You want to put a fence around your large yard. There are two companies that you have found to do the work. They have each given you a quote for how much the work will cost. Of course, you want to find out which company will be the cheapest. The boundary of your yard is determined by five trees. The lines connecting them form the edge of your property. Shown below are the descriptions for the positions of the trees relative to your house.
TREE Position (relative to your house)
1 100 ft. east 2 40 ft east, 80 ft south 3 40 ft west, 120 ft south 4 90 ft west, 60 ft north 5 20 ft east, 110 ft north
STEP 1: On graph paper, mark the position of each of the trees on your land. Let each block of the graph paper represent a 10-foot by 10-foot square. Using a straightedge, connect Tree 1 to Tree 2, Tree 2 to Tree 3, Tree 3 to Tree 4, and so on.
STEP 2: Use the Pythagorean Theorem to find the length of each side of your property. Round
each answer to the nearest hundredth, if necessary.
STEP 3: Determine the perimeter of your property by adding up all of the sides.
STEP 4: Company 1 says that they will complete the job for $12 per foot of fencing. Company 2
says that they will charge you $250 for the first 100 feet of fencing and $15 for each additional foot. Determine the cost of fencing for both companies.
Answers
Answer:
STEP 1: See attached drawing on graph paper
STEP 2:
Length of segment 1 - 2 = 100 feet
Length of segment 2 - 3 = 89.44 ft.
Length of segment 3 - 4 = 186.82 ft.
Length of segment 4 - 5 = 120.83 ft.
Length of segment 5 - 1 = 136.01 ft.
STEP 3:
The perimeter of the property is 633.103 ft.
STEP 4:
The cost of fencing by Company 1 is $7597.24
The cost of fencing by Company 2 is $8246.55
Therefore, the company that provides the cheapest quote for fencing the property is Company 1
Step-by-step explanation:
STEP 1: See attached drawing on graph paper
STEP 2:
Therefore, we have
Length of segment 1 - 2 = √(8² + 6²) = 10 × 10 = 100 feet
Length of segment 2 - 3 = √(4² + 8²) = 4·√5× 10 = 40·√5 feet = 89.44 ft.
Length of segment 3 - 4 = √(5² + 18²) = √349 = 10·√349 feet = 186.82 ft.
Length of segment 4 - 5 = √(11² + 5²) = √146 = 10·√146 feet = 120.83 ft.
Length of segment 5 - 1 = √(11² + 8²) = √185 = 10·√185 feet = 136.01 ft.
STEP 3:
Therefore, the perimeter of the property = 100 + 89.44 + 186.82 + 120.83 + 136.01 = 633.103 ft.
STEP 4:
Hence the cost of fencing the property by Company 1 = $12 × 633.103 = $7597.24
The cost of fencing the property by Company 2 = $250 + $15 × 533.103 = $8246.55.
Related Questions
The number of goldfish in a tank is 19, and the volume of the tank is 52 cubic feet. What is the density of the tank?
Answers
Answer:
0.37 goldfish per cubic feet
Step-by-step explanation:
Density has the formula = number/volume
Density = 19/52 = 0.36538 which is rounded to 0.37
Answer:
0.37 goldfish / cu ft. (to the nearest hundredth).
Step-by-step explanation:
Density = number of goldfish / volume of the tank.
That is 19 / 52
= 0.37 goldfish / cu ft.
Factor the perfect square trinomial 25x^2-60x+36
Answers
Since it is a perfect square trinomial, it is of the form:
a^2x^2-2abx+b^2 which simplifies to (ax-b)^2
Therefore:
sqrt(a)=sqrt(25)=5
sqrt(b)=sqrt(36)=6
Plug in a and b:
(ax-b)^2
(5x-6)^2
Test to make sure it did fit the formula:
-2abx=-60 (where x is 1)
-2(5)(6)=-60
-2(30)=-60
-60=-60
Answer:
(5x-6)^2
Please help and show work and steps
Answers
Answer:
I and III
Step-by-step explanation:
On a unit circle, the only two angles whose sine is [tex]-\dfrac{\sqrt{3}}{2}[/tex] are [tex]\dfrac{4\pi}{3}[/tex] and [tex]\dfrac{5\pi}{3}[/tex], otherwise known as [tex]-\dfrac{\pi}{3}[/tex]. Therefore, the correct answers are I and III. You can see the unit circle below, where the y coordinates of the above angles show [tex]-\dfrac{\sqrt{3}}{2}[/tex].
What is the area of the composite figure
Answers
to find the area of the figure, you first need to find the area of the separate figures: a triangle and a square.
first, find the area of the triangle:
multiply 13 and 5 to get 65.
divide 65 by 2.
