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.

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.

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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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

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

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]

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:

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

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]

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.

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

Answer:

-1 -8

Step-by-step explanation:

Answer:

(1,8)

Step-by-step explanation:

only point that doesn't go through other lines

Answer:

d. 13 raise power 3/5

Step-by-step explanation:

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

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.

Answer:

B,C,E

Step-by-step explanation:

khan academy

Side length of the scaled copy of square is smaller than original.

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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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.

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

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

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].

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

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

Answer:

23

Step-by-step explanation:

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.

[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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Answer:

Step-by-step explanation:

Answer of this question is 2

Answer:

Step-by-step explanation:

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

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.

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.

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.

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