Triangle A B C is shown. The length of side A is 12 inches, the length of side B is 6 StartRoot 3 EndRoot, and the length of side C is 6 inches.

What are the angle measures in triangle ABC?
m∠A = 90°, m∠B = 30°, m∠C = 60°
m∠A = 60°, m∠B = 90°, m∠C = 30°
m∠A = 90°, m∠B = 60°, m∠C = 30°
m∠A = 60°, m∠B = 30°, m∠C = 90°

By using triangle properties and the law of the cosine twice, we find that the distance between points M and N is approximately 9.8 meters.

In this problem we must determine the distance between two points that are part of a triangle and we can take advantage of properties of triangles to find it. First, we determine the measure of angle L by the law of the cosine:

[tex]\cos L = \frac{(19.6\,m)^{2}-(14.8\,m)^{2}-(21.4\,m)^{2}}{-2\cdot (14.8\,m)\cdot (21.4\,m)}[/tex]

L ≈ 62.464°

Then, we get the distance between points M and N by the law of the cosine once again:

[tex]MN = \sqrt{(7.4\,m)^{2}+(10.7\,m)^{2}-2\cdot (7.4\,m)\cdot (10.7\,m)\cdot \cos 62.464^{\circ}}[/tex]

MN ≈ 9.8 m

By using triangle properties and the law of the cosine twice, we find that the distance between points M and N is approximately 9.8 meters.

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Answer: The answer is option

Step-by-step explanation:

The solution is in the attached

Answer:

He can cut 2 1/3 pieces, so a is the correct answer.

Step-by-step explanation:

[tex] \frac{6}{7} x = 2[/tex]

[tex]x = 2 \div \frac{6}{7} = 2 \times \frac{7}{6} = \frac{7}{3} = 2 \frac{1}{3} [/tex]

Answer:

[tex]2\frac{1}{3}[/tex]

Step-by-step explanation:

So this question is essentially asking how many 6/7s can fit into 2/1. Or in other words, what is 2 divided by 6/7. This gives you the equation: [tex]\frac{2}{1}\div\frac{6}{7}[/tex]. Whenever you're dividing by a fraction, you just keep the first fraction (don't change anything), change the operation (from division to multiplication) and "flip" the fraction so if you had the fraction a/b it's now b/a. This gives you the equation: [tex]\frac{2}{1}*\frac{7}{6}[/tex]. You can now just multiply the denominator and numerator. This gives you the fraction: [tex]\frac{2*7}{1*6}[/tex] which simplifies to [tex]\frac{14}{6}[/tex]. This can be further simplified by dividing both the numerator and denominator by 2. If you don't know why this keeps the original value think of it as multiplying the fraction by [tex]\frac{0.5}{0.5}[/tex] or [tex]\frac{\frac{1}{2}}{\frac{1}{2}}[/tex]. Which is technically multiplying the value by 1, so it should keep the original value, you're just simplifying the numerator and denominator. Simplifying it, gives you the fraction: [tex]\frac{7}{3}[/tex]. This can be a mixed fraction by splitting it up into two parts: [tex]\frac{6}{3}+\frac{1}{3}[/tex]. Which when added is the same thing, except the second side simplifies, and you get [tex]2\frac{1}{3}[/tex]

The measure of angle IMJ is 62.5 degrees

To solve for angle IMJ, we make use of the following arc intercept theorem.

Angle IMJ = 0.5 * (Arc IJ + Arc LK)

So, we have:

Angle IMJ = 0.5 * (40 + 85)

Evaluate the product

Angle IMJ =62.5

Hence, the measure of angle IMJ is 62.5 degrees

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Option D. The description that best fits the intercept of the graph is The initial velocity of the runner was 6 m/s, and the runner stopped after 8 seconds.

The graph has lines that would go through these points, (0,6) and pair (6,8). In the other graph, it goes through 6, 8 and 8, 0.

The initial velocity of this runner is seen to be 6m/s. As he runs this would increase and while he slows down it would fall. The stop time of the runner is going to be at 8 minutes.

Which of the following describes the intercepts on the graph?

The initial acceleration of the runner was 8 m/s2, and the runner stopped after 6 seconds.

The initial acceleration of the runner was 6 m/s2, and the runner stopped after 8 seconds.

The initial velocity of the runner was 8 m/s, and the runner stopped after 6 seconds.

The initial velocity of the runner was 6 m/s, and the runner stopped after 8 seconds.

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Answer:

Step-by-step explanation:

Answer:

I think - option c. 54.22kg

Step-by-step explanation:

Hello !

[tex]5(3y + 2) + 6[/tex]

[tex] = 5 \times 3y + 5 \times 2 + 6[/tex]

[tex] = 15y + 10 + 6[/tex]

[tex] = 15y + 16[/tex]

15y + 16

Fully expanding and simplifying an expression means distributing all values and combining like terms.

Distributing

First, the 5 needs to be distributed to the values within the parentheses. Using the distribution property, the 5 can be multiplied by 3y and 2.

Then, just simplify

Combine Like Terms

Now that all values are distributed like terms need to be added together.

The terms 10 and 6 are of the same power and do not have variables. So, they can be added together.

This expression is the most expanded and simplified version.

Step-by-step explanation:

Answer:

The lodge is 21 feet tall.

Step-by-step explanation:

Ski Lodge:

object/shadow

x/3

Ski Pole:

object/shadow

3.5/0.5

Solve for x:

x/3 = 3.5/0.5

0.5x = 10.5

x = 21

Three common tangents is illustrated when two circles touch each other externally at one point and they'll have three tangents.

It should be noted that a common tangent simply means a line the bus tangent to more than one circle.

In this case, three common tangents is illustrated when two circles touch each other externally at one point and they'll have three tangents.

A diagram is attached to illustrate the tangent.

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The solution of the given expression [tex]\sqrt{7xy^7}\sqrt{21x^5y^5}[/tex]will be 7x³y⁶√3.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

The given expression will be solved as follows:-

E =  [tex]\sqrt{7xy^7}\sqrt{21x^5y^5}[/tex]

E = [tex]\sqrt{7\times 7\times 3\times xy^7\times x^5y^5[/tex]

E=[tex]\sqrt{7\times 7\times 3\times x^6y^{12}[/tex]

E = 7x³y⁶√3.

Therefore the solution of the given expression [tex]\sqrt{7xy^7}\sqrt{21x^5y^5}[/tex]will be 7x³y⁶√3.

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Answer:

C. Yes, she used stratified random sampling.

Explanation :

Stratified random sampling is a random method of sampling where researcher divided the population into sub group and the randomly select from these group to find the final sample.

Answer:

C

Step-by-step explanation:

The measure of angles x and y are 90 degrees and 59 degrees.

A rhombus is a two-dimensional shape having four parallel opposite pairs of straight, equal sides. This shape resembles a diamond and is what you'd find on a deck of cards to represent the diamond suit. Rhombuses can be encountered in a variety of common situations.

We have shown the rhombus in the picture.

As we know the diagonals bisect at a 90-degree angle.

So angle x = 90 degree

To find the value of y:

31 + y + 90 = 180

y = 59 degrees

Thus, the measure of angles x and y are 90 degrees and 59 degrees.

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When 'c' is negative both p and q would have the same sign and when opposite signs whereas when b is positive and negative, both would have positive and negative signs respectively.

The ways in which the signs of 'b' and 'c' affect the form include;

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The explicit equation of the function is t(n) = 5 * 8^(n-1)

The function definition is given as:

t(1)=5

t(n+1)=8t(n)

Let n = 1

So, we have:

t(2) = 8t(1)

Divide through by t(1)

t(2)/t(1) = 8

The common ratio of the function is:

r = t(2)/t(1) = 8

The explicit rule is then calculated as:

t(n) = t(1) * r^(n-1)

So, we have:

t(n) = 5 * 8^(n-1)

Hence, the explicit equation of the function is t(n) = 5 * 8^(n-1)

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Answer:

Slope = 0

Step-by-step explanation:

This is a HORIZONTAL line  ....horizontal lines have slope = 0

VERTICAL lines like   x =2    have  UNDEFINED slope.

Answer:

m = 0

Step-by-step explanation:

This type of linear equation would be a horizontal line when graphed meaning that the slope would equal zero.

So in the equation y = -2, the slope is missing as the ' mx ' because it is horizontal.

The 0.375 terminating decimals are equivalent to 3/8 option second is correct.

Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.

The fraction is:

= 3/8

After dividing with 8

= 0.375

Thus, the 0.375 terminating decimals are equivalent to 3/8 option second is correct.

The question is incomplete.

The complete question is:

Which of the following terminating decimals is equivalent to 3/8?

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[tex]y = \frac{1}{x - 3} + 7[/tex]

[tex]x = \frac{1}{y - 3} + 7[/tex]

[tex]x - 7 = \frac{1}{y - 3} [/tex]

[tex]y - 3 = \frac{1}{x - 7} [/tex]

[tex]y = \frac{1}{x - 7} + 3[/tex]

Answer is 41

Hope it help you

The next step in constructing a line perpendicular to a segment is; With compass at P, draw an arc that intersects a in two places.

