Will give brainliest!
given that the slope of the consecutive sides is -2/3 and 3/2
can you prove that it is a parallelogram or a rectangle.
explain your answer.

Answers

Answer 1

A figure with slope of consecutive sides -2/3 and 3/2 is a rectangle and it is not a parallelogram.

To prove that it is a parallelogram or a rectangle, we need to show that the opposite sides are parallel and the adjacent sides are perpendicular.

Let's first check if the opposite sides are parallel. The slope of one side is -2/3, and the slope of the adjacent side is 3/2. For opposite sides to be parallel, the slopes must be equal. However, -2/3 and 3/2 are not equal, so we can conclude that the given figure is not a parallelogram.

Now, let's check if the adjacent sides are perpendicular. The product of the slopes of the adjacent sides is

(-2/3) x (3/2) = -1, which is the slope of a line perpendicular to both sides. Since the product of the slopes is -1, we can conclude that the adjacent sides are perpendicular.

Therefore, figure is not a parallelogram, but it is a rectangle.

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Related Questions

if you complete it and it's correct I give you (brainlist)​help

if you complete it and it's correct I give you (brainlist)help

Answers

Answer:

1. 9

2. 122cm squared

3. 189m

4. 30

5. b

Step-by-step explanation:

1. 27,36,45,54,63,72,81,90,99

2. 12x6=72 10x5=50 50+72=122

3. 21x9=189

4. 5x12=60 60/2=30

5  b because 150 divided by 4 doesn't give you a whole number.

a- is there truncation in the sales data? is there censoring in the sales data? explain b- is there sample selection (or selection bias) in the sales data? explain

Answers

Truncation refers to the situation when values in the sales data are missing due to certain criteria not being met. For example, if the sales data only includes transactions above a certain threshold, all transactions below that threshold would be truncated.

Censoring, on the other hand, occurs when certain values in the sales data are not observed or recorded. This could happen if there is a limit on the highest or lowest sales amounts that can be recorded.

Sample selection, also known as selection bias, may exist in the sales data if the sample is not representative of the entire population. This can occur if certain groups or types of sales are overrepresented or underrepresented in the data.

For example, if the sales data primarily includes transactions from a specific region or demographic, it may not accurately reflect the overall sales patterns. To determine if there is selection bias, it is important to assess how the sample was chosen and whether it is truly representative of the population of interest.

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evaluate the integral. (remember to use absolute values where appropriate. use c for the constant of integration.) 9 tan2(x) sec(x) dx

Answers

Integration of 9 tan²(x) sec(x) dx  is 9 (  1/2secx × tanx -  1/2 ln |secx+tanx|) +C

Rewrite integral as ∫(sec²x-1)*(secx)dx = ∫sec³x dx - ∫secx dx

∫sec³x dx integrating by parts as ∫sec²x secx dx

=> secx × tanx - ∫secx(sec²x-1) dx

=>  secx × tanx - ∫sec³x dx + ∫secxdx

so  ∫sec³x dx =  secx × tanx - ∫sec³x dx + ∫secxdx

=> 2  ∫sec³x dx = secx × tanx + ∫secxdx

=>  ∫sec³x dx = 1/2secx × tanx - ln |secx+tanx|

so now final integral is

1/2secx × tanx - ln |secx+tanx| + ∫secx dx

=> 1/2secx × tanx - ln |secx+tanx| +  1/2 ln |secx+tanx|

=> 1/2secx × tanx -  1/2 ln |secx+tanx|

so final integral is 9 (  1/2secx × tanx -  1/2 ln |secx+tanx|) +C

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Brady has $20,000 in student loans with 3.3% interest that he plans to pay off in 5 years. Find the total cost of repayment.

Answers

The total cost of repayment over 5 years is $23,300.

What is the total cost of repayment?

A loan repayment refers to the act of paying back money previously borrowed from a lender.

To get total cost of repayment, we must principal amount, the interest rate and the duration of the loan.

