Find the perimeter of the polygon with the given vertices. Round your answer to the nearest hundredth.
4
4(1.4)
2
N(2.0)
14
-2
x
(Pl-1, -2)
M(4,0)
The perimeter is about
units.
Answers
Check the picture below, now the distance from 2,0 to 4,0 there's no need to do much calculation since that's just 2 units, as you see there.
[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\\\\ (\stackrel{x_1}{2}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{4}) ~\hfill d1=\sqrt{[ 1- 2]^2 + [ 4- 0]^2} \\\\\\ d1=\sqrt{(-1)^2+4^2}\implies \boxed{d1=\sqrt{17}} \\\\[-0.35em] ~\dotfill[/tex]
[tex](\stackrel{x_1}{1}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{-1}~,~\stackrel{y_2}{-2}) ~\hfill d2=\sqrt{[ -1- 1]^2 + [ -2- 4]^2} \\\\\\ d2=\sqrt{(-2)^2+(-6)^2}\implies \boxed{d2=\sqrt{40}} \\\\[-0.35em] ~\dotfill\\\\ (\stackrel{x_1}{-1}~,~\stackrel{y_1}{-2})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{0}) ~\hfill d3=\sqrt{[ 4- (-1)]^2 + [ 0- (-2)]^2} \\\\\\ d3=\sqrt{(4+1)^2+(0+2)^2}\implies \boxed{d3=\sqrt{29}}[/tex]
[tex]~\dotfill\\\\ \stackrel{\textit{\Large Perimeter}}{2~~ + ~~\sqrt{17}~~ + ~~\sqrt{40}~~ + ~~\sqrt{29}~~\approx~~17.83}[/tex]
The perimeter of the polygon with the vertices L = (1, 4), P = (-1, -2),
N = (2, 0) and M = (4, 0) is approximately 17.93 units.
We have,
The polygon has the following sides:
LP, PN, NM, and ML.
The coordinates for each point are:
L = (1, 4)
P = (-1, -2)
N = (2, 0)
M = (4, 0)
The perimeter of the polygons.
= LP + PN + NM + ML
Using the distance formula for the distance between two points (a, b) and (c, d):
Distance = √((c - a)² + (d - b)²)
Let's calculate the distances between the points:
LP:
Distance(LP)
= √((-1 - 1)² + (-2 - 4)²)
= √((-2)² + (-6)²)
= √(4 + 36)
= √40
= 6.32
PN:
Distance(PN)
= √((2 - (-1))² + (0 - (-2))²)
= √((2 + 1)² + (0 + 2)²)
= √(3² + 2²)
= √(9 + 4)
= √13
≈ 3.61
NM:
Distance(NM)
= √((4 - 2)² + (0 - 0)²)
= √(2² + 0²)
= √4
= 2
ML:
Distance(ML)
= √((4 - 1)² + (0 - 4)²)
= √((4 - 1)² + (-4)²)
= √(3² + 16)
= √(9 + 16)
= √25
= 5
Now,
Perimeter = LP + PN + NM + ML
Perimeter ≈ 6.32 + 3.61 + 2 + 5 ≈ 16.93
Thus,
The perimeter of the polygon is approximately 17.93 units.
Learn more about polygons here:
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Related Questions
Alex is 12 years older than George.
Carl is three times older than Alex
The sum of their ages is 68
Find the ratio of George's age to Carl's age to Alex's age.