32.5.
then, find the area of the rectangle:
multiply 5 and 14 to get 70.
add those answers up, and you get:
102.5
2.5 kg of potatoes cost £1.40
Work out the cost of 4.25 kg of potatoes.
Answers
Step-by-step explanation:
if 2.5kg=£1.40
then 4.25kg=!
then cross multiply
4.25×1.40=2.5
5.95÷2.5kg=£2.38
Answer:
4.25 kg = £2.38
Step-by-step explanation:
The formula for working out the price per quantity is : [tex]\frac{Price}{Amount}[/tex]
To work this out you would first need to convert the mass of 2.5 kilograms into grams. You can do this by multiplying 2.5 by 1000, this gives you 2500 grams. This is because 1 Kg is equivalent to 1000 g and so by multiplying it by 1000 we are converting the kilograms into grams.
Then the next step is to divide the price of £1.40 by the quantity of 2500, this gives you 0.00056. This is because we are working out how much it costs for 1 g of potatoes.
Now that we know the price per gram we can now start working out the price of 4.25 kg. You can do this by first multiplying the mass of 4.25 kg by 1000, this gives you 4250. This is because we are converting the kilograms into grams.
The final step is to multiply the price per gram which is 0.00056 by 4250, this gives you £2.38.
1) Multiply 2.5 by 1000.
[tex]2.5*1000=2500[/tex]
2) Divide 1.40 by 2500.
[tex]1.40/2500=0.00056[/tex]
3) Multiply 4.25 by 1000.
[tex]4.25*1000=4250[/tex]
4) Multiply 0.00056 by 4250.
[tex]0.00056*4250=2.38[/tex]
Given a triangle with side lengths 4.1 and 1.3, what is the range of possible sizes for x
Answers
Answer:
2.8-5.4
Step-by-step explanation:
4.1 minus 1.3 =2.8 4.1+1.3= 5.4 the answer will look like x<x< or something with the numbers idk for sure how it will look but i know the numbers are right
Aaron baked two identical cakes. He cut one into 9 equal
slices and the other into 18 equal slices.show that 2/3 of the 9-slice cake gives the same
number of pieces as 1/3 of the 18-slice cake.
Answers
Answer:
23
Step-by-step explanation:
Pls help me answer this if ur good at algebra. Thanks .
Answers
Answer:
Step-by-step explanation:
Answer of this question is 2
Answer:
Step-by-step explanation:
Find the area of a rectangle with the given base and height 9ft , 3in
Answers
Answer:
324 in^2
Step-by-step explanation:
If you transfer the 9 ft to inches you get 108 in
108x3=324
Answer:
21
Step-by-step explanation: 9 + 9 = 18 , 3 + 3 = 6 , 18 + 6 = 21.
Two rectangular prisms, M and N, are mathematically similar. The volumes of M and N are 17 cm^3 and 136 cm^3, respectively. The height of N is 18 cm. Find the corresponding height of M.
Answers
We have been given that two rectangular prisms, M and N, are mathematically similar. The volumes of M and N are 17 cm^3 and 136 cm^3, respectively. The height of N is 18 cm. We are asked to find the height of M.
First of all, we will find the ratio between sides of rectangle M and N using proportions.
[tex]\frac{\text{Side of N}}{\text{Side of M}}=\frac{\text{ Volume of N}}{\text{ Volume of M}}[/tex]
[tex]\frac{\text{Side of N}}{\text{Side of M}}=\frac{136\text{ cm}^3}{17\text{ cm}^3}[/tex]
[tex]\frac{\text{Side of N}}{\text{Side of M}}=\frac{8\text{ cm}^3}{1\text{ cm}^3}[/tex]
Now we will take cube root on right side to find length in cm.
[tex]\frac{\text{Side of N}}{\text{Side of M}}=\frac{\sqrt[3]{\text{8 cm}^3}}{\sqrt[3]{\text{1 cm}^3}}[/tex]
[tex]\frac{\text{Side of N}}{\text{Side of M}}=\frac{\text{2 cm}}{\text{1 cm}}[/tex]
Therefore, sides of rectangle N is 2 times greater than sides of rectangle M.
To find height of rectangle M, we will divide side of rectangle N by 2.
[tex]\text{Height of rectangle M}=\frac{18}{2}=9[/tex]
Therefore, height of rectangle M is 9 cm.
What is the probability that 2 randomly selected months have 31 days?
Answers
Answer:
31.8%
Step-by-step explanation:There are 7 months that have 31 days so,
The odds the first selected month has 31 days is 7/12
The next month there are only 6 months left with 31 days of only 11 months to choose from
so the odds for the second are 6/11
To calculate the odds they BOTH have 31 months you multiply the two odds:
(7/12) x (6/11) = 42/132 = .318 so 31.8%
The required probability is 0.318 or 31.8% (in the form of a percentage) that 2 randomly selected months have 31 days.
