Fernando also learns in math class that the rule Add 1 to the side length of a pentagon with equal sides length results the rule Add 5 to the perimeter. Write four ordered pairs that relate the side length of a pentagon to the perimeter of the pentagon.

Answer:

  37.98°

Step-by-step explanation:

You want the value of θ in a right triangle with a hypotenuse of 13 cm and a side opposite the angle of 8 cm.

The sine relation is ...

  Sin = Opposite/Hypotenuse

In this figure, that means ...

  sin(θ°) = (8 cm)/(13 cm)

The value of θ is found using the arcsin function:

  θ° = arcsin(8/13) ≈ 37.98°

__

Additional comment

You will note the calculator mode is set to DEGrees.

The inverse function of the sine function is called the "arcsine" function. It is represented on most calculator keypads using a -1 exponent. (-1 is usually used with a function name to signify the inverse function. Here, the inverse sine function gives "the angle whose sine is ...".)

Typical units used for angles are degrees, radians, and gradians. The number that is the argument of the inverse sine function is a "pure number" with no units. If you find your calculation causes it to have units, then you need to check your work. (Here the units of cm in numerator and denominator cancel, leaving the unitless value 8/13.)

The missing measures in the triangle are given as follows:

m < F = 111.4º, m < D = 28.6º, f = 35.1.

Suppose we have a triangle in which:

The lengths and the sine of the angles are related as follows:

[tex]\frac{\sin{A}}{a} = \frac{\sin{B}}{b} = \frac{\sin{C}}{c}[/tex]

Considering the triangle in this problem, the relation is given as follows:

sin(D)/18 = sin(40º)/24.2.

Hence the measure of angle D is obtained as follows:

sin(D) = 18 x sine of 40 degrees/24.2

sin(D) = 0.4781

m < D = arcsin(0.4781)

m < D = 28.6º.

The sum of the internal angle measures of a triangle is of 180º, hence the measure of angle F is obtained as follows:

m < F + 40 + 28.6 = 180

m < F = 180 - (40 + 28.6)

m < F = 111.4º

Then the length f is obtained as follows:

sin(111.4º)/f = sin(40º)/24.2

f = 24.2 x sine of 111.4 degrees/sine of 40 degrees

f = 35.1.

More can be learned about the law of sines at https://brainly.com/question/4372174

#SPJ1

Answer:

The top and middle shelves are parallel.

Step-by-step explanation:

<1 and <5 are corresponding angles.

When two lines are cut by a transversal such that corresponding angles are congruent, the lines are parallel.

If angles 1 and 5 are congruent, the shelves are parallel.

We are given m<5 = 60°.

Also, m<2 = 120°.

Angles 1 and 2 are a linear pair and are supplementary.

The measures of angles 1 and 2 add to 180°.

m<1 + m<2 = 180°

m<1 + 120° = 180°

Subtract 120° from both sides.

m<1 = 60°

m<1 = m<5 = 60°

Since angles 1 and 2 have the same measure, 60°, angles 1 and 2 are congruent.

Answer: The top and middle shelves are parallel.

Answer:

The sample space describing all possible outcomes is:

{H1, H2, H3, H4, T1, T2, T3, T4}

The outcomes for the event that the coin toss is heads are:

{H1, H2, H3, H4}

Step-by-step explanation:

If it pertains to using the format H1 to mean that the coin toss is heads and the number chosen is 1.

Let's assume that the video game system and games cost a total of $x. Marshall has saved $68.50 so far. To represent the amount of money, a, that Marshall still needs to save, we can write the following inequality:

a ≥ x - 68.50

This inequality states that the amount Marshall still needs to save (a) must be greater than or equal to the cost of the video game system and games (x) minus the amount he has already saved ($68.50).

The set that could not represent the side of a right triangle are {27, 36, 46}.

A right angle triangle is a triangle that has one of its angles as 90 degrees. The sides of a right angle triangle can be found using Pythagoras's theorem.

