The following is an incomplete paragraph proving that ∠WRS ≅ ∠VQT, given the information in the figure where segment UV is parallel to segment WZ.:

Segments UV and WZ are parallel with line ST intersecting both at points Q and R respectively

According to the given information, segment UV is parallel to segment WZ while angles SQU and VQT are vertical angles. Angle VQT is congruent to angle SQU by the Vertical Angles Theorem. Because angles SQU and WRS are corresponding angles, they are congruent according to the Corresponding Angles Postulate. Finally, angle VQT is congruent to angle WRS by the _____________________.

Which Property of Equality accurately completes the proof?

Reflexive
Substitution
Subtraction
Transitive

The appropriate model of the function is:

                        Linear model

We are given a table of values as:

           x               f(x)

           1                15

           2               12

           3                9

           4                6

           5                 3

Clearly we could observe that with each increasing value of x the value of function decreases by 3.

This means that the range of change is constant.

Hence, the relation is linear ( as the rate of change is constant )

Also, the equation that models this data set is given by:

                       [tex]y=f(x)=18-3x[/tex]

Answer:

P(x)= 0.0198

Step-by-step explanation:

Given : 65% men are knowledgeable football fans, 12 are randomly selected ,

To find :  Probability that exactly four of them will consider themselves knowledgeable fans.

Solution : Let P is the success rate = 65% = 0.65  

               Let Q is the failure rate = 100-65= 35%= 0.35

               Let n be the total number of fans selected = 12

               Let r be the probability of getting exactly four = 4

Formula used : The binomial probability

[tex]P(x)= \frac{n!}{(n-r)!r!}P^rQ^{n-r}[/tex]

putting values in the formula we get ,

[tex]P(x)= \frac{12!}{(12-4)!4!}(0.65)^4(0.35)^{12-4}[/tex]

[tex]P(x)= (495)(0.1785)(o.ooo22 )[/tex]

 P(x)= 0.0198

The probability that exactly four out of the twelve randomly selected men will consider themselves knowledgeable football fans is approximately 0.236 or 23.6%.

Step 1: Model Selection (Binomial Distribution)

This scenario can be modeled using the binomial distribution if the following conditions are met:

Since these conditions seem reasonable, the binomial distribution is a suitable model for this scenario.

Step 2: Formula and Values

The probability (P(x)) of exactly x successes (knowledgeable fans) in n trials (men selected) with probability p of success (knowledgeable fan) can be calculated using the binomial probability formula:

P(x) = nCx * p^x * (1 - p)^(n-x)

where:

Step 3: Apply the Formula

Step 4: Calculate Using Calculator or Software

Step 5: Complete the Calculation

if they were rounded to the tens place

18 would round to 20

16 would round to 20

17 would round to 20

 14 would round to 10

 so April would be different.

Answer:

Option C. 1.047 radians

Step-by-step explanation:

We have to find the measure of angle AOT in radians.

To convert measure of an angle from degree to radians we use the formula

[tex]\text{radians}=\frac{\pi(\text{degrees})}{180}[/tex]

= [tex]\frac{\pi(60)}{180}=\frac{\pi }{3}[/tex]

(Since measure of angle AOT is 60°)

= [tex]\frac{3.14}{3}[/tex] (since π = 3.14)

= 1.047 radians

Therefore, option C. 1.047 radians is the correct option.

The given problem supplies as with the surface area of the beach ball and we are to look for the required radius. Assuming that the beach ball is perfectly shaped in the form of a sphere, then the formula for calculating the surface area of a sphere is given as:

SA = 4 π r^2

where r is the radius of the sphere and SA is the surface area which is given to be 7238 in^2

Rewriting the formula in terms of r:

r^2 = SA / 4 π

r = sqrt (SA / 4 π)

Solving for r:

r = sqrt (7238 in^2 / 4 π)

r = 24 in

Answer:

24 inches

The segment addition problem was given below which gives the value of x as 20.

Segment addition problem:

Consider three points on a line: A, B, and C. Point B is located between points A and C.

