Find the perimeter of triangle ABC. Round your answer to two decimal places.

Find The Perimeter Of Triangle ABC. Round Your Answer To Two Decimal Places.

Answers

Answer 1

Check the picture below.

[tex]~\hfill \stackrel{\textit{\large distance between 2 points}}{d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}}~\hfill~ \\\\[-0.35em] ~\dotfill\\\\ A(\stackrel{x_1}{-7}~,~\stackrel{y_1}{2})\qquad B(\stackrel{x_2}{3}~,~\stackrel{y_2}{-8}) ~\hfill AB=\sqrt{(~~ 3- (-7)~~)^2 + (~~ -8- 2~~)^2} \\\\\\ ~\hfill AB=\sqrt{( 10)^2 + ( -10)^2} \implies \boxed{AB=\sqrt{ 200 }}[/tex]

[tex]B(\stackrel{x_1}{3}~,~\stackrel{y_1}{-8})\qquad C(\stackrel{x_2}{-4}~,~\stackrel{y_2}{-9}) ~\hfill BC=\sqrt{(~~ -4- 3~~)^2 + (~~ -9- (-8)~~)^2} \\\\\\ ~\hfill BC=\sqrt{( -7)^2 + ( -1)^2} \implies \boxed{BC=\sqrt{ 50 }} \\\\\\ C(\stackrel{x_1}{-4}~,~\stackrel{y_1}{-9})\qquad A(\stackrel{x_2}{-7}~,~\stackrel{y_2}{2}) ~\hfill CA=\sqrt{(~~ -7- (-4)~~)^2 + (~~ 2- (-9)~~)^2} \\\\\\ ~\hfill CA=\sqrt{( -3)^2 + (11)^2} \implies \boxed{CA=\sqrt{ 130 }} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{\LARGE perimeter}}{\sqrt{200}~~ + ~~\sqrt{50}~~ + ~~\sqrt{130}} ~~ \approx ~~ \text{\LARGE 32.61}[/tex]

Find The Perimeter Of Triangle ABC. Round Your Answer To Two Decimal Places.

Related Questions

Change the following problem to an addition problem.
-5-4

Answers

Answer:-9

Step-by-step explanation:

-(5+4)

-(9)

The answer is -1
-5+4
Will be -1

Between which two integers does the square root of 92 lie?

Answers

The square root of 92 lies between 9 and 10.

According to the question,

We have the following information:

Square root of 92

Now, we have to find the two integers between which its square root lie.

So, we will first find the perfect squares of positive integers to get an idea where the square root of 92 lies.

Perfect squares are given below:

1 = 1

2 = 4

3 = 9

4 = 16

5 = 25

6 = 36

7 = 49

8 = 64

9 = 81

10 = 100

Now, the square of 10 is greater than 92 and square of 9 is less than 92. So, it will lie between these two integers.

Hence, the square root of 92 lies between 9 and 10.

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for each pair of points, find the slope of the line that passes through both points. If you get stuck, try plotting the points on graph paper and drawing the line thoruhg them wiht a ruler

Answers

The slope of points (1,3) and (4,5) will be 2/3.

What is a slope?

Slope or the gradient is the number or the ratio which determines the direction or the steepness of the line. The slope is also defined as the ratio of the rise and the run of the line.

Given that the line is passing through points (1,3) and (4,5). The slope of the line will be calculated as,

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

Slope = ( 5 - 3 ) / ( 4 - 1)

Slope = 2 / 3

Therefore, the slope of points (1,3) and (4,5) will be 2/3.

The complete question is given below.

Find the slope of the line that passes through both points (11,3) and (4,5).

