Maya is using a coordinate plane to create a map of her yard drawn to scale. Each unit
on the coordinate plane represents 1 meter. Her yard forms a quadrilateral with vertices
A(5, -3), B(10, -3), C(12, -11), and D(7, -11). Maya would like to fence in her entire
yard. Fencing costs $200 per meter. How much will it cost Maya to fence in her yard?
Answers
Answer:
$5,298.48
Step-by-step explanation:
Given vertices:
A = (5, -3)B = (10, -3)C = (12, -11)D = (7, -11)As points A and B, and points C and D, have the same y-coordinates, AB is parallel to CD.
As there is a difference of 5 units between points A and B, and C and D, AB = CD.
As AB is parallel to CD and AB = CD ⇒ AD = BD and AD is parallel to BD.
Therefore, the quadrilateral ABCD is a parallelogram (see attachment).
To find the perimeter of ABCD, calculate the side lengths of AB and AD using the Distance Formula.
[tex]\boxed{\begin{minipage}{4.7 cm}\underline{Distance Formula}\\\\$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are the two endpoints.\end{minipage}}[/tex]
[tex]\begin{aligned}AB & =\sqrt{(x_B-x_A)^2+(y_B-y_A)^2}\\& =\sqrt{(10-5)^2+(-3-(-3))^2}\\& =\sqrt{(5)^2+(0)^2}\\& =\sqrt{25}\\& =5\:\:\sf units\end{aligned}[/tex]
[tex]\begin{aligned}AD & =\sqrt{(x_D-x_A)^2+(y_D-y_A)^2}\\& =\sqrt{(7-5)^2+(-11-(-3))^2}\\& =\sqrt{(2)^2+(-8)^2}\\& =\sqrt{4+64}\\& =\sqrt{68}\:\:\sf units\end{aligned}[/tex]
The perimeter of a two-dimensional shape is the distance all the way around the outside.
[tex]\begin{aligned}\textsf{Perimeter of $ABCD$} & = AB + CD + AD + BC\\& = 2\:AB + 2\:AD\\& = 2 \cdot 5+2 \cdot \sqrt{68}\\& = 10+2 \sqrt{68}\\& = 10+2\sqrt{4 \cdot 17}\\& = 10+2\sqrt{4}\sqrt{17}\\& = 10+2 \cdot2\sqrt{17}\\& = 10+4\sqrt{17}\:\:\sf units\end{aligned}[/tex]
As 1 unit = 1 meter, the perimeter of the fence is (10 + 4√17) m.
If fencing costs $200 per meter:
[tex]\begin{aligned}\sf \implies Cost \:of\:fencing& = 200(10 + 4 \sqrt{17})\\& = 2000+800 \sqrt{17}\\& = 5298.4845\\ & = \$5298.48\end{aligned}[/tex]
Therefore, it will cost Maya $5,298.48 to fence her yard.
Related Questions
Find the volume generated by rotating the given region about the specified line. I tried it 4 different times and have 1 try left! Please help only if you're sure of how to do it
Answers
Using integrals, the volume generated by rotating the given region about the specified line is of 0.8π cubic units.
How to use integrals to find the volume of a curve?Rotating a function f(x) around a function g(x), the volume is given by the following integral:
[tex]V = \pi \int_{a}^{b}[f(x) - g(x)]^2 dx[/tex]
In which a and b are the intersection points of the curve.
For this problem, from the graph, we have that:
[tex]f(x) = 2\sqrt[4]{x}[/tex].g(x) = 2x.a = 0.b = 1.Hence:
[tex]V = \pi \int_{0}^{1}[2\sqrt[4]{x} - 2x]^2 dx[/tex]
[tex]V = \pi [\int_{0}^{1} 4\sqrt{x} - 8x\sqrt{x} + 4x^2 dx][/tex]
[tex]V = \pi \left[\frac{8}{3}x^{\frac{3}{2}} - \frac{16}{5}x^{\frac{5}{2}} + \frac{4}{3}x^3}\right]_{x=0}^{x=1}[/tex]
[tex]V = \pi \left[\frac{8}{3} - \frac{16}{5} + \frac{4}{3}\right][/tex]
[tex]V = \pi \left[4 - \frac{16}{5}\right][/tex]
[tex]V = \frac{4\pi}{5}[/tex]
V = 0.8π cubic units.
