If ALMN - ALOP by the SAS similarity theorem, what is LM? Show your work.

If ALMN - ALOP By The SAS Similarity Theorem, What Is LM? Show Your Work.

Answers

Answer 1

Answer:

LM = 40

Step-by-step explanation:

since the triangles are similar then the ratios of corresponding sides are in proportion, that is

[tex]\frac{LM}{LO}[/tex] = [tex]\frac{LN}{LP}[/tex] ( substitute values )

[tex]\frac{LM}{5}[/tex] = [tex]\frac{14+2}{2}[/tex] = [tex]\frac{16}{2}[/tex] = 8 ( multiply both sides by 5 )

LM = 5 × 8 = 40


Related Questions

Match each sum or difference with the correct simplified expression.
(x-5)-(x + 1)
(x-5)+ (x + 1)
(x-5)+ (x-1)
(x-5)-(x-1)
Intro
-4
2x-6
-6
2x-4

Answers

Answer:

Step-by-step explanation:

[tex](x-5)-(x + 1)=x-5-x-1=-6[/tex]

[tex](x-5)+ (x + 1)=x-5+x+1=2x-4[/tex]

[tex](x-5)+ (x-1)=x-5+x-1=2x-6[/tex]

[tex](x-5)-(x-1)=x-5-x+1=-4[/tex]

Translate the verbal phrase into a mathematical expression. Use x to represent the unknown number.
the product of 6 less than a number and 2 more than the number

The complete verbal phrase translates to
(Do not perform the calculation.)

Answers

The expression represents the product of two terms = (x - 6) × (x + 2)

What do you mean by Linear Equation ?

An equation in mathematics that is linear has a variable whose maximum power is 1. Alternatively said, it is an algebraic equation of the following form:

ax+ b = 0

where an is a constant that cannot equal zero, b is a constant, and x is a variable. Another way to express a linear equation in its general form is as follows:

y = mx + b

where the y variable is the dependent variable, the independent variable is x, the slope is m, and the y-intercept is b.

The product of 6 less than a number and 2 more than the number can be translated into the mathematical expression:

(x - 6) × (x + 2)

Here, x represents the unknown number, and the expression represents the product of two terms: "6 less than a number" (x - 6) and "2 more than the number" (x + 2).

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evaluate the expression -5+7-(-3)

Answers

Answer:

the answer is 5........

Answer: I rechecked and confirmed the answer. The answer is 5.

Lynne read 2.5 chapters of her book on Tuesday, 4.25 chapters on Wednesday, and 5 chapters on Thursday. How many chapters did she read in total during those three days? I think you have to add them

Answers

Answer:

11.75

Step-by-step explanation:

2.5 + 4.25 + 5

Answer:

11.75 chapters in total

Step-by-step explanation:

Given:

2.5, 4.25, 5

The question ask for total

2.5 + 4.25 + 5 = 11.75

How many different committees can be formed from 12 teachers and 43 students if the committee consists of 2 teachers and 2 students

Answers

Answer: 59598

Step-by-step explanation:

It would be 12C2 for the teachers

and 43C2 for the students

12C2=66

43C2=903

66*903=59598

pls help lol it’s due tomorrow

Answers

Answer: 100 degrees
(If you need an explanation, just comment)
(Also if you can please give me brainliest)

You spin the spinner once. 123 What is P(odd or divisor of 54)? Simplify your answer and write it as a fraction or whole number.

Answers

After answering the given question, we can conclude that As a result, the probability of receiving an odd or a divisor of 54 is one, or 100% confidence.

What is probability?

Probability is a gauge of how likely an occurrence is to occur. It is represented by a figure between 0 and 1, with 0 representing an unlikely occurrence and 1 representing an inevitable event. Switching a fair coin and coin turns has a chance of 0.5 or 50% because there are two equally likely results. (Heads or tails). Probability theory is a branch of mathematics that studies random occurrences rather than their characteristics. It is applied in many areas, including statistics, economics, science, and engineering.

There are three equally probable results from the spinner: 1, 2, and 3. To determine the likelihood of receiving an odd or divisor of 54, we must tally the number of events that meet this requirement.

54 has divisors of 1, 2, 3, 6, 9, 18, 27, and 54. Only one, three, and nine are unusual. As a result, the potential results that are either odd or divisors of 54 are 1, 3, and 2.

