what is the area of the triangle? 6 , 3

What Is The Area Of The Triangle? 6 , 3

Answers

Answer 1

Answer:

9

Step-by-step explanation:

Answer 2
i think the area of the triangle is 9

Related Questions

find the statement that is incorrect. Then, correct and rewrite the statement in the space provided. Show any necessary work.

find the statement that is incorrect. Then, correct and rewrite the statement in the space provided.

Answers

The incorrect statement is

The transformation can be represented by (7/3x, 7/3y)

What is Dilation in Transformation?

In mathematics, dilation can be defined as a transformation which alters the size of an object, though its shape remains unchanged. It is described as a specific similarity transformation where all dimensions associated with the given object (i.e. height, width and length) are increased or decreased uniformly by a particular scale factor.

A dilation thus produces an alteration in size, with the figure being either magnified or diminished while keeping its unique shape intact.

The scale factor used in the dilation is 9/7 instead of 7/3.

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What does the term basic mean as used in the advertisement? (2)​

Answers

Answer:

Step-by-step explanation:

it’s d

Marta walked at 3.1 miles per hour for 0.62 hours. How far did you walk?

Answers

Answer:

1.922  miles

Step-by-step explanation:

3.1 times 0.62 = 1.922

There are 20 chocolate candies in a bag.
What is the probability of reaching in the
bag and pulling out a strawberry?

There are 20 chocolate candies in a bag.What is the probability of reaching in thebag and pulling out

Answers

Answer:

C (prob = 0)

Step-by-step explanation:

There are only chocolate in the bag, so no probability of finding any non-chocolate.

0Answer:

Step-by-step explanation:

NO strawberries

(I NEED THIS RIGHT NOW!! PLEASE GIVE EXPLANATION!!) Millie and her brother, Jack, sold candy baes for the band fund-raiser. Millie sold three times as many candy bars as Jack. If Jack sold 30 candy bars, which equation and solution can be used to represent y, the number of candy bars Millie sold?

A. 3y = 30; y = 10
B. 30 = y/3; y = 103
C. 30 = y/3; y = 90
D. 3y = 30; y = 90

Answers

The answer is C: 30=y/3; y=90

The reason for this is that we know that Millie sold 3 times as much as Jack, and, if we use x to represent the number that Jack sold, and y to represent the number that Millie sold, we can form the equation y=3x which is equivalent to x=y/3.

By substituting x=30, we get to 30=y/3 and multiplying both sides by 3, we get to y=90

Answer:

C

Step-by-step explanation:

When we do 30=y/3 we get 90 because of the fraction symbol and its says in the problem 3 times as much so more not less so 3x30 equals 90 so we already take out A and B and when there is nothing but a simple equation like 30=3 we dived so it cant be D Ethier so its C

PLS GIVE BRAINLIST

Happy Easter

Pls help me i will give the crown thing
Question 4 Part B (2 points): Drag and
drop the units of measurement that
correctly represent the composite
function you created in part A. Click on
the image to refer back to Part A.
The composite function for part a was 20d-(80) = 67

Pls help me i will give the crown thingQuestion 4 Part B (2 points): Drag anddrop the units of measurement
Pls help me i will give the crown thingQuestion 4 Part B (2 points): Drag anddrop the units of measurement

Answers

Answer:

Given function:

t(s) = 3s + 20

where:

t(s) = number of palm trees growns = number of seeds planted

Given function:

s(d) = 20d

where:

s(d) = number of seeds planted per dayd = number of days

To determine the composite function that represents how many palm trees Carlos can expect to grow over a certain number of days, simply substitute s = 20d into t(s) = 3s + 20:

⇒ t(d) = 3(20d) + 20

⇒ t(d) = 60d + 20

The unit of measurement is how many palm trees Carlos can expect to grow over a certain number of days:

\(\sf \dfrac{palm \ trees}{days}\)

An artist can draw 3 illustrations in 3.5 hours. How many hours will it take to
draw 15 illustrations? Explain or show how you found your answer.

Answers

Answer:

17.5 hours

Step-by-step explanation:

divide 15 by 3 to get 5,

multiply 5 by the amount of hours it takes to draw 3 illustrations so 5 x 3.5, the answer is 17.5

the respone times for a certain ambulance company are normally distributed with a mean of 13 minutes.95% of the response times are between 10 and 16 minutes

Answers

The standard deviation of the response time is 1.53 minutes.