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How do this?Help pls give answer

Answers

Answer:

Step-by-step explanation:

Ok! So apparently I think you are learning about pre algebra. So the questions are saying what times 1/4=8 in that case it would be x = 32. x is just a fancy way to say you don’t know what it is.

write a linear function f with the given values. f(-10) = 4, f (8) = -5 Can someone please help me with this question​

Answers

Answer: y=-0.5x-1

Step-by-step explanation:

                                              y=mx+b

Convert the given values f(-10) = 4, f (8) = -5 to coordinates (-10,4)  (8,-5)

Hence we use the formula for finding the slope m:

[tex]\displaystyle\\\boxed{m=\frac{y_2-y_1}{x_2-x_1} }\\\\x_1=-1\ \ \ \ \ x_2=8\ \ \ \ \ \ y_1=4\ \ \ \ \ y_2=-5\\\\m=\frac{-5-4}{8-(-10)}\\\\m=\frac{-9}{8+10} \\\\m=\frac{-9}{18} \\\\m=-0.5\\\\Thus, y=-0.5x+b\ \ \ \ (1)\\\\[/tex]

We substitute the value of (-10,4) into equation (1):

[tex]4=-0.5(-10)+b\\\\4=5+b\\\\-1=b\\\\Thus, b=-1[/tex]

Hence, y=-0.5x-1

4. Find x.

78°
65°

This is problem number 4

I will mark brainless if I get this question right when I turn it in

Answers

The answer would be 78 degrees, or 70 degrees


What is the angle of elevation of the sun when a 47-ft mast casts a 14 ft
shadow?
O
The angle of elevation is
(Simplify your answer. Type an integer. Round to the nearest degree.)
***

Answers

The sun's angle of elevation when a 47-foot mast casts a 14-foot shadow 73.4127

What is the angle of elevation ?

At the foot of the mast, place the 90 degree (right) angle of a right triangle. When the sun hits the mast, it casts a 47-foot shadow. Consider the mask's height to be on the "opposite side" of the elevation angle, and this shadow to be on the "adjacent side."

The "tangent" trig function includes the following variables:

Tan = (opposite side) (elevation angle) (adjacent side).

In this case, tan (angle of elevation) equals opposing side / adj opposing side.

is used for

radians, or tan (angle of elevation)

= 47/14 = 3.3571

3.3571 is equal to 73.4127 degree.

The angle of elevation of the sun when a 47-ft mast casts a 14 ft

shadow 73.4127 degree

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On a math quiz, Tatiana earns 5 points for each question she answers correctly. She wrote this
equation to find how many points she earns (p) based on how many questions she answers
correctly (g):
p = 5q
Identify the dependent and independent variables.
Points earned (p)
Questions correct (g)
Dependent variable Independent variable

Answers

Answer:

For points earned (p), the button should be on the left, and for questions correct (q), its on the right.

Step-by-step explanation:

me not know how to speak English!

In the given equation p = 5q, p is the dependent variable and g is the independent variable.

Given that Tatiana earns 5 points for each question she answers.

So, the equation is p = 5q

The above equation explains that for every question she answers, she earns 5 points. That means answering questions which is "q" is an independent variable as it is not depending on any other factor.

The points earned which is "p", is completely depending on answering questions, so the "p" which is points earned is a dependent variable.

From the above explanation, we can conclude that p is dependent variable and q is independent variable.

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Valentina measured a kitchen and made a scale drawing. She used the scale 1 inch : 2 feet. A countertop in the kitchen is 2 inches wide in the drawing. How wide is the actual counter?

Answers

The actual width of the countertop is 4 feet

Given,

Valentina measured a kitchen and made a scale drawing;

The scale she used for the drawing = 1 inch ; 2 feet

The width of countertop of kitchen in drawing = 2 inches.

We have to find the actual width of the countertop;

Here,

The scale factor used in the drawing = 1 inch = 2 feet

1 inch  = 2 feet

2 inch = 2 x 2 = 4 feet

Now,

The actual width of the countertop = Width in drawing x 2

= 2 x 2 = 4 feet

That is,

The actual width of the countertop is 4 feet

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What does 25 DIVIDE by 3 equal?

Answers

Step-by-step explanation:

25/3 = 8.33

hope it's helpful

25 divided by 3 equals

8.3333
OR
8 1/3
OR
8 remainder 1

Really need help!
Graph the equation y =x²
+ 4x - 5 on the accompanying set of axes. You must plot 5 points including the roots and the vertex. Using the graph, determine the roots
of the equation x² + 4x − 5 = 0.

Answers

Answer:

See picture below

Step-by-step explanation:

Use Desmos the free calcualtor.

