Recreating the Original Triangle

You will be using the following original triangle in the following activity.

With a ruler, measure the sides of the original triangle to the nearest millimeter. Write down the length of each side in your math journal.
With a protractor, measure the angles of the original triangle to the nearest degree. Write down the measure of each angle in your math journal.

SSS: Cut three pieces of string. Make each piece of string the length of one of the sides of the original triangle. Put the string together to form a triangle and trace the triangle on a separate piece of paper. Measure the angles of the triangle with your protractor.

Are the lengths of the sides and the measures of the angles of the triangle you created the same as the original triangle?
Rearrange the string to make a different triangle. Is there any way to create a triangle that has different angle measures?
SAS: Choose two sides of the original triangle. Cut two pieces of string and make each piece of string the length of one of those sides. Measure the angle between the sides that you chose and draw an angle of that measure on a separate sheet of paper. Put the string together to form the sides of that angle and trace them. Draw in the third side of the triangle. Measure the third side that you drew and the two angles adjacent to that side.

Are the lengths of the sides and the measures of the angles of the triangle you created the same as the original triangle?
Draw the starting angle elsewhere on your paper and rearrange the string to make a different triangle. Is there any way to create a triangle whose third side has a different length?
ASA: Choose one side of the original triangle. Cut one piece of string and make the piece of string the length of that side. Trace the string on a separate sheet of paper. Measure the angles on either side of the side that you chose, and draw angle of those measures on either side of the line you traced on the paper. Extend the sides of the angles until they intersect and form a triangle. Measure the two sides that you drew and the angle between them.

Are the lengths of the sides and the measures of the angles of the triangle you created the same as the original triangle?
Rearrange the string and re-draw the two starting angles to make a different triangle. Is there any way to create a triangle that has different side lengths?


The original triangle⬇️

there are 10 clubs on campus. how many ways are there if you want to choose 3 student clubs out of 10 to join is 120

A fractional factorial experiment utilizes subset of combinations that are gotten from the full factorial experiment. They are applicable when there are too many inputs to screen practically or cost or time would be excessive.

Also, using the fractional factorial experiment makes running the experiments faster and cheaper.

10C3 = 10! / (7!*3!)

        = 10*9*8/6

        = 120

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Answer:

2(x+8)=126

Step-by-step explanation:

GD is the bisector of CGE and 126 and the angle CGE are equal

Answer:

I tried as I can to solve it

Using the roller coaster as an example, draw a right triangle.

Use h to symbolize the horizontal distance.

The following expression can be used to get h given that roller coaster serves as a representation of the hypotenuse side length.

30² = h² + 25².

Assemble similar phrases.

h² = 30² - 25².

horizontal separation

In (a), there is:

h² = 30² - 25².

This results:

h² = 275

Take both sides' roots.

h = 16.58

Consequently, 16.58 feet are the horizontal distance.

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Answer:

554

Step-by-step explanation:

x + 2551 - 2551 = 3105 - 2551

x = 554

Answer:

[tex]x + 2551 = 3105 \\ x + 2551 - 2551 = 3105 - 2551 \\ x = 554[/tex]

By using the formula for area of rectangle, it can be calculated that Area of the median is 2400 sq. feet

What is area of rectangle?

The area of a rectangle is calculated by multiplying the length by the width. For example, if a rectangle has a length of 10 feet and a width of 6 feet, the area would be 10 x 6 = 60 square feet. The area of a rectangle is a two-dimensional measurement and is typically expressed in units squared, such as square feet or meters squared. Other shapes, such as a triangle or a circle, also have areas and are calculated differently.

If l is the length of the rectangle and b is the breadth of the rectangle, then area of rectangle is calculated by the formula

Area = [tex]l \times b[/tex]

Length of the median = 300 feet

Width of the median = 8 feet

Area of the median = 300 [tex]\times[/tex] 8 = 2400 sq. feet

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if there are 720 different classes in one quarter at time, each in its own room, different rooms will be required 720 rooms.

To answer this question, we need to understand that each class needs its own room. Therefore, the number of rooms required will be equal to the number of classes. In this case, there are 720 different classes in one quarter, so 720 different rooms will be required. Each room can accommodate one class at a time, so the total number of rooms needed is 720.

Number of Classes = 720

Number of Rooms Required = Number of Classes = 720

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In  linear equation, He travels at a greater speed from his friend's house, at a rate of 0.6667 miles per minute, that is, 2 miles in 3 minutes.