What is probability?Probability is defined as the possibility of an event being equal to the ratio of the number of favorable outcomes and the total number of outcomes.
There are 7 months with 31 days, therefore
The probability that the first picked month has 31 days is 7/12.
There are just 6 months left with 31 days of only 11 months to choose from the following month.
As a result, the odds for the second are 6/11.
To determine the probabilities that they both have 31 months, multiply the two odds:
⇒ (7/12) × (6/11)
⇒ 42/132
Apply the division operation,
⇒ 0.318
⇒ 31.8% in the form of a percentage
Thus, the required probability is 0.318 or 31.8% that 2 randomly selected months have 31 days.
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A point has a position vector given by [tex]r(t)=(2t,t^2)[/tex] for all time t ≥ 0 seconds. Find the speed of the object at t = 1 seconds.
8
4
2
[tex]2\sqrt{2}[/tex]
Answers
Answer:
2√2
Step-by-step explanation:
r(t) = (2t, t²)
v(t) = dr/dt
v(t) = (2, 2t)
v(1) = (2, 2)
|v(1)| = √(2² + 2²)
|v(1)| = 2√2
The mean age of 5 people in a room is 37 years.
A person enters the room.
The mean age is now 38.
What is the age of the person who entered the room?
my hegarty work lol im 2 lazy 2 answer
Answers
Answer:39?
Step-by-step explanation:
Answer:
43
Step-by-step explanation:
+ Total age of 5 people: 37 x5 = 185
+ Total age of 6 people (when 1 person enters the room): 38 x 6 = 228
+ The age of the person who enter the room is: 228 - 185 = 43 age
!!!TIMED REVIEW PLS ANSWER QUICKLY WILL LIST BRAINLIEST♡
three fifths multiplied by two tenths
Answers
Answer:
0.12 in decimal form and fraction form is 3/25
Step-by-step explanation:
:)
Answer:
Step-by-step explanation:
three fifths times two tenths = six over fifty simplified version = three over twenty-five
A carpenter leans an extension ladder against a house to reach the bottom of a window 30 feet
above the ground. As shown in the diagram below, the ladder makes a 70° angle with the ground.
To the nearest foot, determine and state the length of the ladder.
Answers
Answer:The answer will be 35ft
Step-by-step explanation:
One way that you can answer this is by using sin law. You will put the length of a side on top and the corresponding angle that faces towards that side at the bottom of a fraction. So for this one it will be 30/sin(70) = x/sin(90) The 90 comes from the bottom of the building with the ground. And the side the angle faces is the ladder. After that you put 30sin(90)/sin(70) to find x. And you get 34.655 which rounds to 35 ft.
Starting at 1:00 p.M., The temperature changes -4 degrees Fahrenheit per hour. Write and solve an equation to find how many hours (x) it will take to reach -1 °F.
Answers
Answer: it will take 5 hours to reach -1 °F.
Step-by-step explanation:
The temperature changes -4 degrees Fahrenheit per hour. This is a linear rate. The rate at which the temperature is decreasing is in arithmetic progression. The formula for determining the nth term of an arithmetic sequence is expressed as
Tn = a + (n - 1)d
Where
a represents the first term of the sequence(the starting point)
d represents the common difference.
n = x = the number of terms in the sequence(number of hours)
From the information given,
a = 0(at 1 pm, number of hours is 0)
d = - 4 degrees (it is decreasing)
Tn = -1 °F.
We want to determine the number of hours, x when Tn = -1 °F
Therefore,
- 1 = 0 + (x - 1)- 4
- 1 = - x + 4
x = 4 + 1
x = 5 hours
Please help, thank you.
Answers
Answer:
Photoreceptors
Step-by-step explanation:
This is the answer but I don't see it on there . . .
Question:This is a light sensitive tissue that lines the back of the eye
Answer: Retina
these 2 questions please will mark brainly
Answers
Answer:
[tex]28\sqrt{2}[/tex]
Step-by-step explanation:
To answer this question, you must split 98 into 2 factors:
98
2 49
7 7
2 and 49 can be multiplied to get 98. 49 is also a perfect square, meaning the factors are going to be the same number, which is 7. Since there are two 7's you take that out of the radical, like so:
[tex](7)4\sqrt{2}[/tex]
[tex]28\sqrt{2}[/tex]
Ronny is selling coffee mugs for $3.00. So far, he has earned $228.00. Ronny needs to earn more than $372.00 in order to meet his sales goal. How many more coffee mugs, x, does Ronny need to sell in order to reach his sales goal?
Answers
Answer:
He needs to sell at least 49 mugs.
Step-by-step explanation:
Since Ronny earned $228 and needs to earn more than $372, he needs to earn more than 372-228 = 144.