What is the standard deviation of the response time?

To get standard deviation, we will determine z-scores corresponding to the given percentiles and use them to calculate the standard deviation.

Z-score = z = (x - μ) / σ

For the lower bound of 10 minutes:

z = (10 - 13) / σ

For the upper bound of 16 minutes:

z = (16 - 13) / σ

As normal distribution is symmetric, the z-score corresponding to the lower tail of 2.5% is -1.96, and the z-score corresponding to the upper tail of 2.5% is 1.96.

Using z-scores, we set up  equations:

(10 - 13) / σ = -1.96

(16 - 13) / σ = 1.96

Solving the first equation:

-3 / σ = -1.96

σ = -3 / -1.96

Solving the second equation:

3 / σ = 1.96

σ = 3 / 1.96

Dividing both sides by 1.96:

-3 / 1.96 = σ

1.53 = σ

Full question:

The respone times for a certain ambulance company are normally distributed with a mean of 13 minutes.95% of the response times are between 10 and 16 minutes. What is S.D. of the response time.

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in a party everyone present received 2 gifts from each of the other people present. If 480 gifts were exchanged,how many people attended the party

Answers

Answer:240

Step-by-step explanation:

divide 480 by the amount of gift everybody gets . 2

Answer:

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

Step-by-step explanation:

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

Why?

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

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

Select the correct answer.
You work for a flower company. You sell roses at these prices: 3 roses for $4.80, 6 roses for $9, 12 roses for $14.40, and 36 roses for $45. What is
the approximate percentage difference of the best and worst rose deals according to their unit costs?
OA. 696
ОВ.
18%
Ос.
22%
OD. 29%

Answers

The approximate percentage difference of the best and worst rose deals according to their unit costs is; 25%

How to find the percentage difference?

Percent difference formula is obtained by dividing the absolute value of change by the average of the values and then multiplying it with 100. Thus;

Percentage difference = (x2 - x1)/x1

where;

x2 is final value

x1 is initial value

3 roses cost $4.80. Thus;

Unit cost of this is; 4.8/3 = $1.60 each

6 roses cost $9.. Thus;

Unit cost = 9/6 = $1.50

12 roses cost $14.40. Thus;

Unit Cost = 14.40/12 = $1.2

36 roses cost $45. Thus;

Unit cost = 45/36 = $1.25

Best deal = $1.6 and worse deal = $1.2

Percentage difference = (1.6 - 1.2)/1.6 * 100% = 25%

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Peter is going to visit 5 cities this summer. He will choose from 7 different cities, and the order in which he visits the cities does not matter. How many different city combinations are possible for the summer traveling?

Peter is going to visit 5 cities this summer. He will choose from 7 different cities, and the order in

Answers

There are 21 different city combinations possible for Peter's summer traveling.

To determine the number of different city combinations possible for Peter's summer traveling, we need to calculate the number of combinations of choosing 5 cities out of the 7 available cities.

Since the order in which he visits the cities does not matter, we are dealing with combinations rather than permutations.

The formula to calculate the number of combinations is given by the binomial coefficient, also known as "n choose k," denoted as C(n, k) or (nCk).

In this case, we have 7 cities to choose from, and Peter will visit 5 cities. Thus, we can calculate the number of city combinations as follows:

C(7, 5) = 7! / (5! * (7-5)!)

= 7! / (5! * 2!)

= (7 * 6 * 5!) / (5! * 2)

= (7 * 6) / 2

= 42 / 2

= 21

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Rewrite 6 as a fraction with the denominator being 7

Answers

Answer:

42/7

Step-by-step explanation:

Change 6 to a fraction by putting a 1 under the 6.

6 becomes 6/1

Then multiply by 7/7 to change the denominator to 7 as was asked for in the question.

6/1 × 7/7

= 42/7

When you multiply fraction × fraction, you multiply top×top and bottom×bottom.

6 rewritten as a fraction with the 7 on the bottom is 42/7

Suppose Manuela flips a coin three times. What is the theoretical probability of flipping tails at least two times? Express your answer as a fraction in simplest form.