P(odd or divisor of 54) = P(1) + P(2) + P(3) + P(9) = 1/3 + 1/3 + 1/3 + 0 (because 9 is not a spinning choice) = 1

As a result, the chance of receiving an odd or a divisor of 54 is one, or 100% confidence.

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What would be the total amount of money she made in the month if she babysat 10
days?
The total would be ____ dollars

Answers

The total earnings for the month if she babysat 10 days would be $360.

How are the total earnings determined?

Using the mathematical operation of multiplication, the total earnings can be determined as follows:

Multiplication operation involves the multiplicand, the multiplier, and the product.

Hourly pay rate = $4.50

Daily working hours = 8 hours

The number of days worked in the month = 10 days

Total working hours for the month = 80 hours (10 x 8)

Total earnings for the month = $360 ($4.50 x 80)

Thus, we can conclude that she earned $360 gross for the month.

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Question Completion:

Assuming that the Hourly pay rate is $4.50 and she worked for 8 hours daily.

2. You check 50 cartons of eggs. Eight of the cartons have at least one
cracked egg. What is the experimental probability that a carton of ega
has no cracked eggs?

Answers

Answer: 3/20 and 15%

Step-by-step explanation:

I NEED HELP ON THIS

Answers

The expression that correctly name the angle below is ∠K, So correct option is C.

Describe Angles?

In geometry, an angle is a figure formed by two rays, or half-lines, that originate from a common endpoint, which is called the vertex. The rays can be thought of as emanating from the vertex and extending infinitely in opposite directions.

The measure of an angle is typically given in degrees, where a full circle is 360 degrees. Angles can be classified according to their size:

An acute angle is less than 90 degrees.

A right angle measures exactly 90 degrees.

An obtuse angle is greater than 90 degrees but less than 180 degrees.

A straight angle measures exactly 180 degrees.

A reflex angle is greater than 180 degrees but less than 360 degrees.

A full angle measures exactly 360 degrees.

Angles can also be classified based on their position relative to other angles or lines:

Adjacent angles share a common vertex and one common side.

Complementary angles add up to 90 degrees.

Supplementary angles add up to 180 degrees.

Vertical angles are formed by two intersecting lines and are opposite each other.

The expression that correctly name the angle below is ∠K.

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The answer C is accurate since the formula that correctly identifies the angle below is ∠K.

Describe Angles?

An angle is a figure in geometry made up of two rays, or half-lines, that start from a single endpoint known as the vertex. You can imagine the rays coming from the vertex and continuing in opposing directions indefinitely.

A whole circle has 360 degrees, hence an angle is commonly measured in degrees. Angles can be grouped based on their size:

Any angle that is below ninety degrees is considered acute.

Obtuse angles are those that are greater than 90 degrees but below 180 degrees.

The length of a straight angle is 180 degrees.

A reflex angle is one that is above 180 degrees and less than 360 degrees.

Angles can also be categorised according on where they are situated in relation to other angles or lines:

Adjacent angles have one shared side as well as a common vertex.

Complementary angles add up to 90 degrees.

The sum of all supplementary angles is 180 degrees.

Two intersecting lines that are opposite one another form vertical angles.

The formula K accurately identifies the angle below.

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PLEASE I REALLY NEED HELP PLEASE

A car was valued at $45,000 in the year 1991. The value depreciated to $12,000 by the year 2000.

A) What was the annual rate of change between 1991 and 2000?
r=-------------Round the rate of decrease to 4 decimal places.

B) What is the correct answer to part A written in percentage form?
r=------------%

C) Assume that the car value continues to drop by the same percentage. What will the value be in the year 2003 ?
value = $----------------Round to the nearest 50 dollars.

Answers

A)  The annual rate of change or APR between 1991 and 2000 is approximately -0.1091.

B) The correct answer to part A in percentage form is approximately -10.91%.

C) The value of the car in 2003 is $7,750.

What is annual rate?

The car depreciated from $45,000 to $12,000 in 9 years. Using the formula for annual rate of change or annual percentage rate (APR):

r = [tex](Vf/Vi)^{1/n}[/tex] - 1

where Vf is the final value, Vi is the initial value, n is the number of years, and r is the annual rate of change or APR.

