Lines (1) and (2) are parallel. Find sides M
and N. Round your answer to the nearest
tenth.
P
A
M
(2)->
155⁰
N

The value of x is 12.

The triangles which are similar have the same shape and measure of three angles are also same. The only thing that varies is their sides. However, the ratio of the sides of one triangle is equivalent to the ratio of the sides of another triangle, which is called here the scale factor.

By dividing the long sides and short sides, find the scale factor:

96 / 24 = 4

28 / 7 = 4

So, the large triangle is four times bigger than the small one.

Now applying the scale factor to calculate the hypotenuse:

The length of the smaller hypotenuse is 25, a scale that by 4 to get 25 * 4  =100

This means that the larger hypotenuse needs to equal 100 and  the hypotenuse is labeled 6x +28:

6x+28 = 100

Subtract 28 from each side:

⇒6x = 72

Divide both sides by 6:

⇒x = 72/6

∴x = 12

So, the value of x is 12.

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Aspect ratio refers to the proportion of the width to the height of a rectangular image or screen. It is commonly represented as two numbers separated by a colon, such as 4:3 or 16:9.

An aspect ratio of 1:3 means that the width of the image or screen is one-third of its height. This aspect ratio is not commonly used for standard images or screen sizes but it can be used for special cases such as vertical videos.

In general, for images and videos, the aspect ratio of 4:3 was used in the past, but now the aspect ratio of 16:9 is more common, and it's the standard aspect ratio used in most modern televisions, computer monitors, and digital cameras.

Also, it's worth noting that the aspect ratio of 1:3 represents a very elongated shape, and it's not suitable for most practical uses, as it would not be able to display most standard content without black bars on the top and bottom of the screen.

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Answer: X = -4

Step-by-step explanation:

Well, we are given two functions. We know that both of these functions are to be having the same value (they are both f(x) equations).

Therefore, we can create this equation:

6x = -24

We divide both sides by x to get:

x = -4

Answer:

This equation is a simple algebraic equation. It can be solved by isolating the variable on one side of the equation.

a-2=-5

Add 2 to both sides:

a = -5+2

a = -3

So, the solution of the equation is a = -3

[tex] \tt \: a - 2 = - 5[/tex]

[tex] \: [/tex]

[tex] \tt \: a = - 5 + 2[/tex]

[tex] \: [/tex]

[tex] \large \underline{ \boxed{ \tt \color{red} a = - 3}}[/tex]

[tex] \: [/tex]

hope it helps! :)

Answer:

b. x = 62 degree, y = 118 degree

Step-by-step explanation:

x is the vertical angle to the 62-degree angle, so x = 62 degree

We see that the angle x add with the angle y equal to 180 degrees, so to find y, we take

180 - 62 = 118 degree.

So, the answer is b. x = 62 degree, y = 118 degree

Ratnam will have to pay Rs. (x+50y) to the agency for a journey of 50 kilometers.

A word problem is a few sentences describing a 'real-life' scenario where a problem needs to be solved by way of a mathematical calculation.

Given that, Ratnam hired a car from a car renting agency which charges a flat amount of Rs. x for travelling up to 40 kilometers and Rs. y per km for every kilometer travelled thereafter.

We need to find how much should Ratnam pay the agency for a journey of 50 kilometers,

The amount for travelling a km is Rs. y

Therefore, for 50 km it will cost = 50y

Since, they are charging Rs. x as a flat amount,

Therefore, the total cost of travelling 50 km is = x+50y

Hence, Ratnam will have to pay Rs. (x+50y) to the agency for a journey of 50 kilometers.

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Answer: The result is a composite number

Hope this helps :)

Step-by-step explanation:

C

12x + 12, x=8

12*8 + 12

96 + 12

108

The number 108 is a composite number, but not prime and it is a whole number.

Answer:

  2/15

Step-by-step explanation:

You want to know the fraction that is 2/3 of 1/5.

In this context, "of" means "times."

  2/3 of 1/5 = (2/3)×(1/5) = (2·1)/(3·5) = 2/15

2/15 of the pets are alley cats.

The sample space, S: {WW, WL, LW, LL} represent the experiment Playing a video game twice.

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.

The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.

The degree to which something is likely to happen is basically what probability means.

1. Rolling a number cube twice

Drawing a possibility space allows us to see all the 36 outcomes of throwing a cube twice.

So, this is not the required case.

2. Rolling a number cube once

Drawing a possibility space allows us to see all the 6 outcomes of throwing a cube once.

So, this is not the required case.

3. Playing a video game twice

This case can be considered because it gives 4 outcome of Winning(W) and Losing(L).

4. Playing a video game twice

This case cannot be considered because it gives 2 outcome of Winning(W) and Losing(L).

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Answer:

yep its C :)

Step-by-step explanation:

I got it right on my quiz.

Answer:

A Venn diagram is used to visually represent the differences and the similarities between two concepts.

Step-by-step explanation:

hope this helps:)

Answer:

Down below

Step-by-step explanation:

A venn diagram is two circles that overlap in the middle to create the similarities area. The rest of the circles that haven't overlapped are for listing the differences.

Hope this helps! :)

Answer:

Radius =21,  height = 45  
Lateral Surface Area = [tex]5937.61[/tex] cm²
Total Surface Area = [tex]8708.49[/tex]  cm²

Radius = 28, height =28
Lateral Surface Area =  [tex]4926.01[/tex] cm²

Total Surface Area  =  [tex]9852.03[/tex] cm²

Step-by-step explanation:

If r is the radius of a cylinder with height h

Lateral surface area

[tex]L = 2\pi rh[/tex]

Top and bottom surface area for each which is a circle is [tex]\pi r^2[/tex]

So total bottom and top surface area = [tex]2 \pi r^2[/tex]

Total surface area =

[tex]2\pi rh + 2\pi r^2 = 2\pi r(h + r)[/tex]

For r = 21, h = 45
[tex]L = 2 \pi \cdot 21 \cdot 45 = 1890 \pi = 5937.61 \;cm^2[/tex]

[tex]T = 2\pi \cdot 21 (21 + 45) = 2772 \pi = 8708.4948\;cm^2[/tex]

For r = 28, h = 28

[tex]L = 1568\pi = 4926.01 cm^2[/tex]

[tex]T = 3136\pi = 9852.03 \;cm^2[/tex]

In order to have length twice width the answer should be 28 feet.

Let x be the width of the garden.

The length of the garden is 2x.

The perimeter of a rectangle is equal to 2(length + width)

So 42 = 2(2x + x)

42 = 2(3x)

x = 14

The width of the garden is 14 feet and the length is 2x = 2(14) = 28 feet.

The answer is 28 feet (Option a).

Mensuration is the branch of mathematics that deals with the measurement of geometric shapes and figures, such as length, area, and volume. It typically includes the study of geometric shapes, such as circles, triangles, and polygons, and their properties, such as perimeter, area, and volume. Mensuration is used in many fields, including engineering, physics, and computer graphics.

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Answer:

9.) -32 thousand ft per hour

10.) 9/4° per hour

Step-by-step explanation:

9.) To solve this problem, we first need to know the time that the plane landed, which is after 5 hours. Now, we need to find the altitude of the plane a four hours and thirty minutes, which is 16 thousand ft. Lastly, we need to know the formula for rate of change, which is change in y over change in x. Below is the work for how to solve the problem:

change in y / change in x = [tex]\frac{16-0}{4.5-5}[/tex]

[Note: four hours and thirty minutes is equal to 4.5 hours.]

[tex]\frac{16-0}{4.5-5} = \frac{16}{-0.5} =32[/tex]

So, the rate of change from four hours and thirty minutes to when the plane landed is -32 thousand ft per hour.

10.) You did number 10 for the most part, except that the denominator is 8 not 9-0. The reason for this is that is is 8 hours between 6am and 2pm, not 9. This means our final answer is 18/8, or 9/4° per hour.

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Answer: $0.67/eraser

Step-by-step explanation:

Simply divide the cost by the number of eraser in the pack which is 4 eraser.

Solution:

Let x (cost of an eraser)

x = 2.68/4

x = $0.67/eraser

One way to remember multiples of 8 is to think of them as being one less than a multiple of 10. Also another method that can be used to remember multiples of 8 is using them as a double of the multiplies of 4.

For example, 8 is one less than 10, 16 is one less than 18, and so on. This can help make it easier to remember and recall multiples of 8. Another way to remember multiples of 8 is to think of them as being double the multiples of 4. For example, 8 is double of 4, 16 is double of 8 and so on.

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A diagonal of a rectangle will intersect the same number of squares as the length of the rectangle. The rectangle has a length of 7 squares and a width of 4 squares, so the diagonal will intersect 12 squares.

A diagonal of a rectangle will always intersect the same number of squares as the length of the rectangle. In this case, the rectangle has been outlined on a grid paper with dimensions of 7x4. This means that the length of the rectangle is 7 squares and the width is 4 squares. Therefore, the diagonal of this rectangle will intersect 12 squares in total. This is because the length of the rectangle is greater than the width and so the diagonal must intersect the entire length of the rectangle and all of the squares the width intersects. As a result, the diagonal of this rectangle will intersect 12 squares.

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Answer: 28 and 40

Step-by-step explanation:

64 / 2 = 32

32 - 8 = 28

32 + 8 = 40

Answer:28 and 36

Step-by-step explanation:

Rearrange the equation and we get: 2X = 56. Solve for X and we see that X=28

The particles contain 5.199 mol. The result is obtained by dividing the number of particles by the Avogadro number.

Avogadro number is the number of particles contained in 1 mol of any substance. It is 6.022 × 10²³ particles/mol.

The number of particles of a substance can be expressed as

N = n × NA

Where

The number of particles of a substance is 3.131 × 10²⁴ particles. Find the number of moles!

With the Avogadro number, the number of moles would be

N = n × NA

3.131 × 10²⁴ = n × 6.022 × 10²³

n = (3.131 × 10²⁴) / (6.022 × 10²³)

n = 0.5199 × 10¹

n = 5.199 mol

Hence, there are 5.199 mol contained in the particles.

The answer is A.

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Four numbers forming a geometric sequence such that the second term is 35 less than the first term and the third term is 560 more than the fourth term are -35/3, -140/3, - 560/3, -2240/3 and 7, -28, 112, - 448  

Four numbers forming a geometric sequence can be calculate as follows

these terms: a₁, a₂, a₃, a₄

a₁ = a₂ + 35

a₃ = a₄ + 560

Use the formula for the n-term:

a₂ = a₁r

a₃ = a₁r²

a₄ = a₁r³

replace

a₁ = a₁r + 35 ⇒ a₁(1 - r) = 35

a₁r² = a₁r³ + 560  ⇒ a₁(1 - r)r² = 560

Subtracting from the first equation to  the second:

r² = 560/35

r² = 16

r = √16

r = ± 4

Use the first equation to find the first term:

a₁( 1 ± 4) = 35

1. a₁ = 35/-3 = -35/3

2. a₁ = 35/5 = 7

We have two sequences:

r = 4

-35/3, -140/3, - 560/3, -2240/3

r = -4

7, -28, 112, - 448  

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In this function, y = x + 6, the points at x = -2 will be solid and in this function y = 1, there will be a circle at x = - 2. And the correct graph is given below.

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

The function is given below.

y = x + 6,  x ≤ -2

y = 1, x > - 2

In this function, y = x + 6, the points at x = -2 will be solid and in this function y = 1, there will be a circle at x = - 2.

And the correct graph is given below.

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If rotating a graph around a point leaves the graph intact, the graph is said to be symmetric with respect to that point.

Since anything that is mirrored around a horizontal line will fail the Vertical Line Test, no function can by definition be symmetric about the x-axis (or any other horizontal line).

If rotating a graph around a point leaves the graph intact, the graph is said to be symmetric with respect to that point. When two points are always present on a graph, the graph is symmetric with respect to the origin.

If there is a point (a, b) on the graph for every (a, b) on the graph, then the graph is said to be symmetric with respect to the x axis, and f(x, y) = f(x, y).

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The value of y for the given conditions is 82.2.

Repetitive subtraction is the process of division. It is the multiplication operation's opposite. It is described as the process of creating equitable groups. When dividing numbers, we divide a larger number down into smaller ones such that the larger number obtained will be equal to the multiplication of the smaller numbers.

Given a phrase, y divided by 6.85=1.2

y ÷ 6.85 = 12

y/6.85 = 12

multiply both sides by 6.85

y/6.85(6.85) = 12 x 6.85

y = 82.2

Hence the value of y is 82.2.

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Answer:

9 1/2

Step-by-step explanation:

1/2 + 9

Answer:

19/2

Step-by-step explanation:

I am in 8th grade Ik wut the answer is bro

The single Trigonometric function is √2/2.

Trigonometric Function:

In mathematics, trigonometric functions (also called circular functions, trigonometric functions, angular functions) are real functions that relate the angles of a right-angled triangle to the ratio of the lengths of its two sides. They are widely used in all geometry-related sciences such as navigation, solid mechanics, celestial mechanics, and geodesy. They are one of the simplest periodic functions and are often used to study periodic phenomena using Fourier analysis.

The most commonly used trigonometric functions in modern mathematics are sine, cosine, and tangent. Their reciprocals are cosecane, secane, and cotangent, respectively, and are seldom used. Each of these six trigonometric functions has a corresponding inverse and a hyperbolic analogue.

According to the question:

Following are the solution to the given expression:

Given:

0 < x < π/2

[tex]\frac{sin \frac{x}{2} + cos \frac{x}{2} }{1-cos \frac{x}{2} }[/tex]

To find:

value=?

Solution:

0 < x < π/2

[tex]\frac{sin \frac{x}{2} + cos \frac{x}{2} }{1-cos \frac{x}{2} }[/tex]

Now,

Let x = π/2

[tex]\frac{sin \frac{x}{2} + cos \frac{x}{2} }{1-cos \frac{x}{2} }[/tex]

[tex]\frac{\frac{1}{\sqrt{2} * 1} }{1-0}[/tex]

[tex]\frac{1}{\sqrt{2} } * \frac{\sqrt{2} }{\sqrt{2} }[/tex]

[tex]\frac{\sqrt{2} }{2}[/tex]

Therefore, the answer is [tex]\frac{\sqrt{2} }{2}[/tex].

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===================================================

Explanation:

The sequence appears to be geometric. Let's test that claim out.

Divide each term by the previous term.

Each time we get the result 0.2, which is the common ratio r. It tells us this sequence is indeed geometric.

To get the next term in a geometric sequence, we multiply the last term 2500 by this common ratio.

Follow similar steps for terms 6 through 8.

Terms 5 through 8 are 500, 100, 20, and 4 in that order.

The area of the rectangle is [tex]60x^{7y^{9} }[/tex] whoe ide are 12x to the power of 6 y quared and 5xy to the power of 7.

What is rectangle ?

A rectangle is a type of quadrilateral that has its parallel sides equal to each other and all the four vertices are equal to 90 degrees. Hence, it is also called an equiangular quadrilateral. Since, the opposite sides are equal and parallel, in rectangle, therefore, it can also be termed as a parallelogram.

The area of a rectangle is found by multiplying its length by its width. In this case, the length is given as [tex]12x^{6y^{2} }[/tex]and the width is given as [tex]5xy^{7}[/tex]. To find the area, we simply multiply these two values together:

Area = ([tex]12x^{6y^{2} }[/tex]) * ([tex]5xy^{7}[/tex]) = [tex]60x^{7y^{9} }[/tex]

So the area of the rectangle is [tex]60x^{7y^{9} }[/tex]  whoe ide are 12x to the power of 6 y quared and 5xy to the power of 7.

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Exponential growth occurs when an entity experiences a rapid increase in size or output. This type of growth can be seen in companies, economies, and populations, and it requires certain conditions to be in place in order to be successful.

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Charlotte and her sister enjoyed a special dinner in a restaurant, and the bill was $53.86. 11.99%  tip did she leave.

Percent tip she give:

[tex]\frac{6.46}{53.86}[/tex] × 100

= 11.99 %

A percentage, or percent, is a number smaller than or equal to 100. The term "per 100" refers to a percentage of a total amount. 45 percent, for instance, is 45 out of 100. Finding the share of a whole in terms of 100 is what percentage means. You can use online calculators or manually calculate it.

Percentages are utilized extensively and in numerous contexts. Discounts in stores, interest rates at banks, inflation rates, and numerous media statistics are all expressed as percentages. Understanding the financial aspects of everyday life requires knowledge of percentages.

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