If A=[a11a12a21a22] and B=[b11b12b21b22] are arbitrary vectors in R2×2, then the mapping 〈A,B〉=a11b11+a12b12+a21b21+a22b22 defines an inner product in R2×2. Use this inner product to determine 〈A,B〉, ∥A∥, ∥B∥, and the angle αA,B between A and B for A=[3 −2 2 −1] and B=[3 3 −5 −4].

The total area of all the Circles used by Princess is 4710 square centimeters.

The total area of all the circles used by Princess, The formula for the area of a circle is given by:

A = πr²

where A represents the area and r is the radius of the circle. Since we are given the diameter of each circle (20 cm), we can calculate the radius by dividing the diameter by 2:

r = 20 cm / 2 = 10 cm

Substituting this value into the area formula, we have:

A = π(10 cm)²

Now, let's calculate the area of one circle:

A = 3.14 * (10 cm)² ≈ 314 cm²

Therefore, the area of one circle is approximately 314 square centimeters.

Since Princess used 15 circles, we can find the total area by multiplying the area of one circle by the number of circles:

Total area = 314 cm² * 15 = 4710 cm²

Hence, the total area of all the circles used by Princess is 4710 square centimeters.

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To find C∇f·dr, where C is a constant and f has parametric equations[tex]x = t^2 + 1[/tex] and [tex]y = t^3 + t[/tex] for 0 ≤ t ≤ 1, we need to evaluate the line integral. The line integral ∇f·dr represents the work done along the curve defined by the parametric equations.

To calculate C∇f·dr, we first need to find the gradient of the function f. The gradient of f is given by ∇f = (∂f/∂x, ∂f/∂y), where ∂f/∂x and ∂f/∂y are the partial derivatives of f with respect to x and y, respectively.

Taking the partial derivatives of f = (x, y) with respect to x and y, we get ∂f/∂x = 2t and ∂f/∂y = [tex]3t^2[/tex] + 1.

Next, we need to parameterize the curve defined by the given parametric equations. The curve is defined for 0 ≤ t ≤ 1.

To evaluate the line integral C∇f·dr, we substitute the gradient components (∂f/∂x, ∂f/∂y) and the differential elements (dx, dy) with their corresponding expressions in terms of t.

Finally, we integrate the dot product C(∂f/∂x dx + ∂f/∂y dy) along the curve from t = 0 to t = 1. The result will depend on the constant C and can be computed using the given table of values for x and y.

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The complete question is:

A Table Of Values Of A Functionfwith Continuous Gradient Is Given. Find

A table of values of a functionfwith continuous gradient is given. FindCnablaf�dr, whereChas parametric equationsx=t2+ 1,y=t3+t, 0t1.

x\y 0 1 2

0 2 7 5

1 4 6 8

2 9 3 10

To perform the hypothesis test to determine whether the mean GPA for business students differs from the mean GPA at the whole university, we will use the critical value method.

Given:

Sample size (n) = 18

Sample mean (x(bar)) = calculated using the provided GPAs

Population mean (μ) = 2.88

Population standard deviation (σ) = 0.5

Significance level (α) = 0.05

Step 1: Define the null and alternative hypotheses:

Null hypothesis (H0): The mean GPA for business students is equal to the mean GPA at the whole university (μ = 2.88).

Alternative hypothesis (Ha): The mean GPA for business students differs from the mean GPA at the whole university (μ ≠ 2.88).

Step 2: Determine the critical value(s):

Since we are using the critical value method and have a two-tailed test, we need to find the critical values for the given significance level (α = 0.05) and degrees of freedom (df = n - 1 = 18 - 1 = 17). We can consult the t-distribution table or use statistical software. For α = 0.05 and df = 17, the critical values are approximately ±2.110.

Step 3: Calculate the test statistic:

The test statistic for this scenario is the t-statistic, which measures how far the sample mean deviates from the population mean, taking into account the sample size and standard deviation. The formula for the t-statistic is:

t = (x(bar) - μ) / (σ / sqrt(n))

Using the given values, we can calculate the t-statistic:

t = (x(bar) - μ) / (σ / sqrt(n))

t = (sample mean - population mean) / (population standard deviation / sqrt(sample size))

Step 4: Evaluate the test statistic:

Calculate the t-statistic using the provided values:

t = (x(bar) - μ) / (σ / sqrt(n))

Calculate the sample mean (x(bar)) using the provided GPAs.