Substituting the given values:

r = [tex]($12,000/$45,000)^{1/9}[/tex] - 1

r ≈ -0.1091

Therefore, the annual rate of change or APR between 1991 and 2000 is approximately -0.1091.

B) The correct answer to part A in percentage form is approximately -10.91%.

What is APR?

To express the answer as a percentage, multiply the annual rate of change by 100 and round to the nearest 0.01%:

r = -0.1091 × 100

r ≈ -10.91%

Therefore, the correct answer to part A in percentage form is approximately -10.91%.

C) The value of the car in 2003 is $7,750.

What is the value?

To find the value of the car in 2003, we need to use the same percentage rate of decrease from 2000 to 2003. Since 2003 is 3 years after 2000, the value will be:

value = $12,000 × (1 + r)³

value ≈ $7,729.18

Rounding to the nearest 50 dollars, the value of the car in 2003 is $7,750.

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Pls help, Micheal tracked the value of his boat each year after he purchased it. Determine whether the data are linear, quadratic, or exponential. Use regression to the function that models the data.

Answers

This means that after two years since the purchase, the boat was worth $24.57.

What is worth?

In general, worth refers to the value or monetary equivalent of something. It can be used to describe the financial value of assets such as property, stocks, or commodities, or to describe the value of something in terms of its usefulness, importance, or significance.

Michael tracked the value of his boat each year after he purchased it. Determine whether the data are linear, quadratic, or exponential. Use regression to find the function that models the data.

16.75

19.5

4

3

22.9

27.25

2

1

32

0

Years Since Purchase

To better understand the exponential function that models the data, let's break it down:

y = 10.92 * 1.50ˣ

The constant "10.92" represents the initial value of the boat when it was purchased. This means that the boat was worth $10.92 when Michael first bought it.

The constant "1.50" represents the growth factor of the boat's value. This means that each year, the value of the boat increases by a factor of 1.50.

The variable "x" represents the number of years since the boat was purchased. The function takes this input and returns the value of the boat at that time.

For example, if we plug in x=1 into the function, we get:

y = 10.92 * 1.50¹

y = 16.38

This means that after one year since the purchase, the boat was worth $16.38. Similarly, if we plug in x=2 into the function, we get:

y = 10.92 * 1.50²

y = 24.57

This means that after two years since the purchase, the boat was worth $24.57.

It's important to note that the exponential function assumes that the growth rate remains constant over time. In reality, the value of the boat may be affected by other factors such as wear and tear, maintenance, and market fluctuations. Nevertheless, the exponential function provides a useful model for understanding the trend in the data and making predictions about the future value of the boat.

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Use substitution to determine whether the given number is a zero of the given
polynomial.
3; f(x) = -x^4 -8x²-x-5


also

Answers

As f(3) is not equal to zero, 3 is not a zero of the polynomial f(x) = -x⁴ -8x²-x-5.

How to determine whether a given number is a zero of the a polynomial?

Given the polynomial in the question;

f(x) = -x⁴ -8x²-x-5

Given number: 3

To check if 3 is a zero of the polynomial f(x) = -x⁴ -8x²-x-5, we need to substitute x = 3 into the polynomial and see if the result will give zero.

f(x) = -x⁴ -8x²-x-5

plug i x = 3

f(3) = -3⁴ - 8(3)² - 3 - 5

= -81 - 72 - 3 - 5

= -161

Therefore, 3 is not a zero of the polynomial f(x) = -x⁴ -8x²-x-5.

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A triangle is shown with its exterior angles. The interior angles of the triangle are angles 2, 3, 5. The exterior angle at angle 2 is angle 1. The exterior angle at angle 3 is angle 4. The exterior angle at angle 5 is angle 6. Which statements are always true regarding the diagram? Select three options. m∠5 + m∠3 = m∠4 m∠3 + m∠4 + m∠5 = 180° m∠5 + m∠6 =180° m∠2 + m∠3 = m∠6 m∠2 + m∠3 + m∠5 = 180°

Answers

Answer:

1.  m∠5 + m∠6 = 180°

2. ∠ 2+ ∠ 3 = ∠ 6

3. m∠2 + m∠3 + m∠5 = 180°

Step-by-step explanation:

