Write three equations that involve adding negative numbers?

The toast will land with buttered side 50% of the time.

First,

H₀:p=0.5, H₁: p₀ ≠0.5

P(butttered side down)= 19/51

π₀= 0.5

n= 51

Now, z = (p- π₀)/ √π₀(1-π₀)/n

z= (19/51 -0.5)/√0.5(1-0.5)/51

z= -1.82

as, α= 0.01 and [tex]z_{\alpha/2[/tex]=  2.58

So, |z| < | [tex]z_{\alpha/2[/tex]|

Thus, it reject H₀.

Thus, the toast will land with buttered side 50% of the time.

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e. Hourly rate = $975.84 / 38 = $25.68

f. Overtime rate = $25.68 * 1.5 = $38.52

g. Earnings (4 hours OT) = $38.52 * 4 = $154.08

h. Overtime hours = ($1226.22 - $975.84) / $38.52 ≈ 6.5 hours

Begin by determining the number of overtime hours worked by evaluating the discrepancy between his weekly salary and his regular wage:

Take note that the difference = $250.38, specifically from a calculation derived by subtracting $975.84 from $1226.22.

Next, divide this incongruity by his rate of pay for working overtime to establish the actual quantity of time augmented:

Upon performing our overall assessment with $38.52 as the hourly short-term remuneration rate towards supplementing regular pay projections, we determine roughly 6.5 additional work hours incrementally added onto one's overall timesheet.

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An important concept of unit circle in geometry and trigonometry is it helps us to understand and visualize the values of sine, cosine, and tangent functions for different angles.

The unit circle is a circle with a radius of 1 unit, centered at the origin of a coordinate plane.

The coordinates of points on the unit circle correspond to the values of sine and cosine of the corresponding angle.

For example, if we draw a line from the origin to a point on the unit circle that makes an angle of θ with the positive x-axis.

The x-coordinate of that point is cos(θ) and the y-coordinate is sin(θ).

The unit circle is also useful for understanding and visualizing the properties of periodic functions, such as sine and cosine.

Since sine and cosine are periodic with a period of 2π, the unit circle repeats itself every 2π radians or 360 degrees.

Which makes it easier to analyze and graph these functions.

In addition, the unit circle helps us understand the relationships between trigonometric functions.

Pythagorean identity (sin²(θ) + cos²(θ) = 1) is a fundamental relationship that is easy to see and prove using the unit circle.

Overall, the unit circle is an important concept that provides a visual and geometric representation of trigonometric functions and their properties.

It can be a useful tool for solving problems in geometry and trigonometry.

As well as for understanding more advanced concepts in calculus and other branches of mathematics.

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The sum of interior angles in the polygon is 3240 degrees.

The equation used to find x is 180 = 12x - 6.

We have,

The sum of the interior angles of a polygon with n sides can be calculated using the formula (n-2) x 180 degrees.

So, for a regular icosagon with 20 sides, the sum of interior angles.

= (20-2) x 180

= 3240 degrees.

Therefore, the answer is option C, 3240.

Part B:

The sum of the interior angles of a regular polygon can also be calculated using the formula:

Sum of interior angles = n(180 - exterior angle)/2,

where n is the number of sides.

For a regular icosagon, the exterior angle can be found by subtracting the interior angle from 180 degrees.

= 180 - (12x - 6)

= 186 - 12x.

Substituting the values in the formula, we get:

3240 = 20(180 - (12x - 6))/2

Simplifying this equation, we get:

3240 = 1800 - 60x + 30

Combining like terms, we get:

1410 = -60x

Dividing both sides by -60, we get:

x = -23.5

Therefore,

The sum of interior angles is 3240 degrees.

The equation used to find x is 180 = 12x - 6.

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Therefore the set S = {v1, v2, v3, v4} is linearly independent.

The set S = {v1, v2, v3, v4} of vectors in R4 is linearly independent if the only solution of

c1v1 + c2v2 + c3v3 + c4v4 = 0

is c1, c2, c3, c4 = 0

Otherwise (i.e., if a solution with at least some nonzero values exists), S is linearly dependent.