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9. Your family is looking for a new Internet company. Comcast has a $50 installation fee
and $60 per month for Internet. Centurylink has no installation fee and $60 per month.
Your grandparents decide to register with Comcast the sametime your family registers
with Centurylink. At what month will your family pay the same as your grandparents?
Answers
Answer:
in the heaven or hell hhhvgvcgdgghh
There are 35 students in a class. Fifteen of them are men and 20 of them are women. The mean height of the men is 69.65 inches, and the mean height of all 35 students is 66.85 inches. What is the mean height of the women?
Answers
Answer:
64.75
Step-by-step explanation:
The total heights of men is m
so m/15 = 69.65 => m = 1044.75
The total heights of all students is s
so s/35 = 66.85 => s = 2339.75
so the total heights of women = 2339.75 - 1044.75 = 1295
The mean height of women = 1295/20 = 64.75
An English instructor asserted that students' test grades are directly proportional to the amount of time spent studying.
Lisa studies 6 hr for a particular test and gets a score of 76. At this rate, how many hours would she have had to
study to get a
score of 91?
Answers
Answer:
7.18421051
Step-by-step explanation:
76 ÷ 6 = 12.6666667
91 ÷ 12.6666667 = 7.18421051
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what is |x|-7=1 what is the answer
Answers
Answer:
it is x=8 or x=-8
Step-by-step explanation:
|x|-7=1
+7 +7
x=8 or x=-8
i'm doing absolute value in math rn so this should be right!! have a good day
Calculate the length of a chord of a circle of radius 26cm if the chord is 10cm from the center of the circle
Answers
Answer: see explanation
Step-by-step explanation:
The 10 cm distance is measured perpendicularly to the chord, forming a right angle and bisecting the chord. Thus half of the chord, the segment from the center of the chord, and a radius to the end of the chord form a right triangle. The hypotenuse is 26 cm and one leg is 10 cm, so the other leg is given by the Pythagorean theorem: a^2 + 10^2 = 26^2, giving a = 24 cm. Since a is half the chord, the chord is 2a = 48 cm in length.
Hence, the length of a chord of a circle is [tex]48cm[/tex].
What is the circle?
A circle is defined as a two-dimensional figure, which is round in shape where all the points on the surface of the circle are equidistant from the center point is called “[tex]P[/tex]”.
Here given that,
A circle of radius [tex]26[/tex]cm if the chord is [tex]10[/tex]cm from the center of the circle.
So,
The [tex]10[/tex]cm from the center of the circle is perpendicular of the chord and the hypotenuse is [tex]26[/tex]cm .
As we know
[tex]H^2=B^2+P^2[/tex] .......[tex](1)[/tex]
Substituting the values in the equation [tex](1)[/tex], we get
[tex](26)^2=(10)^2+B^2\\B^2=676-100\\B^2=576\\B=\sqrt{576}\\B=24cm[/tex]
Hence, the length of a chord of a circle is [tex]48cm[/tex].
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0.50x +0.15(30) = 23.5
Answers
Explanation:
Isolate the x
Multiply the .15x30=4.5
.50x + 4.5 = 23.5
Subtract 4.5
.50x = 19
Divide by .50
19/.50 = 38
X = 38
Answer: x=38
Step-by-step explanation:
SOLVE FOR X
STEPS FOR SOLVING LINEAR EQUATION
0.50x+0.15(30)=23.5
Multiply 0.15 and 30 to get 4.5.
0.5x+4.5=23.5
Subtract 4.5 from both sides.
0.5x=23.5−4.5
Subtract 4.5 from 23.5 to get 19.
0.5x=19
Divide both sides by 0.5.
[tex]x=\frac{19}{0.5}[/tex]
Expand [tex]\frac{19}{0.5}[/tex] by multiplying both numerator and the denominator by 10.
[tex]x=\frac{190}{5}[/tex]
Divide 190 by 5 to get 38.
x=38
What kind of numbers are −5 and 7?
Answers
-5 and 7 are real and rational numbers also they are integers.
What is a rational number ?Numbers which can be written in the form of p/q are rational numbers where q must not be zero.
According to the given question we have to determine what kind of numbers are -5 and 7.
In a most simple way we can say that - 5 is an negative integer and 7 is a positive integer.
But -5 can be written as -5/1 which is a rational number also and 7 can also be written as 7/1 so we can also say they are integers al well as rational numbers.Lastly they are real numbers as they don't have any imaginary part 'i' in it.
