Find m of angle ZLK if m of angle ZLK= x+86, m of angle MLK =130 degrees, and m of angle MLZ = x+ 66

Certainly! I can help you with trigonometry. To find the lengths of a triangle and the angles, we typically use the trigonometric ratios: sine, cosine, and tangent. These ratios relate the angles of a right triangle to the lengths of its sides.

To find the lengths of a triangle:

To find the angles of a triangle:

Remember to use the appropriate trigonometric ratio or trigonometric formula depending on the given information. Also, keep in mind the restrictions and conventions for angles and sides in triangles, such as the Pythagorean theorem and the sum of angles in a triangle.

I hope this helps! Good luck with your exam. If you have any specific questions or examples, feel free to ask.

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The value of y for the right triangle is equal to 48, which makes the first option correct.

The perpendicular height of the right triangle divides the triangle in two triangles with the same proportions as the original triangle.

60/x = 36/60 {opposite/hypotenuse}

x = (60 × 60)/36 {cross multiplication}

x = 100

by Pythagoras rule the unlabeled side of the entire triangle is calculated as:

√(100² - 60²) = 80

so;

y/80 = 60/100 {opposite/hypotenuse}

y = (60 × 80)/100 {cross multiplication}

y = 48

Therefore, the value of y for the right triangle derived to be 48.

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Answer:  

Step-by-step explanation:

The degree is 4 the leading coefficient is even/positive.  There are 3 distinct real 0's and 3 relative extreme values

Explanation:

4th degree.   Degree is the highest exponent.  The number of 0's (times it hits the curve)tells you the degree.  The curve goes through the x 2 times, which means 2 x's. Then it bounces off x 1 time which means there are 2 x's there too but because this one bounces off it means it's not a distint solution it's a multiplicity ex (x-3)².  So that accounts for 4 solutions

Even/positive coefficient.  That's the first number in the equation.  Because it's facing up it's a positive but all the ends are both facing up so that tells you it's even.  Think of a parabola that is an even function, this follows those rules too.

3 distinct zeroes.    This is explained in 4th degree.   Zeroes are solutions, when it hits x axis.  Goes through x 2 times and bounces once.  So there are 3 distinct zeroes

3 relative extreme values. This is how many "mini" max and mins you have.  

Answer:

You're multiplying each of those numbers by 3.

Step-by-step explanation:

1 * 3 = 3

3 * 3 = 9

9 * 3 = 27
27 * 3 = 81

81 * 3 = 243

Each number is multiplied by 3.

1 x3=3 -> 3x3=9 -> 9x3=27 -> 27x3=81 and so on.

Happy to help; have a great day! :)

Answer:

3

Step-by-step explanation:

3

The equation of the directrix of the parabola found in part A is [tex]x^2 = -2cy + c^2.[/tex]

The equation of the parabola formed when a cross section is taken through the reflector's central axis is

[tex]y = (1/12)(x - 0)^2 + 0.[/tex]

In this equation, the vertex is at the origin (0, 0) and the coefficient 1/12 determines the shape of the parabola.

The equation implies that the parabola opens upward because the coefficient of [tex]x^2[/tex] is positive.

To find the equation of the directrix, we can use the distance formula. The directrix is a horizontal line that is equidistant from the vertex as any point on the parabola.

Since the parabola is symmetric with respect to the y-axis, the directrix will also be symmetric with respect to the y-axis.

Let's assume that the directrix is a horizontal line with the equation y = c, where c is a constant.

To find the value of c, we need to consider a point (x, y) on the parabola. The distance from the point (x, y) to the directrix y = c should be equal to the distance from the point (x, y) to the vertex (0, 0).

