13) y = 8x + 13
- 4x - 5y = 23

The missing sides of the right triangles are listed below:

Case 1

x = 13, y = 13√2

Case 2

x = 15√2, y = 15√2

Case 3

x = 6, y = √3

Case 4

x = 17√3, y = 17

Case 5

x = 10, y = 10

Case 6

x = 50, y = 25

Case 7

x = 2√7, y = 2√7

Case 8

x = 16√3, y = 48

Case 9

x = 11√3, y = 33

Case 10

x = 3√2, y = 2√6

Case 11

x = √10, y = 2√5

Case 12

x = 4√7, y = 8√7

Herein we find twelve cases of right triangles with two sides that must be determined by means of trigonometric functions. The fundamental trigonometric functions are defined below:

sin θ = y / r

cos θ = x / r

tan θ = y / x

Where:

Now we proceed to determine the missing sides for each case:

Case 1

y = 13 / sin 45°

y = 13√2

x = 13 · tan 45°

x = 13

Case 2

x = 30 · sin 45°

x = 15√2

y = 30 · cos 45°

y = 15√2

Case 3

x = 3 / cos 60°

x = 6

y = 3 / tan 60°

y = √3

Case 4

x = 34 · cos 30°

x = 17√3

y = 34 · sin 30°

y = 17

Case 5

x = 10√2 · cos 45°

x = 10

y = 10√2 · sin 45°

y = 10

Case 6

x = 25√3 / sin 60°

x = 50

y = 25√3 / tan 60°

y = 25

Case 7

x = 2√14 · cos 45°

x = 2√7

y = 2√14 · sin 45°

y = 2√7

Case 8

x = 24 / cos 30°

x = 16√3

y = 24 / sin 30°

y = 48

Case 9

x = 22√3 · cos 60°

x = 11√3

y = 22√3 · sin 60°

y = 33

Case 10

x = √6 / tan 30°

x = 3√2

y = √6 / sin 30°

y = 2√6

Case 11

y = √10 / cos 45°

y = 2√5

x = √10 · tan 45°

x = √10

Case 12

x = 4√21 / tan 60°

x = 4√7

y = 4√21 / sin 60°

y = 8√7

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Figure C appears to have all sides and angles the same.

A regular polygon is a closed shape that has straight sides of equal length and interior angles of equal measure.

This means that all of the sides and angles of a regular polygon are congruent (i.e., have the same size).

We have,

Some examples of regular polygons include equilateral triangles, squares, pentagons, hexagons, and so on.

A regular polygon can have any number of sides, and its name reflects the number of sides it has.

For example, a polygon with three sides is called a triangle, a polygon with four sides is called a quadrilateral, a polygon with five sides is called a pentagon, and so on.

Thus,

Figure C appears to have all sides and angles the same.

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Answer:

232

Step-by-step explanation:

→ Find the percentage multipier

( 100 + 45 )÷ 100 = 1.45

→ Multiply this by the original amount

1.45 × 160 = 232

Answer:

Unfortunately, without additional information or data, it is not possible to estimate the number of people running right now using the given equation N/Ntotal = T/Ttotal.

The equation only relates the fraction of people engaged in an activity to the fraction of time spent on that activity. It does not provide any information about the actual number of people or the total population size.

To estimate the number of people running right now, we would need additional data, such as the total population size, the fraction of people who typically engage in running as an activity, and the total time spent running by the people who do engage in the activity.

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Answer:156

Step-by-step explanation:

Answer: 1) slope of 2/3.

2) slope of -1/2

3) slope of 3

4) slope of -2/3

5) slope of undefined

6) slope of -1 1/2

7) slope of 1

8) slope of 0

Step-by-step explanation:

Answer: -18

Step-by-step explanation:

Answer:

value of f is 6

Step-by-step explanation:

100% correct

the work is in the image below. Hope this help!

Answer: ok?

Step-by-step explanation:

Answer:

5v2 – 125 = 0

5(v2−25)=0

v2−25=0

a couple more steps and the answer is...

v=-5

Answer:

6n-3

Step-by-step explanation:

You can see the sequence is ascending by 6 each time so the nth term is 6n.

The 'zero term' would be -3 so the equation would be 6n-3.

The length of the base of the triangle is 8 yards whose height is half of 28 yards.

A triangle is a two-dimensional geometric shape that is formed by three straight lines that connect three non-collinear points. These three lines are called the sides of the triangle, and the points where the sides meet are called the vertices of the triangle.

The following formula provides the area of a triangle:

Area = (1/2) x base x height

We are given that the height of the triangle is half of 28 yards, which is:

height = 1/2 x 28 = 14 yards

We are also given that the area of the triangle is 56 square yards. Substituting these values into the formula for the area, we get:

56 = (1/2) x base x 14

Simplifying this equation, we get:

56 = 7 x base

Dividing both sides by 7, we get:

base = 8

Therefore, the length of the base of the triangle is 8 yards.

The vertices are typically denoted by letters, such as A, B, and C. The three angles formed by the sides are also part of the triangle.

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The correct answer is: O Yes, distance and angle measure are preserved.

When a triangle ABC is reflected across the line y = x, the pre-image and image are congruent.

This is because the line y = x is the perpendicular bisector of the segment joining each corresponding point of the pre-image and image.

Reflection across the line y = x is a type of transformation known as an isometry, which preserves both distance and angle measure.

Here's why:

Distance preservation:

When a point is reflected across the line y = x, the distance between the original point and its reflection remains the same.

This holds true for all corresponding points of the triangle.

Therefore, the distance between any two corresponding points in the pre-image and image triangle will be equal, resulting in distance preservation.

Angle preservation: When a line segment is reflected across the line y = x, the angle between the line segment and the line y = x is preserved. This means that the corresponding angles in the pre-image and image triangle will be congruent.

Since both distance and angle measure are preserved during reflection across the line y = x, the pre-image and image triangles are congruent.

It's important to note that congruence under reflection across a line holds only when the line of reflection is the same for both the pre-image and image.

If the line of reflection were different, the triangles would not be congruent.

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Answer:

Es una pregunta doble, calcule una y grafíquela, calcule la otra y grafíquela, ps: dame lo más inteligente.

a) The rule that represents the height as a function of the number of bounces is described by H(n) = 1.5 · (71 / 100)ˣ⁻¹. (Correct choice: B)

b) The height at the top of the sixth path is equal to 0.27 meters. (Correct choice: B)

In this problem we need to derive the equation that represents maximum height as a function of the number of bounces:

H(n) = a · (r / 100)ˣ⁻¹

Where:

If we know that a = 1.5 m and r = 71, then the rule for the sequence is:

H(n) = 1.5 · (71 / 100)ˣ⁻¹

And the height at the top of the sixth path:

H(6) = 1.5 · (71 / 100)⁶⁻¹

H(6) = 0.27 m

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To solve the expression 1 - (1 + 0.04/12)^(-12x10), you can follow these steps: Step 1: Simplify the exponent. In this case, -12x10 simplifies to -120.

Step 2: Evaluate the term within the parentheses first. 0.04/12 simplifies to 0.0033333 (approximately).

Step 3: Add 1 to 0.0033333 to get 1.0033333.

Step 4: Raise 1.0033333 to the power of -120.

Step 5: Calculate the value inside the parentheses using a calculator or software. The result is approximately 0.742657.

Step 6: Subtract the value obtained in Step 5 from 1.

1 - 0.742657 = 0.257343 (approximately).

Hence, the value of the expression 1 - (1 + 0.04/12)^(-12x10) is approximately 0.257343.

It's important to follow the order of operations (PEMDAS/BODMAS) when solving mathematical expressions. In this case, the exponent is evaluated first, followed by addition and subtraction. Utilizing a calculator or software that supports exponentiation and parentheses can help simplify complex expressions and obtain accurate results efficiently.

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The vertex of point A' in the dilated triangle A'B'C' is (6, 4.5).

1. Start by calculating the distance between the vertices of the original triangle ABC:

  - Distance between A(4, 3) and B(3, -2):

    Δx = 3 - 4 = -1

    Δy = -2 - 3 = -5

    Distance = √((-\(1)^2\) + (-\(5)^2\)) = √26

  - Distance between B(3, -2) and C(-3, 1):

    Δx = -3 - 3 = -6

    Δy = 1 - (-2) = 3

    Distance = √((-6)² + 3²) = √45 = 3√5

  - Distance between C(-3, 1) and A(4, 3):

    Δx = 4 - (-3) = 7

    Δy = 3 - 1 = 2

    Distance = √(7² + 2²) = √53

2. Apply the scale factor of 1.5 to the distances calculated above:

  - Distance between A' and B' = 1.5 * √26

  - Distance between B' and C' = 1.5 * 3√5

  - Distance between C' and A' = 1.5 * √53

3. Determine the coordinates of A' by using the distance formula and the given coordinates of A(4, 3):

  - A' is located Δx units horizontally and Δy units vertically from A.

  - Δx = 1.5 * (-1) = -1.5

  - Δy = 1.5 * (-5) = -7.5

  - Coordinates of A':

    x-coordinate: 4 + (-1.5) = 2.5

    y-coordinate: 3 + (-7.5) = -4.5

4. Thus, the vertex of point A' in the dilated triangle A'B'C' is (2.5, -4.5).

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Answer:

Yes, Anna and Sharon both created triangles that are congruent. Their triangles are congruent because they have 2 corresponding, congruent side-lengths and an included angle that is congruent. Therefore, their triangles are congruent by SAS (Side-Angle-Side).

Answer:-2

Step-by-step explanation:

Ok so I’m assuming the x stands for the multiplication sign

7/2-4.5*3+8

Use pemdas

Multiplication first

7/2-4.5*3+8

-4.5*3

7/2-13.5+8

Then addition

-13.5+8

Lastly subtraction

7/2-5

-2

Answer:

the solution is 5.7

Answer:

The Y intercept of this line is -3.

Step-by-step explanation:

The X intercept of the crossing line is about -1.4.
On finding the Y intercept:
Step 1: look at the vertical black line (Y Axis)

Step 2: Locate where the blue line crosses on this line.
Step 3: graph Y function of the point as your answer.

Hope this helped a bunch!
Have a great day!
- Kit-Kat~

To find out the box number the boxes, extract the same number of balls as the number of the box, calculate the total weight.

Considering you can only weigh the balls extracted once and you need to find the box with balls that are 1-kilo lighter; here are the steps you can follow:

The total weight using this method would be 6,300 kg which is the result of adding 30 kg (first box) + 60 kg (second box)... However, since there is a box with lighter balls the total weight will be less.

Let's imagine the weight is 6,290, this means there are 10 fewer kilos and therefore the box with the lighter balls is box 10 since this is the box number from which 10 balls were extracted.

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The measure of distance x, that is, the distance between a point P and the point of horizon, is equal to 284.372 miles.

In this problem we must determine the distance between a point P located about earth's circumference and the point of horizon, located on earth's circumference. Since the line between these two points is tangent to earth, then, distance x can be found by Pythagorean theorem:

x = √[(3959 mi + 10.2 mi)² - (3959 mi)²]

x = 284.372 mi

The distance x is equal to 284.372 miles.

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Answer:

6 to the power of 3 =396 x 36=6 to the power of 2

Step-by-step explanation:

answer =14256

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Answer:

Type II error.

Step-by-step explanation:

We have a hypothesis test for the claim that placing a seasonal cookie product on an end cap (the shelf at the end of an aisle at a store) will make a difference in sales.

The null hypothesis will state that there is no difference, while the alternative hypothesis will state that there is significant positive difference.

The result is a P-value of 0.1288 and the null hypothesis failing to be rejected.

As the null hypothesis failed to be rejected, if an error has been made in the conclusion, is that we erroneusly accept a false null hypothesis.

This is a Type II error, where the null hypothesis is accepted although the alternative hypothesis is true.

Step-by-step explanation:

Slope 1/2    point    5,1  

  in point slope form would be

    (y-1) = 1/2 (x-5)

Transformation involves rotating a shape in clockwise or counterclockwise direction

The coordinates of the image are: M' = (6,7), N' = (2,1) and P = (0,6)

The coordinates are given as:

M = (-7,6)

N = (-1,2)

P = (-6,0)

The rule of 270 degrees clockwise rotation is:

\((x,y) \to (y, -x)\)

Hence, the coordinates of the image are:

M' = (6,7)

N' = (2,1)

P = (0,6)

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