STATISTICS The most familiar statistical measure is the arithmetic mean, or average. A second important statistical measure is the standard deviation, which is a measure of how far the individual scores are from the mean. For example, the mean score on the Wechsler IQ test is 100 and the standard deviation is 15. This means that people within one deviation of the mean have IQ scores that are 15 points higher or lower than the mean.

Answers

An absolute value equation that can be used to find the maximum and minimum scores within one standard deviation of the mean is |x - 20.9| = 5.3.

The minimum score that is within one standard deviation of the mean is equal to 15.6.

What is an absolute value function?

In Mathematics, an absolute value function can be defined as a type of function that consist of an algebraic expression, which is placed within absolute value symbols and measures the distance of a point on the x-coordinate to the x-origin (0).

Mathematically, an absolute value function can be represented by this mathematical expression:

|x| = x, x ≥ 0.|x| = x, x < 0.

Since the standard deviation is 5.3 and the mean is 20.9, an absolute value equation for the scores that is within one standard deviation of the mean is given by:

|x - 20.9| = 5.3.

x - 20.9 = ±5.3

Evaluating the absolute value function, the maximum score is given by:

x - 20.9 = 5.3

x = 20.9 + 5.3

x = 26.2.

Evaluating the absolute value function, the minimum score is given by:

x - 20.9 = -5.3

x = 20.9 - 5.3

x = 15.6.

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Complete Question:

The most familiar statistical measure is the arithmetic mean, or average. A second important statistical measure is the standard deviation, which is a measure of how far the data are from the mean. For example, the mean score on the Wechsler IQ test is 100 and the standard deviation is 15. This means that people within one standard deviation of the mean have IQ scores that are 15 points higher or lower than the mean. One year, the mean mathematics score on the ACT test was 20.9 with a standard deviation of 5.3. Write an absolute value equation to find the maximum and minimum scores within one standard deviation of the mean. Use your equation to find the minimum score that is within one standard deviation of the mean

which choice does not determine the sampling distribution? the population size the population variance the population mean the sample size

Answers

The population size does not determine the sampling distribution.

In the give question we have to find which choice does not determine the sampling distribution.

We firstly learn more about sampling distribution

A sampling distribution is a probability distribution of a statistic that is derived from a bigger sample size of individuals chosen at random from a given population. The sampling distribution of a particular population is the distribution of frequencies of a variety of potential outcomes for a population statistic.

So, the population size does not determine the sampling distribution.

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find the growth or decay rate: y=2.5(0.72)^x

Answers

Answer: decay

Step-by-step explanation: decay is when the input is less than 1 and greater than 0. 0.75 falls in between these numbers

the tell-tale factor is the value inside the parenthesis, if that's less than 1 is Decay, if more than 1 is Growth

[tex]\qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{current amount}\\ P=\textit{initial amount}\dotfill &2.5\\ r=rate\to \text{\LARGE 28\%}\to \frac{28}{100}\dotfill &0.28\\ t=\textit{elapsed time}\dotfill &x\\ \end{cases} \\\\\\ A=2.5(1 - 0.28)^{x} \implies A = 2.5(0.72)^x\hspace{5em}y= 2.5(0.72)^x[/tex]

if -3 + i is a root of the polynomial function f(x), which of the following must also be a root of f(x)?

Answers

Answer:

-3 - i

Step-by-step explanation:

This is true, because when solving for an imaginary solution through a polynomial, the form A ± Bi will always be adhered. A and B are both constants.

(Constants are just any real number, like 1, 2.35, or [tex]\frac{1}{2}[/tex].)

Greg mow and rakes lawn to earn extra money He makes 45 for every lawn he mows and an extra 15 for raking his goal is to earn at least 250 per week

Answers

The inequality is 45m + 14 n ≥ 250.

What is Inequality?

Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

Given:

He makes 45 for every lawn he mows

and an extra 15 for raking

His goal earning= at least 250 per week

let the number of lawn he mow is m and the number of lawn rakes is n.

Then the inequality is

45m + 14 n ≥ 250

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Amadou and his children went into a grocery store and he bought $9 worth of apples and bananas. Each apple costs $1 and each banana costs $0.50. He bought 4 times as many apples as bananas. By following the steps below, determine the number of apples, x, and the number of bananas, y, that Amadou bought.

Determine THREE ways to have 4 times as many apples as bananas.

There are 3 other ways so please try to answer them!

Answers

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

The number of apples is 8.

The number of bananas is 2.

What is an expression?

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Total cost = $9

Cost of one apple = $1

Cost of one banana = $0.50

The number of bananas = x

The number of apples:

y = 4x

Now,

1y + 0.50x = 9

4x + 0.50x = 9

4.50x = 9

x = 9/4.50

x = 2

Now,

y = 4 x 2 = 8

Thus,

The number of apples 8.

The number of bananas is 2.

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What is the next fraction
in this sequence?
Simplify your answer

5/14, 3/7, 1/2, 4/7 …

Answers

Closed form:
an=n+4/14 (for all terms given)

Next fraction would be 9/14.

rohit studies 5⅖ hrs daily. He devotes 1¼ hrs of his time for English abd 1½ hrs for Mathematics. How much time does he devote for other subjects​

Answers

Answer:3 1/2 hours

Step-by-step explanation: 5 2/5 - 1 1/4 -1 1/2= 3 1/2

A retailer needs to purchase 12 printers. The first printer costs $54, and each additional printer costs 5% less than the price of the previous printer, up to 15 printers. What is the total cost of 12 printers?.

Answers

The total cost of 12 printers is; $493.41

Cost of first printer; C1 = $54

Cost of second printer is; 95% × 54 = $51.3

Cost of third printer is; 0.95 × 51.3 = $48.735

Cost of fourth printer = 0.95 × 48.735 = $46.298

Now, let us apply same pattern using a calculator for the remaining costs and we will have them as follows;

Cost of 5th printer = $43.983

Cost of 6th printer = $41.784

Cost of 7th printer = $39.695

Cost of 8th printer = $37.710

Cost of 9th printer = $35.825

Cost of 10th printer = $34.033

Cost of 11th printer = $32.332

Cost of 12th printer = $30.715

Total cos is; 54 + 51.3 + 48.735 + 46.298 + 43.983 + 41.784 + 36.695 + 37.710 + 35.825 + 34.033 + 32.332 + 30.715 = $493.41

Therefore, the total cost of 12 printers is $493.41

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Which of the following is not an isometry
A). Translation
B). Line reflection
3). Point reflection
4). Rotation

Answers

The option that is not an isometry from the given transformations is 3). Point reflection.

What is an isometry?

An Isometry refers to a transformation that leads to the distance and length  of a shape being preserved when it is transformed.

Translations and rotations preserve the shape of a figure during transformation which means they preserve length which makes them an isometry. The same is true of line reflections.

Point reflections on the other hand, will lead to a change in dimensions for the figure being transformed.

In conclusion, `a point reflection is not an isometry.

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8x1 4* 28 × +8 help me ​

Answers

Answer:

8x1 4* 28 × +8 = 28x + 12

8x^1 + 4 times 28 + 8

Add common Factors which are 8x and 28x added they equals 36x and 4 and 8 which equals 12 so now we got 28x + 12 and that is the answer

PLEASE GIVE BRAINLIEST THANK YOU!!!

Beatrice makes a jar of dry soup mix. The ingredients are:

1 3/4 = 7/4cups uncooked rice

1/2 cup dry lentils

1 2/3 = 5/3 cups uncooked pasta

1/3 cup beef bouillon

1/4 cup dried onion flakes

1/2cup dried peas

How much soup mix does this recipe make?

Answer the questions to find out.

The sum 7/4+ 1/2+5/3 +1/3 +1/4 +1/2 gives the amount of mix.


1. Which property could you use to change the grouping of the addends?

Answers

The soup mix that this recipe makes is 5.

The property could you use to change the grouping of the addends is the associative property of addition.

How to calculate the value of the mix?

From the information, the following can be deduced:

7/4cups uncooked rice

1/2 cup dry lentils

1 2/3 = 5/3 cups uncooked pasta

1/3 cup beef bouillon

1/4 cup dried onion flakes

1/2cup dried peas

The soup mix that this recipe make will be the addition of all the values. This will be:

= 7/4+ 1/2+5/3 +1/3 +1/4 +1/2

= 5

The associative property of addition can change the grouping.

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Mrs. Nicholas baked two batches of cookies. The first batch consisted of 120 gingerbread cookies and the second batch consisted of 150 shortbread cookies. Mrs. Nicholas saved the same fraction of cookies from each batch. If Mrs. Nicholas saved 20 more shortbread cookies than gingerbread cookies, what fraction of the cookies did she save?

Answers

Answer:

i think 2/15 of the cookies

Step-by-step explanation:

hope this helps

what is 6,000 lb/day = ____ t/wk?

Answers

Answer: 21 tons/wk

Step-by-step explanation:

6000 lb/day = 3 tons/day

3 t/day * 7 = 21 t/wk

A car moves at a speed of 80km/h from P at 0800 hours and reaches Q at 0930 hours. A lorry takes the same route from Q at 0800 hours to P at a speed of 70km/h. At what time do both vehicles meet?​

Answers

The vehicles will meet at 0845 at a distance of 64 km from P when they move at the respective speeds.

The car moves at a speed of 80km/h from P to Q and it takes time t

t = 9.30 - 8.00 = 1 hour 30 minutes or 1.5 hours

Distance covered = speed × time

Distance = 80 × 1.5 = 120 km

Now et the cars meets at a distance of x km from P.

times taken by the car to cover x km = x/80 hours

The lorry travels 120 - x in that same time.

time taken = 70/(120 - x)

Now the time taken must be equal.

Therefore we will form an equation to calculate x.

(120 - x) / 70 = x / 80

or, 960 - 8x = 7x

or, 15x = 960

or, x = 64

Therefore the cars will meet at 64 km from P.

Now time taken by the car to cover 64 km = 64/80 = 0.8 hours = 48 minutes

Hence the cars will meet at 0845 hours.

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Please help
What equation is represented by the values in this table

Answers

Answer:

y=2x-2

Step-by-step explanation:

use y2-y1/x2-x1 to find slope

4-2/3-2

2/1

2 is the slope

A and B are the only possible answers so far

Now to find y intercept

We know it can’t be +2 because at 2 x is equal to 2 so -2 is the only option

Hopes this helps please mark brainliest

Solve this system of equations using the SUBSTITUTION method, then answer the questions below.

x + 2y = 4
3x + 6y = 18

What did you get for the (x, y) solution to this system? If you were to graph these equations, would their lines cross? Explain why or why not.

Answers

The x and y do not have the values in the equation because both the equations don't intersect each other.

given that the equation,

x + 2y = 4 ..........i

3x + 6y = 18 ...........ii

now multiply i with 3 and subtract with from ii,

3x + 6y = 18

-(3x + 6y ) = 12

0x + 0y = 6

which is not possible so x and y do not have the values at the intersection of the both equations which states that both the equation do not intersect at each other.

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a wheat farmer is investigating the effectiveness of a treatment for controlling a pest. a random sample of 500 plants shows that 47 of them are infected by the pest. what does this sample indicate about the claim that 20% of the plants are infected?

Answers

The sample indicates that the data does not provide sufficient evidence to support the claim that 20% of plants are infected.

This given test is a test for single sample proportion

The test hypothesis are:

[tex]H_{o} :p=0.20[/tex], null hypothesis

[tex]H_{1} :p\neq 0.20[/tex], alternative hypothesis

The test statistic fallows a standard normal distribution and is given by:

[tex]Z=\frac{x-p}{{\sqrt{p(1-p)/n} } }[/tex]

p=0.20

X=47 plants

Sample size, n=500

x, is the sample mean:

x=X/n=47/500

x=0.094

So, test statistic is calculated as:

[tex]Z=\frac{0.094-0.20}{\sqrt{0.20(1-0.20)/500} }[/tex]

Z=-5.93

From the z-table, the p-value associated with Z=-5.93 is approximately 0

The decision rule based on p-vale, is to reject the null hypothesis if p-value is less than confidence level

In this case, the p-value is very small and less than confidence level of 0.20, we therefore reject the null hypothesis or the claim

So we conclude that the data does not provide sufficient evidence to support the claim that 20% of plants are infected.

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What are the coordinates of the point on the directed line segment from (-9, -10)
to (1,5) that partitions the segment into a ratio of 2 to 3?