Using the distance formula, the distance from (x, y) to the directrix y = c is given by |y - c|, and the distance from (x, y) to the vertex (0, 0) is given by [tex]\sqrt{(x^2 + y^2)}[/tex]

Setting these distances equal, we have:

[tex]|y - c| = \sqrt{(x^2 + y^2)}[/tex]

Squaring both sides of the equation, we get:

[tex](y - c)^2 = x^2 + y^2[/tex]

Expanding and simplifying the equation, we have:

[tex]y^2 - 2cy + c^2 = x^2 + y^2[/tex]

Simplifying further, we obtain:

[tex]-2cy + c^2 = x^2[/tex]

Rearranging the terms, we get:

[tex]x^2 = -2cy + c^2[/tex]

This equation represents the equation of the directrix of the parabola formed by the reflector.

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Answer:

slope m = - [tex]\frac{1}{3}[/tex]

Step-by-step explanation:

calculate the slope m of the line using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (0, 3) and (x₂, y₂ ) = (3, 2) ← 2 points on the line

m = [tex]\frac{2-3}{3-0}[/tex] = [tex]\frac{-1}{3}[/tex] = - [tex]\frac{1}{3}[/tex]

• Parallel lines have equal slopes

then parallel line will have a slope of - [tex]\frac{1}{3}[/tex]

The Growth functions are:

[tex]N = 2000(1.12)^{t}[/tex]

[tex]N = N_{0} e^{kt}[/tex] where k > 0

The Decay Functions are:

[tex]A = A_{0}(0.95)^{t}[/tex]

[tex]N = N_{0} e^{kt}[/tex] where k < 0

[tex]A = Pe^{-rt}[/tex]

[tex]A = A_{0}(1 - \frac{r}{n})^{nt}[/tex]

Exponential growth and decay function:

Exponential growth refers to when the quantity is increasing over time, while exponential decay refers to when the quantity is decreasing over time.

The general form of growth functions is:

y = [tex]ab^{kt}[/tex]

where: a ≠ 0 and b ≠ 0

The conditions for the functions are:

1) When b > 1, k > 0, it represents exponential growth function

2) When 0 < b < 1, k > 0, it represents exponential decay function

3) When b > 1, k < 0, it represents exponential decay function

Thus:

Growth functions are:

[tex]N = 2000(1.12)^{t}[/tex]

[tex]N = N_{0} e^{kt}[/tex] where k > 0

Decay Functions are:

[tex]A = A_{0}(0.95)^{t}[/tex]

[tex]N = N_{0} e^{kt}[/tex] where k < 0

[tex]A = Pe^{-rt}[/tex]

[tex]A = A_{0}(1 - \frac{r}{n})^{nt}[/tex]

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Answer: $204

Step-by-step explanation:

203 plus 195 plus 180 plus 238 equals 816

816 divided by 4 equals 204

203+195=398

398+180=578

578+238=816

816/4=204

Step-by-step explanation:

The quadratic expression f(x) = 2x^2 - 9x - 18 can be factored as (2x + 3)(x - 6). So, the missing values in the given expression (2x + [?])(x - [ ]) are 3 and 6, respectively.

Answer:

(2x + 3)(x -6)

Step-by-step explanation:

2x² -9x -18

2 × -18 = -36

Find factors of -36 which you multiply will give -36 but when same factors are added will give -9.

-12 × 3 = -36

-12 + 3 = -9

2x²-12x +3x -18

2x(x - 6) + 3(x -6)

(2x + 3)(x -6)

[tex]\textit{circumference of a circle}\\\\ C=2\pi r ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ C=280 \end{cases}\implies 280=2\pi r\implies \cfrac{280}{2\pi }=r\implies \cfrac{140}{\pi }=r \\\\[-0.35em] ~\dotfill\\\\ \textit{area of a circle}\\\\ A=\pi r^2 ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=\frac{140}{\pi } \end{cases}\implies A=\pi \left( \cfrac{140}{\pi } \right)^2 \\\\\\ A=\pi \cdot \cfrac{140^2}{\pi^2}\implies A=\cfrac{19600}{\pi }\implies A\approx 6238.87~cm^2[/tex]

Answer:240

Step-by-step explanation:

divide 480 by the amount of gift everybody gets . 2

Answer:

I think the answer would be 240 people that received a gift.