The formula to get total cost of repayment is given by \(Total Cost of Repayment = Principal + Interest\)

Interest = Principal * Interest Rate * Time

Given:

Principal amount is $20,000

Interest rate is 3.3%

Duration is 5 years.

Interest = $20,000 * 0.033 * 5

Interest = $3,300

Total Cost of Repayment = Principal + Interest

= $20,000 + $3,300

= $23,300.

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During the period from 2011 through 2015 the annual returns on small U.S. stocks were - 3.80 percent, 19.15 percent, 45.91 percent, 3.26 percent, and - 3.80 percent, respectively. What would a $1 investment, made at the beginning of 2011 , have been worth at the end of 2015 ? (Round answer to 3 decimol places, eg. 52.750.) Value in 2015$ What average annual return would have been earned on this investment? (Round answer to 2 decimai ploces, eg. 52.75) Average annual return percent per year:

Answers

The average annual return on this investment from 2011 to 2015 is approximately 0.8%.

To calculate the value of a $1 investment made at the beginning of 2011 and its average annual return by the end of 2015, we need to multiply the successive annual returns and calculate the cumulative value.

The successive annual returns on small U.S. stocks from 2011 to 2015 are:

-3.80%, 19.15%, 45.91%, 3.26%, and -3.80%.

To calculate the cumulative value, we multiply the successive returns by the initial investment value of $1:

(1 + (-3.80%/100)) * (1 + (19.15%/100)) * (1 + (45.91%/100)) * (1 + (3.26%/100)) * (1 + (-3.80%/100))

Calculating this expression, we find that the cumulative value is approximately $1.044, rounded to three decimal places.

Therefore, a $1 investment made at the beginning of 2011 would have been worth approximately $1.044 at the end of 2015.

To calculate the average annual return, we need to find the geometric mean of the annual returns. We can use the following formula:

Average annual return = (Cumulative value)^(1/number of years) - 1

In this case, the number of years is 5 (from 2011 to 2015).

Average annual return = (1.044)^(1/5) - 1

Calculating this expression, we find that the average annual return is approximately 0.008 or 0.8% per year, rounded to two decimal places.

Therefore, the average annual return on this investment from 2011 to 2015 is approximately 0.8%.

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Select all the relations that represent a function.A. (1,3), (2,5), (2,7) (4,9)B. (1,3), (2,5), (3, 7) (4,9)C. (1, 3), (1,5), (1, 7) (4,9)D. (1,3), (2, 3), (3, 3) (4, 3)E. (1, 2), (2,5), (2, 1) (4,5)

Answers

Explanation:

A relation is a function if and only if for each value of x there's only one value of y. In other words, if we find one value of x more than once, the relation is not a function.

Relation A is not a function because x = 2 shows up twice: (2, 5) and (2, 7)

Relation C is not a function because x = 1 shows up three times: (1, 3), (1, 5) and (1, 7)

Relation E is not a function because x = 2 shows up twice: (2, 5) and (2, 1)

Relations B and D have only one time each value of x

Answers:

The table shows the results of rolling a number cube with sides labeled 1 through 6 several times. Outcome Number of times outcome occurred 1 10 What is the experimental probability of rolling a 3 or a 6? 2 6 Enter your answer as a fraction in simplest form in the box.. 3 4 4 8 5 6 Basic 6 6 7 8 9 L: X y​

Answers

Answer:

Because a 2 or a 4 was rolled 3 out of 12 times in the experiment, t so the fraction would be 3/12 (or 3 over 12).

Simplified: 1/4 (or 1 over 4)

Step-by-step explanation:

What is the MEAN of the data set below?(0.2,0.8,0.4,0.3,0.4,0.4,0.4,0.8,1.3)

Answers

Answer:

5/9

Step-by-step explanation:

we add all of the values and divide by the total number in this case 9, all of them add to make 5 so we do 5÷9 to get 5/9

There are 101 girls and 105 boys in Year 11 in a school. One girl is going to be chosen to be Head Girl and a different girl to be the Deputy Head Girl. One boy is going to be chosen to be Head Boy and a different boy to be the Deputy Head boy. How many different possible selections could be made?​

Answers

110,664,000 possible selections for Head Girl, Deputy Head Girl, Head Boy, and Deputy Head Boy from a group of 101 girls and 105 boys.