Answers

The probability of flipping tails at least two times in three flips is 1/2.

When flipping a coin, there are two possible outcomes: heads or tails. Each flip is independent of the previous flips, so the probability of getting tails on any given flip is always 1/2 (assuming the coin is fair).

To find the theoretical probability of flipping tails at least two times in three flips, we can use the binomial probability formula:

P(x ≥ k) = 1 - P(x < k)

where P(x < k) is the probability of getting tails fewer than k times in three flips.

To find P(x < k), we can add up the probabilities of getting tails 0 times and getting tails 1 time:

P(x < 2) = P(0 tails) + P(1 tail)

P(0 tails) = (1/2)⁰ x (1/2)³ = 1/8

P(1 tail) = 3 x (1/2)  (1/2)² = 3/8 (since there are three ways to get exactly one tail: TTH, THT, HTT)

P(x < 2) = 1/8 + 3/8 = 1/2

Therefore, the probability of flipping tails at least two times in three flips is:

P(x ≥ 2) = 1 - P(x < 2) = 1 - 1/2 = 1/2

So the theoretical probability of flipping tails at least two times in three flips is 1/2 or 0.5 as a decimal.

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A person ears $16,700 one year and gets a 5% raise in salary. What is the new salary?

Answers

Answer:

$17,535

Step-by-step explanation:

 Original (old) salary:  $16,700/year

+ raise:                          0.05($16,700/year) = $835/year

---------------------------------------------------------------------------------

 New salary:  Original salary plus amount of raise:

                        $16,700/year + $835/year   =  $17,535

A faster but still valid approach to finding the new salary involves multiplying the original salary by 1.05:

1.05($16,700) = $17,535.  Here the '1.00' represents the original salary and the '0.05) the raise.

An instructor at a major research university occasionally teaches summer session and notices that that there are often students repeating the class. Out of curiosity, she designs a random sample of students enrolled in summer sessions and counts the number repeating a class. She counts 105 students in the sample, of which 19 are repeating the class. She decides a confidence interval provides a good estimate of the proportion of students repeating a class. She wants a 95% confidence interval with a margin of error at most =0.025
. She has no idea what the true proportion could be.
How large a sample should she take?

Answers

The instructor would need to take a sample size of at least 385 students in order to construct a 95% confidence interval with a margin of error of 0.025 or less.

What is confidence interval?

A confidence interval is a range of values that, with a certain degree of certainty, is likely to contain the real value of a population parameter. It is typically used in inferential statistics, where we use a sample to make inferences about a larger population.

According to question:

To determine the sample size required to construct a 95% confidence interval with a margin of error of 0.025 or less, we need to use the formula:

n = (Z² * p * (1 - p)) / E²

where:

n = sample size

Z = Z-score corresponding to the desired level of confidence (in this case, 95%, which corresponds to a Z-score of 1.96)

p = estimated proportion of students repeating the class (since we have no prior information, we will use 0.5 as a conservative estimate)

E = maximum allowable margin of error (in this case, 0.025)

Plugging in the values, we get:

n = (1.96² * 0.5 * (1 - 0.5)) / 0.025²

n = 384.16

Rounding up to the nearest whole number, the instructor would need to take a sample size of at least 385 students in order to construct a 95% confidence interval with a margin of error of 0.025 or less.

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BOWLING The cost for Nobu to go bowling is $4 per game plus an additional flat fee of $3.50 for the rental of bowling shoes. The cost can be modeled by the function f(x)=4x+3.5, where x represents the number of games bowled. Describe the graph of g(x) as it relates to f(x) if Nobu does not rent bowling shoes.



g(x) = , 1 of 3.
Select Choice
, which is the translation of f(x) , 2 of 3.
Select Choice
units , 3 of 3.
Select Choice

Answers

The graph of g(x) = 4x, is the translation of f(x) by subtracting 3.5 units, 2 of 3.

What is a graph?

A graph can be defined as a pictorial representation or a diagram that represents data or values.

The cost can be modeled by the function f(x)=4x+3.5, where x represents the number of games bowled.

As per the given question, the required solution would be as:

g(x) = 4x , is the translation of f(x) by subtracting 3.5 units, 2 of 3.