Step-by-step explanation:

If there were 240 people at the party that received gift then we would check by dividing 480 and 2.

Why?

Simply because if there was 480 gifts and 2 were given to each person then it would only make sense that , that’s as the amount.

(2 persons would have 4 gifts, and if there was 240 people then there would be 480 gift brought to the party)

The solution for the system of equations is (x, y) = B. (3, -5).

The correct option is B. (3, -5).

To find the solution for the system of equations:

{4x + y = 7

{2y + 3 = 3x - 16

We can solve it using the method of substitution or elimination. Let's use the method of elimination:

First, let's multiply the second equation by 2 to eliminate the variable y:

2(2y + 3) = 2(3x - 16)

4y + 6 = 6x - 32

Rearranging this equation, we get:

6x - 4y = 38 ----(1)

Now we have the system of equations:

4x + y = 7 ----(2)

6x - 4y = 38 ----(1)

Next, let's multiply equation (2) by 4 to eliminate the variable y:

4(4x + y) = 4(7)

16x + 4y = 28

Now we have the system of equations:

16x + 4y = 28 ----(3)

6x - 4y = 38 ----(1)

Adding equations (3) and (1) eliminates the variable y:

(16x + 4y) + (6x - 4y) = 28 + 38

22x = 66

x = 66/22

x = 3

Substituting the value of x into equation (2), we can solve for y:

4(3) + y = 7

12 + y = 7

y = 7 - 12

y = -5

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Answer:

the volume of 8 identical cubes is approximately 386.744 cm³.

Step-by-step explanation:

Let's assume the side length of a cube is represented by "s."

The total shaded area of two identical cubes is given as 162 cm². Since there are two cubes, each cube contributes half of the total shaded area.

Area of a single cube = (Total shaded area) / 2

= 162 cm² / 2

= 81 cm²

The area of each face of a cube is equal to the side length squared. Therefore, we can set up the equation:

6s² = 81 cm²

Dividing both sides by 6:

s² = 81 cm² / 6

= 13.5 cm²

Taking the square root of both sides:

s = √(13.5 cm²)

≈ 3.674 cm (rounded to three decimal places)

Now that we know the side length of a single cube, we can calculate the volume of 8 identical cubes.

Volume of a single cube = s³

= (3.674 cm)³

≈ 48.343 cm³ (rounded to three decimal places)

Volume of 8 cubes = Volume of a single cube * 8

= 48.343 cm³ * 8

= 386.744 cm³

Megan is wrong because the square root of a number can be either smaller or larger, depending on whether the number is less than or greater than 1.

Megan's statement that "when you square root a number, the answer is always smaller" is incorrect.

In fact, the square root of a number can be either smaller or larger than the original number, depending on the value of the number.

To demonstrate that Megan is wrong, let's consider a few examples:

Square root of 4:

The square root of 4 is 2.

In this case, the square root is smaller than the original number.

Square root of 1:

The square root of 1 is also 1.

Here, the square root is equal to the original number.

Square root of 9:

The square root of 9 is 3.

In this case, the square root is larger than the original number.

Square root of 16:

The square root of 16 is 4.

Again, the square root is larger than the original number.

From these examples, we can see that the square root of a number can be smaller, equal to, or larger than the original number.

It depends on the specific value of the number.

Megan's statement oversimplifies the relationship between a number and its square root.

In general, the square root of a number is a value that, when multiplied by itself, gives the original number.

It is not always smaller but rather a value that satisfies the mathematical relationship.

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Alright, so let's assume your phone number has no repeated digits. The first task is to select the first digit of the two-digit number. Since phone numbers don't start with zero, you have 9 choices (1 through 9).

The next task is to select the second digit. Because we've already used one digit, and we're assuming there are no repeats in the phone number, we have 9 choices left (0 and the 8 digits that were not selected first).