Therefore, using Pythagoras's theorem,

c² = a² + b²

where

Therefore, the hypotenuse is the longest side of the right angle triangle.

27² + 36² ≠ 46²

729 + 1296 ≠ 2116

2025 ≠ 2116

Hence, the sides that can't form a right triangle is {27, 36, 46}

learn more on right triangle here: https://brainly.com/question/6322314

#SPJ1

The perimeter of the parallelogram is 90 ft while it's area is calculated to be 900 square feet.

The sum of the boundary length of the parallelogram is it's perimeter so;

perimeter of the parallelogram = 15ft + 15ft + 30ft + 30ft

perimeter of the parallelogram = 90 ft

In calculating for the area of parallelogram, the base is multiplied by the height, as the same way for calculating the area of a rectangle.

height of the parallelogram = 30ft × tan 45°

height of the parallelogram = 30ft {recall tan 45° = 1}

area of the parallelogram = 30ft × 30ft

area of the parallelogram = 900 ft²

Therefore, the perimeter of the parallelogram is 90 ft while it's area is calculated to be 900 square feet.

Read more area of parallelogram here: https://brainly.com/question/970600

#SPJ1

Answer: The correct answer is option A. a reference point.

Step-by-step explanation:

An reference point is required to determine whether or not an object moves.

The amount of the sample remaining after 10 years is approximately 514 grams.

The amount of the sample remaining after 80 years is approximately 102 grams.

Using the exponential function given by in the problem as

A(t) = 647 (1/2) ^ (1/30 x t) the numbers remaining are calculated

For 10 years

substitute t = 10

A(10) = 647 * (1/2)^(1/30 * 10)

A(10) = 647 * (1/2)^(1/3)

A(10) ≈ 647 * 0.7937

A(10) ≈ 513.52 grams

A(10) ≈ 514 grams to the nearest gram

For 80 years

substitute t = 80

A(80) = 647 * (1/2)^(1/30 * 80)

A(80) = 647 * (1/2)^(8/3)

A(80) ≈ 647 * 0.1575

A(80) ≈ 101.9025 grams

A(80) ≈ 102 grams to the nearest gram

Learn more about half-life at

https://brainly.com/question/1160651

#SPJ1

The missing terms in the geometric progression given are:

x = 10      y = 20

The nth term of a Geometric progression is expressed by the formula:

an = ar^(n - 1)

Where we have:

an = nth term

a = first term of the geometric progression

n = number of terms

r = common ratio

We are given the geometric progression 5, x, y, and 40, where:

a1 = 5

a4 = 40

Therefore, we have:

40 = 5 * r^(4 - 1)

40 = 5 * r³

40/5 = r³

8 = r³

r = ∛8

r = 2

Since we know a and r, find the 2nd and 3rd which are represented by x and y respectively, by applying an = ar^(n - 1):

a2 = 5 * 2^(2 - 1)

a2 = 5 * 2^1

a2 = 10

x = 10

a3 = 5 * 2^(3 - 1)

a3 = 5 * 2²

a3 = 20

y = 20

Learn more about geometric progression on:

https://brainly.com/question/12006112

#SPJ1

Step-by-step explanation:

dependingon h o w m a n y bedrooms that are added to the

apartment, an additional $150will be added to $850.

Answer:

17/50

Step-by-step explanation:

When the bus is on time 4/5 of the time, it is late 1/5 of the time.

Mason arrives at 9 am when the bus is on time 3/4 of the time, so he doesn't arrive at 9 am 1/4 of the time.

Mason arrives at 9 am when the bus is late 3/10 of the time, so he doesn't arrive at 9 am 7/10 of the time.

The probability for Mason not to arrive at 9 am when the bus is on time is:

4/5 × 1/4 = 1/5

The probability for Mason not to arrive at 9 am when the bus is late is:

1/5 × 7/10 = 7/50

The probability for Mason not to arrive at work by 9 am is:

1/5 + 7/50 = 17/50.

Answer:

The slope is [tex]\frac{-1}{2}[/tex]

Step-by-step explanation:

the slope is the number before the x.