The graph of g(x) would be identical to the graph of f(x), but shifted 3.5 units downward, 3 of 3.

This is because the flat fee for the rental of bowling shoes is not present in the function g(x), so the y-intercept of the graph would be at (0,-3.5) instead of (0,0) in f(x) function.

The slope and the shape of the function will remain the same.

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Use substitution to solve the system of equations. Show your work (30 Points!!!)

Use substitution to solve the system of equations. Show your work (30 Points!!!)

Answers

Using the substitution method, the values of x and y are 1 and 10 respectively

What is simultaneous equation?

There are times when you come across two or more unknown quantities and two or more equations relating to them. These are called Simultaneous Equations.

The given equations are

4x + y = 14

y=8+2x

By substitution, put y=8+2x in equation 1

4x+8+2x=14

6x=14-8

6x=6

x=1

Recall that y=8+2(1)

y=8+2

Therefore the value of y=10

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The values are given as;

x = 1

y = 10

How to determine the value

From the information given, we have that;

4x + y = 14

y = 8 + 2x

Substitute the value of y in equation (1), we get;

4x + 8 + 2x = 14

collect the like terms

4x + 2x = 14 - 8

Add or subtract the like terms

6x = 6

Make 'x' the subject

x = 1

Substitute the value

y = 8 + 2x

y = 8 + 2(1)

expand the bracket

y = 8 + 2

Add the values

y = 10

Hence, the values are 1 and 10

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3/4 ^ 5/12 = 3/4 x _______

Answers

2/3 I think I hope it’s right

A turkey cost $1.05 per pound. There are going to be fifteen people at Thanksgiving dinner. Plan for each person to eat two, 3/8-pound servings if turkey. How much will the turkey for Thanksgiving dinner cost?

Answers

Answer:

5.90625

Step-by-step explanation:

15*3/8=5 5/8

5 5/8=5.625

1.05*5.625=5.90625

The cost of the turkey for Thanksgiving dinner is $ 11.8125

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the cost of 1 pound of turkey = $ 1.05

Total number of people at the Thanksgiving dinner = 15 people

The number of servings for each person = 2 servings

The amount of turkey servings for each person = 2 x 3/8 pound servings

                                                                               = 3/4 pound servings

Now , the equation will be

So , the total cost of 3/4 pound servings of turkey =
3/4 x cost of 1 pound of turkey

The total cost of 3/4 pound servings of turkey = 3/4 x 1.05

                                                                             = $ 0.7875

Now , the cost for 15 people at the Thanksgiving dinner =
15 x total cost of 3/4 pound servings of turkey

The cost for 15 people at the Thanksgiving dinner = 15 x 0.7875

                                                                                    = $ 11.8125

Hence , The cost of the turkey for Thanksgiving dinner is $ 11.8125

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Raina drove 464 miles in 8 hours.
At the same rate, how long would it take her to drive 638 miles?
0 hours
X
S

Answers

s= d/t
s= 464/8 = 58mi/hr
t = d/s
= 638/58 = 11 hours

Liza and Kelly rode their bikes everyday for five days. They each rode the same distance everyday. Lisa rode 60 miles in all and Kelly rode 25 miles in all. How many more miles per day did Lisa ride than Kelly?​

Answers

Answer:

60/5=12  25/5=5   7 more miles a day

Step-by-step explanation:

plzz mark brainiest

translate in terms of x then solve the algebra equation the sum of a number and 3 is subtracted from 10 the result is 5

Answers

Answer:

x=2

Step-by-step explanation:

10 - (x + 3) = 5

To solve for x, we can start by simplifying the left side of the equation:

10 - (x + 3) = 5

10 - x - 3 = 5

7 - x = 5

Next, we can isolate x on one side of the equation by subtracting 7 from both sides:

7 - x = 5

7 - x - 7 = 5 - 7

-x = -2

Finally, we can solve for x by dividing both sides of the equation by -1:

-x = -2

x = 2

Therefore, the solution to the equation is x = 2.