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The angles of a triangle add up to 180 degrees.
The second angle is 20 degrees larger than the smallest angle.
The third angle is 3 times as big as the smallest angle.
Find the measure of the smallest angle (in degrees).
Answers
Answer:
32 degrees
Step-by-step explanation:
You want the smallest angle of a triangle in which the other two angles are 20 degrees larger than the smallest, and 3 times the smallest.
SetupThe sum of angles is 180 degrees. The three angles are x, (x+20), and (3x). Their sum is ...
x +(x +20) +3x = 180
SolutionCollecting terms gives ...
5x +20 = 180
5x = 160 . . . . . . subtract 20
x = 32 . . . . . . divide by 5
The smallest angle is 32 degrees.
A line passes through the point (-2, 6) and has a slope of -8.
Write an equation in slope-intercept form for this line.
Answers
The given equation of the straight line is y +8x+10=0
We are required to find the equation of a straight line passing through the point (-2, 6) and has a slope of -8.
An equation of a straight line can be easily found if the slope and any of the points is given
The general form of equation is given by
y-y1 = m (x-x1)
where x1,y1 is the coordinate of the known point
m is the slope of the line
It is given that the coordinate of the known point is (-2,6)
the slope is given to be -8
Thus using these values to form the equation,
y-6 = -8 (x--2)
y-6 = -8 (x+2)
y-6 = -8x-16
y+8x-6+16=0
y+8x+`10=0
Hence, The straight line equation is y +8x+10=0
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One integer is selected at random from integers 8 through 38. Find the probability that the number is odd
Answers
Answer: 0.48387
Step-by-step explanation:
Solution set = {9,11,13,15,17,19,21,23,25,27,29,31,33,35,37}
Sample Set = {8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38}
out of the 31 numbers, 15 are odd
15/31 = 0.48387 probability.
. Compare the value of the 4's in this number
64,432
Write your statement
Answers
The 4 on the right is 10 times larger than the 4 on the left! (=^.^=)
How many even 2 digit positive integers can be written using the numbers 2,4,5,8
Answers
Answer: 12 different even 2 digit positive numbers can be witten
Step-by-step explanation:
the even numbers are 44, 24, 54, 84, 22, 42, 52, 82, 28, 48, 58, 88
Please answer the screenshot
Answers
The set of ordered pairs that represents a function is the third option.
{ (4, 1), (-6, 6), (5, -2), (-4, 1)}
Which set of ordered pairs represents a function?
For a relation that maps elements x (inputs) into elements y (outputs), we will have ordered pairs of the form (x, y) that define the relation.
Now, a relation is only a function if input are only mapped to only one output.
For example, if you look at the first set of ordered pairs, you can see that the input x = -4 appears twice with two different outputs, then this relation does not represent a function.
For the second set the same thing happens for the input x = -8, and for the last set the same happens for the input x = -8
The only set where each input appears only once is the third one:
{ (4, 1), (-6, 6), (5, -2), (-4, 1)}
This relation represents a function, so this is the correct option.
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|3x|-4=2x-4 Solve for x
Answers
Answer:
Your answer is x=0
Which expression has the same value as 4^2 - 6 x 2?
A. 1 - 8^0 + 2^2
B. 3^2 x 6^-2
C. 10 - 3 x 2 + 4^1
Answers
The expression which has the same value as the given expression; 4² - 6 × 2 among the answer choices is; Choice C; 10 - 3 x 2 + 4¹.
Which expression has the same value as the given expression?According to the task content; the given expression whose equivalent is to be determined is;
Given;
4² -6 ×2.
It follows from PEMDAS that the exponent should be evaluated and then the multiplication.
Hence, the value of the expression is; 16 - 8
= 8.
For answer choice C, which is correct, the evaluation is as follows;
10 - 3 × 2 + 4¹
= 10 -6 + 4
= 8.
Ultimately, choice C has the same value as the given expression.
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m/NMG = 46°, m/NML = 11x + 11, and m/GML = 8x-5. Find x.
Answers
we get that, the value of x for the given angles in the diagram is 10°.
We can see that:
∠ NMG + ∠ GML = ∠ NML
Substituting the values of the angles in the equation, we get that:
46 ° + 8 x - 5° = 11 x + 11 °
Combining the like terms:
8 x + 41° = 11 x + 11°
Taking variables on one side:
11 x - 8 x = 41° - 11°
Combining the like terms again:
3 x = 30°
Divide both sides by 3:
x = 30° / 3
x = 10°
Therefore, we get that, the value of x for the given angles in the diagram is 10°.