Helping in the name of Jesus.

When the transformation is preformed on a coordinate plane, the coordinates of the new point would be located in a different quadrant.

The coordinates of the new point on this figure are (-6, -2).

In Geometry, the rotation of a point 180° about the origin in a clockwise or counterclockwise direction would produce a point that has these coordinates (-x, -y).

Furthermore, the mapping rule for the rotation of a geometric figure about the origin is given by this mathematical expression:

(x, y)                                            →            (-x, -y)

Coordinates of point A = (6, 2)  →  Coordinates of point A' = (-6, -2)

In conclusion, the transformation rule (x, y) → (-x, -y) is used for the rotation of a geometric figure about the origin in a clockwise or counterclockwise (anticlockwise) direction.

Read more on rotation here: brainly.com/question/28515054

#SPJ1

The numbers arranged from greatest to least based on their absolute value is; |-34|, |-25|, |0.5|, |0.35|

The absolute value of a number is the expression or value of the distance of the number from 0 on the number line.

The numbers are; |-25|, |0.5|, |-34|, |0.35|

The absolute value of a number is positive, which indicates;

|-25| = 25

|0.5| = 0.5

|-34| = 34

|0.35| = 0.35

The above numbers arranged from greatest to least is therefore;

34 > 25 > 0.5 > 0.35

The numbers arranged from greatest to least based on their absolute value is therefore;

Learn more on absolute values here: https://brainly.com/question/24368848

#SPJ1

The insurance will pay toward Bob's expenses: $10,000.00.

The insurance will pay toward the wife and daughter's expenses: $11,000.00.

John will be responsible for paying the remaining amount, which is $3,000.00.

The insurance coverage of 10/20 means that the insurance company will pay up to $10,000.00 per person and up to a total of $20,000.00 for the entire accident.

The insurance will pay toward Bob's expenses: $10,000.00 (maximum coverage for one person).

The insurance will pay toward the wife and daughter's expenses: $11,000.00 ($8,000.00 for Mrs. Brownlee and $3,000.00 for the daughter).

John will be responsible for paying the remaining amount, which is $3,000.00 ($12,000.00 + $8,000.00 + $3,000.00 - $20,000.00 insurance coverage).

To learn more about the addition;

brainly.com/question/29464370

#SPJ1

Answer:

The insurance will pay toward Bob's expenses: $10,000.00.

The insurance will pay toward the wife and daughter's expenses: $11,000.00.

John will be responsible for paying the remaining amount, which is $3,000.00.

Step-by-step explanation:

The relative frequency of "tails" when the companions coalesce their results is close to 0.524.

In order to ascertain the relative frequency of "tails" when the friends amalgamate their outcomes, one must accumulate the amount of tails, then divide that sum by the entirety of trials:

Relative frequency of "tails" = total number of tails / cumulative number of trials

= 129 / (117 + 129)

= 129 / 246

≈ 0.524

Consequently, the relative frequency of "tails" when the companions coalesce their results is close to 0.524.

Learn more about frequency on

https://brainly.com/question/254161

#SPJ1

Thermal energy and heat transfer principles guide the design of efficient systems, minimizing heat loss and maximizing performance.

It is crucial to take into account a number of aspects that may impact the functionality and efficiency of systems and objects that include thermal energy and heat transmission. You would need to take into account things like the kind and quantity of heat source, the materials utilized, the insulation, and the processes employed for heat transfer, for instance.

Additionally, you would have to think about ways to increase heat transmission effectiveness and reduce heat loss. High thermal conductivity materials may be used, or the system may be designed to have more heat-transfer surface area.

More about the heat transfer link is given below.

https://brainly.com/question/31065010

#SPJ1

Answer: The difference in temperatures was 19°F.

Step-by-step explanation:

Answer:

19F

Step-by-step explanation:

The lines intercept at the point (3, 9), and:

A system of linear equations can have one solution, no solutions, and infinite solutions, these are the only options.