With our vectors v1, v2, v3, v4, (*) becomes:

c1

3

0

-3

6 + c2

0

2

3

1 + c3

0

-2

-2

0 + c4

-2

1

2

1 =

0

0

0

0

Rearranging the left hand side yields

3 c1 +0 c2 +0 c3-2 c4

0 c1 +2 c2-2 c3 +1 c4

-3 c1 +3 c2-2 c3 +2 c4

6 c1 +1 c2 +0 c3 +1 c4 =

0

0

0

0

The matrix equation above is equivalent to the following homogeneous system of equations

3 c1

We now transform the coefficient matrix of the homogeneous system above to the reduced row echelon form to determine whether the system has

the trivial solution only (meaning that S is linearly independent), or

the trivial solution as well as nontrivial ones (S is linearly dependent).

Row

Operation

1:

3 0 0 -2

0 2 -2 1

-3 3 -2 2

6 1 0 1 multiply the 1st row by 1/3

1 0 0 -2/3

0 2 -2 1

-3 3 -2 2

6 1 0 1

Row

Operation

2:

1 0 0 -2/3

0 2 -2 1

-3 3 -2 2

6 1 0 1 add 3 times the 1st row to the 3rd row

1 0 0 -2/3

0 2 -2 1

0 3 -2 0

6 1 0 1

Row

Operation

3:

1 0 0 -2/3

0 2 -2 1

0 3 -2 0

6 1 0 1 add -6 times the 1st row to the 4th row

1 0 0 -2/3

0 2 -2 1

0 3 -2 0

0 1 0 5

Row

Operation

4:

1 0 0 -2/3

0 2 -2 1

0 3 -2 0

0 1 0 5 multiply the 2nd row by 1/2

1 0 0 -2/3

0 1 -1 1/ 2

0 3 -2 0

0 1 0 5

Row

Operation

5:

1 0 0 -2/3

0 1 -1 1/2

0 3 -2 0

0 1 0 5 add -3 times the 2nd row to the 3rd row

1 0 0 -2/3

0 1 -1 1/2

0 0 1 -3/2

0 1 0 5

Row

Operation

6:

1 0 0 -2/3

0 1 -1 1/2

0 0 1 -3/2

0 1 0 5 add -1 times the 2nd row to the 4th row

1 0 0 -2/3

0 1 -1 1/2

0 0 1 -3/2

0 0 1 9/2

Row

Operation

7:

1 0 0 -2/3

0 1 -1 1/2

0 0 1 -3/2

0 0 1 9/2 add -1 times the 3rd row to the 4th row

1 0 0 -2 /3

0 1 -1 1/2

0 0 1 -3/2

0 0 0 6

Row

Operation

8:

1 0 0 -2/3

0 1 -1 1 2

0 0 1 -3 2

0 0 0 6 multiply the 4th row by 1/6

1 0 0 -2/3

0 1 -1 1 /2

0 0 1 -3/ 2

0 0 0 1

Row

Operation

9:

1 0 0 -2/3

0 1 -1 1/2

0 0 1 -3/2

0 0 0 1 add 3/2 times the 4th row to the 3rd row

1 0 0 -2/3

0 1 -1 1/2

0 0 1 0

0 0 0 1

Row

Operation

10:

1 0 0 -2/3

0 1 -1 1/ 2

0 0 1 0

0 0 0 1 add -1/2 times the 4th row to the 2nd row

1 0 0 -2/3

0 1 -1 0

0 0 1 0

0 0 0 1

Row

Operation

11:

1 0 0 -2/3

0 1 -1 0

0 0 1 0

0 0 0 1 add 2/3 times the 4th row to the 1st row

1 0 0 0

0 1 -1 0

0 0 1 0

0 0 0 1

Row

Operation

12:

1 0 0 0

0 1 -1 0

0 0 1 0

0 0 0 1 add 1 times the 3rd row to the 2nd row

1 0 0 0

0 1 0 0

0 0 1 0

0 0 0 1

The reduced row echelon form of the coefficient matrix of the homogeneous system (**) is

1 0 0 0

0 1 0 0

0 0 1 0

0 0 0 1

Since each column contains a leading entry (highlighted in yellow), then the system has only the trivial solution, so that the only solution of is c1, c2, c3, c4 = 0.