What in mathematics is a linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.  

                             Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

Using linear function concepts, it is found that:

Seth starts closer to the school in the bus.

He travels at a greater speed from his friend's house, at a rate of 0.6667 miles per minute, that is, 2 miles in 3 minutes.

From the graph of the bus, when he takes the bus, he is 13 miles from the school, as he starts at position 4 and ends at 17.

At his friend house, he is 13 miles from the school only after 3 minutes, which means that the bus will be closer.

The scenario with the greater speed is the one with the higher slope, that is, higher rate of change, which is the change in distance divided by the change in time.

In the bus, change of 13 miles in 24 minutes, thus

       mᵇ = 13/24 = 0.5417

   From the friend's house, change of 2 miles in 3 minutes, thus

   mf = 2/3 = 0.6667

Thus, he travels at a greater speed from his friend's house, at a rate of 0.6667 miles per minute, that is, 2 miles in 3 minutes.

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Answer:

Yes, the lines are parallel. This is because the lines have the same slope. The slope of a line is a measure of how steep the line is, and it is calculated by taking the difference of the y-coordinates of two points on the line and dividing it by the difference of the x-coordinates of the same two points. In this case, the slope of line a is -1, and the slope of line b is also -1. Because the lines have the same slope, they are parallel to each other.

One exponential function with the given features is y = 2^x - 3, and is graphed at the end of the answer.

An exponential function is defined as follows:

y = a(b)^x + c.

In which:

The graph of the function has a horizontal asymptote at y = -3, hence:

c = -3.

For a and b, they can assume any non-negative values, hence we attribute these following values:

a = 1, b = 2.

The graph is given at the end of the answer.

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Answer:

(8.25, 9.75)

Step-by-step explanation:

To find the point that is ¼ of the distance from A to D, we first need to find the coordinates of D. Since A is located at the point (3, 7) and D is located at the point (11, 11), we can use the distance formula to find the distance between these two points. The distance formula is given by:

distance = √((x2 - x1)^2 + (y2 - y1)^2)

where (x1, y1) and (x2, y2) are the coordinates of the two points. In this case, we have x1 = 3, y1 = 7, x2 = 11, and y2 = 11, so the distance between A and D is:

distance = √((11 - 3)^2 + (11 - 7)^2) = √(8^2 + 4^2) = √(64 + 16) = √80 = 8.944

Now that we know the distance between A and D, we can use this information to find the point that is ¼ of the distance from A to D. Since C is ¼ of the distance from A to D, it is located ¼ of the way along the line between A and D. This means that we can find the coordinates of C by taking the average of the coordinates of A and D, weighted by ¼ and ¾, respectively. In other words, the coordinates of C are given by:

C = ¼ * A + ¾ * D

where A and D are the coordinates of points A and D, respectively. Plugging in the coordinates of A and D, we get:

C = ¼ * (3, 7) + ¾ * (11, 11) = (0.75 * 3 + 2.25 * 11, 0.75 * 7 + 2.25 * 11) = (8.25, 9.75)

Therefore, the point C is located at the coordinates (8.25, 9.75).

Answer:

The value of n in this equation is 5.

Step-by-step explanation:

This can be determined by using the property of exponents that states that x^n * x^m = x^(n+m). In this case, 10^n * 10^5 = 14,521, so 10^(n+5) = 14,521. Solving for n, we get n = 5.

Answer:

Step-by-step explanation:

Answer:

Your answer should be [tex]\frac{\pi }{7}[/tex]

Step-by-step explanation:

Looking at the x-axis we can say that is our b.

Period Formula: 2π/b.

x-axis is from 0 to 20.

b = 14 because of the rise to rise.

2π/14 = π/7

The solution is given as,
Two-digit  numbers                 Multiples of 3             Three-digit numbers
     30                                      3,30, 333,                            333    

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

here,
Place the given number in the appropriate place.
Numbers are 3, 30, 333, 3001,
Two digit number among the numbers = 30
Multiples of 3 among numbers = 30, 333, 3
Three-digit numbers among the numbers = 333

Thus, It is shown that the numbers are placed in their appropriate positions.

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Based on the above, the number of 3-points that they make is 25.

Simultaneous equation is a form of two equations that have to be solved at the same time. Thus, the number of 2 points made is 17, while that of 3 points is 25.

A set of equations that has to be solved simultaneously so as to determine the values of the unknown variables is termed simultaneous equation.

