A landscape architect wants to plant a circle of flowers around a triangular garden. She has sketched the triangle on a coordinate grid with vertices at A (0, 0), B (8, 12), and C (18, 0). Explain how the architect can find the center of the circle that will circumscribe triangle ABC. Then find the radius of the circumscribed circle.

Answer:

Step-by-step explanation:

Yep!

Answer:

Step-by-step explanation:

We have 6 numbers, the mean is the average of all 6, so adding all 6 numbers together and dividing by 6 will give you 3. Because of this we know the 6 numbers will have to add up to 18.

The median is the middle number, but we have an even number so the median is found by adding the 2 middle numbers and dividing by 2.

Because the mean is low, we can guess the first 2 numbers will be small, so let's try 1.  

1 + 1 + _ + _ + _ + _

The remaining 4 numbers will have to add up to 16, and the next 2 numbers need to add up to 12. There would not be any possible combination where this would work. Now we know our first 2 numbers are too big.

Now we try 0.

0 + 0 + _ + _ + _ + _

Now our remaining 4 numbers neet to be 18, but the middle 2 need to add to 12 (so when we divide by 2 we get 6) so 0 is still too big!

-2 + -2 + _ + _ + _ + _  

If we try -2 now the next 4 numbers need to add to 22, but that's still not going to work because 22-12 = 10 and the last 2 numbers have to be the same, or larger than the middle 2.

-3 + -3 + _ + _ + _ + _  

With -3 then our total of the remaining 4 numbers needs to be 24 and 24-12 = 12 so this could be an option!

Our numbers could be:

-3, -3, 6, 6, 6, 6

Let's check:

-3 + -3 + 6 + 6 + 6 + 6 = 18   18/6 = 3    and our middle 2 numbers are 6 so our median would be 6.

If the numbers all have to be different we can come up with a different solution by making our first 2 numbers smaller.

-9, -5, 5, 7, 9, 11  

Let's check

-9 + -5 + 5 + 7 + 9 + 11

-14 + 32 = 18  mean  18/6 = 3      median 5+7 = 12 and 12/2 = 6

So that could also work! There are actually many options that would be correct!

One of the set of numbers whose mean is 3 and median is 6 is 0, 1, 5, 7, 2 and 3.

Mean of a set of numbers is the average value of the numbers. Mean is calculated by taking the sum of the given numbers divided by the total number of numbers.

Let x₁, x₂, x₃, x₄, x₅ and x₆ be the six numbers.

We have mean = 3

⇒ (x₁ + x₂ + x₃ + x₄ + x₅ + x₆) / 6 = 3

⇒ x₁ + x₂ + x₃ + x₄ + x₅ + x₆ = 18

Median is the midpoint of the set of numbers arranged in ascending or descending orders.

If the number of set of numbers are odd, then median is the midpoint of the set and if the number of the set is even, then median is the average of the middle two elements.

Median = 6

Since there are 6 numbers here median = (x₃ + x₄) / 2

(x₃ + x₄) / 2 = 6

(x₃ + x₄) = 12

So x₁ + x₂ + x₅ + x₆ = 18 - 12 = 6

Lets just say x₁ = 0, x₂ = 1, x₅ = 2 and x₆ = 3, the sum of which equals 6.

Now, let x₃ = 5 and x₄ = 7, such that x₃ + x₄ = 12

So one of the set which satisfies the given conditions is x₁, x₂, x₃, x₄, x₅ and x₆ = 0, 1, 5, 7, 2 and 3 respectively.

Hence, one of the list of 6 numbers whose mean equals 3 and median equals 6 is 0, 1, 5, 7, 2 and 3.

To learn more about Mean, click:

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The true statements are,

π is irrational because π is a repeating decimal.

7√ is irrational because 7 is not a perfect square.

7.1234… is irrational because it is a nonterminating, nonrepeating decimal.

7√ is rational because 7 is not a perfect square.

Irrational number are real numbers that cannot be expressed as a ratio of two integers.

Now we have,

→π is irrational because π is a repeating decimal.

Since, the value of π is called as infinite decimal-after the decimal point the digits go on forever and repeating.