Therefore the set S = {v1, v2, v3, v4} is linearly independent.

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The predicted distance the puck will travel at a speed of 50 miles per hour is 3054.12 yards

Given data ,

The equation for the line of fit is given as y = 3.12 + 61.02s, where y represents the predicted distance (in yards) the puck will travel and s represents the speed of the puck (in miles per hour).

So , y = 3.12 + 61.02s

Now , when the speed of the hockey player is s = 50 miles per hour

On simplifying , we get

y = 3.12 + 61.02 ( 50 )

y = 3.12 + 3051

y = 3,054.12 yards

Hence , the distance traveled by the puck is 3,054.12 yards

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An exponential function showing the relationship between y and t is y = 2500(1.11ˣ)

To write an exponential function for this situation, we can start with the initial number of cells (2500) and then multiply by 1.11 for each hour that has passed. We can use the variable t to represent the number of hours since the start of the study, and the variable y to represent the number of bacteria cells. Then, our exponential function is:

y = 2500(1.11ˣ)

This function tells us that the number of bacteria cells (y) is equal to the initial number of cells (2500) multiplied by 1.11 raised to the power of the number of hours since the start of the study (x).

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Step-by-step explanation:

If slope r and slope m are perpendicular , their product must give negative one.

That is r ×m = -1

r = -1 /m

m = -1 /r

To solve the equation (x - 3)^2 = 49, we can take the square root of both sides to eliminate the exponent of 2. However, when taking the square root, we need to consider both the positive and negative square roots.

(x - 3)^2 = 49

Taking the square root of both sides, we get:

√((x - 3)^2) = ±√49

Simplifying, we get:

x - 3 = ±7

Adding 3 to both sides, we get:

x = 3 ± 7

So the possible values of x are:

x = 3 + 7 = 10

x = 3 - 7 = -4

Therefore, the correct values of x are -4 and 10. The options given are -46, -4, 10, and 52. So the correct values of x from the options are -4 and 10.

Answer:

-4 and 10.

Step-by-step explanation:

c ≥ 6 and d > 4, the common solutions are all values of (c,d) that satisfy these two conditions simultaneously of inequalities

The given inequalities are -2(c-4)≤-4 and 1/2 d - 6 >-4

The first inequality is  -2(c-4)≤-4

-2c + 8 ≤ -4

Subtracting 8 from both sides, we get:

-2c ≤ -12

Dividing both sides by -2

c ≥ 6

Now, let's look at the second inequality:

1/2 d - 6 > -4

Adding 6 to both sides, we get:

1/2 d > 2

Multiplying both sides by 2, we get:

d > 4

So, the solutions for these two inequalities are: c ≥ 6 and d > 4

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The value of x is 50° from the given set of parallel lines.

Give that, two parallel lines cut by a transversal.

The interior angles are (2x+10)° and (2x-30)°.

Here, (2x+10)°+(2x-30)°=180° (Sum of co-interior angles is 180°)

4x-20=180

4x=200

x=200/4

x=50°

Therefore, the value of x is 50° from the given set of parallel lines.

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As the sample size increases, it does not necessarily mean that the range of the sample population also increases.

The range of a sample population is simply the difference between the maximum and minimum values of the data set. It is possible for the range to increase or decrease as the sample size increases, depending on the distribution of the data.

For example, if the data is evenly distributed with no outliers, increasing the sample size may not change the range significantly. However, if the data has outliers or a skewed distribution, increasing the sample size may result in capturing more extreme values, which could increase the range of the sample population.

Therefore, it is important to consider the distribution of the data and not assume that increasing the sample size will always result in an increased range of the sample population.

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The area of the circle is 50.24.

The area of the square is 32.

The area of the shaded region is 18.24.

We have,

From the figure,

Area of the circle.

= πr²

Radius = 4

So,

= 3.14 x 4 x 4

= 50.24

In the triangle QST,

TS and TQ are congruent.

TS = TQ = x

QS = 8

This means,

From the Pythagorean theorem,

8² = x² + x²

64 = 2x²

x² = 32

x = √(16 x 2)

x = 4√2

Area of the square.