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Your question was incomplete. Please refer the content below:
∠ NMG = 46°, ∠ NML = 11x + 11, and ∠ GML = 8x-5. Find x.
There are 15 floors of an office building each floor is 10 2/5 feet tall 24 9/10 feet of the building are completed 1 1/4 feet of the building can be finished each day how many days are needed to complete the building
Answers
The days it would take to complete the building is 104 22/25 days.
How many days would it take to complete the building?A fraction is a non-integer that has a numerator and a denominator. The numerator is the number above. While the denominator is the number below. An example of a fraction is 1/4.
A mixed number is a number that has a whole number and a proper fraction. A proper fraction is a non-integer in which the numerator is less than the denominator. An example of a mixed number is 3 1/2.
The first step is to determine the total height of the office bulding = height of each floor x total number of floors
15 x 10 2/5
15 x 52/5 = 780 /5 = 156
The next step is to determine the floors left to complete the office building :
156 - 24 9/10 = 131 1/10 feet
The last step is to divide the feet that can be built each day by the number of floors needed to complete the builfing :
1311/10 ÷ 1 1/4
1311 / 110 ÷ 5/4
1311 / 10 x 4/5 = 104 days 44/50
104 22/25 days
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Un terreno tiene 205 metros y cada metro cuesta 315 cuánto vale el terreno
Answers
Answer:
64,765
Step-by-step explanation:
multiplicas porque dice que uno cuesta 315 entonces si hay 205 hay 64,765
Six friends each use $2-off coupons to but themselves a movie ticket. They spend a total of $42. What is the price of one movie ticket without coupon?
Answers
Modelling the situation, it is found the price of the ticket without the coupon is of $9 when all the six friends spent $ 42 to buy the tickets.
Total money spent by 6 friends on purchasing of the movie tickets = $ 42
So, the money spent for the purchase of 1 ticket will be calculated by dividing the $ 42 by 6.
So, cost of 1 ticket = 4 42 / 6 = $ 7
Coupon is of $2-off.
This means that with the coupon, $2 is subtracted from the ticket price.
So, price of ticket will be = $ 7 + $ 2 = $ 9.
Therefore, the price of the ticket without the coupons will be $ 9.
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6216÷21 please show me the work
Answers
Therefore, on dividing 6216 by 21 we get 126
Given 6216 / 21
21 ) 6216 ( 296
42
(-)................... (By subtracting these two numbers we get )
201
189
(-)..................
126
126
.(-)..........................
0
Therefore 6216 / 21 = 126
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Ann and Ben translate documents from German into English.
A set of documents that would take Ann 10 days would take Ben 12 days.
Ann starts to translate the documents.
After 2 days Ann and Ben both work on translating the documents.
How many more days will it take to complete the work?
You must show your working.
Answers
Using the together rate, it will take more 3.45 days to complete the work.
Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers. The other operations are addition, subtraction, and multiplication.
The together rate is given by the sum of each separate rate.
For this problem, the rates are given as follows,
Ann,1/10 = 0.1
Ben,1/12 = 0.0833
Together,1/x
Hence the amount completed in 2 days is:
2 x (0.1 + 0.0833) = 0.3666
The amount it would take them to complete 100% of the project working together is found by the together rate as follows,
x = 60/11
x = 5.45 days.
The time it would take to do the remaining 100 - 36.66 = 63.34% of the project is,
0.6334 x 5.45 = 3.45 days.
It will take more 3.45 days to complete the work.
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ANSWER RIGHT AWAY PLEASE!
question one: simply the exponents. (show your work)
- 21^0 = ?
- (2/3)^-2 = ?
question two: Solve the problem. (leave your answer as a base number with an exponent and show your work)
- 4^6 / 4^2 = ?
question three: Convert the number into numerical form. (show your work)
- 8.723 x 10^-10 = ?
question four: Solve the problem. (leave your answer in scientific notion and show your work)
- 5.1 x 10^8 - 2.3 x 10^3 = ?
- 6 x 10^5 x 1.1 x 10^7 = ?