If we have an equation system, the solutions are the spots where the graphs of the equations intersect.

We know that the solution of the system of linear equations is (3, 9), which signifies that the linear equations intersect at that location.

Can  we have more than one solutions?

Yes, you can have

These are the 3 options.

Learn more about systems of equations:

https://brainly.com/question/24065247

#SPJ1

The graph of the population equation is on the image at the end.

Here we know that the function p(h) models the population of bacteria as the function of h, the number of hours.

And we can write this as the exponential function:

p(h) = 150*(3)^h

The graph of this will be an exponential that starts at 150 and triples for each increase in the horizontal variable, then the graph of this will be like the one you can see at the end of the answer.

Learn more about exponential functions at.

https://brainly.com/question/2456547

#SPJ1

The radius of circle M is equal to 3.99 cm.

In Mathematics and Geometry, the area of a sector can be calculated by using the following formula:

Area of sector = θπr²/360

Where:

By substituting the given parameters into the area of a sector formula, we have the following;

Area of sector = θπr²/360

12.36 = 89(3.142/360) × r²

12.36 = 0.7768r²

Radius, r = √15.9114

Radius, r = 3.99 cm.

Read more on arc length here: brainly.com/question/28108430

#SPJ1

The smallest positive integer a that satisfies the conditions of the problem is a = 2.

The Intermediate Value Theorem states that if a function f(x) is continuous on the interval [a, b] and takes on values f(a) and f(b) at the endpoints a and b, respectively, then for any value c between f(a) and f(b), there exists at least one value x in the interval [a, b] such that f(x) = c.

In this problem, we are asked to find the smallest positive integer a such that the Intermediate Value Theorem guarantees a zero exists between 0 and a for the polynomial f(x) = 3x³ - 4x² - 3x - 1.

To find this value of a, we need to evaluate f(0) and f(a) and look for a value of a such that f(0) and f(a) have opposite signs. This will guarantee the existence of a root of f(x) between 0 and a.

Evaluating f(0), we get:

f(0) = 3(0)³ - 4(0)² - 3(0) - 1 = -1

To find f(a), we need to solve for a using the equation f(a) = 0. We can use a numerical method, such as the Newton-Raphson method or the bisection method, to find the root of f(x) = 0. Using a calculator or a computer program, we find that f(a) = 0 for a ≈ 1.353.

Since f(0) = -1 and f(a) = 0 have opposite signs, the Intermediate Value Theorem guarantees the existence of at least one zero of f(x) between 0 and a = 1.353. Therefore, the smallest positive integer a that satisfies the conditions of the problem is a = 2.

To learn more about polynomial click on,

https://brainly.com/question/23006670

#SPJ1

a. A translation on a coordinate plane involves moving every point on the plane a certain distance in a particular direction without distrupting their orientation. The shape and size of the figure do not change, only that the position shifts.

b. If the translation is moving 3 units to the right, it is affecting the x-coordinate. Basically, the x-coordinate of each point on the plane is increased by 3 units, while the y-coordinate remains the same.

c. If the translation is moving 8 units down, it is affecting the y-coordinate. Basically, the y-coordinate of each point on the plane is decreased by 8 units, while the x-coordinate remains the same.

learn more about translation: https://brainly.com/question/1574635

#SPJ1

The volume of the given composite figure is: 1,283.33 ft³

The given composite figure is made up of a cone and a cylinder.

The formula for the volume of a cone is:

V = ¹/₃πr²h

Where:

r is radius

h is height

The formula for volume of a cylinder is:

V = πr²h

Where:

r is radius

h is height

Thus:

Total volume of composite figure is:

V =  (¹/₃* (22/7) * 7² * 7) + ((22/7) * 7² * 6)

V = 359.33 + 924

V = 1,283.33 ft³

Read more about Volume of Composite figure at: https://brainly.com/question/12693294

#SPJ1

The 3 : 5 ratio of the number of cups of sparkling water to the number of cups of apple juice indicates;

7. a) 12 cups of sparkling water

b) 15 cups of apple juice

c) Please find attached the required graph of the pairs of measurements, which are plotted as points using MS Excel

A ratio expresses the quantitative relationship between two quantities, and it is obtained by dividing the quantity of one by the other.