The given question would result to a simultaneous equation as follows;

let the number of 2 points made by represented by m, and that of 3 points by n.So that;

m + n = 42  ..................

i2m + 3n = 109  ...............

ii multiply equation 1 by 3 and equation 2 by 1 to have;3m + 3n = 126 ............

iii 2m + 3n = 109 .............

iv subtract eqaution iv from iii

m = 17

substitute the value of m in equation 1 to have:

m + n = 4217 + n = 42n = 42 - 17   = 25m = 17, n = 25

Thus the number of 2 points made was 17, while that of 3 points made was 25.

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Answer:

y=-3

Step-by-step explanation:

A line of symmetry is the line where a function can be folded in half evenly. Here it occurs at y=-3

line of symmetry, the line at which point the graph begins to mirror itself, Check the picture below.

The Area of the circle will be = is 144.87 [tex]cm^{2}[/tex]

Given in the question,

The sector of the circle has an area of = 121 [tex]cm^{2}[/tex]

The measure of an arc = is 36 inches.

According to the attached figure,

Let us consider the arc length = L

Let radius = r

As per the question L = 36'

Let the radius be

To calculate the length of the arc we need to use the formula,

L = r x θ

36 = r x θ

θ = [tex]\frac{36}{r}[/tex] degrees ------- equation 1

Now according to the area of the sector of the circle,

A = [tex]r^{2}[/tex] x θ / 2

121 = [tex]r^{2}[/tex] x θ / 2

[tex]r^{2}[/tex] = 2 x 121 / ( [tex]\frac{36}{r}[/tex] )

[tex]r^{2}[/tex] = [tex]\frac{2 * 121 * r}{36}[/tex]  ----- equation 2

r = [tex]\frac{2 * 121 }{36}[/tex]

r = 6.72 cm.

Now if the radius is = 6.72 cm

Diameter = 2 x radius

= 2 x 6.72

= 13.44 cm

Area of the circle = [tex]\pi r^{2}[/tex]

= [tex]\pi[/tex] x 6.72 x 6.72

= 144.87 [tex]cm^{2}[/tex]

Therefore, the area of the circle = is 144.87 [tex]cm^{2}[/tex]

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Answer:

y=-2/3x+4

Step-by-step explanation:

Rise/run (from the y-intercept to the next point you go down 2 and then to the right 3)

Y-intercept (where the line touches the y-axis) 4

When the spring is stretched and the distance from point a to point b is 5.3 feet, the value of θ is 53.13  degrees

The distance between point a to point b = 5.3 feet

The length of the top side = 3 feet

Therefore, it will form a right triangle

Here we have to use trigonometric function

Here adjacent side and the hypotenuse of the triangle is given

The trigonometric function that suitable for the given conditions is

cos θ = Adjacent side / Hypotenuse

Substitute the values in the equation

cos θ = 3 / 5

θ = cos^-1(3 / 5)

θ = cos^-1(0.6)

θ = 53.13 degrees

Therefore, the value of θ is 53.13  degrees

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A sampling error is the difference between a population parameter and a sample statistic.

Parameters are numbers that describe the properties of entire populations. Statistics are numbers that describe the properties of samples. For example, the average income for the United States is a population parameter. Conversely, the average income for a sample drawn from the U.S. is a sample statistic. The difference between a parameter vs a statistic is that a parameter is a fixed measure describing the whole population, while a statistic is a characteristic of a sample, a portion of the target population.

Thus, the difference is defined as sampling error.

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Five water glasses each minute, one minute to fill the cooler.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units. what kinds of values and units

Let's say you go to the store to buy six apples.

You are informed by the shopkeeper that he is offering 10 apples for Rs 100. In this instance, the value and the units are the price of the apples. Recognizing the units and values is crucial when using the unitary technique to a problem.

Always write the items that need to be computed on the right side and the things that are known on the left side to simplify things.

We are aware of the quantity of apples and the amount of money in the aforesaid problem.

According to our question-

divide 150 by 30 equal 5

= 5

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The linear functions defined in this problem are given as follows:

1. y = -x + 3.

2. y = x - 3.

3. y = 3x + 1.

4. y = -2x - 2.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

The coefficients and their meaning are given as follows:

From the second bullet point above,  the intercepts for each function in this problem are given as follows:

The slopes are given as follows:

The problem is incomplete, hence we just define the linear functions.

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The time presently is 8:15 a.m, and the rocket will launch in 3.75 hours, at 11:20 a.m.