How to calculate different possible selections could be made?​

To find the number of possible selections that can be made, we need to multiply the number of choices available for each position.

For the Head Girl position, there are 101 girls to choose from. After one girl is selected for Head Girl, there are 100 girls remaining to choose from for the Deputy Head Girl position. So there are a total of 101 x 100 = 10,100 possible combinations of girls that can be chosen for these two positions.

Similarly, there are 105 boys to choose from for Head Boy, and 104 boys remaining to choose from for Deputy Head Boy. So there are a total of 105 x 104 = 10,920 possible combinations of boys that can be chosen for these two positions.

To find the total number of possible selections, we multiply the number of combinations for the girls by the number of combinations for the boys:

10,100 x 10,920 = 110,664,000

Therefore, there are 110,664,000 different possible selections that could be made.

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Someone help what is the answer

4h + 14 > 38 =
19 points

Answers

Answer:

its in there

Step-by-step explanation:

Answer: Solve the Inequality for h

Solve for h

Graph

Convert to Interval Notation

Evaluate

Write in y=mx+b Form

Find the Exact Value

Solve the Absolute Value Inequality for h

Convert to Set Notation

Plot

Write in Slope-Intercept Form

Solve the Rational Equation for h

Simplify

Add

Solve by Factoring

Describe the Transformation

Evaluate the Summation

Find the Absolute Max and Min over the Interval

Find the Product

Convert from Degrees to Radians

Convert to a Decimal

Subtract

Find the Slope

Find the Domain and Range

Find the Derivative - d/dh

Solve Using the Square Root Property

Find the Direction Angle of the Vector

Multiply

Find the Function Rule

Convert to a Simplified Fraction

Find the Area Between the Curves

Solve the Function Operation

Solve the System of Inequalities

Solve for h in Degrees

Find Where Increasing/Decreasing

Find the Maximum/Minimum Value

Write with Rational (Fractional) Exponents

Evaluate the Limit

Find the Slope and y-intercept

Solve by Isolating the Absolute Value for h

Find All Complex Solutions

Factor over the Complex Numbers

Find the Intersection

Find the Center and Radius

Convert to Radical Form

Find the Integral

Evaluate Using Summation Formulas

Evaluate Using Scientific Notation

Simplify/Condense

Determine if Linear

Graph Using a Table of Values

Reduce

Rationalize the Denominator

Find the Union

Find the Critical Points

Solve for h in Radians

Find the x and y Intercepts

Find the Inverse

Find the Perpendicular Line

Convert from Interval to Inequality

Solve by Completing the Square

Simplify the Matrix

Maximize the Equation given the Constraints

Convert to Regular Notation

Determine if the Relation is a Function

Write in Standard Form

Convert to Trigonometric Form

Split Using Partial Fraction Decomposition

Find the Zeros by Completing the Square

Find the Prime Factorization

Find the Local Maxima and Minima

Find the Quotient

Multiply the Matrices

Factor

1. Differentiate the function f(x) = ln (81 sin^2 (x)) f’(x) 2. Differentiate the function P(t) = in ( √t2 + 9) p' (t) 3. if x2 + y2 + z2 = 9, dx/dt = B, and dy/dt = 4, find dz/dt when (x,y,z) = (2,2,1)
dz/dt =

Answers

First you will get 4dz

The weather in Columbus is either good, indifferent, or bad on any given day. If the weather is good today, there is a 70% chance it will be good tomorrow, a 20% chance it will be indifferent, and a 10% chance it will be bad. If the weather is indifferent today, there is a 60% chance it will be good tomorrow, and a 30% chance it will be indifferent. Finally, if the weather is bad today, there is a 40% chance it will be good tomorrow and a 40% chance it will be indifferent. Questions: 1. What is the stochastic matrix M in this situation? M = Answer: 2. Suppose there is a 20% chance of good weather today and a 80% chance of indifferent weather. What are the chances of bad weather tomorrow?