Hence π is irrational.

⇒This statement is true.

→√7 is irrational because 7 is not a perfect square.

Since, 7 is a prime number this means 7 is without its pair and is not in the power of 2.

Therefore,√7 is irrational

⇒This statement is true.

→7.1234… is irrational because it is a non terminating, non repeating decimal.

Since,the value of decimal in 7.1234… goes on forever and repeating.

Therefore,7.1234… is irrational.

⇒This statement is true.

→√7 is rational because 7 is not a perfect square.

Since, 7 is a prime number this means 7 is without its pair and is not in the power of 2.

Therefore,√7 is irrational

⇒This statement is true.

→π is irrational because π is not a repeating decimal.

π is irrational because  the value of π is called as infinite decimal-after the decimal point the digits go on forever and repeating.

⇒This statement is false.

More about irrational numbers :

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Answer:

[See Below]

Step-by-step explanation:

✦ [tex]\sqrt{95} =9.74679434[/tex]

~Hope this helps Mate. If you need anything feel free to message me.

-I have included a number line as well...

Answer:

7

Step-by-step explanation:

Just put it

Answer:

7

Step-by-step explanation:

Did it in I ready

Answer:

No solution

Step-by-step explanation:

Step 1: Write equation

-6(3 + x) + 2(3x + 5) = 0

Step 2: Solve for x

Distribute: -18 - 6x + 6x + 10 = 0

Combine like terms: -8 ≠ 0

∴ No solution

No answer

Step-by-step explanation:

-6(3+x) Multiply -6 by 3=-18. -18+-6x     2(3x+5) 6x+10

(-18+-6x) + (10+6x) = (-8 = 0).

Answer:

  -0.8 m/s^2

Step-by-step explanation:

Acceleration is the slope of the velocity curve. Here the velocity decreases from 12 m/s to zero in 15 seconds. So, the slope is ...

  (-12 m/s)/(15 s) = -0.8 m/s^2

Answer:

9 people

Step-by-step explanation:

9 pieces of the 10 pieces of pie were left. If all 9 of those are gone and each took 1, there were 9 employees.

Answer:

6 yards

Step-by-step explanation:

she need 1 yard of ribbon for each hairbow and 6 friends to make them for

Answer:

h ≈ 174.3 m

Step-by-step explanation:

Step 1: Define variables

∅ = 71°

b = 60 meters (horizontal leg of the triangle)

We are solving for height h (vertical leg of the triangle)

Step 2: Use Trig

tan∅ = opposite over adjacent

tan71° = h/60

Step 3: Evaluate

60tan71° = h

h = 174.253 m

h ≈ 174.3 m

Answer:

the height of the building is 174.3 m

Step-by-step explanation:

see attached image

height of building (h) = x tan Ф

where x = 60m

Ф = 71°

plugin values into the formula

h = 60 tan (71)

h = 174.3 m

therefore

the height of the building is 174.3 m

Answer:

See below

Step-by-step explanation:

So you are moving the decimal to the right, right?

This action would make the number bigger.

For this explanation I will use the example 7.2

So lets move the decimal 3 to the right.

You get 7200.

Now try dividing 7200 by 100 = 72

This did not get us the original # 7.2

Now lets divide 7200 by 1000 = 7.2

Now that we got the original #, switch the operation and multiply 7.2 by 1000

7.2 x 1000 = 7200

Answer = multiplying the number by 1,000

Answer:

6

Step-by-step explanation:

I hope this helps!

Answer:

erxytfgnb

Step-by-step explanation:

Answer: C

Definition of a conditional:

A conditional statement is a statement that can be written in the form “If P then Q,” where P and Q are sentences. For this conditional statement, P is called the hypothesis and Q is called the conclusion. Intuitively, “If P then Q” means that Q must be true whenever P is true.

I hope it will help you :)

Answer:

52,920

Step-by-step explanation:

Answer:

52,920^^

Step-by-step explanation:

brains plss

Answer:

[tex](x - 3)^{2} = 17[/tex]

Step-by-step explanation:

[tex] {x}^{2} - 6x = 8 \\ {x}^{2} - 6x + 9 = 8 + 9 \\ (x - 3)^{2} = 17[/tex]

Answer:

4x-2

Step-by-step explanation:

First, distribute the minus sign.