IF ITS WRONG CONTACT ME AND I WILL FIX IT

please send the correct answer

Answers

The values that complete the missing segments are shown below

Completing the missing segments

From the question, we have the following parameters that can be used in our computation:

Blue segment = length of the rectangle

Where

length of the rectangle = radius of circle

So, we have

Blue segment = 12 units

Similarly, we have

Violet segment = width of rectangle

So, we have

Violet segment = 18 units

The green segment is the base circumference

So, we have

Green segment = 2 * 22/7 * 12

Green segment = 75.4 units

The orange segment is the diameter

So, we have

Orange segment = 2 * 12

Orange segment = 24

The area of one base is

Area of one base = 22/7 * 12^2

Area of one base = 452.4

The area of one rectangle is

Area of rectangle = 12 * 18

Area of rectangle = 216

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Solve the right
triangle.
...
$
Find the measure of ZB.
A
35°
19
B
C
mZB= (Round to one decimal place as needed.)
C

Answers

Answer:

∠ B = 55°

Step-by-step explanation:

the sum of the 3 angles in triangle = 180° , that is

∠ B + 35° + 90° = 180°

∠ B + 125° = 180° ( subtract 125° from both sides )

∠ B = 55°

At this year's State Fair, there was a dice rolling gamne. If you rolled two dice and got a sum of 2 or 12, you won $12. If you rolled a 7, you won $5. Any other roll was a loss. It cost $1 to play one game with one roll of the dice. What is the expectation of the game? Round your answer to the nearest cent.
The expectation of this game is approximately dollars.

Answers

the expectation of the game is $0.22 per game. This means that on average, for every game played, the player can expect to win $0.22. However, this does not guarantee that the player will actually win $0.22 every time they play the game. It simply means that over many plays of the game, the player's winnings will average out to $0.22 per game.

How to solve the probability?

To find the expectation of the game, we need to calculate the probability of winning and losing and multiply them by their corresponding payoffs.

First, let's calculate the probability of rolling a sum of 2 or 12. There is only one way to roll a sum of 2 or 12, which is by rolling a pair of ones or a pair of sixes, respectively. So, the probability of rolling a sum of 2 or 12 is:

P(2 or 12) = P(1,1) + P(6,6) = (1/6) * (1/6) + (1/6) * (1/6) = 1/18

Next, let's calculate the probability of rolling a 7. There are six ways to roll a sum of 7, which are: (1,6), (2,5), (3,4), (4,3), (5,2), and (6,1). So, the probability of rolling a 7 is:

P(7) = P(1,6) + P(2,5) + P(3,4) + P(4,3) + P(5,2) + P(6,1) = 6 * (1/6) * (1/6) = 1/6

Finally, the probability of losing is:

P(loss) = 1 - P(2 or 12) - P(7) = 1 - 1/18 - 1/6 = 11/18

Now, we can calculate the expectation of the game as follows:

E(X) = (12 * P(2 or 12)) + (5 * P(7)) - (1 * P(loss))

= (12 * 1/18) + (5 * 1/6) - (1 * 11/18)

= 2/9 + 5/6 - 11/18

= 0.22

So, the expectation of the game is $0.22 per game. This means that on average, for every game played, the player can expect to win $0.22. However, this does not guarantee that the player will actually win $0.22 every time they play the game. It simply means that over many plays of the game, the player's winnings will average out to $0.22 per game.

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What was the age distribution of prehistoric Native Americans? Suppose an extensive anthropological studies in the southwestern United States gave the following information about a prehistoric extended family group of 84 members on what is now a Native American reservation.
Age range (years) 1-10 11-20 21-30 31 and over
Number of individuals 35 22 20 7
For this community, estimate the mean age expressed in years, the sample variance, and the sample standard deviation. For the class 31 and over, use 35.5 as the class midpoint. (Round your answers to one decimal place.)
x =
years
s2 =
s =
years

Answers

Mean age: 16.1 years, Sample variance: 50.47 square years and Sample standard deviation: 7.10 years for the given problem.