Since he sells a mug for $3 and needs more than $144, his earning must be greater than 144:
→ 3x > 144, x represents the number of coffee mugs
→ x > 48
→ x must be at least 49
Seth's mother brought home 3/4 of a chocolate cake and 1/2 of a vanilla cake that was left from a party at her work. Seth ate 1/3 of the chocolate cake that was left. How much of the whole chocolate cake did he eat?
Answers
Answer:
1/4 of the cake.
Step-by-step explanation:
Since he ate 1/3 of 3/4 of the chocolate cake, we will need to multiply fractions to solve this.
[tex]\frac{3}{4} * \frac{1}{3} = \frac{3}{12} = \frac{1}{4}[/tex]
Therefore, he ate 1/4 of the entire cake.
The triangle has side lengths 7, 10, and 12. Is it a right triangle? Explain your reasoning.
Answers
Answer: it is not a right triangle
12^2=7^2+10^2
144=49+100
144=149
To prove this we try the pitagor teorem which the largest side is the hypotenuse
It is not a right triangle.
We have given that,
The triangle has side lengths 7, 10, and 12.
What is the Pythagoraus theorem?
[tex]hypotenous^2=side^2+side^2[/tex]
12^2=7^2+10^2
144=49+100
144=149
The pitagor theorem which the largest side is the hypotenuse.
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Order each set of the numbers from LEAST to GREATEST
0.23, 19%, 1/5
Answers
If Quadrilateral JKLM is a square, where points J(-6, 0), K(?, ?), L(9, -1) and M(2, 7) are known. Find the coordinates of point K.
Group of answer choices
(-1, -8)
(5, -15)
(1,8)
(1, -8)
Answers
Answer:
-1 -8
Step-by-step explanation:
Answer:
(1,8)
Step-by-step explanation:
only point that doesn't go through other lines
What is 20 divided by 2
Answers
Answer:
10
Step-by-step explanation:
10 x 2 = 20
10 = 20 / 2
Answer:
10
Step-by-step explanation:
2×1=2
2×2=4
2×3=6
2×4=8
2×5=10
2×6=12
2×7=14
2×8=16
2×9=18
2×10=20
Someone please help me. ASAP
Answers
Answer:
x=2
Step-by-step explanation:
4x+6=x+12
-x -x
3x+6=12
-6 -6
3x=6
/3 /3
x=2
Answer:
x=2
Step-by-step explanation:
4x+6 = x+12
Subtract x from each side
4x-x +6 =x-x+12
3x +6 = 12
Subtract 6 from each side
3x+6-6=12-6
3x = 6
Divide each side by 3
3x/3 =6/3
x =2
Maggie buys 1 1/2 pounds of walnuts pounds of walnuts 8 ounces 8 ounces of pecans of pecans and 3/4 pounds of almonds how much do the nuts weigh in all
Answers
Answer:
[tex]2\frac{3}{4}[/tex] pounds
Step-by-step explanation:
Maggie buys 1 1/2 pounds of walnuts, 8 ounces of pecans and 3/4 pounds of almonds.
To find the total weight of nuts that she buys, let us first put all the weights in a single unit, pounds.
She buys 8 ounces of pecans.
1 ounce = 0.0625 pounds
8 ounces = 8 * 0.0625 = 0.5 pounds = 1/2 pounds
Therefore, the total weight of nuts that she buys is:
[tex]1\frac{1}{2} + \frac{1}{2} + \frac{3}{4}\\ \\\frac{3}{2} + \frac{1}{2} + \frac{3}{4} = 2\frac{3}{4}[/tex]
The nuts weight [tex]2\frac{3}{4}[/tex] pounds in all.
Answer:
the answer is 2 3/4 pounds
Step-by-step explanation:
To divide two powers with the same base, (fill the blank)
the exponents.
Answers
Kendra made a scaled copy of the following square. She used a scale factor less than 111. What could be the side length of the scaled copy of the square.
Answers
Answer:
B,C,E
Step-by-step explanation:
khan academy
Side length of the scaled copy of square is smaller than original.
What is scale factor?A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size (bigger or smaller).
Given,
Scale factor of scaled copy of square is less than 1.
Scale factor basically defines the ratio between the sides of the constructed square to that of the original square.
if scale factor is less than 1 then the sides of the constructed square is smaller than that of the original square.
Hence, side length of constructed square is smaller than the original square.
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which of the following is equivalent to 5 cube root 13^3
Answers
Answer:
d. 13 raise power 3/5
Step-by-step explanation:
helpppppp pros only helppppppp me plzzzzzzzzzzz ill reporte you if you do bad qweshtones
Answers
Answer:
A
Step-by-step explanation:
We are looking for 2 numbers with a product of -35 and a sum of -2. These are -7 and 5, so the factored version would be (w + 5)(w - 7), or A.