Step 5: Determine whether to reject the null hypothesis:

Compare the absolute value of the calculated t-statistic with the critical value(s) from Step 2. If the absolute value of the t-statistic is greater than the critical value(s), we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.

If there is enough evidence to conclude that the mean GPA for business students differs from the mean GPA at the whole university, we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.

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The part in the steering column that allows for changes in the angle between the upper and lower shafts is the universal joint.

The universal joint, also known as a U-joint or Cardan joint, is a mechanical device that enables changes in the angle between two shafts that are not in a straight line. In the context of a steering column, the upper and lower shafts are connected by a universal joint.

As the steering wheel is turned, it exerts rotational force on the upper shaft of the steering column. The universal joint allows for the transmission of this rotational motion while accommodating changes in the angle between the upper and lower shafts. It provides flexibility and compensates for any misalignment between the two shafts, ensuring smooth and continuous rotation of the steering column.

The universal joint typically consists of two yokes connected by a cross-shaped component with needle bearings. These bearings allow for rotation in multiple axes, allowing the steering column to handle variations in the angle between the upper and lower shafts during steering movements.

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[tex]-(5\cdot(-4))=-(-20)=20[/tex]

Distributive property works only for addition.

[tex]a(b+c)=ab+ac[/tex] but [tex]a(bc)=abc[/tex], not [tex]ab+ac[/tex] or something like that.

Answer:

[tex]-(-5\times(-4))=-(-20)=20[/tex]

Step-by-step explanation:

Notice that the product within the brackets is:

[tex]5\times(-4)=-20[/tex]

Then, by first evaluating the product within the brackets, we get the following:

[tex]-(5\times(-4))=-(-20)[/tex]

Finally, note that the negative of negative twenty is twenty as follows:

[tex]-(-20)=20[/tex]

*Note on your mistake:

You cannot distribute the negative sign to each component of a product.

This can only happen if the expression within the bracket is a sum, for instance:

[tex]-(5+(-4))=-5+4[/tex]

Answer:

x=77°

Step-by-step explanation:

angles in triangle add to 180°

180°-43°-60°=x°

77°=x°

The corresponding angle to angle 9, according to the figure  is

angle 11

Corresponding angles are a pair of angles that are formed on the same side of a transversal line and in the same relative position with respect to the parallel lines being intersected by the transversal.

In simpler terms corresponding angles are formed when a line crosses two parallel lines  and the angles are in corresponding positions on each of the parallel lines.

Using the figure, the parallel lines are l and m and angle 9 and angle 11  are at the vertex of he triangles formed.

The two triangles formed are congruent (parallel lines l and line m ensures equal length of sides), According  to CPCTC theorem

angle 9 ≅ angle 11

angle 20 ≅ angle 6

angle 16 ≅ angle 7

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complete question

What is/are two corresponding angles to angle 9?

Answer: To match the shapes produced by the slice through the triangular prism, we need to consider the orientation of the slice relative to the prism. Here are the matching options:

A. Perpendicular to the base: Rectangle

B. Parallel to the base: Triangle with dimensions equal to the base

C. Diagonal from vertex to vertex: Triangle with unknown dimensions

We have shown that for any connected graph G with at least one cycle, we can remove some edges such that the resulting subgraph is bipartite and connected.

A graph is a graphic or visual representation of facts or values. The points on a graph are frequently used to depict the relationships between two or more objects.

To prove the statement, let's consider a connected graph G with at least one cycle.

Case 1: G is already bipartite.

If G is already bipartite, then the statement is trivially true. We don't need to remove any edges because G is already bipartite and connected.

Case 2: G is not bipartite.

If G is not bipartite, it means that there exists at least one odd cycle in G. In order to make G bipartite, we can remove any one of the edges from the odd cycle. Removing a single edge will break the cycle and create two separate connected components.

Let's denote the original graph with the odd cycle as G', and the resulting subgraph after removing one edge as G''. By removing a single edge, G'' will consist of two connected components, each of which is bipartite. This is because removing one edge from the odd cycle creates two separate paths, and each path can be assigned a different color to form a bipartite graph.

Since G'' is the result of removing one edge from G', it is still connected because all the vertices in G' are still connected through the remaining edges. Thus, G'' is a connected subgraph of G and is also bipartite.

Therefore, we have shown that for any connected graph G with at least one cycle, we can remove some edges such that the resulting subgraph is bipartite and connected.

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The value of arc RS is 105⁰.

The value of angle GHJ is 73⁰.

The value of angle GIJ is 73⁰.

The value of angle ABC is calculated by applying intersecting chord theorem, which states that the angle at tangent is half of the arc angle of the two intersecting chords.

m∠ABC = ¹/₂ (arc AC ) (interior angle of intersecting secants)

m∠ABC = ¹/₂ ( 34⁰ )

m∠ABC = 17⁰

The value of arc RS is calculated as follows;

arc RT = 2 x ( 42⁰) (interior angles of intersecting secants)

arc RT = 84⁰

arc RS = 360 - (RT + TS) (sum of angles in a circle)

arc RS = 360 - ( 84 + 171)

arc RS = 360 - 255

arc RS = 105⁰

The value of angle GHJ is calculated as follows;

arc GJ = 360 - (68 + 31 + 115)

arc GJ = 146⁰

angle GHJ = ¹/₂ x 146⁰ = 73⁰

angle GIJ = angle GHJ = 73⁰ (vertical opposite angles are equal).

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Answer:

Step-by-step explanation:

BD = 100.8

AB² = BC×BD = 2096.64

AC = [tex]\sqrt{AB^{2}- BC^{2} }[/tex] = [tex]8\sqrt{26}[/tex]

The complex number z = 2 - 8i in Trigonometric form ,the correct option is: 8.246(cos 75.964° + isin 75.964°).

The complex number z = 2 - 8i in trigonometric form, The trigonometric form is typically written as z = r(cos θ + isin θ), where r represents the magnitude and θ represents the argument.

The magnitude of z, we use the formula: |z| = sqrt(Re(z)^2 + Im(z)^2), where Re(z) is the real part and Im(z) is the imaginary part of z.

In this case, Re(z) = 2 and Im(z) = -8, so we have:

|z| = sqrt(2^2 + (-8)^2) = sqrt(4 + 64) = sqrt(68) ≈ 8.246

The argument (angle) of z, we use the formula: θ = atan(Im(z)/Re(z)), where atan is the arctangent function.

In this case, θ = atan((-8)/2) = atan(-4) ≈ -75.964° or 284.036° (adding or subtracting multiples of 360° does not change the angle).

Putting it all together, the complex number z = 2 - 8i can be expressed in trigonometric form as:

8.246(cos 75.964° + isin 75.964°) or 8.246(cos 284.036° + isin 284.036°).

Therefore, the correct option is: 8.246(cos 75.964° + isin 75.964°).

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The equation Y=-3x-1 represents a linear relationship between x and y, and can be used to model real-world situations such as distance vs. time or cost vs. quantity.

The equation Y=-3x-1 represents a straight line on a coordinate plane. The "slope-intercept" form of the equation is y=mx+b, where m is the slope and b is the y-intercept.

In this case, the slope is -3 and the y-intercept is -1. This means that the line goes downwards at a rate of 3 units for every 1 unit to the right, and intersects the y-axis at -1.

To find the solution to this equation, you would need to have a specific value for either x or y.

If you were given a value for x, you could plug it into the equation to find the corresponding value for y. If you were given a value for y, you could solve for x by rearranging the equation.

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The required bearing angle of town B from Thomas is 75°.

We have,

Bearing is basically an angle that is measured clockwise from the north. Bearing are generally written in three figure.

Given that

Thomas is facing towards town A, which is at a bearing of 300°.

Implies that town A is 300° from north.

If Thomas turns 135° clockwise, then he faces towards town B,

The bearing angle will be 300+135 = 435°

Since, one complete round makes angle 360°, therefore

The required bearing angle = 435 - 360 = 75

The bearing angle of town B from Thomas is 75°.

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The given statement "non-linear quality constraints can sometimes be rewritten as linear constraints" is TRUE because this process, known as linearization, involves transforming non-linear expressions into equivalent linear expressions.

Linearization simplifies complex problems, allowing them to be solved using linear programming techniques. However, this may not always be possible for all non-linear constraints, and some trade-offs in accuracy might occur.

Linearization techniques, such as piecewise linear approximation or variable substitution, can be applied to rewrite non-linear constraints into linear ones, facilitating the use of linear programming methods for more efficient and tractable solutions.

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The number of bags of maize loaded is A = 50 bags

Given data ,

A lorry weighs 3.2 tonnes when empty. It weighed 7.7 tonnes when loaded with 90 kg bags of maize.

To find the number of bags of maize loaded onto the lorry, we need to calculate the difference in weight between the loaded and empty states, and then convert that difference into the weight of the bags.

The weight of the lorry when loaded with bags of maize is 7.7 tonnes, and when empty, it weighs 3.2 tonnes. Therefore, the weight of the bags of maize is:

7.7 tonnes - 3.2 tonnes = 4.5 tonnes

On simplifying the equation , we get

Number of bags = (Weight of maize) / (Weight per bag)

= 4.5 tonnes / 0.09 tonnes

= 50 bags

Hence , there were 50 bags of maize loaded onto the lorry

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1.) Sherelle:

Q₁: 60

Me: 68

Q₃: 74

Minimum: 26

Maximum: 85

Venita:

Q₁: 53

Me: 62

Q₃: 70

Minimum: 44

Maximum: 79

2.) A) This could mean that Venita's coins are evenly spread out based time.

B) Venita's plot has a larger within box spread than Shrella.

C) Shrella's plot has a median value of about 68 while Venita's has a median value of 60.

3.) Sherelle remembers seeing an old coin in her bag earlier, then her bag would be more likely to have the 1916 coin.

Here, we have,

1.)

The five-number summary comprehends the minimum and maximum values, the 1st and 3rd quartiles and the median.

1st step: is to arrange the data sets from least to greatest.

Sherelle:

26 39 56 58 60 62 65 66 66 68 71 72 72 73 74 75 81 83 84 85

Venita:

44 45 51 51 53 53 55 57 58 62 65 66 69 69 70 73 75 77 78 79

2nd step: To calculate each quartile you have to determine their position and then identify which observation sits in that position:

Quartile 1:

PosQ₁: n/4= 20/4= 5

Quartile 2 (Median)

PosMe: n/2= 20/2= 10

Quartile 3

PosQ₃: n*(3/4)= 20*(3/4)= 15

Since both samples have the same size, the 1st quartile will be the fifth observation of each sample, the median will be the tenth observation and the 3rd quartile will be the fifteenth.

Sherelle:

Q₁: 60

Me: 68

Q₃: 74

Minimum: 26

Maximum: 85

Venita:

Q₁: 53

Me: 62

Q₃: 70

Minimum: 44

Maximum: 79

2.)

A.)

Differentiating based on the shape of the box and whisker plot.

The first plot, named shrella depicts a skewed distribution, (negative skew) highlighted by the long whisker (tail) to the left with the median also shifting towatds to the right of the box away from the box center. This could mean that the time difference between the coins aren't even and older coins seem to exhibit a larger time gap than newer coins.

The second plot however. VENITA, depicts a distribution which could be described as normal, as the whiskers are aodt of equal length and the median centered in the middle of the box. This could mean that Venita's coins are evenly spread out based time.

B.)

As for the overall spread, Shrella's plot covers a wider range, hence (larger spread) than Venita's plot. Thanks to the long whiskers in Shrella's plot.

For the spread within the boxes, Venita's plot has a larger within box spread than Shrella. With Venita's plot has a wider box tham Shrella's box plot.

C)

The appropriate measure of centre to be used is the median which is denoted by the vertical line in between the box. Shrella's plot has a median value of about 68 while Venita's has a median value of 60. The median value are still s bit close or similar.

3.)

If Sherelle remembers seeing an old coin in her bag earlier, then her bag would be more likely to have the 1916 coin.

We have,

It is a branch of mathematics that deals with the occurrence of a random event.

Sherelle might say that she remembers seeing an old coin in her bag earlier and that she rarely removes things from her bag.

She might also argue that she has not used her bag as frequently as Venita, so the coin is more likely to be in her bag.

Venita might argue that she has used her bag more frequently than Sherelle, so the coin is more likely to be in her bag.

She might also say that she has checked her bag multiple times and has not seen the coin, so it must be in Sherelle's bag.

if Sherelle remembers seeing an old coin in her bag earlier, then her bag would be more likely to have the 1916 coin.

On the other hand, if the coin was recently added to one of the bags, then Venita's bag could also be a likely candidate.

Hence, if Sherelle remembers seeing an old coin in her bag earlier, then her bag would be more likely to have the 1916 coin.

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Answer:21.9

Step-by-step explanation:

The theoretical probability of spinning green on the spinner, divided into 4 equal-size sections colored red, green, orange, and blue, is ¼ or 25%.

In this scenario, the spinner has four equal-size sections. Since each section is of equal size, the probability of landing on any specific section is the same. Therefore, the probability of spinning green, which is one out of the four possible outcomes, is 1/4 or 25%.

To calculate the theoretical probability, we divide the favorable outcomes (spinning green) by the total possible outcomes. In this case, there is one favorable outcome (green) out of four possible outcomes (red, green, orange, and blue), resulting in a probability of 1/4 or 25%.

It's important to note that theoretical probability is based on the assumption of equally likely outcomes and assumes a large number of trials. In practice, actual outcomes may deviate from theoretical probabilities due to factors like imbalances in the spinner or inherent randomness.

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To find the general expressions for the autocorrelation function rzz() of z(t) in terms of the autocorrelation functions of x(t) and y(t), we need to consider the relationship between z(t), x(t), and y(t).

If z(t) is a linear combination of x(t) and y(t), we can express it as:

z(t) = a * x(t) + b * y(t)

where a and b are constants.

The autocorrelation function of z(t), denoted as rzz(), can be calculated as:

rzz() = E[z(t) * z(t + )]

Substituting the expression for z(t), we have:

rzz() = E[(a * x(t) + b * y(t)) * (a * x(t + ) + b * y(t + ))]

Expanding this expression and applying the linearity property of expectation, we get:

rzz() = a^2 * Exx() + b^2 * Eyy() + 2ab * Exy()

where Exx(), Eyy(), and Exy() are the autocorrelation functions of x(t), y(t), and the cross-correlation function between x(t) and y(t), respectively.

Therefore, the general expression for the autocorrelation function rzz() of z(t) in terms of the autocorrelation functions of x(t) and y(t) is given by:

rzz() = a^2 * Exx() + b^2 * Eyy() + 2ab * Exy()

This expression demonstrates how the autocorrelation of z(t) can be determined based on the autocorrelation functions of x(t) and y(t) along with their cross-correlation.

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The answer choices that correctly describe the points labeled A, B, and C in the box plot include the following:

B. point C represents Q₃.

C. point A represents Q₁.

E. point B represents the median.

In Mathematics and Statistics, a box plot is sometimes referred to as box-and-whisker plot and it can be defined as a type of chart that can be used to graphically or visually represent the five-number summary of a data set with respect to locality, skewness, and spread.

Based on the information provided about the box-and-whisker plot, the five-number summary for the given data set include the following:

Minimum (Min) = 1.

First quartile (Q₁) = 4.

Median (Med) = 7.

Third quartile (Q₃) = 10.

Maximum (Max) = 12.

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Number of Data points with z-score less than 0.7 = P(Z < 0.7) * N

The data set have a z-score less than 0.7, the properties of the standard normal distribution. The standard normal distribution has a mean of 0 and a standard deviation of 1.

Given that the mean of the data set is 34 and the standard deviation is 9, we can calculate the z-score for each data point using the formula:

z = (x - mean) / standard deviation

Substituting the values, we have:

z = (x - 34) / 9

The number of data points with a z-score less than 0.7, we need to determine the proportion of data points that fall within that range.

To do this, we can use a standard normal distribution table or a statistical software to find the cumulative probability associated with a z-score of 0.7. Let's assume that the cumulative probability is P(Z < 0.7).

Using the standard normal distribution table or software, we find that P(Z < 0.7) is approximately 0.7580.

This means that approximately 75.80% of the data points in a standard normal distribution have a z-score less than 0.7.

The number of data points in our specific data set with a z-score less than 0.7, we can multiply the proportion by the total number of data points.

the total number of data points in the data set is N.

Number of data points with z-score less than 0.7 = P(Z < 0.7) * N

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To calculate the probabilities of the given events when randomly selecting a permutation of {1, 2, 3}, we need to consider the total number of possible permutations and the number of permutations that satisfy each event.

Total number of permutations:

There are 3 elements in the set {1, 2, 3}, so the total number of permutations is 3! = 3 × 2 × 1 = 6.

(a) 1 precedes 3:

In this case, we want to find the number of permutations where 1 appears before 3. The valid permutations are {1, 2, 3} and {2, 1, 3}, which means there are 2 permutations that satisfy this event.

Probability of 1 precedes 3: P(1 precedes 3) = Number of permutations satisfying the event / Total number of permutations = 2 / 6 = 1/3.

(b) 3 precedes 1:

Here, we want to find the number of permutations where 3 appears before 1. The valid permutations are {3, 1, 2} and {3, 2, 1}, so there are 2 permutations that satisfy this event.

Probability of 3 precedes 1: P(3 precedes 1) = Number of permutations satisfying the event / Total number of permutations = 2 / 6 = 1/3.

(c) 3 precedes 1 and 3 precedes 2:

To find the number of permutations where 3 appears before 1 and 3 appears before 2, we can examine the valid permutations: {3, 1, 2} and {3, 2, 1}. Only these two permutations satisfy both conditions.

Probability of both events: P(3 precedes 1 and 3 precedes 2) = Number of permutations satisfying the events / Total number of permutations = 2 / 6 = 1/3.

Therefore, the probabilities are:

(a) P(1 precedes 3) = 1/3

(b) P(3 precedes 1) = 1/3

(c) P(3 precedes 1 and 3 precedes 2) = 1/3

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The value of SS (Sum of Squares) for this population is 30. The answer is c.

To calculate SS, we use the formula:

SS = ΣX² - ((ΣX)² / N)

Given that ΣX = 12, ΣX² = 54, and N = 6, we can substitute these values into the formula:

SS = 54 - ((12)² / 6)

  = 54 - (144 / 6)

  = 54 - 24

  = 30

The value of SS represents the sum of the squared deviations of each score from the mean. It quantifies the variability or dispersion within the data set. In this case, the given values of ΣX and ΣX² allow us to calculate SS by substituting them into the formula.

By performing the necessary calculations, we find that SS for this population is 30. It is important to note that SS is commonly used in various statistical analyses, such as calculating variance and standard deviation, to assess the spread of data points from the mean.

Hence, the correct option is: c. 30

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The equation of the tangent plane to f(x, y) = x^2 - 2xy + 3y^2, with slopes 2 in the positive x direction and 2 in the positive y direction, is 2x + 4y - 8 = 0.

To locate the equation of the tangent airplane to the floor described with the aid of the feature f(x, y) = [tex]x^2 - 2xy + 3y^2[/tex], we need to decide the gradient vector and consider it at a given point.

The gradient vector will grant the ordinary vector to the tangent plane, and by way of the use of the slope information, we can discover the equation of the plane.

Calculate the partial derivatives of the feature with recognize to x and y:

f_x = 2x - 2y

f_y = -2x + 6y

Set up a device of equations the use of the given slope information:

f_x = 2

f_y = 2

Solve the machine of equations to discover the factor where the slopes are satisfied:

2x - 2y = 2 --> x - y = 1 --> x = y + 1

-2x + 6y = 2 --> -x + 3y = 1 --> -x = 1 - 3y --> x = 3y - 1

Setting the two expressions for x equal to every other:

y + 1 = 3y - 1

2 = 2y

y = 1

Substitute y = 1 into both expression for x:

x = 1 + 1

x = 2

Therefore, the factor the place the slopes are comfy is (2, 1).

Evaluate the gradient vector at the factor (2, 1):

grad(f) = (f_x, f_y) = (2x - 2y, -2x + 6y)

= (2(2) - 2(1), -2(2) + 6(1))

= (2, 4)

The ordinary vector to the tangent airplane is the gradient vector (2, 4).

Using the point-normal structure of the equation for a plane, the equation of the tangent airplane is:

2(x - 2) + 4(y - 1) + d = 0

To decide the price of d, alternative the coordinates of the factor (2, 1):

2(2 - 2) + 4(1 - 1) + d = 0

0 + 0 + d = 0

d = 0

The equation of the tangent airplane is:

2(x - 2) + 4(y - 1) = 0

Simplifying the equation, we have:

2x - 4 + 4y - 4 = 0

2x + 4y - 8 = 8

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Answer:

∠ XYW = 52° , ∠ X = 97°

Step-by-step explanation:

∠ XYW and ∠ VWY are alternate angles and are congruent , then

∠ XYW = ∠ VWY = 52°

the opposite angles of a parallelogram are congruent , then

∠ X = ∠ Y = 97°