To estimate the mean age, we need to find the midpoint of each age range and multiply it by the number of individuals in that range. Then we add up these products and divide by the total number of individuals:

Mean age = [(1+10)/2 x 35 + (11+20)/2 x 22 + (21+30)/2 x 20 + 35.5 x 7] / 84

= (5.5 x 35 + 15.5 x 22 + 25.5 x 20 + 35.5 x 7) / 84

= 16.1

Therefore, the estimated mean age of this extended family group is 16.1 years.

To calculate the sample variance, we need to find the deviation of each age from the mean, square each deviation, and add up these squared deviations. Then we divide this sum by the total number of individuals minus one:

s2 = [(1-16.1)2 x 35 + (11-16.1)2 x 22 + (21-16.1)2 x 20 + (35.5-16.1)2 x 7] / (84-1)

= (2254.05 + 537.08 + 220.89 + 253.68) / 83

= 50.47

Therefore, the estimated sample variance is 50.47 square years.

We simply take the square root of the sample variance to calculate the sample standard deviation:

s = [tex]\sqrt{s2}[/tex]

= s[tex]\sqrt{50.47}[/tex]

= 7.10

Therefore, the estimated sample standard deviation is 7.10 years.

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1. Solve the following system of equations graphically. Make sure to check the solution.

y = 1/2x - 3
y = 3/4x + 2

Answers

Answer:

Step-by-step explanation:

The average retail price of gasoline (all types) for the first half of 2005 was 212.2 cents. What would the standard deviation have to be in order for a 11% probability that a gallon of gas costs less than $1.80? Round z-value calculations to two decimal places and final answer to the nearest cent.

Answers

Given:

Average retail price of gasoline (all types) for the first half of 2005 = 212.2 cents
Probability that a gallon of gas costs less than $1.80 = 11%
We need to find the standard deviation required for this probability
First, we need to convert the price of $1.80 to cents:
$1.80 = 180 cents

Next, we need to find the z-score corresponding to the 11th percentile (since we want the probability of a price less than $1.80):
Using a standard normal distribution table or calculator, we find that the z-score for the 11th percentile is approximately -1.22.

Now, we can use the formula for z-score to find the standard deviation:
z = (x - μ) / σ
where:
z = -1.22
x = 180 cents (price of gas)
μ = 212.2 cents (average price of gas)
σ = standard deviation

Rearranging the formula and substituting the values, we get:
σ = (x - μ) / z
σ = (180 - 212.2) / (-1.22)
σ = 26.2 / 1.22
σ ≈ 21.48

Therefore, the standard deviation required for an 11% probability that a gallon of gas costs less than $1.80 is approximately 21.48 cents.

Select "Growth" or "Decay" to classify each function.


y=200(0.5)2t = DECAY

y=12(2.5)t6 = GROWTH

y=(0.65)t4 = DECAY

just took the test

Answers

y=200(0.5)2t  this functiοn represents decay, y=12(2.5)t6 this functiοn represents grοwth and y=(0.65)t4 this functiοn represents decay.

What is functiοn?

In mathematics, a functiοn is a relatiοnship between twο sets οf elements, called the dοmain and the range, such that each element in the dοmain is assοciated with a unique element in the range.

In general, we can determine whether a functiοn represents grοwth οr decay by examining the base οf the expοnential term.

If the base is greater than 1, the functiοn represents grοwth.

If the base is between 0 and 1, the functiοn represents decay.

Here are the classificatiοns fοr each οf the given functiοns:

y=200(0.5)2t

The base οf the expοnential term is 0.5, which is between 0 and 1. Therefοre, this functiοn represents decay.

y=12(2.5)t6

The base οf the expοnential term is 2.5, which is greater than 1. Therefοre, this functiοn represents grοwth.

y=(0.65)t4

The base οf the expοnential term is 0.65, which is between 0 and 1. Therefοre, this functiοn represents decay.

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Complete Question:

Select "Growth" or "Decay" to classify each function.

Function Which ones are growth or decay

f(x)=(1.05)t4

y=100(0.4)t

f(x)=14(10)t12

how many degrees is a obtuce angel

Answers

Obtuse*

Angels between 90 and 180 degrees are obtuse angels.

Solve using the substitution method
2x -y = 7 and -6x + 3y = 21

Answers

There is no solution to the given system of equations. Therefore, the system is inconsistent.

How to solve the equation using substitution method?

