will take Emma to airport is much more cheaper even though the entry price is a bit expensive .

Answer:

60

Step-by-step explanation:

Colton is 60 because Polly is 21 and plus 39 is 60.

The system of linear equations will be 2x+3y=8,  4x+6y=15.

Which mathematical equation is the most challenging?

A mathematics issue have baffled the finest scientists in the world for decades. The Diophantine equation x3+y3+z3=k, where k is the sum of all of the numbers from 1 to 100, is sometimes referred to as the "sum of three cubes."

What is an equation's most basic form?

The lowest corresponding fraction of the integer is its simplest form. How to determine the simplest form: Look for shared components in the denominator and numerator. Verify if a fractional integer includes a prime number.

For example:

2x+3y=8

4x+6y=15

Part C:

Using the example above,

2x+3y=8

4x+6y=15

If we multiply the first equation by , we get:

4x+6y=16

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The rate of change is 961.37 gallons/hour. This means that the water level decreases by 961.37 gallons every hour.

In mathematics, comparing two related quantities stated in different units is known as a rate. A rate is the ratio of two distinct values that are gauged in various ways. It is not the same as a unit rate to compare a certain number of units of the first quantity to one unit of the second. In general, the rate can be expressed as the ratio of two quantities with distinct units. With the help of rate, we can create a connection between two otherwise unconnected components. By doing this, we can gain a deeper understanding of a scenario.

Given,

The total amount of water the pool can hold =  9613.7 gallons

The time taken to drain the pool completely = 10 hours

We are asked to find the change in water level per hour of the pool.

This can be called the rate of change.

Rate of change = Total amount of water/ Time taken to drain

                       = 9613.7 / 10 = 961.37 gallons / hour

Therefore the rate of change is 961.37 gallons/hour. This means that the water level decreases by 961.37 gallons every hour.

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The solution to the given system of equations is x = 2.67 and y = 5.

The given system of equations can be solved by adding the two equations together.


3x + 4y = 20
-6x - 8y = -38


Adding the two equations together, we get:

-3x - 4y = -18


Subtracting 3x from both sides, we get:

-4y = -20
y = 5


Substituting the value of y in either of the given equations, we get:

3x + 4(5) = 20
3x = 8
x = 8/3

x = 2.67

After solving system of equations is x = 2.67 and y = 5.

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Answer:

12345,13345,14345,15345,16345

Step-by-step explanation:

Answer:
To calculate the time at which they flash together we need to find the least common multiple of 3 and 8.

Multiples of 3 =

3 x 1 = 3​

3 x 2 = 6​

3 x 3 = 9​

3 x 4 = 12​

3 x 5 = 15​

3 x 6 = 18​

3 x 7 = 21​

3 x 8 = 24​

3 x 9 =27​

3 x 10 = 30

Multiples of 8 =

8 x 1 = 8​

8 x 2 = 16​

8 x 3 = 24

8 x 4 = 32

8 x 5 = 40​

8 x 6 = 48

8 x 7 = 56​

8 x 8 = 64​

8 x 9 =72​

8 x 10 = 80

So LCM of 3 and 8 = 24

So both the lights will flash next at 7:24

Step-by-step explanation:

A linear function is a polynomial function with a degree of 1, and a degree 4 polynomial function is a polynomial function with a degree of 4. The leading coefficient of a polynomial function is the coefficient of the term with the highest degree. The y-intercept of a graph is the point where the graph crosses the y-axis.

To create the linear function, h(x), we can use the slope-intercept form: y = mx + b, where m is the slope and b is the y-intercept. Since the y-intercept can not be 0, we can choose a value for b that is not 0. For example, b = 2. We can also choose a value for m that is not 0, so that h(x) is not a horizontal or vertical line. For example, m = 3. Therefore, h(x) = 3x + 2.