Answers

The coordinates of the point on the directed line segment from (-9, -10) to (1,5) that partitions the segment into a ratio of 2 to 3 is (-5,-4)

The end points of the line segment = (-9, -10) and (1, 5)

The partition ratio = 2 : 3

According to the partition rule

The x coordinate of the point = [tex]x_1+\frac{A(x_2-x_1)}{A+B}[/tex]

A = 2

B = 3

Substitute the values in the equation

The x coordinate of the point = -9 + [2(1--9) / 2+3]

= -9 + [2×10 / 5]

= -9 + [20/5]

= -9 + 4

= -5

Similarly,

The y coordinate of the point = [tex]y_1+\frac{A(y_2-y_1)}{A+B}[/tex]

= -10+[2(5--10)/2+3]

= -10+[2×15/5]

= -10+[30/5]

= -10 + 6

= -4

Hence, the coordinates of the point on the directed line segment from (-9, -10) to (1,5) that partitions the segment into a ratio of 2 to 3 is (-5,-4)

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Calcium plays an essential role in all of the following except ______. a. DNA synthesis b. muscle contraction c. blood clotting d. exocytosis e. communication true or false If a space ship traveling at 1000 miles per hour enters an area free of gravitational forces, its engine must run at some minimum level in order to maintain the ships velocity. According to equity theory, a person who feels equitably treated is motivated to ________. Describe how the graph of g(x)= ||x+2||+4 is related to the graph of the parent function. Use properties to rewrite the given equation. Which equations have the same solution as 2.3p 10.1 = 6.5p 4 0.01p? Select two options. 2.3p 10.1 = 6.4p 4 2.3p 10.1 = 6.49p 4 230p 1010 = 650p 400 p 23p 101 = 65p 40 p 2.3p 14.1 = 6.4p 4 in his work, artist patrick dougherty intentionally references ideas of home, architecture, and dwellings. true or false the swivel chair company manufacturers a standard recliner. during february, the firm's assembly department started production of 145,000 chairs. during the month, the firm completed 175,000 chairs and transferred them to the finishing department. the firm ended the month with 18,000 chairs in ending inventory. all direct materials costs are added at the beginning of the production cycle. weighted-average costing is used by swivel. what were the equivalent units for conversion costs for february if the beginning inventory was 70% complete as to conversion costs and the ending inventory was 40% complete as to conversion costs? Please help. Look at photo Question 510 Points(1) Al Smith, the Democratic candidate for President in 1928, was known for his ready wit and quick comebacks. (2) Once he washeckled while making a campaign speech. (3) "Tell 'em everything you know, Al," yelled the heckler. (4) "It won't take very long."(5) Al Smith answered with a grin, "I'll tell em everything we both know-it won't take any longer."The primary purpose of this passage is toA) a. inform students about a humorous aspect of a historical figure.b. persuade people to support the Democrats.c. both of the above. Can anyone help me with the answer for number 5 & 6 I really need my math homework done , it will be graded. Thank you. the council of trent did all the following When jamel went to the store, he spent $7 on 2. 5 pounds of hamburger meat. What are two different ways to express the rate in this situation?. Suppose the equilibrium aggregate price level is rising and the equilibrium level of real GDP is falling. Which of the following most likely caused these changes?A) The average price of homes begins to fall.B) Labor unions successfully negotiate an increase in nominal wages for their workers.C) Congress decides to reduce purchases of new weapon systems.D) A recession overseas causes foreigners to buy fewer U.S. goods. Which relation represents a function? New york city will pay two men $36 million for their wrongful conviction in the 1965 assassination of civil rights activist. ?. instructions:explain the different types of racism that happens tying back to Enviromental racism and how it affects people of color. use references which of the following is a feature of language? group of answer choices it is stable it is inherently illogical its written and spoken forms are usually the same it consists of sounds organized into words according to some sort of grammar a mortgage that builds up equity faster while interest costs are cut by more than one-half. multiple choice question. interest-only mortgage graduated payment mortgage 15-year fixed-rate mortgage adjustable rate mortgag what ideologies threaten the free world today why does it matter to know about mobile phone art and computer-generated images?