The lengths of the line segments are as follows:

Length of segment AB: 12

Length of segment BC: x

Length of segment AC: 32

Find the value of x.

We have the equation for segment addition: AB + BC = AC

Substitute the given values:

12 + x = 32

Now, solve for x:

x = 32 - 12

x = 20

Therefore, the value of x is indeed 20, and the lengths of the segments satisfy the segment addition property.

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To construct a segment addition problem with a solution of x = 20, use three collinear points A, B, and C and set AB = x and BC = 20 - x, with the entire segment AC being 20 units. Solving the equation x + (20 - x) = 20 confirms that x = 20 is the solution.

To write a segment addition problem that solves for x where the solution is x = 20, let’s use three collinear points A, B, and C with point B between A and C. We can then express the lengths of segments AB and BC in terms of x. For instance, if AB is x units long and BC is 20 - x units long, the total length of AC would be 20 units. We can write an equation based on this:

AB + BC = AC

x + (20 - x) = 20

By simplifying, x cancels out on the left-hand side, leaving 20 = 20, which is true for x = 20. Therefore, this is a valid segment addition problem where solving for x yields 20 as the solution.

Here is the step-by-step problem phrased as a question:

The distance and speed are illustrations of linear equations

The given parameters are:

[tex]\mathbf{Rate = 6}[/tex]

[tex]\mathbf{Initial = 9}[/tex]

(a) The standard equation

Because the distance reduces with time, the equation is:

[tex]\mathbf{y = Initial-Rate \times x}[/tex]

This gives

[tex]\mathbf{y = 9 - 6\times x}[/tex]

[tex]\mathbf{y = 9 - 6x}[/tex]

Add 6x to both sides

[tex]\mathbf{6x + y = 9}[/tex]

(b) The y-intercept

This is the initial distance away from home.

So, the y-intercept is 9

(c) The x-intercept

Set y to 0, to calculate the x-intercept

[tex]\mathbf{6x + y = 9}[/tex]

[tex]\mathbf{6x + 0 = 9}[/tex]

[tex]\mathbf{6x = 9}[/tex]

Divide both sides by 6

[tex]\mathbf{x = 1.5}[/tex]

This is the initial time away from home.

So, the x-intercept is 1.5

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Answer: 6 units

Step-by-step explanation:

Given: Line segment LM is dilated to create L'M' using point Q as the center of dilation and a scale factor of 2.

Since in dilation , to calculate the distance of a point on image from center point we need to multiply scale factor to the distance of corresponding point on pre-image from center point .

Thus we have,

[tex]QM'=2\times QM\\\\\Rightarrow QM'=2\times3\\\\\Rightarrow QM'=6[/tex]

Hence, the length of segment QM' = 6 units.

Answer:

6 units

Step-by-step explanation:

Answer:

Selling price of an item is $256.50 (A).

Step-by-step explanation:

Given : WE have  given an item listed at $400 subject to a discounted series of $25%, 10%, and 5% .

To find : Find the selling price of an item.

Formula used : Selling price = marked price - discount.

Solution : We have an item listed at = $400.

Discount percentage = $25% , $10% , $5.

Discount 1  = $400 ×[tex]\frac{25}{100}[/tex] = $100.

Selling price = $400-100 = $300.

Discount 2 = $300 ×[tex]\frac{10}{100}[/tex] = $30.

Selling price = $300-30 = $270.

Discount 3  = $270 ×[tex]\frac{5}{100}[/tex] = $13.50.

Final selling price = $270-13.50 = $256.50.

Therefore, Selling price of an item is $256.50 (A).

The point on the terminal side is (1,-1) and this can be determined by using the trigonometric functions.

Given :

The point on the terminal side of θ = negative three [tex]\pi[/tex] divided by four that has an x coordinate of negative 1.

The following steps can be used in order to determine the point on the terminal side:

Step 1 - Write the given expression.

[tex]\theta = -\dfrac{3\pi}{4}[/tex]

Step 2 - The value of the trigonometric function is given by:

[tex]\rm tan \dfrac{3\pi}{4} =-1[/tex]

Step 3 - The trigonometric function can also be written as:

[tex]\rm tan \theta=\dfrac{y}{x}=-1[/tex]

Step 4 - Substitute the value of 'x' in the above expression.

y = -1

So, the point on the terminal side is (1,-1).

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area = 4 x 5.5 = 22 square inches

cost is 0.99 per sq. inch

22 * 0.99 = 21.78

 cost is $21.98

To find the cost of the glass for a 4.0 inch by 5.5 inch picture frame, calculate the frame's area and multiply it by the cost per square inch. The glass would cost $21.78.

To calculate the cost of the glass needed to cover the picture, you first need to determine the area of the glass required. The frame measures 4.0 inches by 5.5 inches, so the area can be found using the formula for the area of a rectangle, which is length multiplied by width.

The area is therefore 4.0 inches × 5.5 inches = 22.0 square inches. With the cost of glass being $0.99 per square inch, the total cost can be calculated by multiplying the area of the glass by the cost per square inch:

Total cost = 22.0 square inches × $0.99/square inch = $21.78.

Therefore, the cost of the glass to cover the picture would be $21.78.

when numbers are in parenthesis the first number is x the second is y

(x,y)

sine they give you (2, blank)

2 = x so replace x in the equation with 2

 so y=2x+5 becomes y=2(2)+5

 so y = 2*2+5 = 9

 y=9

 so it should be (2,9)

True or false an inscribed angle is formed by two radii that share an endpoint

the correct answer is : FALSE

Answer:

The given statement : an inscribed angle is formed by two radii that share an endpoint is an FALSE statement.

Step-by-step explanation:

Inscribed angle is a angle which is formed inside the circle by joining of two intersecting chords inside a circle.

The inscribed angle is explained with the help of a diagram below :

In the diagram attached below, ∠ABC is an inscribed angle with an intercepted minor arc from A to C.

Thus, the inscribed angle is not formed with the help of radii that share a common end point.

Hence, The given statement : an inscribed angle is formed by two radii that share an endpoint is an FALSE statement.

The required exact value of the given trigonometric function is sin(17π/12) = (√6 + √2)/4

Trigonometric functions are defined as the functions which show the relationship between the angle and sides of a right-angled triangle.

The trigonometric function is given in the question, as follows:

sin(17π/12)

To find the value of sin(17π/12), we can use the following trigonometric identity:

sin(a + b) = sin(a)cos(b) + cos(a)sin(b)

In this case, we can write:

sin(17π/12) = sin(π/3 + π/4)

We know that sin(π/3) = √3/2 and cos(π/3) = 1/2, and sin(π/4) = cos(π/4) = √2/2.

Therefore, we can use the above identity to get:

sin(17π/12) = sin(π/3)cos(π/4) + cos(π/3)sin(π/4)

         = (√3/2)(√2/2) + (1/2)(√2/2)

         = (√6/4) + (√2/4)

         = (√6 + √2)/4

So the answer is option (c): √6 + √2 / 4.

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The given equation is a hyperbola, and by converting it to standard form we find a = 2 and b = 3. Therefore, the slopes of the asymptotes are ±3/2.

The equation given is in the form of a hyperbola equation which could be written as [tex]x^2/a^2 - y^2/b^2 = 1.[/tex] This suggests that the transverse axis is horizontal meaning the hyperbola opens to the left and right. The slopes of the asymptotes for hyperbola is given by ±b/a.

First, we need to rewrite our equation in standard form. The equation given is [tex]36 = 9x^{2} - 4y^{2}.[/tex] To convert it into the standard form, we divide whole equation by 36 to isolate 1 on one side. This yields [tex](x^2/4) - (y^2/9) = 1.[/tex] Now, it is in the standard form of hyperbola.

By comparing it with the standard equation, we see that  [tex]a^2 = 4 \ and\ b^2 = 9[/tex]which gives a = 2 and b = 3. Based on these, we can now find the slope of the asymptotes which is ±b/a = ±3/2.

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