To create the degree 4 polynomial function, P(x), we can use the factored form: P(x) = a(x - r1)(x - r2)(x - r3)(x - r4), where a is the leading coefficient, and r1, r2, r3, and r4 are the zeros of the function. Since the leading coefficient can not be |1|, we can choose a value for a that is not 1 or -1. For example, a = 2. Since one of the factors must be repeated 2 times, we can choose a value for r1 and set r2 equal to r1. For example, r1 = 1 and r2 = 1. Since one of the zeros must be a fraction, we can choose a value for r3 that is a fraction. For example, r3 = 1/2. Since the zeros should have a mix of positive and negative numbers, we can choose a value for r4 that is negative. For example, r4 = -2. Therefore, P(x) = 2(x - 1)(x - 1)(x - 1/2)(x + 2).

To find the points of intersection between h(x) and P(x), we can set h(x) equal to P(x) and solve for x:
3x + 2 = 2(x - 1)(x - 1)(x - 1/2)(x + 2)
This equation can be solved algebraically by expanding the right-hand side and rearranging the terms to form a degree 4 polynomial equation. Then, we can use the Rational Root Theorem and synthetic division to find the possible rational roots of the equation. Once we find the rational roots, we can use them to factor the equation and find the remaining roots. The x-coordinates of the points of intersection are the roots of the equation.

To determine the intervals when h(x)≥P(x), we can use the points of intersection and the signs of h(x) and P(x) on either side of the points of intersection. If h(x) is greater than or equal to P(x) on an interval, then the graph of h(x) is above or coincident with the graph of P(x) on that interval. We can use a sign chart or a graph to determine the intervals when h(x)≥P(x).

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B' is the reflection of the x-axis at position B(1,3) (1,-3) as a consequence of B (1, 3) being reflected over the x-axis.

A coordinate is a group of integers used to describe a point's location in space in mathematics. Cartesian coordinates are the most widely used form of coordinates. They are made up of an ordered pair of numbers (x, y) that represent a point's horizontal and vertical distances from a constant point of reference known as the origin. The y-coordinate indicates the point's vertical distance from the origin, while the x-coordinate represents the point's horizontal distance from it.

given

The x-coordinate remains constant while the sign of the y-coordinate varies when a point is reflected over the x-axis.

Therefore, we only need to alter the sign of the y-coordinate of B in order to determine the reflection B' of the point B(1,3) over the x-axis.

B' is the reflection of the x-axis at position B(1,3) (1,-3) as a consequence of B (1, 3) being reflected over the x-axis.

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These statistics can help us better understand the data and make comparisons between the two classes.

The given data shows the results of two classes, Class A and Class B.

Class A: 34, 31, 29, 24, 27, 37, 26, 24, 20, 37, 22, 18, 36, 26, 28, 23, 23, 27, 33, 25, 36, 32, 33, 25, 28, 35

Class B: (no data given)

In order to analyze the data, we can use statistics. Statistics is the science of collecting, analyzing, and interpreting data. One way to analyze the data is to find the mean, median, and mode of the data set.

Mean: The mean is the average of the data set. To find the mean, add up all the numbers and divide by the total number of data points.

Mean of Class A = (34+31+29+24+27+37+26+24+20+37+22+18+36+26+28+23+23+27+33+25+36+32+33+25+28+35) / 26 = 28.42

Median: The median is the middle number in the data set. To find the median, sort the data set in ascending or descending order and find the middle number. If there are an even number of data points, the median is the average of the two middle numbers.

Sorted Class A: 18, 20, 22, 23, 23, 24, 24, 25, 25, 26, 26, 27, 27, 28, 28, 29, 31, 32, 33, 33, 34, 35, 36, 36, 37, 37

Median of Class A = (26+27) / 2 = 26.5

Mode: The mode is the number that appears most frequently in the data set.

Mode of Class A = 24, 26, 27, 33, 36, 37 (all appear twice)

These statistics can help us better understand the data and make comparisons between the two classes.