That gives us a total of 9 * 9 = 81 possible two-digit numbers.

Now, your phone number has a specific first two digits, right? There's only one such combination that matches your phone number.

So the probability that the two-digit number you've selected matches the first two digits of your phone number is 1 in 81, or 1/81.

Think of it this way, my friend: Imagine you have a bag with 81 marbles, each marble has a unique two-digit number on it. You close your eyes and reach into the bag to pick a marble. The chance that you'll pick out the marble with your phone number's first two digits is just like finding one special marble in a bag of 81. It's quite the quest, isn't it? But that's what makes the game of probability so interesting!

The chi-square test of independence is a useful statistical method that can be used to test the null hypothesis that there is no association between two categorical variables. When the assumptions of the test are satisfied, this hypothesis can be tested using the chi-square statistic. The following problem can be solved using the chi-square test of independence:

Is gender associated with a person's environmental awareness? Two hundred randomly selected individuals were surveyed about their environmental awareness. Participants were asked about recycling, use of aerosol sprays, and various other environmental concerns.

A point system was developed to score the individuals' responses. Once the points were tallied, individuals were broken up into categories of environmental awareness.

Those with scores of 8 to 10 were considered to be very environmentally aware, scores of 4 to 6 moderately aware, and 3 or less not aware.

The results are shown in the following table: Very environmentally aware Moderately environmentally aware Not environmentally aware Male 302145 Female 423428 We will use a chi-square test of independence to test the null hypothesis that gender is not associated with one's environmental awareness.

We begin by specifying the null and alternative hypotheses: H0: Gender and environmental awareness are independent.

Ha: Gender and environmental awareness are dependent. We choose a significance level of α = 0.05. We can now proceed with the chi-square test of independence.

First, we will calculate the expected frequencies. The expected frequency for each cell can be found by multiplying the row total by the column total and then dividing by the sample size.

The expected frequencies are shown in the following table: Very environmentally aware Moderately environmentally aware not environmentally aware Male 22.5716.6176.81 Female 49.424.826.19 Next, we calculate the chi-square statistic using the formula: X2 = ∑(O - E)2/E where O is the observed frequency and E is the expected frequency.

The chi-square statistic is 18.66. We now need to find the degrees of freedom.

The degrees of freedom for a chi-square test of independence are given by df = (r - 1)(c - 1) where r is the number of rows and c is the number of columns. In this case, there are 2 rows and 3 columns, so df = (2 - 1)(3 - 1) = 2.

We can now use a chi-square distribution table to find the critical value of the chi-square distribution with 2 degrees of freedom and a significance level of 0.05.

The critical value is 5.99. Since the calculated value of the chi-square statistic (18.66) is greater than the critical value (5.99), we reject the null hypothesis.

We have sufficient evidence to conclude that gender and environmental awareness are dependent. Therefore, we can conclude that gender is associated with a person's environmental awareness.

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Answer: The fuction with the greatest intercept is 0,2

Step-by-step explanation:

None of the answer choices (2,4), (2,-4), (4,2), or (4,-2) are applicable to the function f(x) = 3/(x-4) + 2. The function does not have a center point in the traditional geometric sense. Option E.

he function f(x) = 3/(x-4) + 2 does not have a center in the traditional sense. The concept of a center is typically associated with geometric figures such as circles or ellipses.

The function f(x) = 3/(x-4) + 2 represents a rational function. It does not have a central point or location like a circle, which has a center at (h, k). In this case, we are dealing with a rational expression involving x.

The equation f(x) = 3/(x-4) + 2 describes a vertical shift of the graph of the function 3/(x-4) by 2 units upward. However, this vertical shift does not correspond to a center point.

The function f(x) = 3/(x-4) + 2 does not have a center point. The concept of a center is not applicable in this context as it is commonly associated with geometric figures rather than rational functions. Option E is correct.

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a. The new technology leads to an increase in the supply of beginner-level violins, resulting in a rightward shift of the supply curve. The demand curve remains unchanged unless otherwise specified.

b. The new technology increases consumer surplus by $2400, as represented by the shaded area between the original demand curve and the new demand curve up to the new equilibrium quantity.

c. The new technology increases producer surplus by $2400, represented by the shaded area between the original supply curve and the new supply curve up to the new equilibrium quantity.

d. The new technology increases total surplus by $4800, which is the sum of the increase in consumer surplus and the increase in producer surplus.

a. To illustrate the effect of the new technology on the supply and demand of beginner-level violins, we need to consider the following:

Supply: The new technology allows beginner-level violin producers to make violins at a substantially lower marginal cost while maintaining the same quality. This means that the supply of beginner-level violins will increase. We can show this on the graph by shifting the supply curve to the right.

Demand: The demand for beginner-level violins will depend on factors other than the new technology. If there is no change in demand, the demand curve will remain the same. However, if there is an increase in demand due to factors such as increased interest in learning the violin, we would see a shift in the demand curve to the right.

By shifting the supply curve to the right or the demand curve to the right, or both, we can represent the effect of the new technology on the market for beginner-level violins.

b. The increase in consumer surplus can be calculated by finding the area of the triangle formed by the original demand curve, the new demand curve, and the new equilibrium quantity of violins. This represents the additional benefit consumers receive from the lower price due to the new technology.

In the given graph, the increase in consumer surplus is represented by the shaded area between the original demand curve and the new demand curve, up to the new equilibrium quantity. The dollar value of this increase can be calculated by multiplying the increase in quantity by the average difference in price between the original and new equilibrium.

c. The increase in producer surplus can be calculated by finding the area of the triangle formed by the original supply curve, the new supply curve, and the new equilibrium quantity of violins. This represents the additional profit that producers receive from the higher quantity sold at the same or slightly reduced price due to the lower marginal cost from the new technology.

In the given graph, the increase in producer surplus is represented by the shaded area between the original supply curve and the new supply curve, up to the new equilibrium quantity. The dollar value of this increase can be calculated by multiplying the increase in quantity by the average difference in price between the original and new equilibrium.

d. The increase in total (or social) surplus is the sum of the increase in consumer surplus and the increase in producer surplus. In this case, the increase in total surplus would be the sum of the increases calculated in parts b and c.

Therefore, the increase in total surplus due to the new technology is represented by the shaded area between the original supply and demand curves and the new supply and demand curves, up to the new equilibrium quantity. The dollar value of this increase can be calculated by adding the dollar values of the increase in consumer surplus and the increase in producer surplus. In this example, the increase in total surplus is $4800.

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Answer:

$858

Step-by-step explanation:

You are paying 11 months of rent for 1 year.

11 × $936 = $10,296

The total rent paid in 1 year for 11 months of rent is $10,296.

Divide the total by 12:

$10,296/12 = $858

The monthly amount averages to $858.

There are 17,576,000 possible license plates that can be issued using this system.

To calculate the number of possible license plates that can be issued using this system, we need to determine the number of options for each character in the license plate.

For the first character, there are 26 letters in the English alphabet. Therefore, we have 26 options for the first character.

Similarly, for the second and third characters, we also have 26 options each.

For the fourth character, there are 10 possible numbers (0-9).

And for the fifth character, we again have 10 possible numbers.

To find the total number of possible license plates, we multiply the number of options for each character together:

Number of possible license plates = Number of options for the first character × Number of options for the second character × Number of options for the third character × Number of options for the fourth character × Number of options for the fifth character

Number of possible license plates = 26 × 26 × 26 × 10 × 10

Calculating this expression gives us:

Number of possible license plates = 17,576,000

Therefore, there are 17,576,000 possible license plates that can be issued using this system.

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Using sine law and cosine law, the value of the missing sides are

B = 17.94°, C = 124.03° and c = 403.57m

To solve the missing side, we have to use the sine angle formula.

The law of sine or the sine law states that the ratio of the side length of a triangle to the sine of the opposite angle, which is the same for all three sides.

The formula is given as;

a / sin A = b / sin B

A = 38° 18' = 38.03°

Substituting the values into the formula

300 / sin 38.03 = 150 / sin B

sin B = 150 * sin 38.03 / 300

sin B = 0.3080

B = sin⁻¹(0.3080)

B = 17.94°

From the sum of angles in a triangle;

A + B + C = 180°

38.03 + 17.94 + C = 180

C = 124.03°

Using cosine rule;

c² = a² + b² - 2(a)(b)cos C

c² = 300² + 150² - 2(300)(150)cos 124.03°

c² = 162866.422

c = √162866.422

c = 403.57m

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The given expression -4x^2 + 2x - 5(1+x) is equivalent to -4x^2 - 3x - 5, not -5 - 5x.

To simplify the expression -4x^2 + 2x - 5(1+x), we can distribute the -5 to the terms inside the parentheses:

-4x^2 + 2x - 5(1+x) = -4x^2 + 2x - 5 - 5x

Next, we can combine like terms:

-4x^2 + 2x - 5 - 5x = -4x^2 + (2x - 5x) - 5

Simplifying further, we have:

-4x^2 + (2x - 5x) - 5 = -4x^2 - 3x - 5

Therefore, the expression -4x^2 + 2x - 5(1+x) is equivalent to -4x^2 - 3x - 5.

It's important to note that when we distribute the -5 to the terms inside the parentheses, we multiply each term by -5. So, the expression becomes -5(1) - 5(x). However, -5(1) simplifies to -5, and -5(x) simplifies to -5x. Hence, the expression simplifies to -5 - 5x.

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The kinetic energy of this car is equal to 77160.49 Joules.

In Mathematics, the kinetic energy of a physical object can be calculated by using the following equation (formula):

K.E = 1/2 × mv²

Where:

Note: 50 km/h to m/s = 50 × 1000/3600 = 13.89 m/s

By substituting the given parameters into the formula for the kinetic energy of a physical object, we have the following:

Kinetic energy, K.E = 1/2 × 800 × 13.89²

Kinetic energy, K.E = 400 × 192.90

Kinetic energy, K.E = 77160.49 Joules.

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Complete Question:

An 800 kg car travels at 50 km/h, what will its kinetic energy be?

The product of 22.12 and 0.6 is indeed 13.272.

To compute the product of 22.12 and 0.6, we can perform the multiplication using the standard algorithm for decimal multiplication.

Multiply the decimal part (the digits after the decimal point) first.

0.12 x 0.6 = 0.072 (Multiply 12 by 6, which gives 72, and then move the decimal point two places to the left.)

Multiply the whole numbers.

22 x 0.6 = 13.2 (Multiply 22 by 6, which gives 132, and then move the decimal point one place to the left.)

Add the results from Step 1 and Step 2.

0.072 + 13.2 = 13.272

Therefore, when multiplying 22.12 by 0.6, the result is 13.272.

To verify the calculation, we can check by using estimation. 22.12 is approximately 22 and 0.6 is approximately 0.6. Multiplying 22 by 0.6 gives 13.2, which is close to our calculated result of 13.272. This further confirms that our multiplication is correct.

Hence, the product of 22.12 and 0.6 is indeed 13.272.

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The statement about the points (0, 3), (2, 8), (8, 2), and (0, 1) that is true is All but one of the points are in Quadrant I. Option C

The first quadrant, positioned at the upper-right area of the Cartesian plane, involves coordinates that have favorable values for both x and y.

The coordinates (0,3), (2,8), and (0,1) all fall under quadrant I since their x and y values are positive.

The point located in Quadrant IV can be identified as (8, 2) due to its positive x-coordinate and negative y-coordinate.

Hence, it can be said with precision that Quadrant I contains all but one point.

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