Answers

The stochastic matrix M in this situation is:

| 0.7  0.2  0.1 |

| 0.6  0.3  0.1 |

| 0.4  0.4  0.2 |

B. To find the chances of bad weather tomorrow, we need to multiply today's weather probabilities with the corresponding transition probabilities to get the probabilities of each weather condition tomorrow, and then add up the probabilities of bad weather tomorrow.

Let the weather today be represented by the row vector P = [0.2 0.8 0], where the first entry is the probability of good weather, the second entry is the probability of indifferent weather, and the third entry is the probability of bad weather.

To find the weather probabilities tomorrow, we multiply P by the stochastic matrix M:

P' = P * M = [0.7*0.2+0.6*0.8+0.4*0, 0.2*0.7+0.3*0.8+0.4*0.4, 0.1*0.7+0.1*0.3+0.2*0.4]

= [0.62, 0.37, 0.11]

Therefore, the probability of bad weather tomorrow is 0.11, or 11%.

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The equation x2 - 7x=0 when solved is:

Answers

Answer:

x =0   x=7

Step-by-step explanation:

x^2 - 7x=0

Factor out an x

x(x-7) =0

Using the zero product property

x =0   x-7 =0

x =0   x=7

Joseph alexander obtained and installment loan of 1500. He ahreed to repay the loan in 18 monthly payments. The fiance charge is 146. 25. What is the apr?

Answers

The APR for Joseph Alexander's loan is 19.125 percent.

An installment loan is a sort of loan that is repaid in a series of installments, each of which includes a portion of the loan principal plus interest. If a person is unable to repay the full amount of the loan upfront, installment loans are a good alternative.

Joseph Alexander got an installment loan for 1500 and agreed to pay it back over 18 monthly payments. The finance charge on the loan is 146.25, and we have to determine the APR (annual percentage rate).

The APR is a measure of the total cost of borrowing money, which includes both the interest rate and any extra costs associated with the loan.

The APR is the best way to compare loans since it considers both the interest rate and the fees charged for the loan. To calculate the APR for Joseph Alexander's loan, we'll need to use a formula.

The formula is APR = (2 * n * F) / (P * (n + 1)) Here, n is the number of payments (18), F is the finance charge ($146.25), and P is the loan principal ($1500). So, let's plug in these values and solve for the APR: APR = (2 * 18 * 146.25) / (1500 * (18 + 1))APR = 0.19125, which means the APR is 19.125 percent.

As a result, the APR for Joseph Alexander's loan is 19.125 percent.

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Plot Z + 22-Im876532+++> Re2 3 4 5 6 7 8 9S G1A++ ++-9-8-7-6-5 -4 -3 -222-2 +-3 +-4--5--6-721B

Plot Z + 22-Im876532+++> Re2 3 4 5 6 7 8 9S G1A++ ++-9-8-7-6-5 -4 -3 -222-2 +-3 +-4--5--6-721B

Answers

Answer:

Explanation:

Here, we want to plot the graph of z1 plus z2

Firstly,let us identify the coordinates of z1 and z2

We can get this from the graph provided

z1 is (8,-4)

z2 is (-2,-3)

The sum of these two will be : (6,-7)

To plot this, we draw dotted vertical line at the point x = 6 and dotted horizontal line at the point y = -7

Wherever these two dotted lines meet is the point z

Reposting This question cuz no one answered it!!! :) please help quickly

Reposting This question cuz no one answered it!!! :) please help quickly

Answers

Answer:

1 and 3

Step-by-step explanation:

I learned this today so I'm not 100% sure

Acellus
The translation of ABCD to A'B'C'D'
is given by (x+[?],y-[ ]).
5
4
B
С
3
2
А
В'
C'
-7
-6 -5
-4
-3
-2
0
1
2.
3
4
5
A1
A
D
Enter

AcellusThe translation of ABCD to A'B'C'D'is given by (x+[?],y-[ ]).54B32'C'-7-6 -5-4-3-2012.345A1ADEnter

Answers

Answer:

Step-by-step explanation:

its (x+1,y+-3)

x/2 = 7
A) x=5
B) x=7
C) x=9
D) x=14

Answers

Answer:

D. x = 14

Step-by-step explanation:

Because 14 ÷ 7 = 2

7 × 2 = 14

Answer:

x=14

Step-by-step explanation:

2(x/2)=(7)2

multiply both sides by 2

x=14

Seven less than four times a number, x, is 37.
What is a possible solution of x?

Answers

4x-7=37
4x=37+7
4x=44
4x/4=44/4
X=11

The equation for the given phrase is 4x-7=37 and the solution for the obtained equation is 11.

The given unknown number is x.

Seven less than four times a number, x is

4x-7

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

So, the equation is

4x-7=37

The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.

Now, the solution is

4x=37+7

4x=44

x=44/4

x=11

Therefore, the equation for the given phrase is 4x-7=37 and the solution for the obtained equation is 11.

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What expression should be used to access the first element of an array of integers called numbers? What expression should be used to access the last element of numbers, assuming it contains 10 elements? What expression can be used to access its last element, regardless of its length?

Answers

To access the first element of an array of integers called "numbers," you can use the expression:
numbers[0]`
This expression uses the array name "numbers" and the index "0" to access the first element.

To access the last element of "numbers," assuming it contains 10 elements, use the expression:

`numbers[9]`

Here, we use the index "9" since arrays are zero-indexed, meaning the last element in a 10-element array has an index of 9.
To access the first element of the array called numbers, we would use the expression "numbers[0]."

To access the last element of the array, assuming it contains 10 elements, we would use the expression "numbers [9]" since arrays are zero-indexed in most programming languages.

To access the last element of the array regardless of its length, we can use the expression "numbers [numbers.length-1]," which subtracts 1 from the length of the array to access the last element.
To access the last element, regardless of its length, use the expression:

'numbers [numbers. length - 1]'

This expression uses the "length" property of the array to find the total number of elements and subtracts 1 to get the correct index for the last element.

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danielle is facing towards town A which is at a bearing of 300 from her.if she turn 135 clockwise she will be facing town b what is the bearing of town b from danielle

Answers

The bearing of Town B from Danielle is

435 degrees.

How to find the bearing

If Danielle is initially facing towards Town A at a bearing of 300 degrees, and she turns 135 degrees clockwise, we can determine the bearing of Town B from Danielle.

To calculate the new bearing, we add the initial bearing and the clockwise turn.

Initial bearing: 300 degrees

Clockwise turn: 135 degrees

Bearing of Town B = Initial bearing + Clockwise turn

Bearing of Town B = 300 degrees + 135 degrees

Bearing of Town B = 435 degrees

Therefore, the bearing of Town B from Danielle is 435 degrees.

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What is the value of a in the equation a = 2 + 3a + 8? (5 points)

Group of answer choices

5

10

−5

−10

Answers

Step-by-step explanation:

a = 2 + 3a + 8

a = 10 + 3a

a - 3a = 10

-2a = 10

a = -5

Math help: Variables
I need help solving these two questions, explanations would be greatly appreciated.

Math help: VariablesI need help solving these two questions, explanations would be greatly appreciated.

Answers

Answer:

1. h = 11 cm

2. d = 220 km

Step-by-step explanation:

1. A = 1/2bh

Where,

A = 66 cm²

b = 12 cm

A = 1/2bh

66 = 1/2 * 12 * h

66 = 6h

h = 66/6

h = 11 cm

2. s = d/t

Where,

s = 110 km/h

t = 2h

s = d/t

110 = d/2

Cross multiply

110 * 2 = d

d = 220 km

fill in the blank. In a 4x3x2x2 factorial experiment, you have ___ independent variables and potentially ___ main effect hypotheses.
4; 4

Answers

In a 4x3x2x2 factorial experiment, you have 4 independent variables and potentially 4 main effect hypotheses.

The 4 independent variables are represented by the four numbers in the experimental design

(i.e., 4 levels of variable A, 3 levels of variable B, 2 levels of variable C, and 2 levels of variable D).

The potentially 4 main effect hypotheses are one for each independent variable, which states that there is a significant effect of that independent variable on the outcome variable.

Factorial experiment:

A factorial experiment includes multiple factors simultaneously, each consisting of two or more

levels. Many factors simultaneously influence what is studied in a factorial experiment, and

experimenters consider the main effects and interactions between factors.

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Given that 113 out of a random sample of 310 adults indicated that they support the practice of changing clocks twice a year in observance of Daylight Saving Time, what will the sample proportion (or ) be

Answers

We can say that approximately 36.45% of the adults in the sample support the practice of changing clocks twice a year in observance of Daylight Saving Time.

The sample proportion, denoted by p-hat, is a measure of the proportion of individuals in the sample who support the practice of changing clocks twice a year in observance of Daylight Saving Time. To find p-hat, we divide the number of individuals in the sample who support the practice by the total number of individuals in the sample.

In this case, we have 113 individuals who support the practice out of a total sample size of 310. Thus, the sample proportion (p-hat) is:

p-hat = 113/310

p-hat = 0.3645 (rounded to four decimal places)

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Complete Question

Given that 1 13 out of a random sample of 310 adults indicated that they support the practice of changing clocks twice a year in observance of Daylight Saving Time, what will the sample proportion (or p) be? Please compute this value below and round your answer to three decimal places.

(help) Miller’s Farm had apples on sale for $1.78 a pound. Maria spent $15.21 on apples. How many pounds did she buy?

Answers

Answer:

8.5 pounds

Step-by-step explanation:

$ 1.78 - 1 pound

$ 15.21 - 15.21/1.78

= 8.5

Benjamin ran a total of 21 miles last month. This is 75% of the number of miles he wants to run this month. Slove the equation 0. 75m =21 to find out how many miles ,m, Benjamin wants to run this month. Show your work

Answers

The equation 0.75m = 21 can be solved to find the number of miles, m, Benjamin wants to run this month.To solve the equation 0.75m = 21, we need to isolate the variable m.

Let's divide both sides of the equation by 0.75 to isolate m: (0.75m) / 0.75 = 21 / 0.75 Simplifying the equation, we have: m = 28 Therefore, Benjamin wants to run 28 miles this month.The equation 0.75m = 21 represents the relationship between the number of miles Benjamin wants to run this month (m) and the fact that he ran 21 miles last month, which is 75% of his goal. To solve the equation, we isolate the variable m by dividing both sides of the equation by 0.75. This step is necessary to cancel out the coefficient of m. Dividing both sides by 0.75, we have: (0.75m) / 0.75 = 21 / 0.75 The division of 0.75m by 0.75 on the left side of the equation cancels out the coefficient, leaving us with m. On the right side, we divide 21 by 0.75 to obtain the value of m. Dividing 21 by 0.75, we find: m = 28 Therefore, Benjamin wants to run 28 miles this month to achieve his goal. In summary, by solving the equation 0.75m = 21, we find that Benjamin's goal for this month is to run 28 miles. This equation represents the relationship between the miles he ran last month (21) and the percentage (75%) of his goal for this month.

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The angle lies in Quadrant II.
sin0=3/4
What is cos 0?

The angle lies in Quadrant II.sin0=3/4What is cos 0?