Answers
Answer:
George : Carl : Alex = 1 : 12 : 4
Step-by-step explanation:
let a = Alex's age in years
let g = George's age in years
let c = Carl's age in years
Given:
Alex is 12 years older than George⇒ a = 12 + g
⇒ g = a - 12
Given:
Carl is three times older than Alex⇒ c = 3a
Given:
The sum of their ages is 68⇒ a + g + c = 68
Substitute the first two equations in the last equation and solve for a:
⇒ a + (a - 12) + 3a = 68
⇒ 5a - 12 = 68
⇒ 5a = 80
⇒ a = 16
Substitute the found value of a into the other equations to find g and c:
⇒ g = 16 - 12 = 4
⇒ c = 3(16) = 48
Therefore:
Alex = 16 years oldGeorge = 4 years oldCarl = 48 years oldRatio
George : Carl : Alex = 4 : 48 : 16
Reduce by dividing by 4 → 1 : 12 : 4
In which quadrant does Ø lie if the following statement is true:
Answers
The total amount of deductions from an employee’s gross pay is $83.20. if the gross pay is $378.18, what percent of their gross pay is being withheld? a. 21% b. 22% c. 23% d. 24% please select the best answer from the choices provided a b c d
Answers
The total amount of deduction in percentage is 22%. Then the correct option is B.
What is the percentage?The amount of something is expressed as if it is a part of the total which is a hundred. The ratio can be expressed as a fraction of 100. The word percent means per 100. It is represented by the symbol ‘%’.
The total amount of deductions from an employee’s gross pay is $83.20. if the gross pay is $378.18.
Then the percentage will be given as
[tex]\rm P = \dfrac{83.20}{378.18}\times 100\\\\P = 0.220 \ or \ 22\%[/tex]
More about the percentage link is given below.
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Kobe's overtime pay is $5 an hour more than his regular pay. He worked 8 hours at his regular wage and 3 hours at his overtime wage. He earned $114.
What is Kobe's regular wage per hour?
Answers
Answer:
anwer 9$ and hour
Step-by-step explanation:
9×8=72
9+5=14
14×3=42
42+72=114
mean absolute deviation of 290
Answers
Answer:
3.5555555555556
Step-by-step explanation:
you cannot find the Mean Absolute Deviation of one number. This answer is the data set 2, 9, and 0. 3.5555555555556 is the Mean Absolute Deviation of 2, 9, 0.
Jenny scored a 70% on a 50 point test while Hannah scored 80% on the same test. Enter the difference.
Answers
Answer:
5
Step-by-step explanation:
70% is 0.7, multiply 0.7×50=35 points on Jenny's test. Hannah scored 0.8×50=40 points on the test. Subtract 40-35 for the answer of 5
Really appreciate it!!! Have a blessed day!!!!
Answers
Answer:
A.
Divide each dimension by scale factor of 5
Big Δ dimensions : Small Δ dimensions
35 : 7
30 : 6
15 : 3
a = 7 in
b = 6 in
c = 3 in
Hope this helps and God bless!
Vlad spent 20 minutes on his history homework and then completely solved x math problems that each took 2 minutes to complete. what is the equation that can be used to find the value of y, the total time that vlad spent on his homework, and what are the constraints on the values of x and y? y=2x 20; x is any integer greater than or equal to 0, and y is an integer greater than or equal to 20. y=2x 20; x is any real number greater than or equal to 0, and y is any real number greater than or equal to 20. y=20x 2; x is any integer greater than or equal to 0, and y is an integer greater than or equal to 20. y=20x 2; x is any real number greater than or equal to 0, and y is any real number greater than or equal to 20.
Answers
The expression for y is y = 2x +20; x is any integer greater than or equal to 0, and y is an integer greater than or equal to 20
How to form mathematical expression from the given description?You can represent the unknown amounts by the use of variables. Follow whatever the description is and convert it one by one mathematically. For example if it is asked to increase some item by 4 , then you can add 4 in that item to increase it by 4. If something is for example, doubled, then you can multiply that thing by 2 and so on methods can be used to convert description to mathematical expressions.
What is domain and range of a function?Domain is the set of values for which the given function is defined.
Range is the set of all values which the given function can output.
We're given that:
Time spent by Vlad on history homework = 20 minutesTime spent by Vlad on math homework (x math problems) = 2 minutes on each problemy = time he spent on doing overall homeworkThen we have:
y = time on math homework + history homework
y = 2 +2 +2 ... (x times) + 20 minutes
[tex]y = 2x + 20[/tex]
x is "number of math problems". Thus, x can be 0,1,2,... These numbers are called non-negative integers(or integers greater or equal to 0) or whole numbers.
y is the time taken, but we see that
y = 2 times (non-negative integer) + 20
y = positive integer times non-negative integer + positive integer
Thus, we have:
y = non-negative integer + positive integer = positive integer
Thus, y assumes positive integral values only (in minutes).