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Answer:

35%

Step-by-step explanation:

26/40 = 0.65
1-0.65=35

A company will make a profit of 63.9%

Here, the cost of making pins = £1.10

the number of pins = 1000

Using unitary method, the total cost for making 1000 pins would be,

= Cost of each pin × Number of pins

= 1.10 × 1000

= £1110

Now we find the number of pins that sold in charities.

35 percent of pins in charities.

Using percentage formula, we find 35% of total number of pins.

= 35% of 1000

= (35/100) × 1000

= 350 pins

This means that 350 pins were sold in charities.

So, the number of pins left = 1000 - 350

                                          = 650 pins

Out of these remaining pins, 60% are sold at £3. 00 each

So, the number of pins sold at £3.00:

= 60% of 650

= (60/100) × 650

= 390

And the selling price of these 390 pins would be:

= 390 × £3.00

= £1170                           .................(1)

40% of 650 pins were sold at £5. 00 for 2

So, using percentage formula the number of pins sold at £5.00 for 2 would be:

= 40% of 650

= (40/100) × 650

= 260

These 260 pins were sold in pairs for £5.

Therefore, number of pairs sold

= 260/2

= 130 pairs

The selling price of these 130 pairs of pins would be,

= 130 × 5.00

= £650                    ...............(2)

Therefore, from (1) and (2) the total selling price would be,

= £1170 + £650

= £1820

So, the Profit would be:

= Selling price - Cost price

= 1820 - 1110

= £710

Now using  we find the profit percentage:

= Profit × 100 / Total cost price

= 710 × 100 / 1110

= 63.9%

Therefore, the required percentage profit = 63.9%

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The graph of the linear equation, y = 5x + 2, is shown below in the attachment.

To graph the linear equation, y = 5x + 2, first plot the y-intercept at (0, 2) on the coordinate plane. Then, use the slope of 5 to move up 5 units and right 1 unit from the y-intercept to find another point on the line.

Continue this process to plot several more points, and then connect the points with a straight line to complete the graph of the equation. The resulting graph will be a straight line with a positive slope of 5 and y-intercept of 2.

See the attachment below for the graph.

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This is the vertex form equation of the parabola with the given information.

From the information provided, we can write the vertex form equation of the parabola as follows:

First, we need to determine the value of "a" in the equation y = a(x - h)^2 + k, where (h,k) is the vertex and "a" determines the width and direction of the parabola.

The distance between the vertex and the focus is equal to 1/4a, so we can use this to find "a":

1/4a = (41/4 - 10)

1/4a = 1/4

a = 1

Now we can plug in the values for the vertex and "a" into the equation:

y = 1(x - 10)^2 - 8

This is the vertex form equation of the parabola with the given information.

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Answer:

5

Step-by-step explanation:

Using prοperties οf quadrilaterals, The line segment in the image that cοrrespοnds tο BC¯¯¯¯¯ in the pre-image is the line segment FG¯¯¯¯¯.

A pοlygοn with fοur sides and fοur vertices is called a quadrilateral (cοrners). It is a twο-dimensiοnal οbject that is flat and can take οn a number οf fοrms.

We knοw that matching sides οf the pre-image and image are identical in length since a reflectiοn maintains the size and shape οf the figure.

Since a reflectiοn preserves the shape and size οf the figure, we knοw that cοrrespοnding sides οf the pre-image and image are equal in length.

Therefοre, the line segment in the image that cοrrespοnds tο BC¯¯¯¯¯ in the pre-image is the line segment FG¯¯¯¯¯.

Tο see why, imagine fοlding the figure alοng the line οf reflectiοn sο that the pre-image and image cοincide. In this fοlded pοsitiοn, the cοrrespοnding sides οf the twο quadrilaterals will be οn tοp οf each οther. In particular, side BC¯¯¯¯¯ οf the pre-image will be οn tοp οf side FG¯¯¯¯¯ οf the image, cοnfirming that FG¯¯¯¯¯ cοrrespοnds tο BC¯¯¯¯¯ in the pre-image.

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