7. The ratio of the number of cups of sparkling water to the number of cups of apple juice = 3 to 5

a) Where the number of cups of apple juice = 20, we get;

20 = 4 × 5

Therefore, the number of cups of apple juice in the current mixture is 4 times the amount that is mixed with 3 cups of sparkling water

b) 9 cups of sparkling water is 3 times the amount required per 5 cups of apple juice

c) The plot of the points can be presented as follows;

(3, 5), (9, 15), (12, 20)

Please find attached the graph showing the pairs of measurements, plotted as points, created with MS Excel

Learn more on ratios here: https://brainly.com/question/12024093

#SPJ1

Answer:

19.8 units

Step-by-step explanation:

From the diagram attached, to find the length of side AB, we need to use Pythagoras theorem on the right triangles. We can see that AB is the base of the two right triangle.

For the first right triangle with hypotenuse of 13 and height of 12, let x be the base, therefore using hypotenuse:

13² = 12² + x²

169 = 144 + x²

x² = 169 - 144

x² = 25

x = √25 = 5

For the second right triangle with hypotenuse of 15 and height of 12, let y be the base, therefore using hypotenuse:

15² = 12² + y²

225 = 144 + y²

y² = 225 - 144

y² = 81

y = √81 = 9

The length of AB = x + y = 9 + 5 = 14 unit

Since for a square all the sides are equal, therefore the length of each side of the square ABCD is 14 units.

In triangle ADC, the hypotenuse = AC, AD = DC = 14 unit. Using Pythagoras:

AC² = AD² + DC²

AC² = 14² + 14²

AC² = 196 + 196 = 392

AC = √392 = 19.8

The length of its diagonal is about 19.8 units

The polynomial long division of (5x^4 − 2x^3 − 7x^2 − 39) ÷ (x^2 + 2x − 4) gives a quotient of 5x^2 - 12x + 37

From the question, we have the following parameters that can be used in our computation:

(5x^4 − 2x^3 − 7x^2 − 39) ÷ (x^2 + 2x − 4)

Using the polynomial long division setup, we have

x^2 + 2x − 4   |  5x^4 − 2x^3 − 7x^2 − 39

Evaluating the division, we have

                         5x^2 - 12x + 37

x^2 + 2x − 4   |  5x^4 − 2x^3 − 7x^2 − 39

                         5x^4  + 10x^3 - 20x^2

                         ---------------------------------------

                                      -12x^3 + 13x^2 - 39

                                      -12x^3 - 24x^2 - 48

                         ---------------------------------------

                                                    37x^2 + 9

                                                    37x^2 + 74x - 148

                         ---------------------------------------

                                                    -74x + 157

Hence, the quotient is 5x^2 - 12x + 37

Read more about long division at

https://brainly.com/question/30989082

#SPJ1

The expected number of education majors in the sample is 20.

Since 80 out of 200 freshmen are education majors, the probability of randomly selecting an education major from the population is:

P(edu major) = 80/200 = 0.4

To find the expected number of education majors in a sample of 50 freshmen, we can use the formula for the expected value of a discrete random variable:

E(X) = n x p

Substituting the given values, we get:

E(X) = 50 x 0.4 = 20

Therefore, the expected number of education majors in a sample of 50 freshmen is 20.

More on probability can be found here: https://brainly.com/question/30034780

#SPJ1

The length of the arc of a circle of radius 12 is 37.68.

The arc of a circle is defined as the part or segment of the circumference of a circle.

To calculate the arc of the circle, we the formula below.

Formula:

Where:

From the question,

Given:

Note: 360° = 2π radian

Substitute these values into equation 1

Hence, the length of the arc is 37.68.

Learn more about arc here: https://brainly.com/question/28108430

#SPJ1