Also, y is always going to be at least 20 (as history homework is going to take 20 minutes, even if math homework is nill ).
Thus, the expression for y is y = 2x +20; x is any integer greater than or equal to 0, and y is an integer greater than or equal to 20
Learn more about domain here:
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solve for n: -1/2 (n + 8) +3/4
Answers
[tex]\frac{1}{2} (n+8) + \frac{3}{4} [/tex]
[tex]\frac{1(n+8)}{2} + \frac{3}{4} [/tex]
[tex]\frac{n+8}{2} + \frac{3}{4} [/tex]
[tex]\frac{2(n+8)}{4} + \frac{3}{4} [/tex]
[tex]\frac{2(n+8) + 3}{4} [/tex]
[tex]\frac{2n + 16 +3}{4} [/tex]
[tex] \frac{2n + 19}{4} [/tex]
Find the value of c.
12 cm
с
40 cm
Perimeter
100 centimeters
C=
centimeters
Submit
Answers
Answer:
[tex]c + c \: + 40 + 12 = 100 \\ 2c + 52 = 100 \\ 2c = 100 - 52 \\ 2c = 48 \\ c = \frac{48}{2} \\ c = 24cm[/tex]
Answer: 24
Explanation: 12+40 is 52, perimeter is adding up all the sides. since perimeter is 100, then you have to see what numbers you add to get 100. 100-52 is 48. since there are 2 sides, you divide 48 by 2, which is 24.
I hope this is helpful xx
10 squares and 8 circles. What is the simplest ratio of circles to total shapes?
Answers
Answer:
8:18
Step-by-step explanation:
You are ordering sweatshirts for your baseball team. How many more large sweatshirts than medium sweatshirts do you order?
Answers
Answer:
The answer is 10 and i know because im smart
Step-by-step explanation:
because im smart
Answer:
24
Step-by-step explanation:
add 8 and 12 and 4 and its 24
three teachers handed out math and science textbooks for their classes two teachers had 21 students each and the last teacher had 22 how many textbooks were handed out altogether
help me pls with this problem sooon
Answers
Answer:
64 textbooks
Step-by-step explanation:
the first two teachers had 21 students each that's 21+21=42
the other teacher had 22 students so apparently all the textbooks handed to the students are,21+21+22=64
To solve the following problem, use the 5-D Process. Define
a variable and write an expression for each column of your
table. In the first three football games of the season, Carlos gained three times as many yards as Alston. Travis gained ten yards
more than Carlos. Altogether, the three players gained a total
of 430 yards. How many yards did Carlos gain?
Answers
Answer:
c=3a=180
Step-by-step explanation:
c=3a,t=c+10 and a +t=430
a+3a+3a+10=430
7a=420
a=60
c=3a=180
6 Résolvez les équations suivantes.
a. x + 4 = 12
d. -14 = 2x
b. x + 5,1 = x + x
e. 5 = 4x
C. 6x = x – 15
f. x + 8 = 2x + 3
=
=
X égal à combien
Answers
Answer:
Yo espero yo ayuda tu résolve estes équations
Step-by-step explanation:
a) x=8
b) x=-7
c) x=5,1
d) x=5/4
e) x=-3
f) x=5
Lo siento, mi español no son muy bien.
Which function is graphed on the right? y = 2x 3 – 2 y = 2x–3 2 y = 2x–2 3 y = 2x–2 – 3
Answers
The equation of the function which is graphed on the right is specified by: Option C: y = 2^{x-2} + 3
How to find the function which was used to make graph?There are many tools we can use to find the information of the relation which was used to form the graph.
A graph contains data of which input maps to which output.
Analysis of this leads to the relations which were used to make it.
For example, if the graph of a function is rising upwards after a certain value of x, then the function must be having increasingly output for inputs greater than that value of x.
If we know that the function crosses x axis at some point, then for some polynomial functions, we have those as roots of the polynomial.
Since there is no graph available, we will work with the image attached below.
The function, as visible is tending to output 3 and x goes more and more negative.
That means:
[tex]\lim_{x\rightarrow -\infty}f(x) = 3[/tex] (assuming the predicted pattern is true).
Checking this for all the options:
Case 1: [tex]y = f(x) = 2^{x+3} - 2[/tex]
[tex]\lim_{x\rightarrow -\infty}f(x) = \lim_{x\rightarrow -\infty} 2^{x+3} -2 = -2[/tex]
Thus, the graph doesn't belong to this function.
Case 2: [tex]y = f(x) = 2^{x-3} + 2[/tex]
[tex]\lim_{x\rightarrow -\infty} f(x) = \lim_{x\rightarrow -\infty}2^{x-3} + 2 = 2[/tex]
Thus, the graph doesn't belong to this function.
Case 3: [tex]y = f(x) = 2^{x-2} +3[/tex]
[tex]\lim_{x\rightarrow -\infty}f(x) = \lim_{x\rightarrow -\infty} 2^{x-2} +3 = 3[/tex]
Thus, the graph may belong to this function. (we are still not sure since the last option may also have same limit, which if is found to be true, then additional findings would've to be done too).
Case 4: [tex]y = f(x) = 2^{x-2} - 3[/tex]
[tex]\lim_{x\rightarrow -\infty}f(x) = \lim_{x\rightarrow -\infty} 2^{x-2} -3 = -3[/tex]
Thus, the graph doesn't belong to this function.
Thus, assuming at least one option is true, the graph of the considered function on the right is of the function [tex]y = f(x) = 2^{x-2} +3[/tex]
Learn more about graphing functions here:
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Answer:
c
Step-by-step explanation:
The radius of a circle is 4 m. Find its area in terms of
π
π.
Answers
Answer:
16π
Step-by-step explanation:
Given:
[tex]\text{Radius of circle}: 4 \ \text{m}[/tex]
Formula:
[tex]\text{Area of circle} = \pi r^{2}[/tex]
Replace the radius in the formula:
[tex]\implies \text{Area of circle} = \pi (4)^{2}[/tex]
Evaluate the area:
[tex]\implies \text{Area of circle} = \pi (4)(4)[/tex]
[tex]\implies \text{Area of circle} = 16\pi[/tex]
Since the question says to determine the area in terms of π, the final answer is 16π.
Which statement best describes the equation (x+5)^2+4(x+5)+12=0
Answers
Answer:
x^2 + 14x + 57 = 0
Step-by-step explanation:
(x+5)^2+4(x+5)+12 = 0
x^2 +10x + 25 + 4x + 20 + 12 = 0
x^2 + 14x + 57 = 0
Look at the following rules for two number patterns. Both patterns start with 40.
Pattern P: "Subtract 2"
Pattern Q: "Subtract 4"
Answers are:
Excluding the first term, a term in Pattern P is always 2 greater than its corresponding term in Pattern Q.
Excluding the first term, a term in Pattern Q is always 4 greater than its corresponding term in Pattern P.
Starting with 0, the difference in the corresponding terms in the two patterns decreases by 4.
Starting with 0, the difference in the corresponding terms in the two patterns increases by 2.
Answers
Answer:
Starting with 0, the difference in the corresponding terms in the two patterns increases by 2.
Step-by-step explanation:
P Q Difference
1 40 40 0
2 38 36 2
3 36 32 4
4 34 28 6
5 32 24 8
6 30 20 10
7 28 16 12
8 26 12 14
9 24 8 16
10 22 4 18
==================
Answers are:
Excluding the first term, a term in Pattern P is always 2 greater than its corresponding term in Pattern Q.
Excluding the first term, a term in Pattern Q is always 4 greater than its corresponding term in Pattern P.
Starting with 0, the difference in the corresponding terms in the two patterns decreases by 4.
Starting with 0, the difference in the corresponding terms in the two patterns increases by 2.What is the surface area of this composite solid? Show your work.
Answers
Answer:
357.5ft^3
Step-by-step explanation:
solve for bottom reticular prism
8 * 10 * 4
320ft^3
solve for top triangular prism
((3*5)/2)*5
37.5ft^3
add top and bottom
320+37.5
357.5ft^3
Answer: 268ft^3
Step-by-step explanation: To solve, find the area of each side and add them all together.
8*4=32*2=64
10*4=40*2=80
10*5=50*2=100
8*3/2=12*2=24
64+80+100+24=268
Hope I helped <3
3 . 7 x - x =
Hurry please correct answers only fake answers will get you reported .
Answers
Answer:
20x
Step-by-step explanation:
This is not multiple-choice, I need steps and how we found the answer, help I've been stuck for 2 days now!!!!
Find the surface area of the figure. Be sure to show all of your work and steps in solving for your answer.
Answers
Answer:
The surface area of a figure is the sum of all the sides that consist of it.
Let's first find the base's area, using the formula for the area of a rectangle, L · W:
9(6)
= 54 is the area of the base.
Now let's find the entire front side of this figure's area and double it so we get both the areas of the front and back side (using the formula for the area of a rectangle):
4(9)[bottom front rectangle] + 4(5)[upper front rectangle]
36 + 20
= 56, now double that area to get the area of both the front and back side:
56(2)
= 112 is the area of both the entire front and back side of this figure.
Now let's figure out the area of the right whole side of this figure then double it so we get both the areas for the left and right sides.
But, if we look at the middle rectangle to the right and left sides, we can see that there is no value, so let's find the value first.
The total length across the figure is 9 inches.
And we are given that the rectangle above intersects with the total length, so let's exclude that from 9 inches.
9 - 4 = 5, so now the total length of the two rectangles beside the above rectangle is 5.
But we want to find the value of one side, so divide 5 by 2.
5/2 = 2.5 inches.
Now let's find the whole entire area of the right side to this figure.
5(6)[upper right rectangle] + 2.5(5)[flat middle right rectangle] + 6(4)[bottom right rectangle)
30 + 12.5 + 24
= 66.5, now double that area to get both the area of the right and left side.
66.5(2)
= 133, is the area of both the right and left side of this entire figure.
Finally, we add all those areas together to get the surface area:-
54 + 112 + 133
= 299 inches is the surface area for this figure.
Answer:The surface area of a figure is the sum of all the sides that consist of it.
Let's first find the base's area, using the formula for the area of a rectangle, L · W:
9(6)
= 54 is the area of the base.
Now let's find the entire front side of this figure's area and double it so we get both the areas of the front and back side (using the formula for the area of a rectangle):
4(9)[bottom front rectangle] + 4(5)[upper front rectangle]
36 + 20
= 56, now double that area to get the area of both the front and back side:
56(2)
= 112 is the area of both the entire front and back side of this figure.
Now let's figure out the area of the right whole side of this figure then double it so we get both the areas for the left and right sides.
But, if we look at the middle rectangle to the right and left sides, we can see that there is no value, so let's find the value first.
The total length across the figure is 9 inches.
And we are given that the rectangle above intersects with the total length, so let's exclude that from 9 inches.
9 - 4 = 5, so now the total length of the two rectangles beside the above rectangle is 5.
But we want to find the value of one side, so divide 5 by 2.
5/2 = 2.5 inches.
Now let's find the whole entire area of the right side to this figure.
5(6)[upper right rectangle] + 2.5(5)[flat middle right rectangle] + 6(4)[bottom right rectangle)
30 + 12.5 + 24
= 66.5, now double that area to get both the area of the right and left side.
66.5(2)
= 133, is the area of both the right and left side of this entire figure.
Finally, we add all those areas together to get the surface area:-
54 + 112 + 133
= 299 inches is the surface area for this figure.
Step-by-step explanation:
Help me in math please
Answers
Answer:
1. 27.5
2.32.5
3.30
6.22.5
11. 17.5
16.12.5
21. 7.5
7.27.5
12.22.5
17.17.5
22.12.5
8.25
13.20
18.15
23.10
Find The distance between (5,2) and (5,0) on the coordinate Plane
Answers
Answer:
2
Step-by-step explanation:
2 is 2 away from 0
PLSSS HELP IF YOU TURLY KNOW THISS
Answers
Answer:
[tex]\huge\underline{\red{A}\blue{n}\pink{s}\purple{w}\orange{e}\green{r} -}[/tex]
option ( c ) [tex]\huge\pink{1 \frac{2}{5} }[/tex]
step by step explanation -
well , the question asks us to find the difference between the two terms given as mixed fractions ~
tho it's not that difficult to simplify a problem in mixed fraction , but solving the problem by first converting it to an improper fraction reduces the risk of mistakes ! so let's do the question by that way ~
[tex]4 \frac{4}{5} - 3 \frac{2}{5} \\ \\ converting \: into \: improper \: fraction \: we \: get \\ \\ \implies \: \frac{5 \times 4 + 4}{5} \: \: - \: \: \frac{5 \times 3 + 2}{5} \\ \\ \implies \: \frac{24}{5} \: \: - \: \: \frac{17}{5} \\ \\ since \: the \: denominators \: are \: same \: we \: can \: simply \: subtract \: the \: terms \\ \\ \implies \: \frac{7}{5} [/tex]
we're done with our solution tho , but since the options given are in mixed fraction , so let's convert the improper fraction , obtained as the answer , into a mixed fraction !
[tex] \frac{7}{5} = 1 \frac{2}{5} \\ [/tex]
hope helpful :D
Answer:
1 2/5
Step-by-step explanation:
subtract it and then add it and u will have your answer
This pattern follows the rule add 9. What are the next 3 terms?
An image of a pattern. Term one has 9 triangles, term two has eighteen triangles, term three has twenty seven triangles.
36, 45, 54
39, 48, 57
42, 51, 60
54, 63, 72
Answers
Answer: A
Step-by-step explanation: 27+9 = 36
II. Let us see what you have learned in this module by
completing the following statements.
The Central Limit Theorem implies the following important
ideas in statistics:
1. The sample mean can be considered approximately
normally distributed if the sample size is
2. If the population is not normally distributed, or if we don't
know of its distribution, the
allows us to
conclude that the distribution of the sample mean will be
normal if the sample size is sufficiently large.
3. The population mean is equal to the
of the
sampling distribution. That is u = ur.
4. Mean of the sampling distribution of the sample mean is
equal to the population mean: H. - = H and the
of the sampling distribution of the sample
mean (sampling with replacement)
is equal to: 0,7
5. The Central Limit Theorem describes the
of the sample mean taken from a
population that is not normally distributed
o
Answers
Solve the equation to find X.
2.5+5.5-0.6x
Answers
Answer:
40/3
Step-by-step explanation:
-0.6X=-8
X=-8/-06
X=40/3
The perimeter of a rectanglular pool is 294 m. If thr width of the pool is 54 m what is its length
Answers
Answer:
L=93
Step-by-step explanation:
So basically you need to know the formula beforehand the formula to find the length of a rectangle what is P=2(l+w) so to find for L the equation will be L=P/2-W=294-54=93 Therefore 93 is L
I’ve been stuck on this problem for the last 10 minutes and really need help! Here’s the problem:
Answers
Answer:
25.5
Step-by-step explanation:
the sum of an infinite geometric series with first term a and common ratio r<1 is given by a/(1-r).
------------------------------------
the sum of a given infinite geometric series is 200, and the common ratio is 0.15. What is the second term of this series?
Solve:
a/(1-r) = 200
a/0.85 = 200
a = 170 (that is the 1st term)
----
2nd term: a*r = 170*0.15 = 25.5
--------------------------------------