What is the value of x
83
58
50
70.5

What is the value of x83585070.5

Answers

Answer:

58

Step-by-step explanation:

\(x = \frac{141 - 25}{2} = 58\)

What is the value of x83585070.5

In exercise 5.12, we were given the following joint probabiltiy density function for the random variables Y1 and Y2, which were the proportions of two components in a sample from a mixture of insecticide:f(y1,y2)={2, 0<=y1<=1, 0<=y2<=1, 0<=y1+y2<=1. 0, elsewhere}For the two chemicals under consideration, an important quantity is the total proportion Y1+Y2 found in any sample. Find E(Y1+Y2) and V(Y1+Y2).

Answers

The probability density function is of E(Y1) and E(Y2) is 1/6 and variance is 1/18.

To find the expected value E(Y1+Y2), we can use the linearity of expectation and the fact that the expected value of a constant is that constant:

E(Y1+Y2) = E(Y1) + E(Y2)

To find E(Y1) and E(Y2), we need to integrate y1 and y2 respectively over their joint probability density function:

E(Y1) = ∫∫ y1 f(y1,y2) dy1 dy2

= ∫0^1 ∫0^(1-y1) 2y1 dy2 dy1

= ∫0^1 2y1(1-y1)/2 dy1

= ∫0^1 y1-y1^2 dy1

= [y1^2/2 - y1^3/3] from 0 to 1

= 1/6

Similarly,

E(Y2) = ∫∫ y2 f(y1,y2) dy1 dy2

= ∫0^1 ∫0^(1-y2) 2y2 dy1 dy2

= ∫0^1 2y2(1-y2)/2 dy2

= ∫0^1 y2-y2^2 dy2

= [y2^2/2 - y2^3/3] from 0 to 1

= 1/6

Therefore, E(Y1+Y2) = E(Y1) + E(Y2) = 1/6 + 1/6 = 1/3.

To find the variance V(Y1+Y2), we can use the formula:

V(Y1+Y2) = E((Y1+Y2)^2) - [E(Y1+Y2)]^2

To find E((Y1+Y2)^2), we need to integrate (y1+y2)^2 over their joint probability density function:

E((Y1+Y2)^2) = ∫∫ (y1+y2)^2 f(y1,y2) dy1 dy2

= ∫0^1 ∫0^(1-y1) (y1+y2)^2 2 dy2 dy1

= ∫0^1 [(2/3)y1^3 + y1^2 + (1/3)y1] dy1

= 5/18

Therefore, V(Y1+Y2) = E((Y1+Y2)^2) - [E(Y1+Y2)]^2 = 5/18 - (1/3)^2 = 5/18 - 1/9 = 1/18

The variance is 1/18.

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the first number in the pattern is 32 the rule is to add 27​

Answers

Answer:

59

Step-by-step explanation:

A circle has a radius of 6 meters. What is the circumference of the circle?
OA) 12 m
OB) 9 m
OC) 6am
OD) 37 m

Answers

Your answer would be 37 as the formula for circumference is 2 times pi times your radius

The reciprocal of 5 is 5/2 True False

Answers

Answer:

False

Step-by-step explanation:

FalseFalseFalse

Answer:

true

Step-by-step explanation:

Consider function fand function g.
() = In
g(x) = -5 In
How does the graph of function g compare with the graph of function ?
Unlike the graph of function f, the graph of function ghas a y-intercept.
The graph of function g is the graph of function fvertically stretched by a factor of 5.
Unlike the graph of function f, the graph of function g decreases as x increases.
The graphs of both functions have a vertical asymptote of r = 0.
Unlike the graph of function f, the graph of function g has a domain of {+1 -5 < x < 0}
Reset
Next

Consider function fand function g.() = Ing(x) = -5 InHow does the graph of function g compare with the

Answers

Answer:

I believe it is the first third and fourth options, I am not entirely sure for I mostly guessed on them, but they make the most sense when looking at the graph.

Step-by-step explanation:

It can be deduced that the graph of function f and g compare as:

Unlike the graph of function f, the graph of function g decreases as x increases.The graph of both functions have a vertical asymptote of x = 0.

What is a function?

A function in mathematics simply means the relation between a set of inputs and a set of permissible outputs.

In this case, the graph of both functions have a vertical asymptote of x = 0. This is because the divisor equals to zero for a value of x.

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any jus want to help with this? i attached the picture

any jus want to help with this? i attached the picture

Answers

1. The difference in the distance of Jupiter from the sun than Mercury will be 4.816.

2. The difference in the distance of Neptune from the sun than Mars will be

3. The greatest distance between Earth and Uranus is Uranus.

4. The greatest distance between Venus and Saturn is Saturn

How to calculate the distance?

From the information, the average distance from the sun to each planets have been given. The difference in the distance of Jupiter from the sun than Mercury will be:

= 5.203 - 0.387

= 4.816

The difference in the distance of Jupiter from the sun than Mars will be:

= 30.07 - 1.524

= 28.546

The greatest distance between Earth and Uranus is Uranus and the greatest distance between Venus and Saturn is that of Saturn.

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hey any help? (please make sure this is correct i'd appreciate it)

hey any help? (please make sure this is correct i'd appreciate it)

Answers

Answer:

Below

Step-by-step explanation:

Line AB is of the form y = mx + b    where m is the slope = 2

 Line BC is perpendicular to this and will have slope - 1/m = - 1/2   and includes the point C (0,6)

 The point slope form of line BC will then be

     ( y-6) = - 1/2 ( x - 0)    which can be re-arranged to

       y = - 1/2x + 6     < ==== equation for line BC

       

Other Questions
Why do some systems store the operating system in firmware, while others store it on disk?For certain devices, such as embedded systems, a disk with a file system may be not be available for the device. In this situation, the operating system must be stored in firmware. An 12oz energy drink is advertised as having only 160 calories. How many ounces could a user drink if they wanted to drink just 100 calories?. Choose the best word or phrase from the drop-down boxes to complete each sentence.The Pendleton Act is an example of how reformers pressured the federal government to becomeThe act required people tobefore they could be hired for jobs with the federalgovernment and gave presidents the power to increase the number of jobs it covered. However, presidents in the1880s and 1890s struggled to expand the new civil service because what is your smallest bone in your body The Constitution requires that the House of Representatives select the president when nocandidate has won a majority of the electoral vote.A. TrueB. False Which sentence could best be used to start the second paragraph Relationship A has a greater rate than Relationship B. This table represents Relationship B.Hours worked 2 4 5 8Amount paid 30.40 60.80 76 121.60Which equation could represent Relationship A?Hours worked is represented by x, and the amount paid is represented by y.Select each correct answer.Responsesy = 16.4xy = 15.2xy = 14.9xy = 15.4x the nurse would consider which disaster management plans to be most applicable if an earthquake hits a metropolitan area causing widespread death and injuries? select all that apply. one, some, or all responses may be correct. A manufacturer's raw-material purchasing department would likely be classified as a: Select one: a. investment center. b. cost center. c. profit center. d. contribution center. e. revenue center. What physical properties explain the observation that octane is insoluble in water? Which ordered pairs in the form (x,y) are solutions to the equation?4x - 5y = 24Select each correct answer.- ( 4, 8 ) - ( 1 -4 ) - ( 6, 0 ) - ( -9, -12 ) How does the expected etiquette of the time and society affect Elizabeths characterization?Elizabeths dirty attire and means of travel reflect her lower social ranking.Elizabeths attendance at Bingleys home shows her comfort in different social settings.Elizabeths social skills make up for her familys lack of strong connections.Elizabeths independence and confidence reflect her social rank. In DEF, the measure of F=90, the measure of D=67, and FD = 7.4 feet. Find the length of EF to the nearest tenth of a foot. What did this article of the treaty promise the indigenous groups who signed it?They could start their own farms on the reservation They could set up posts for trading food and other goodsThey could live on any open or unclaimed land in Washington They could continue to hunt and fish on their traditional lands. suppose rock is tossed upwards with an initial velocity of 80 ftisec from an initial height of 150 ft the position function can be written as quadratic function in the ________ are able to turn into many different types of specialized tissue, such as blood or muscle cells What was a goal of the Populist movement? which imaging modality best fits the following description? the modality has limited inter-examiner reliability, best demonstrates the internal structure of dense connective tissue, is inexpensive, and has a limited field of view. The smith family wants to fence their yard. the yard is 96 meters and 52 meters wide. how much fencing will they need? What do you know about the history of dance?