Answers

Answer:

cosФ is \(-\frac{\sqrt{7}}{4}\)  ⇒ B

Step-by-step explanation:

Let us solve the question using one of the identities of trigonometry

sin²Ф + cos²Ф = 1

∵ sinФ = \(\frac{3}{4}\)

→ Substitute it in the rule above to find cos Ф

∴ (\(\frac{3}{4}\))² + cosФ² = 1

∴ \(\frac{9}{16}\) + cosФ² = 1

→ Subtract \(\frac{9}{16}\)  from both sides

∴ cos²Ф = \(\frac{7}{16}\)

→ Take √ for both sides

cosФ = ± \(\frac{\sqrt{7}}{4}\)

∵ Angle Ф lies on the second quadrant

∴ cosФ is a negative value

∴ cosФ = \(-\frac{\sqrt{7}}{4}\)  

cosФ is \(-\frac{\sqrt{7}}{4}\)  

(1). On a set of axes, draw AABC if A(6;-5), B(6; -2) and C(2;-5) are the coordinates of the vertices. (2). If the rule of transformation is (x; y) → (y;x), draw AABC. State the type of transformation and indicate the coordinates of the vertices of AA BC. (3) Write down the value of the following ratios: Area of AA BC (i) Area of AABC Perimeter of AA BC (ii) Perimeter of AABC AB BC AC (iii) and " AB BC AC (c) (1) (2)

Answers

Here is a graph of AABC with vertices A(6, -5), B(6, -2), and C(2, -5):

           |

           |

       A   |    B

     (6,-5)|   (6,-2)

           |

   --------C--------

          (2,-5)    

Applying the transformation (x,y) → (y,x) to the coordinates of the vertices of AABC, we get A'(-5,6), B(-2,6), and C(-5,2). This is a reflection of the original triangle across the line y = x. The new vertices are A'(-5,6), B(-2,6), and C(-5,2).

           ^

           |

       A'  |    B

      (-5,6)|   (-2,6)

           |

   --------C--------

        (2,-5)    

(i) Area of AA BC : Area of AABC = 9/25

(ii) Perimeter of AA BC : Perimeter of AABC = 3/4

(iii) AB BC AC : AB BC AC = 1:3:2

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Which of the following coordinate points have undergone an enlargement and reduction? Select all that apply.Group of answer choices(5, -1) --> (10, 2) --> (20, 4)(1, 1) --> (6, 6) --> (1, 1)(4, 9) --> (20, 34) --> (20/45, 1)(3, 0) --> (9, 0) --> (18, 0)(0, -5) --> (0, 5) --> (0, 30)

Answers

By definition, you know that dilations have a scale factor, this is labeled k. To dilate something in the coordinate plane, multiply each coordinate by the scale factor.

If there is a reduction, then 0 < k < 1.

If there is an enlargement, then k > 1.

\((x,y)\rightarrow(kx,ky)\)

So, you have

\(\begin{gathered} (5,-1)\rightarrow(5\cdot2,-1\cdot-2)=(10,2) \\ \text{ k is not the same for both coordinates of the point} \end{gathered}\)

\(\begin{gathered} (1,1)\rightarrow(6\cdot1,6\cdot1)=(6,6) \\ \text{In this case, k = 6 and k > 1 then the coordinate points have an enlargement} \\ (6,6)\rightarrow(\frac{1}{6}\cdot6,\frac{1}{6}\cdot6)=(1,1) \\ \text{In this case, k = 1 and 0< k < 1 then the coordinate points have an reduction} \end{gathered}\)\(\begin{gathered} (4,9)\rightarrow(4\cdot5,9\cdot\frac{34}{9})=(20,34) \\ \text{ k is not the same for both coordinates of the point} \end{gathered}\)\(\begin{gathered} (3,0)\rightarrow(3\cdot3,3\cdot0)=(9,0) \\ \text{In this case, k = 3 and k > 1 then the coordinate points have an enlargement} \\ (9,0)\rightarrow(2\cdot9,2\cdot0)=(18,0) \\ \text{In this case, k = 2 and k > 1 then the coordinate points have an enlargement} \end{gathered}\)\(\begin{gathered} (0,-5)\rightarrow(-1\cdot0,-1\cdot-5)=(0,5) \\ \text{ In this case, k = -1, and by definition k > 0} \end{gathered}\)

Therefore, the correct answer is

\(B\text{.}(1,1)\rightarrow(6,6)\rightarrow(1,1)\)

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