= Side²

Side = x = 4√2

= (4√2)²

= 16 x 2

= 32

Now,

Area of the shaded region.

= Area of the circle - Area of the square

= 50.24 - 32

= 18.24

Thus,

The area of the circle is 50.24.

The area of the square is 32.

The area of the shaded region is 18.24.

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Answer:

a)

[tex]4ydy = xdx[/tex]

[tex]2 {y}^{2} = \frac{1}{2} {x}^{2} + c[/tex]

[tex] {y}^{2} = \frac{1}{4} {x}^{2} + c [/tex]

[tex] {y}^{2} - \frac{1}{4} {x}^{2} = c [/tex]

b)

c = 4, so

[tex] {y}^{2} = \frac{1}{4} {x}^{2} + 4[/tex]

[tex]y = - \sqrt{ \frac{1}{4} {x}^{2} + 4} [/tex]

[tex]y = - \frac{ \sqrt{ {x}^{2} + 16} }{2} [/tex]

1) Polynomial of 4 terms.

2) The rational roots of the function are,

x = - 2, 1

3) The zeroes of the function are,

x = - 2, - 3, 2

4) The zeroes of the function are,

x = 1, - 1, 2i, - 2i

5) The correct function which shows the cubic equation is, option 1.

We have to given that;

1) Function is,

⇒ 3x⁵ + 5x⁴ - 7x³ + 15

Clearly, There are 4 terms in function.

Hence, Polynomial of 4 terms.

2) Function is,

⇒ x⁴ + 5x³ + 7x² - 3x - 10 = 0

The correct rational roots are satisfy the function,

Hence, We get;

Plug x = 1,

⇒ x⁴ + 5x³ + 7x² - 3x - 10 = 0

⇒ 1⁴ + 5(1)³ + 7 (1)² - 3(1) - 10 = 0

⇒ 0 = 0

Plug x = - 2;

⇒ x⁴ + 5x³ + 7x² - 3x - 10 = 0

⇒ 2⁴ + 5(2)³ + 7 (2)² - 3(2) - 10 = 0

⇒ 0 = 0

Thus, The zeroes of the function are,

x = - 2, 1

3) Function is,

⇒ y = (x + 3) (x + 2) (x - 2)

Hence, The zeroes of the function are,

x = - 3

x = - 2

x = 2

4) Function is,

⇒ 3x² - 4 = - x⁴

⇒ x⁴ + 3x² - 4 = 0

⇒ x⁴ + 4x² - x² - 4 = 0

⇒ x² (x² + 4) - 1 (x² + 4) = 0

⇒ (x² - 1) (x² + 4) = 0

⇒ x² - 1 = 0

⇒ x² = 1

⇒ x = ±1

⇒ x² + 4 = 0

⇒ x² = - 4

⇒ x = ±2i

Hence, The zeroes of the function are,

x = 1, - 1, 2i, - 2i

5) By given graph the  correct function which shows the cubic equation is, Option 1.

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Answer:

(x-1, y) = (x-1, 1/2x + 1/2).

Step-by-step explanation:

To find the point one unit to the left of the given point, we need to subtract 1 from the x-coordinate of the given point.

Let's start with the given point: y = [1/2x - 2] + 3

We can simplify this by combining the constants: y = 1/2x + 1

Now we need to find the point one unit to the left. This means we subtract 1 from the x-coordinate:

y = 1/2(x-1) + 1

Simplifying this expression:

y = 1/2x - 1/2 + 1

y = 1/2x + 1/2

So the point one unit to the left of the original point is (x-1, y) = (x-1, 1/2x + 1/2)

The angle of elevation is 53.1( nearest tenth)

The angle of elevation is an angle that is formed between the horizontal line and the line of sight. Trigonometric ratio is mainly used to solve problems in this case.

A 20ft ladder leans against the wall, the height of the wall will be the opposite to angle of elevation and the height of the ladder will be the hypotenuse.

Therefore using trigonometry ratio;

sin( tetha) = opp/hyp

sin(tetha) = 16/20

sin(tetha) = 0.8

tetha = sin^-1(0.8)

tetha = 53.1°( nearest tenth)

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The profit on this stock transaction is $600 and the percentage return on investment is 7.69%.

To calculate the profit on this stock transaction, we need to subtract the total cost from the total revenue:

Total cost = $7800

Total revenue = $8400

Profit = Total revenue - Total cost

Profit = $8400 - $7800

Profit = $600

Therefore, the profit on this stock transaction is $600.

To calculate the percentage return on investment

we need to divide the profit by the total cost and then multiply by 100 to get the percentage:

Percentage return on investment = (Profit / Total cost) x 100%

= ($600 / $7800) x 100%

= 0.0769 x 100%

= 7.69%

Therefore, the percentage return on investment is 7.69%.

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There are 30 minutes in [tex]\frac{2}{4}[/tex] of an hour.

To find the no. of minutes in an hour we can multiply the no. of hours by 60. Suppose to find the no. of minutes in an hour we can simply multiply 1 by 60 so we can get 60 minutes in an hour.

Similarly to find the no. of minutes are in [tex]\frac{2}{4}[/tex] of an hour we can multiply the [tex]\frac{2}{4}[/tex] by 60 to get the required minutes.

[tex]\frac{2}{4}[/tex] × 60 = [tex]\frac{1}{2}[/tex] × 60 = [tex]\frac{60}{2}[/tex]  = 30.

So, from the above explanation, we can conclude that there will be 30 minutes in the [tex]\frac{2}{4}[/tex] of an hour.

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Answer:

To determine the range of car prices for which the cash-back option will cost less, we need to find the total cost of each option over 60 months for different car prices and compare them. Let's assume the car price ranges from $20,000 to $30,000.

For the 0% financing option, the monthly payment is $16.67 per $1,000 financed, so the monthly payment for a car priced at $20,000 would be:

$20,000 / 1000 * $16.67 = $333.40 per month

Similarly, the monthly payment for a car priced at $30,000 would be:

$30,000 / 1000 * $16.67 = $500.10 per month

Over 60 months, the total cost for the 0% financing option for a car priced at $20,000 would be:

$333.40 * 60 = $20,004

And the total cost for a car priced at $30,000 would be:

$500.10 * 60 = $30,006

For the cash-back option, the cost of the car would be reduced by $2,500, so the total cost over 60 months for a car priced at $20,000 would be:

($20,000 - $2,500) + ($18.41 * $20) * 60 = $19,484

And the total cost for a car priced at $30,000 would be:

($30,000 - $2,500) + ($18.41 * $30) * 60 = $29,222

To find the range of car prices for which the cash back option will cost less, we need to compare the total cost of each option. Setting the two equations equal to each other and solving for x, we get:

($x - $2,500) + ($18.41 * $x) * 60 < $20,004

($x - $2,500) + ($18.41 * $x) * 60 > $30,006

Simplifying, we get:

$17.285x < $22,504

$17.285x > $34,256

Dividing by 17.285, we get:

$1,300.90 < x < $1,978.63

So, for car prices between $13,000.90 and $19,978.63, the cash-back option will cost less.

To find the range of car prices for which the 0% financing option is a better choice, we can simply look at the range of car prices for which the cash-back option is more expensive, which is anything outside of the range of $13,000.90 to $19,978.63. Therefore, for car prices outside of this range, the 0% financing option is the better choice.

The line of reflection is the line y = 0, which is the x-axis.

To see this, imagine folding the image of polygon VWYZ along the x-axis so that the top vertex, V, is reflected down to its corresponding point, V'. Similarly, W is reflected up to W', Y is reflected up to Y', and Z is reflected down to Z'. This produces the image of polygon V'W'Y'Z', which is the reflection of polygon VWYZ across the x-axis.

When reflecting a shape across a line, the line of reflection is the line that serves as the "mirror" for the shape. In this case, the given polygons VWYZ and V'W'Y'Z' are related by a reflection. By examining the vertices of the polygons, we can determine the line of reflection. The x-coordinates of the corresponding vertices are the same, which suggests that the line of reflection is vertical.

However, the y-coordinates are opposites, indicating that the line of reflection is actually the x-axis. Therefore, the reflection of polygon VWYZ onto polygon V'W'Y'Z' is achieved by folding the image along the x-axis so that each vertex is reflected across the x-axis to its corresponding point in the other polygon.

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Answer:

Reflection across x = −1

Step-by-step explanation:

Took test it's right!

The probability of getting exactly 9 heads out of 15 tries when flipping a fair coin is approximately 0.19638 or about 19.64%.

We have,

The probability of getting a head or a tail when flipping a fair coin.

= 1/2 or 0.5

Assuming the coin is unbiased and each flip is independent of the previous flips.

To find the probability of getting 9 heads out of 15 tries, we need to use the binomial probability formula:

= P(9 heads out of 15 tries)

= [tex]^{15}C_9[/tex] x (0.5)^9 x (0.5)^6

Now,

P(9 heads out of 15 tries)

= 5005 x (0.5)^9 x (0.5)^6

= 0.19638 (rounded to five decimal places)

Thus,

The probability of getting exactly 9 heads out of 15 tries when flipping a fair coin is approximately 0.19638 or about 19.64%.

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well the first cylinder is small the other is big and if this dosent help i'm so very sorry

Answer:

20 blue pens

Step-by-step explanation:

Since it is a 3 to 4 ratio (Green to Blue) and you have 15 green pens you need to multiply 5 to the 3(green pens). Since you multiplied 5 it needs to stay equal you need to multiply 5 to the blue pens which would give you 20 blue pens

The average rate of change over is 1.

Given that;

the function is,

⇒ g (t) = - (t - 1)² + 5

Hence, We need to determine the average rate of change over the interval - 4 ≤ t ≤ 5.

The value of G(-4):

The value of G(-4) can be determined by substituting t = -4 in the function

⇒ g (t) = - (t - 1)² + 5

Thus, we have,

⇒ g (t) = - (-4 - 1)² + 5

⇒ g (t) = - 20

Thus, the value of G(-4) = -20

The value of G(5):

The value of G(5) can be determined by substituting t = 5 in the function , we get,

⇒ g (t) = - (t - 1)² + 5

⇒ g (t) = - (5 - 1)² + 5

⇒ g (t) = - 11

Thus, the value of G(5) is, -11

Now, Average rate of change:

The average rate of change can be determined using the formula,

⇒ G(b) - G (a) / (b - a)

where, a = - 4 and b = 5

Substituting the values, we get,

⇒ G(5) - G (-4) / (5 - (-4))

⇒ ( - 11 - (- 20)) / 9

⇒ 9/9

⇒ 1

Thus, the average rate of change over the interval is. 1.

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Answer:

First graph:

y + 7 = C((x + 5)^3)

-3.8 + 7 = C(4^3)

3.2 = 64C, so C = .05

y = .05((x + 5)^3) - 7

Second graph:

y - 38.45 = C((x + 5)^3)

2 - 38.45 = C(4.5^3)

-36.45 = 91.125C

C = -.4

y = -.4((x + 5)^3) + 38.45

Answer:

x = 21.1

y = 18.3

Step-by-step explanation:

                      left triangle     right triangle     large triangle

Short leg:             12                  altitude                    y

Long legs:        altitude                 16                         x

Hypotenuse:         y                       x                          28

The three triangles are similar, so the ratios of the lengths of corresponding sides are equal.

hypotenuse/short leg

28/y = y/12

y² = 12 × 28

y² = 336

y = 18.3

hypotenuse/long leg

28/x = x/16

x² = 28 × 16

x² = 448

x = 21.1

Answer:

The two angles that are directly across the intersection point from each other are called vertical angles. Vertical angles are always congruent.

Step-by-step explanation:

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Vertical angles are two angles that are opposite of each other when two intersect. These angles are congruent.

Vertical angles are angles opposite to each other where two lines cross.

When two lines intersect, they naturally form two pairs of vertical angles. Vertical angles share the same vertex or corner, and are opposite each other.

These pair of angles are congruent which means they have the same angle measure.

Hence, Vertical angles are two angles that are opposite of each other when two intersect. These angles are congruent.

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