PLEASE ANSWER I WILL GIVE 100 POINTS TO ANYONE WHO ANSWERS AND MARK BRAINLIEST AT LEAST ANSWER THE ONES YOU KNOW
Answers
Answer:
1. 1, 9/4
2. 4^4
3. -0.0000000008723
4. -5100023*10^2, -6.6*10^(12)
Step-by-step explanation:
[tex]21^0 = 1;\ n^0\ always\ is\ 1.\\(\frac{2}{3})^{-2} = (\frac{3}{2})^2 = \frac{3^2}{2^2} = \frac{9}{4}; n^m\ is\ performed\ by\ doing\ n*n,\ m\ times.\\i.e.,\\ n^2=n*n;\\n^3=n*n*n;\\ n^4=n*n*n*n\\\\\frac{4^6}{4^2};\ original\\\\\frac{(4^2)^3}{4^2};\ (n^{mc}\ can\ be\ rewritten\ as\ (n^m)^c\\\\\frac{4^2}{4^2}*\frac{(4^2)^2}{1};\ split\ the\ fraction\ into\ two\ parts\ because\ of\ multiplication\ rules.\\\\1*4^4;\ \frac{n}{n}\ can\ be\ written\ as\ 1.\ \frac{n}{1}\ can\ be\ written\ as\ n.\\\\4^4[/tex]
Technically, [tex]4^4[/tex] is 256, but the answer is requested as a number with an exponent.
-8.723 * 10^-10 would be -0.0000000008723.
10^-10 = [tex]\frac{1}{10^{10}}[/tex], which would mean you must move your decimal left by the number of places indicated by the exponent.
[tex]-5.1*10^8-2.3*10^3 = x\\-51*10^7-23*10^2 = x\\10^7=10^{5+2}=10^5*10^2\\-5100000*10^2-23*10^2=x\\-5100023*10^2=x;\ combine\ like\ terms.\\-6*10^5 * 1.1*10^7 = x\\-6*1.1*10^5*10^7;\ rewrite\ for\ simplification.\\-6.6*10^{12}=x[/tex]
Use the graph of the line to answer the questions. what is an equation of the line in slope-point form? _____
How can the point-slope form be written in function notation?
_______
Answers
The slope-point form is y + 1 = (1/4) (x +2)
The function notation for the point-slope form is f(x) = -1 + (1/4) (x +2)
From the graph, we get two points (x₁, y₁) = (-2, -1) and (x₂, y₂) = (2,0)
Slope, m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
= [tex]\frac{0 --1}{2--2}[/tex]
= 1/4
The slope-point form of a line is (y-y₁) = m(x-x₁), where (x, y) is the general point on the line, (x₁, y₁) is a given point on the line and m, the slope of the line.
So here the slope-point form of the line is,
(y- -1) = 1/4(x- -2)
⇒ y + 1 = (1/4) (x +2)
For the function notation, we put y = f(x) simply and write it as,
f(x) = -1 + (1/4) (x +2)
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the first one is c
the second is B
Step-by-step explanation:
If LM = 22 and MN = 15, find LK
Answers
Could you show the work so I can learn? Thank you!
Answers
Answer:
38363
Step-by-step explanation:
1000 divided by 3 answer
Answers
Answer:333R1 or as a mixed fraction 33 1/3. I believe this is right :]
Step-by-step explanation:
PLEASE HELP ME TY!!!!!!
Answers
Answer:
3.82×10^7
Step-by-step explanation:
3.82e+7= 3.82×10^7
Step by step
3.82 x 10^7
Change from scientific to standard form
This is a positive power of 10 so your decimal will go to the right 7 places
3.82 to
38200000.
If the power of 10 was a negative, you move the decimal to the left creating a decimal number less than 1
You decide you need a new computer. The cost of the computer is $864. However, the store also offers a rent to own option which will cost $41 per week for 24 weeksHow much more will the rent to own option cost after you have made all of the payments? $
Answers
The rent option will cost 120 more dollars than the outright cost of the computer .
How to find how much more the rent to own option cost?The outright cost of the computer is $864.
The store also offers a rent to own option which will cost $41 per week for 24 weeks.
Therefore, the total cost for the rent option is as follows:
cost of the computer for rent option = 41 × 24
cost of the computer for rent option = 984 dollars
Therefore,
difference in cost = 984 - 864
difference in cost = 120 dollars
Therefore, the rent option will cost 120 more dollars than the outright cost of the computer.
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How many inches are in 75 mm
Answers
Answer: 2.95 I think
Step-by-step explanation: