The triangles are similar.
What is the value of x?

See the attachment for the problem to be answered.

In rectangle WXYZ, the length of each diagonal are 40.97 units and 39.98 units.

To find the lengths of the diagonals of rectangle WXYZ, we can use the Pythagorean theorem.

The diagonal WX is the hypotenuse of right triangle WXY, so we have:

WX^2 = WY^2 + XY^2

Similarly, the diagonal YZ is the hypotenuse of right triangle XYZ, so we have:

YZ^2 = XY^2 + XZ^2

Substituting the given values for WY and XZ, and x = 2, we get:

WY = 24(2) - 8 = 40

XZ = -18(2) + 13 = -23

Plugging these values into the equations above and simplifying, we get:

WX^2 = 40^2 + XY^2

YZ^2 = XY^2 + (-23)^2

Since XY is a common side of both triangles, we can solve for it by setting the two expressions for XY^2 equal to each other:

40^2 + XY^2 = XY^2 + (-23)^2

Simplifying, we get:

40^2 + 23^2 = 2XY^2

XY^2 = (40^2 + 23^2) / 2 = 1039

Substituting this value for XY^2 in the equations for WX^2 and YZ^2, we get:

WX^2 = 40^2 + 1039 = 1679

YZ^2 = 1039 + (-23)^2 = 1598

Taking the square roots, we get:

WX = sqrt(1679) ≈ 40.97

YZ = sqrt(1598) ≈ 39.98

Therefore, the length of each diagonal of Rectangle are approximately 40.97 units and 39.98 units.

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_____The given question is incomplete, the complete question is given below:

Find the lengths of the diagonals of rectangle WXYZ.

WY = 24x-8

XZ = -18x+13

x= 2

The length of each diagonal is ___ units.

power of ten

Step-by-step explanation:

The factored form of 8x^2+2x-3 is (8x-3)(x+1).

The factored form of 16x^2-1 is (4x+1)(4x-1). The expression 6x^2+1 cannot be factored further,

So the factored form of 36x^2+6 is 6(6x^2+1).

Factoring is a mathematical process that involves breaking down a complex expression into simpler terms that can be multiplied together to obtain the original word. In algebra, factoring is finding the factors or the prime numbers that multiply together to give the original polynomial.

For example, the expression x^2 + 5x + 6 can be factored as (x+2)(x+3). Factoring is a useful tool in solving equations and simplifying expressions, as it allows us to manipulate the original expression in a more manageable way. In addition, factoring is used in various fields such as cryptography, signal processing, and computer science. For instance, factoring large numbers is an important problem in cryptography and is used to secure data transmission.

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Answer:

m<a = 44°

Step-by-step explanation:

Left triangle:

95 + 39 + x = 180

x = 46

Right triangle:

46 + 90 + a = 180

a = 44

Answer:

164 degree is the answer

Answer:

Step-by-step explanation:

Chord PM and PN are equal

arc PM = arc PN

164=5x+4

x=32

arc PN = 5x+4 = 5(32)+4=164

It is not possible to determine the greatest number of people Monica can serve with pasta bake based solely on the information provided.

The amount of milk and other ingredients she has does not necessarily indicate how many portions she can make. Other factors such as the recipe she is using, the size of each serving, and the equipment she has available will also impact how many people she can serve. In order to determine the number of portions she can make, more information is needed about the recipe and the serving size she is aiming for.It is not possible to determine the greatest number of people Monica can serve with pasta bake based solely on the information provided.

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The blue box measures about 641.667 cm in length.

The width and length of a figure indicate its breadth and length, respectively. The term "breadth" is also used to describe width. Although breadth and width are synonymous (thus the idiom hair's breadth, denoting a very small width), there are two significant differences between the two.

We are aware that the blue box's width is 18 cm, which is smaller than the green box's width (70cm).

As a result, the value of "k" must be lower than 1. By creating a proportion, we can determine the value of "k":

width of green box / width of blue box = k

70 / 18 = k

k = 70/18

k ≈ 3.8889

So the factor "k" is approximately 3.8889. To find the length of the blue box, we can use this factor to scale the length of the green box:

length of blue box = k * length of green box

length of blue box = 3.8889 * 165cm

length of blue box ≈ 641.667cm

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Answer:

Option 1 and 5 will be your answer :)

Step-by-step explanation:

Let the equation representing number of sold is,

y - y' = m(x - x')

Where m = number of condo sold per month  

(x', y') is a point from the given table,

Slope of line passing through two points  and  =

Slope of the passing through (1, 8) and (0, 11) will be,

m =  = -3

Therefore, equation of the line passing through (3, 2) and slope (-3),

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

y - 2 = -3(x - 3)

Similarly, equation of the line passing through (0, 1) and slope (-3),

y - 11 = -3(x - 0)

Therefore, Option (1) and (5) will be the answer.

The complete question:

The stem-and-leaf plot shows the test scores for a chemistry class.

How many students had a score greater than 90 points?

A. 6

B. 7

C. 8

D. 9

Solution:

The number of students had a score greater than 90 points is 7. So option B is correct.

A stem-and-leaf plot is a type of data visualization that shows the distribution of a set of data. It is particularly useful for small to medium-sized data sets. In a stem-and-leaf plot, each data point is split into two parts: the stem and the leaf. The stem is the leftmost digit or digits of the data point, and the leaf is the rightmost digit.

To the left of the vertical bar are the tens places.

As we want to find the scores greater than 90, we start at the row in the stem and leaf plot with a 9 to the left.

To the right are 6 values - 1, 2, 3, 4, 6, and 7.

So there are six scores here higher than 90:

91, 92, 93, 94, 96, and 97.

Now we move lower to 10 in the tens place.

There is one score there - 100. (That smart kid.)

Total up the six scores in the 9 row and the 1 in the 10 row to get 7 scores higher than 90 in this stem and leaf plot.

Hence, the number of students is 7

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Answer: D and C

Step-by-step explanation:

To get the value of a market basket you would add up the cost of each year so

2019 market basket = 2.50 + 1.00 + 3.75 = 7.25

2020 market basket = 2.25 + 3.00 + 4.50 = 9.75

2021 market basket = 3.00 + 3.25 + 5.00 = 11.25

now CPI for 2020 would be 9.75 / 7.25 x 100 = 134.828 which is around 135

CPI 2021 would be 11.25 / 7.25 x 100 = 155.172 which is around 155

By inspection, the following products which are multiples of 30 are:

This is referred to as a number that may be divided by another a certain number of times without a remainder.

The multiple of 30 in the options are those who have 2, 3 and 5 as the common values and is therefore the reason why options A, C and D  were chosen as the correct choice.

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The number of elements in the sample space for this experiment is 969.

If a person eating at a cafeteria must choose 3 of 19 vegetables on offer, we can calculate the number of elements in the sample space, or the total number of possible outcomes, using the formula for combinations:

nCr = n! / [r!(n - r)!]

where n is the total number of items in the set and r is the number of items being chosen.

In this case, we have 19 vegetables and we want to choose 3 of them, so we can plug in n = 19 and r = 3:

19C3 = 19! / [3!(19 - 3)!]

= 19! / (3!)(16!)

= 969

Therefore, there are 969 possible combinations of 3 vegetables that a person can choose from a selection of 19 vegetables.

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The account's balance after 5 years is given as follows:

[tex]A(5) = P\left(1 + \frac{r}{4}\right)^{20}[/tex]

In which:

The amount of money earned, in compound interest, after t years, is given by:

[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]

In which:

Quarterly compounding means that the value of n is given as follows:

n = 4.

Then the balance of the account after 5 years, when t = 5, is given as follow:

[tex]A(5) = P\left(1 + \frac{r}{4}\right)^{20}[/tex]

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Exponents, terms in parenthesis, multiplication, division, addition, and finally subtraction. You can use PEMDAS as a helpful acronym to help you remember this.

[tex]$\frac{4 x^2+12 x-16}{\frac{2 x+10}{\frac{6 x+24}{x^2+9 x+20}}}$[/tex]

Here we have two fractions top and bottom

[tex]$\frac{4 x^2+12 x-16}{2 x+10}$ divide by $\frac{6 x+24}{x^2+9 x+20}$[/tex]

We have division in between . we reverse the second fraction and multiply it with first fraction.

[tex]$\frac{4 x^2+12 x-16}{2 x+10} * \frac{x^2+9 x+20}{6 x+24}$[/tex]

Now we factor both numerator and denominator

[tex]$\begin{aligned} & 4 x^{\wedge} 2+12 x-16=4(x+4)(x-1) \\ & 2 x+10=2(x+5) \\ & x^{\wedge} 2+9 x+20=(x+5)(x+4) \\ & 6 x+24=6(x+4)\end{aligned}$[/tex]

Replace the factors,

[tex]$\frac{4(x+4)(x-1)}{2(x+5)} * \frac{(x+5)(x+4)}{6(x+4)}$[/tex]

We cancel out same factors at the top and bottom

So it becomes ,[tex]$\frac{(x-1)(x+4)}{3}$[/tex]

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The force is 80,000 Dynes.

We know that when we talk about the joint variation then we have a lot of variables that are being altered at the same time and this is what we are going to work on in the questions that we have here.

We are told that;

C α mr/t^2

Then;

C = kmr/t^2

k = Ct^2/mr

k = 6000 * 2^2/6 * 10

k = 400

Then, to find C;

C = 400 * 18 * 100/3^2

C = 80,000 Dynes

\

Hence, we can see from the calculation that the centrifugal force that is required is 80,000 Dynes.

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The exponential function that shows Riley's target mileage is y = 12(1.1)ˣ

An equation is an expression that shows how numbers and variables are linked together using mathematical operations such as addition, subtraction, multiplication and division.

The standard exponential equation is:

y = abˣ

where b is the rate of change and a is the initial value.

Let y represent Riley target mileage x weeks after she starts training.

She plans to run 12 miles in her first week of training and will increase her mileage by about 10% each week after. Hence:

a = 12; b = 100% + 10% = 110% = 1.1

The exponential function is y = 12(1.1)ˣ

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For the given equation which shows the relation of temperature in Celsius and Fahrenheit, the correct option is Option D.

What is meant by temperature?

Indicating the direction in which heat energy will naturally flow from a hotter body (one with a higher temperature) to a colder body(one at a lower temperature), the temperature is a measure of hotness or coldness defined in terms of any of several arbitrary scales.

The given equation is:

[tex]C = \frac{5}{9} (F- 32)[/tex]

where C = temperature in Celsius

          F = temperature in Fahrenheit

The above equation can be rewritten as:

C = 5/9F - 160/9

Now, this is an equation of a straight line with a formula,

y = mx + c

Comparing,

m = 5/9 which is the slope of the equation.

This means that for a temperature increase of 1 degree Fahrenheit, the equivalent increase in temperature in Celsius is 5/9.

So the option I is true.

Similarly, an increase in 1 degree Celsius of temperature is equivalent to 9/5 = 1.8 degree increase in Fahrenheit.

So option II is true.

Option III is not true as is discussed above.

Therefore for the given equation of temperature, the correct option is Option D.

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Answer:

D

Step-by-step explanation:

I have nothing else to say- lol

The profit of the company if the company has 1800 customers is 649124 dollars

What is profit ?

A monetary gain, specifically the sum remaining after expenses for purchasing, running, or producing an item have been deducted.

P = 8.5√c³  ------->(1)

c = 1800 customers = 18 hundreds

(1) => P = 8.5√(18)³

           = 8.5 √5832 ( cube of 18=5832

          = 8.5 * 76.3675

          = 649.124 thousands of dollars

( convert into dollars by multiplying by 1000)

          = 649124.025 dollars  

          ≈ 649124 dollars

The profit of the company if the company has 1800 customers is 649124 dollars

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Answer: 48148

Step-by-step explanation:

Answer:

123.88 square units

Step-by-step explanation:

r = radius of circle

  = radius of sector

 = Length of LM

 = Length of MN

 = 13 units

When the angle is measured in degrees:
Area of a sector: [tex]\frac{Angle OfSector}{360^{o}}[/tex]× [tex]\pi r^{2}[/tex]

                = [tex]\frac{84}{360}[/tex]×[tex][\pi (13)^{2}][/tex]

                = 123.883 [tex]units^{2}[/tex]

                = 123.88 square units (Rounded to the nearest hundredth)

The value of the trigonometric relation cos ∠O = 0.849

Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles

The six trigonometric functions are sin , cos , tan , cosec , sec and cot

Let the angle be θ , such that

sin θ = opposite / hypotenuse

cos θ = adjacent / hypotenuse

tan θ = opposite / adjacent

tan θ = sin θ / cos θ

cosec θ = 1/sin θ

sec θ = 1/cos θ

cot θ = 1/tan θ

Given data ,

Let the triangle be represented as ΔPQR

Now , the measure of ∠PQR = 90° and it is a right triangle

The measure of the hypotenuse PO = 53

The measure of adjacent side OQ = 45

The measure of opposite side QP = 28

Now , from the trigonometric relations ,

cos θ = adjacent / hypotenuse

cos θ = OQ / PO

Substituting the values in the equation , we get

cos θ = 45 / 53

cos θ = 0.849

Therefore , the value of cos ∠O is 0.849

Hence , the trigonometric relation cos θ = 0.849

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Answer:

x=-2(3-2√2), -2(3+2√2)

Answer:

75.50 + 14x - (35.50 + 9x) = 40 + 5x

Step-by-step explanation:

The ratio used to find the measurement of angle x is given as follows:

cos(x) = 40/68.

The three trigonometric ratios are defined as follows:

For angle x, we have that:

Hence the ratio is given as follows:

cos(x) = 40/68.

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The distance travelled by Rahul at a speed of 0.5 miles/min in 180 minutes is 90 miles.

What is meant by the speed of an object?

A scalar quantity, speed is defined as the magnitude of the change in an object's location over time. The rate at which an object travels a distance can be thought of as its speed. A fast-moving object travels at a high speed and completes a significant distance in a brief period of time. This is in contrast to an object travelling slowly, which travels a relatively short distance in the same length of time. Zero speed refers to an object that is not moving at all.

The formula of speed = Distance covered /Time taken

Given,

Distance travelled = 10 miles

Time taken to travel 10 miles = 20 minutes

Speed = Distance/ time = 10/20 = 0.5miles/min

Now given the speed remains constant throughout the journey.

So the distance travelled in 3 hours = 3 * 60 = 180 minutes

Distance = speed * time = 0.5 * 180 = 90 miles.

Therefore the distance travelled by Rahul at a speed of 0.5 miles/min in 180 minutes is 90 miles.

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Answer:

1.666... or 1 2/3

Step-by-step explanation:

The table needs to change number of Bags to Clementines.

And we know that they are only sold in pairs of 3 so we divide 5 by 3 to find the unit price

The total surface area of the given prism would be = 504

The formula that can be used to calculate the total surface area of a square prism = 2a² + 4a L

where a = 7

L = 14.5

Area = 2(7²) + 4 ( 7× 14.5)

= 2×49 + 4( 101.5)

= 98 + 406

= 504

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Answer:

B, C, A.

Step-by-step explanation:

In order to find the angles of triangle KLM and their order from least to greatest, we need to use the Law of Cosines and the perimeter equation of the triangle. The Law of Cosines states that in any triangle, the square of the length of one side is equal to the sum of the squares of the lengths of the other two sides minus twice the product of the lengths of these sides and the cosine of the angle between them.

Let's assume that the length of sides KL, LM, and KM are x - 4, x + 4, and 2x - 1, respectively. We can use the Law of Cosines to find the cosine of the angle between KM and KL:

cos A = (x - 4)^2 + (2x - 1)^2 - (x + 4)^2 / 2 * (x - 4) * (2x - 1)

Next, we can use the perimeter equation of the triangle, which is

KL + LM + KM = 27, to find the value of x:

x - 4 + x + 4 + 2x - 1 = 27

4x = 36

x = 9

So, the lengths of the sides of the triangle are

KL = x - 4 = 5, LM = x + 4 = 13, and KM = 2x - 1 = 17.

Next, we can use the Law of Cosines to find the cosine of the angle between KM and KL:

cos A = (5)^2 + (17)^2 - (13)^2 / 2 * (5) * (17)

cos A = 74 / 60

A = cos^-1 (74/60) = approximately 49.7°

Finally, we can use the perimeter equation of the triangle and the Law of Sines to find the other two angles of the triangle:

B + C = 180° - 49.7° = 130.3°

B / sin B = LM / sin A

B = sin^-1 (sin B / sin A) * LM / sin A

C = 130.3° - B

The angles of triangle KLM in order from least to greatest are approximately:

B, C, A.