Subtraction (represented by the minus sign) is one of four mathematical operations, the others being addition, multiplication, and division. Subtraction is the procedure of removing items from a collection. Subtraction may be thought of as the inverse of addition. Counting forwards helps children learn to add. To subtract, they just count backwards.

Here,

launch time=11:20 am

time left to launch=3.75 hour

=0.75*60

=45 minutes

= 3 hours 45 minutes

=11 hours 20 minutes-3 hours 45 minutes

=8 hours 15 minutes

=8:15 AM

The time right now is 8:15 AM when rocket will launch in 3. 75 hour and the launch time is 11:20 am.

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Answer:

70.5%

Step-by-step explanation:

If a continuous random variable X is normally distributed with mean μ and variance σ², it is written as:

[tex]\large\boxed{X \sim\text{N}(\mu,\sigma^2)}[/tex]

Given:

Therefore, if the weights of the 12-month-old baby boys are normally distributed:

[tex]\boxed{X \sim\text{N} \left(22.5,2.2^2 \right)}[/tex]

where X is the weight of the baby boy.

To find the percentage to the nearest tenth of 12-month-old baby boys who weigh between 19.7 and 24.4 pounds find P(19.7 ≤ X ≤ 24.4).

Calculator input for "normal cumulative distribution function (cdf)":

[tex]\implies \text{P}(19.7 \leq X \leq 24.4)=0.704548741[/tex]

[tex]\implies \text{P}(19.7 \leq X \leq 24.4)=70.5\%[/tex]

Therefore, the percentage of 12-month-old baby boys who weigh between 19.7 and 24.4 pounds is 70.5% (nearest tenth).

The length of second lawn is found as the 36 sq. m.

For the stated question-

First lawn:

Area = length x width

A = 6 x 4 = 24 sq. m.

Second lawn:

A2 = length x width

6 x A = L x 4

6 x 24 = L x 4

L = 6 x 6

L = 36 sq. m

Thus, the length of the second lawn is found as the 36 sq. m.

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Answer:

Step-by-step explanation:

36 is the answer

The discount is $3.75 and the amount next week will be $21.25

This has to do with a percentage. A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.

In this case, the pack of tomato plants costs $25. Next week, the plants are on sale for 15% off. Larissa wants to know the price of the tomato plants if she buys them next week.

The discount will be:

= 15% × $25

= $3.75

The amount next week will be:

= $25 - $3.75

= $21.25

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Step-by-step explanation:

A

for a linear function the slope ratio has to be the same between every pair of data points.

between (1, 4) and (2, 8) we have

x changes by +1 (from 1 to 2).

y changes by +4 (from 4 to 8).

the slope is

+4/+1 = 4

between e.g. (2, 8) and (3, 16) we have

x changes by +1 (from 2 to 3).

y changes by +8 (from 8 to 16).

the slope here is +8/+1 = 8.

which is not the same as 4.

so, it is not a linear function.

it is an exponential function.

B.

the function is actually

f(x) = y = 2^(x+1)

an exponential function is of the form

y = a^x

in our case we have

4 = a¹ = 2²

8 = a² = a¹×2 = 2² × 2 = 2^(2+1)

16 = a³ = a²×2 = a¹×2×2 = 2²×2×2

we see

f(n) = a1×2^(n-1) = 2²×2^(n-1) = 2^(n+1)

C.

the average rate of change is

(the difference of the function results at the interval ends) / (the difference of the interval ends).

so, in our case

(f(4) - f(2))/(4 - 2) = (32 - 8)/2 = 24/2 = 12

the average rate of change between stations 2 and 4 is 12 (or 12/1).

Answer:

Um in an old question of mine you said "its been forever". That was my elijahmiraclechild account. I don't really remember you but I would like to

Step-by-step explanation:

The expression which has product of two binomials is (5-n)(n+7).

An expression is combination of variables, numbers and operators.

Binomials are expressions containing the sum (or difference) of two terms.

The expression (x + 3)(x + 2) is the product of two binomials.

(pq)(qp), (5-n)(n+7), 3x(2x+5), 6x-2y

(pq)(qp) is not the product of binomials because pq and qp are products.

3x(2x+5) is not the product of binomials because 3x is not a sum or difference.

6x-2y is also not because it is one binomial, not two multiplied together.

(5-n)(n+7) is the product of two binomials.

Hence, (5-n)(n+7) is the expression which has product of two binomials.

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