The steps in constructing the given line segment in the attached image are;

Looking at the attached line segment the next step is obviously With compass at P, draw an arc that intersects a in two places.

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Answer:

you ;eft the question incomplete, but the answer is:

Increase the compass to almost double the width (the exact setting is not important).

Step-by-step explanation:

The number should be 54, where we can add 36 to get twice the number decreased by 18.

There are only one or two variables in a linear equation. No variable can be multiplied by a number larger than one or used as the denominator of a fraction in a linear equation.

Given that, when we add 36 with a number then it gives twice the number decreased by 18.

Let the number be [tex]x[/tex] .

We get the linear equation

[tex]x+36=2x-18\\\Rightarrow x-2x=-18-36\\\Rightarrow -x=-54\\\Rightarrow x=54[/tex]

Therefore, the number should be 54.

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Answer:  C(10,7)

Reason:

We can numerically compute both C(10, 3) and C(10, 7) and we would get 120 for each result.

Use the nCr combination formula

[tex]nCr = \frac{n!}{r!(n-r)!}[/tex]

In general we have the rule C(n, r) = C(n, n-r)

We conclude that the measure of that angle is 150 degrees.

Notice that  the measure of angle ∠BFE will be equal to:

∠BFE = ∠BFC + ∠CFD + ∠DFE

Where:

∠CFD = 90°

∠DFE = 30°

And we will have that:

∠AFC = 180° - 90° - 30° = 60°

And we know that BF bisects that angle, then:

∠BFC = 30°

So we conclude that:

∠BFE = ∠BFC + ∠CFD + ∠DFE = 30° + 90° + 30° = 150°

We conclude that the measure of that angle is 150 degrees.

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The best fit line for the scatter plot is shown in the graph second option second is correct.

A mathematical notion called the line of the best fit connects points spread throughout a graph. It's a type of linear regression that uses scatter data to figure out the best way to define the dots' relationship.

[tex]\rm m = \dfrac{n\sum xy-\sum x \sum y}{n\sum x^2 - (\sum x)^2} \\\\\\\\\rm c = \dfrac{\sum y -m \sum x}{n}[/tex]

m and c are the slope of and y-intercept of the line of best.

As we can see in the picture there are scatter plots are shown.

The equation of the best fit will be which passes or nears every dot.

In the scatter plot second the line is very close to every point.

Thus, the best fit line for the scatter plot is shown in the graph second option second is correct.

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The average rate of change of the function from n = 1 to n = 5 is 3.36 plants per day

The function is given as:

f(n) = 10(1.02)^n

The maximum height is 11.04

So, we have:

10(1.02)^n = 11.04

Divide by 10

1.02^n = 1.104

Take the log of both sides

n * log(1.02) = log(1.104)

Divide by log(1.02)

n = 5

Hence, the reasonable domain is 0 ≤ n < 5

We have:

f(n) = 10(1.02)^n

Set n to 0

f(0) = 10(1.02)^0

Evaluate

f(0) = 10

Hence, the y-intercept is 10

We have:

f(n) = 10(1.02)^n

Calculate f(1) and f(5)

f(1) = 10(1.02)^1 = 10.2

f(5) = 10(1.02)^5 = 10.2

The average rate is then calculated as:

m = (f(5) - f(1))/(5 - 1)

This gives

m =(11.04 - 10.2)(5 - 1)

Evaluate

m = 3.36

Hence, the average rate of change of the function f(n) from n = 1 to n = 5 is 3.36

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The image of the pentagon under reflections in line m and then line t is shown below.

A spatial transformation is each mapping of feature shapes to itself, and it maintains some spatial correlation between figures.

Reflection does not change the size and shape of the geometry.

The image of the figure under reflections in line m and then line t.

The reflection of the pentagon DEFG will be given in the figure.

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Answer:

80 magazines sold

Step-by-step explanation:

120*2/3=80

The universal set U from which the subset was derived is; U = {keys on a keyboard }

We are told that S is a subset within a universal set, U.

Now, If S = {x, y, 4, 9, ?}  

Given S is a subset within a universal set U;

According to the question S = {x, y, 4, 9, ?}.

Now, we need to find among the given sets the one that describes the best set.

The best Universal set will be {keys on a key board } since the keys on a keyboard will have alphabets, numbers and punctuation marks mentioned in the set

Therefore, U = {keys on a keyboard }

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