Polygon PQRS, shown in the figure, is dilated by a scale factor of 0.5 with the origin as the center of dilation, resulting in polygon P'Q'R'S'. A polygon PQRS is plotted on a coordinate plane. The vertices P is at (10, 8), Q is at (6, 14), R is at (11, 16), and (15, 10). The slope of P'Q' is -1.5 . The length of P'Q' is approximately 5.39 .

Answer:

As the ratio of the length of the arm of the old chair to the length of the arm of the new chair is 3/2, and the length of the old chair is 9 inches, hence the length of the arm of the new chair is 6 inches.

Answer:

Are there answer choices? But when looking at it one side should just be a little bit more than double the length of one side.

Step-by-step explanation:

This is because 20 is less than half of 50

Answer:

The solution I got is (4,2)

Step-by-step explanation:

When I plotted the equations on a graph, they intercepted at (4,2).

Answer:

m = -2/3

Step-by-step explanation:

We can find the slope of the line from the given two points:

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

m = (1-7)/(10-1)

m = -6/9

m = -2/3

To find the z-score for a sales associate who earns $37,500, we can use the formula:

z = (x - μ) / σ

Where:

x is the value we want to convert to a z-score (in this case, $37,500),

μ is the mean of the distribution (in this case, $32,500), and

σ is the standard deviation of the distribution (in this case, $2,500).

Substituting the given values into the formula, we have:

z = (37,500 - 32,500) / 2,500

z = 5,000 / 2,500

z = 2

Therefore, the z-score for a sales associate who earns $37,500 is 2.

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The z-score for a sales associate earning $37,500 in a system where the mean salary is $32,500 and the standard deviation is $2,500 has a z-score of 2. This score indicates that the associate's salary is two standard deviations above the mean.

The z-score represents how many standard deviations a value is from the mean. In this case, the value is the salary of a sales associate, the mean is the average salary, and the standard deviation is the average variation in salaries.

We calculate the z-score by subtracting the mean from the value and dividing by the standard deviation, like so:

Z = (Value - Mean) / Standard Deviation

So, the z-score for an associate earning $37,500 would be:

Z = ($37,500 - $32,500) / $2,500

This gives us a z-score of +2, indicating that a salary of $37,500 is two standard deviations above mean.

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Answer:

22

Step-by-step explanation

Step-by-step explanation:

Sure, here's a step-by-step response you can use:

"Hey, that's a good question! Let me explain why (2x + 1)^2 is not equal to 4x^2 + 1.

When we see an expression like (2x + 1)^2, we know that it means we need to multiply (2x + 1) by itself. So let's do that first:

(2x + 1)^2 = (2x + 1) x (2x + 1)

Now we can use the FOIL method to multiply these two expressions together:

(2x + 1) x (2x + 1) = 4x^2 + 2x + 2x + 1

If we simplify the middle terms by adding them together, we get:

(2x + 1) x (2x + 1) = 4x^2 + 4x + 1

So the expression (2x + 1)^2 simplifies to 4x^2 + 4x + 1, not 4x^2 + 1.

I can see why you might have thought the answer was 4x^2 + 1, since that's the first term in the expression we got. But we can't forget about the two middle terms that come from multiplying 2x and 1 together twice.

I hope that helps clear things up! Let me know if you have any more questions."

To prove that triangle FGE and triangle IJH we need information like the two sides of each triangle and the included angle to be congruent.

To prove two triangles are similar by the SAS is that you need to show that two sides of one triangle are proportional to two corresponding sides of another triangles, with the included corresponding angles being congruent.

For the SAS postulate you need two sides and the included angle in both triangles.

Side-Angle-Side (SAS) postulate:-

If two sides and the included angles of one triangle are congruent to two sides and the included angle of a second triangle, then the two triangles are congruent. SAS postulate relate two triangles and says that two triangles are congruent if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle.

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The value of x if The measure of the angle is = 5x + 4, The measure of the angle is = 146, The lines are parallel, is 6.

Parallel lines are any two or more lines that all lie in the same plane and never cross one another. They are equally spaced apart and have the same incline.

Given:

The measure of the angle is = 5x + 4

The measure of the angle is = 146

The lines are parallel,

Calculate the value of x as shown below,

5x + 4 = 180 - 146  (Parallel line theorem, corresponding angle, and supplementary angles)

5x = 34 - 4

x = 30 / 5

x = 6

Thus, the value of x is 6.

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Answer:

x = 24.99 or 25

Step-by-step explanation:

Using sin to figure out the angle of ABD, we can figure out the angle of CBD by subtracting it from 90°.

sin y = (1/5)

y = 11.54°

90 - 11.54 = 78.46°

Now using Pythagorean Theorem (a²+b²=c²) we can solve for line BD.

1² + b² = 5²

1 + b² = 25

b² = 24

b = √24

Now we can use tan to figure out the length of segment DC.

tan(78.46) = z/√24

z = 23.99

We can now combine the known length of segment AD and the length of DC to get x.

1 + 23.99 = 24.99 or about 25.

The predicted number of runs for the player with only 86 hits can be calculated using the equation Runs = Hits + Walks - Home Runs. Plugging in the values given, we get: Runs = 86 + Walks - Home Runs. Therefore, the predicted number of runs for the player is dependent on the number of walks and home runs they have.

To solve for the predicted number of runs, we can use the following steps:

Therefore, the predicted number of runs for the player with only 86 hits can be calculated by plugging in the values of the number of walks and home runs into the equation Runs = Hits + Walks - Home Runs.

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There are a total of 112 elements shown in the Venn diagram is false statement.

Venn diagrams are used to represent sets, their connections, and set-related actions graphically. The Venn diagram uses circles to represent the relationships between sets and the region that they overlap. A Venn diagram is used in mathematics to represent the logical relationship between sets and their constituent members and aids in the solution of instances based on these sets. A Venn diagram is a type of diagram designed to show every relationship between various sets. Venn diagrams are used in mathematics to show the connection between two or more sets. This approach of articulating sets or specific situations aids in a better comprehension of the problem and makes it easier to draw conclusions. As a result, we frequently utilize circles to illustrate the connections between objects or limited groupings of objects.

Given

Two sets --m and n-- are shown in the Venn diagram

Following statement is false,

c.) there are a total of 112 elements shown in the Venn diagram.

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Answer:

(4,0) and (2,0)

Step-by-step explanation:

For an x-intercept, y=0, so now we have:

(x-4)(x-2)=0

Anything multiplied by 0 is 0, so (x-4)=0 and/or (x-2)=0

(x-4)=0

x=4

(x-2)=0

x=2

The x-intercept co-ordinates are: (4,0), (2,0)

Answer:

x-intercepts are (4,0) and (2,0)

Answer:

150 Miles

Step-by-step explanation:

30 * 5miles = 150

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To calculate the amount of carpentry needed for your bedroom, you should find the area of the bedroom. The answer is A. Area.

When we talk about the amount of carpentry required for a room, we are talking about the number of square feet that need to be covered with carpet. As a result, we'll need to calculate the area of the room to figure out how much carpet we'll need.The area is the amount of space that a two-dimensional object takes up. To calculate the area of a rectangle, multiply the length by the width. The formula for calculating the area of a rectangle is:A = l × wWhere A is the area, l is the length, and w is the width of the rectangle.

For example, if the length of your room is 10 feet and the width is 12 feet, the area of your room will be: A = 10 × 12

= 120 square feet.

To calculate the amount of carpentry needed for your bedroom, you should find the area of the room by multiplying the length by the width.

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£36

20+25=45          Take away 13 and it's 32.   32+4 (the shipping charge) is 36. So Ruth pays 36 pounds.

We need to find the function f(n) whose terms are the same as the series in question. We can then integrate this function from n=1 to infinity and determine if the integral is convergent or divergent. If it is convergent, then the series is convergent. If it is divergent, then the series is also divergent.

To determine whether a series is convergent or divergent using the integral test, we need to first check if the series satisfies three conditions:

1) The terms of the series are positive.

2) The terms of the series are decreasing.

3) The series has an infinite number of terms.

Assuming these conditions are satisfied, we can use the integral test which states that if the integral of the function f(x) from n=1 to infinity is convergent, then the series with terms a_n = f(n) is also convergent. Conversely, if the integral is divergent, then the series is also divergent.

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Answer: always, always

Step-by-step explanation:

Every circle is similar to every other circle.

Answer:

2) f(3) = 2(3)+4

Step-by-step explanation:

From the two column proof we have been able to show that:

m∠6 = 20° and m∠4 = 160°

Two column proof is one of the most common formal proofs in elementary geometry courses. The known or derived statements are written in the left column, and the reason why each statement is known or valid is written in the adjacent right column.  

The complete two column proof is as follows:

Statement 1: a ║ b

Reason 1: Given

Statement 2: m∠6 = ¹/₈m∠4

Reason 2: Given

Statement 3: m∠6 + m∠4 = 180°

Reason 3: Supplementary Angles

Statement 4: m∠6 + 8*m∠4 = 180°

Reason 4: Substitution

Statement 5: m∠6 = 20° and m∠4 = 160°

Reason 5: Algebra

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Answer:

12

Step-by-step explanation:

Given:

3 bags of each color band

4 kits

To "divide equally" we need the greatest number that divides the two numbers 3 and 4 equally.

Find the greatest common factor of 3 and 4:

factors of 3 = 1,3,6,9,12,15,18,21,24....

factors of 4 = 1,2,4,8,12,16,20,24...

How many bands are in each kit?​

12 or any other number that is a factor of both 3 and 4 such as 24,..etc.

We can use Stokes' theorem to evaluate the line integral of the curl of a vector field F around a closed curve C, by integrating the dot product of the curl of F and the unit normal vector to the surface S that is bounded by the curve C.

Mathematically, this can be written as:

∫∫(curl F) · dS = ∫C F · dr

where dS is the differential surface element of S, and dr is the differential vector element of C.

In this problem, we are given the vector field F = (2y cos z, ex sin z, xey), and we need to evaluate the line integral of the curl of F around the hemisphere x^2 + y^2 + z^2 = 9, z ≥ 0, oriented upward.

First, we need to find the curl of F:

curl F = (∂Q/∂y - ∂P/∂z, ∂R/∂z - ∂Q/∂x, ∂P/∂x - ∂R/∂y)

where P = 2y cos z, Q = ex sin z, and R = xey. Taking partial derivatives with respect to x, y, and z, we get:

∂P/∂x = 0

∂Q/∂x = 0

∂R/∂x = ey

∂P/∂y = 2 cos z

∂Q/∂y = 0

∂R/∂y = x e^y

∂P/∂z = -2y sin z

∂Q/∂z = ex cos z

∂R/∂z = 0

Substituting these partial derivatives into the curl formula, we get:

curl F = (x e^y, 2 cos z, 2y sin z - ex cos z)

Next, we need to find the unit normal vector to the surface S that is bounded by the hemisphere x^2 + y^2 + z^2 = 9, z ≥ 0, oriented upward. Since S is a closed surface, its boundary curve C is the circle x^2 + y^2 = 9, z = 0, oriented counterclockwise when viewed from above. Therefore, the unit normal vector to S is:

n = (0, 0, 1)

Now we can apply Stokes' theorem:

∫∫(curl F) · dS = ∫C F · dr

The left-hand side is the surface integral of the curl of F over S. Since S is the hemisphere x^2 + y^2 + z^2 = 9, z ≥ 0, we can use spherical coordinates to parameterize S as:

x = 3 sin θ cos φ

y = 3 sin θ sin φ

z = 3 cos θ

0 ≤ θ ≤ π/2

0 ≤ φ ≤ 2π

The differential surface element dS is then:

dS = (∂x/∂θ x ∂x/∂φ, ∂y/∂θ x ∂y/∂φ, ∂z/∂θ x ∂z/∂φ) dθ dφ

= (9 sin θ cos φ, 9 sin θ sin φ, 9 cos θ) dθ dφ

Substituting the parameterization and the differential surface element into the surface integral, we get:

∫∫(curl F) · dS = ∫C F ·

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Answer:

  15 yd/s

Step-by-step explanation:

You want to know the rate of change of distance to a firework when it is 8 yards away horizontally, 6 yards high, and its height is increasing at 25 yards per second.

The geometry of the problem can be modeled by a 3-4-5 right triangle scaled by a factor of 2 yards. The straight-line distance to the firework is ...

  5 × (2 yd) = 10 yards

The vertical distance is given as 6 yards, increasing at 25 yd/s. Then the cosine of the angle from the line of sight to the direction of travel is ...

  cos(α) = adjacent/hypotenuse = (6 yd)/(10 yd) = 0.6

The speed in the direction of the line of sight is the speed of the firework, multiplied by the cosine of the angle between its direction and the line of sight:

  rate of change of distance away = (25 yd/s) × cos(α) = (25 yd/s)(0.6)

  rate of change of distance away = 15 yd/s

__

Additional comment

The rate of change can also be found using calculus. The distance away can be expressed using the distance formula, and its derivative found. The value of that derivative at the time of interest will give the rate of change of distance to the firework. This is shown in the second attachment, using a graphing calculator to find the derivative.

Here, we have two pairs of similar triangles.

Let's find the values of x and y.

• Sol,vin,g for x:

Given:

Length of longer base = 9

Length of shorter base = 5

Length of smaller leg = 8

Let's solve for x.

Since the triangles are similar, the corresponding sides will be in proportion.

To solve for x, apply the proportionality equation:

Cross multiply and solve for x:

• Solving for y:

Given:

Length of longer base = 3

Length of longer leg = 6

Length of smaller leg = 4

Length of total base = y

To solve for y, we have the equation:

Cross multiply and solve for y:

ANSWER:

• x = 12

• y = 5

Answer: 3/52

Step-by-step explanation:

You want to pick a diamond jack, diamond queen or diamond king

There are only 3 of those so

P(DJ or DQ or DK) = 3/52        There are 3 of those out of 52 total

The height of the object after 3 seconds is 73.5 meters

A model function is a way of describing a real-life system or situation using mathematical concepts and language

Since the equation for the height of the object is given by:

s(t) = -4.9t² + 19.6t + 58.8 and t is the t in seconds

Thus, in order to find the height of the object after 3 seconds, you need to substitute  t = 3 into the equation. That is:

s(t) = -4.9t² + 19.6t + 58.8

s(t) = -4.9×(3)² + 19.6(3) + 58.8

s(t) = 73.5 meters

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Answer

So the unit rate for the nearest cent per ounce for each size is 0.24 : 0.19.

Step-by-step explanation:If 16oz cost 3.89, then 1 oz costs 3.89 ÷ 16 = 0.243125 ≈ 0.24

If 32oz cost 5.98, then 1 oz costs 5.98 ÷ 32 = 0.186875 ≈ 0.19

So the unit rate for the nearest cent per ounce for each size is 0.24 : 0.19.