To solve this system of equations using the substitution method, we need to solve one of the equations for one of the variables, and then substitute that expression into the other equation. Let's solve the first equation for y:

2x - y = 7

-y = -2x + 7

y = 2x - 7

Now we substitute this expression for y into the second equation:

-6x + 3y = 21

-6x + 3(2x - 7) = 21

-6x + 6x - 21 = 21

-21 = 21

This is a contradiction, and there is no solution to the system of equations. Therefore, the system is inconsistent.

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Please help with this

Answers

The probability that a passenger is traveling for business is 67.1%.

The probability of a passenger bringing a laptop on a flight if the passenger is traveling for business is 0.352 or approximately 35.2%.

How to calculate the probability

The probability that a passenger is traveling for business can be calculated by adding the number of passengers traveling for business and dividing by the total number of passengers:

P(traveling for business) = (274 + 397) / 1000 = 0.671

Therefore, the probability that a passenger is traveling for business is 0.671 or approximately 67.1%.

b. The probability of a passenger bringing a laptop on a flight if the passenger is traveling for business can be calculated as follows:

P(laptop | traveling for business) = number of passengers with a laptop and traveling for business / number of passengers traveling for business

P(laptop | traveling for business) = 236 / 671 = 0.352

Therefore, the probability of a passenger bringing a laptop on a flight if the passenger is traveling for business is 0.352 or approximately 35.2%.

c. It should be noted that to determine if there is an association between bringing a laptop on a flight and traveling for business, we can compare the proportion of passengers who bring a laptop when traveling for business versus when not traveling for business. If the proportions are different, it suggests an association.

P(laptop | traveling for business) = 0.352

P(laptop | not traveling for business) = 0.093

The proportions are different, which suggests an association between bringing a laptop on a flight and traveling for business.

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Please help me i need the answers pleasee

Starting with the graph of f(x)=9^x , write the equation of the graph that results when:
(a) f(x) is shifted 2 units upward. y=-----------

(b) f(x) is shifted 4 units to the right. y=----------

(c) f(x) is reflected about the x-axis and the y-axis. y=------------

Answers

Answer: (a) To shift the graph of f(x)=9^x 2 units upward, we can add 2 to the function. Therefore, the new equation is:

y = 9^x + 2

(b) To shift the graph of f(x)=9^x 4 units to the right, we can replace x with (x - 4). Therefore, the new equation is:

y = 9^(x - 4)

(c) To reflect the graph of f(x)=9^x about the x-axis and the y-axis, we can replace x with (-x) and take the negative of the function. Therefore, the new equation is:

y = -9^(-x)

Step-by-step explanation:

A parallelogram has an area of 14.4 square feet. The base is 4.5 centimeters. What is the height?​

Answers

We know that the area of a parallelogram is given by the formula A = bh, where A is the area, b is the base, and h is the height. In this case, we are given the area and the base, and we need to find the height.

We can rearrange the formula to solve for h: h = A/b

Plugging in the given values, we get:

h = 14.4 sq ft / 4.5 cm

Note that the units are different for area and base, so we need to convert them to the same units. Let's convert the base to feet, since the area is given in square feet:

h = 14.4 sq ft / (4.5 cm / 30.48 cm/ft) [converting cm to ft]

h = 14.4 sq ft / 0.148 ft

h ≈ 97.3 cm

Therefore, the height of the parallelogram is approximately 97.3 cm.

HELP PLS THIS IS DUE TOMORROW PLSSSSSSSS

Are ARST and ANSP similar? Use pencil and paper. Find the
measure of the angles in each triangle.

Which two angles must be congruent? What type of angles are they? (1 point)

Answers

The measure of the angles in triangle ARST are: 28 degrees, 28 degrees, 124 degrees, 124 degrees. The measure of the angles in triangle ANSP are: 28 degrees, 51 degrees, 101 degrees, 129 degrees.

What is angle?

An angle is a geοmetric figure fοrmed by twο rays οr lines with a cοmmοn endpοint, called the vertex. Angles are typically measured in degrees οr radians and are used tο describe the amοunt οf turn οr rοtatiοn between twο intersecting lines οr οbjects. Angles can be acute (less than 90 degrees), right (exactly 90 degrees), οbtuse (greater than 90 degrees), straight (exactly 180 degrees), οr reflex (greater than 180 degrees).

Here,

To find the measure of the angles in each triangle, we need to solve for the value of x in both equations.

For the first equation, we can simplify it as follows:

x + 14 = 2x

Subtracting x from both sides, we get:

14 = x

For the second equation, we can simplify it as follows:

3x + 9 = 2x + 23

Subtracting 2x and 9 from both sides, we get:

x = 14

Now that we know x = 14, we can find the measure of the angles in each triangle.

In triangle ARST, we have:

angle A = x + 14

= 14 + 14

= 28 degrees

angle R = 2x

= 2(14)

= 28 degrees

angle S = 180 - (angle A + angle R)

= 180 - (28 + 28)

= 124 degrees

angle T = 180 - (angle A + angle R)

= 180 - (28 + 28)

= 124 degrees

In triangle ANSP, we have:

angle A = x + 14

= 14 + 14

= 28 degrees

angle N = 3x + 9

= 3(14) + 9

= 51 degrees

angle S = 180 - (angle A + angle N)

= 180 - (28 + 51)

= 101 degrees

angle P = 180 - (angle N)

= 180 - 51 = 129 degrees

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A rectangular basket has a height of 6 inches, a width of 4 inches, and a length of 12 inches. What is the volume of the basket? Show how you found your answer.

V= l x w x h

V= B x h

Answers

The volume of a rectangular box or basket can be calculated using the formula:

V = l x w x h

where l is the length, w is the width, and h is the height of the box or basket.

In this case, the height of the basket is 6 inches, the width is 4 inches, and the length is 12 inches. Therefore, we can substitute these values into the formula and calculate the volume:

V = l x w x h

V = 12 x 4 x 6

V = 288 cubic inches

Therefore, the volume of the rectangular basket is 288 cubic inches.

The volume of the basket is 288 cubic inches.

What is Volume?

The area that any three-dimensional solid occupies is known as its volume. These solids can take the form of a cube, cuboid, cone, cylinder, or sphere.

The volume of a rectangular prism can be calculated

= length x  width x height.

Given that the height is 6 inches, the width is 4 inches, and the length is 12 inches, the volume of the basket can be calculated as:

Volume = Length x Width x Height

Volume = 12 inches x 4 inches x 6 inches

Volume = 288 cubic inches

Therefore, the volume of the basket is 288 cubic inches.

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A DVD rotates through an angle of 20pi radians in 1 second. At this speed, the DVD will make ____ revolutions in 1 minute!

Answers

One revolution is equal to 2π radians. Therefore, to find the number of revolutions made by the DVD in 1 minute, we can first find the number of revolutions made by the DVD in 1 second and then multiply by 60 to convert from seconds to minutes.

In 1 second, the DVD rotates through an angle of 20π radians. To find the number of revolutions, we can divide this angle by 2π:

20π radians ÷ 2π radians/revolution = 10 revolutions

Therefore, in 1 second, the DVD makes 10 revolutions. To find the number of revolutions in 1 minute, we can multiply by 60:

10 revolutions/second × 60 seconds/minute = 600 revolutions/minute

So the DVD will make 600 revolutions in 1 minute.

4) Two Truths and a Lie. Use what you know about the patterns in area models to determine which two area models correctly represent a factorable polynomial in the form of ax^2 + bx + c where c = 40. The middle “b” term is unknown

Answers

The correct area models are 4e and none of the given models for 4d and 4c.

What is the quadratic equation?

The solutions to the quadratic equation are the values of the unknown variable x, which satisfy the equation. These solutions are called roots or zeros of quadratic equations. The roots of any polynomial are the solutions for the given equation.

The area model of 4c is incorrect because the last term of the polynomial, which is 40, is represented by the bottom right box of the area model. However, in the given area model, the box representing 40 is in the upper row.

The area model of 4e is correct because it represents the polynomial as the product of two binomials, where the factors are (x-5) and (x-8).

When multiplied using the distributive property, the resulting polynomial is x² - 13x + 40, which matches the given polynomial form.

The area model of 4d is incorrect because it does not properly represent a factorable polynomial.

It only includes three boxes, representing the three terms of the polynomial, but it does not show how the terms can be factored into binomials.

Therefore, the correct area models are 4e and none of the given models for 4d and 4c.

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