-2x+3-(5-6x)

-2x+3+ -1(5)+ -1(-6x)

-2x+3+ (-5) + (6x)

-2x+3-5+6x

Next, combine like terms.

-2x+3-5+6x

(-2x+6x)+(3-5)

4x+(-2)

4x-2

Answer:

4x - 2

Step-by-step explanation:

-2x + 3 - -5 + 6x ( First distribute the parenthess and apply minus-plus rules making it -2x+3-5+6x )

-2x + 6x + 3 - 5 ( Group the equation like this putting like terms together)

4x + 3-5 ( From there add -2x and 6x- like terms to get 4x)

4x -2( After that subtract 3-5 ad the answer is -2)

THE FINAL ANSWER BECOMES 4x - 2

HOPE IT HELPED

Answer:

it is the answer here copy and paste

Step-by-step explanation:

adding and subtracting decimals are different from adding and subtracting whole number because of the values are not going to be the same any more.      

          extra; example 40.04 has hundredths and 4004 has hundreds.

Answer:

The answer is:

In both types of problems you rewrite the problem vertically, line up the decimals, and add zeros or rename where needed.

Step-by-step explanation:

Edge 2021

Answer: the value would be 90

Step-by-step explanation:

Answer:

7.5

Step-by-step explanation:

Answer:

7.5

Step-by-step explanation:

all you need to do is divide 15 by 2

Answer:

[tex] \boxed{ \sf{length \: of \: a \: rectangle = 21 \: in.}}[/tex]

[tex] \boxed{ \sf{width \: of \: a \: rectangle = 10.5 \: in.}}[/tex]

Step-by-step explanation:

Let the length of a rectangle be ' l '

Width of a rectangle ( w ) = [tex] \sf{ \frac{1}{2} l}[/tex]

Perimeter of a rectangle ( P ) = 63 in.

First, finding the length of a rectangle ( l )

[tex] \boxed{ \sf{perimeter \: of \: a \: rectangle = 2(l + b)}} \:[/tex]

[tex] \dashrightarrow{ \sf{63 = 2(l + \frac{1}{2} l}})[/tex]

Distribute 2 through the parentheses

[tex] \dashrightarrow{ \sf{63 = 2l + 2 \times \frac{1}{2} l}}[/tex]

[tex] \dashrightarrow{ \sf{63 = 2l + l}}[/tex]

Add the like terms : 2l and 3l

[tex] \dashrightarrow{ \sf{63 = 3l}}[/tex]

Swap the sides of the equation

[tex] \dashrightarrow {\sf{3l = 63}}[/tex]

Divide both sides by 3

[tex] \dashrightarrow{ \sf{ \frac{3l}{3} = \frac{63}{3}}} [/tex]

Calculate

[tex] \dashrightarrow{ \sf{l = 21 \: in.}}[/tex]

Length of a rectangle = 21 in.

Now, replacing / substituting the value of l in 1/2 l in order to find the width of a rectangle

[tex] \dashrightarrow{ \sf{width = \frac{1}{2} l}}[/tex]

[tex] \dashrightarrow{ \sf{width = \frac{1}{2} \times 21}}[/tex]

[tex] \dashrightarrow{ \sf{width = 10.5 \: in.}}[/tex]

Width of a rectangle = 10.5 in.

Hope I helped!

Best regards! :D

Answer:f(g(0))= 1/5

              g(f(0))= 7

Step-by-step explanation:

for f(g(0))=you solve for g(x) but you plug in 0 for x so g(0)= 8(0)+3

                                                                                                    =3

 so now you plug in the answer of the function of g(x) witch is 3 and plug it in as the x for F(x) so f(3)= 1/(3)+2

                                     = 1/5

so f(g(0)) is equal to 1/5

Now for G(f(0)) you solve for f(x) by pluging 0 for x so F(0)= 1/(0)+2

                                                                                               =1/2

now you plug in 1/2 for the x of g(x) so g(1/2)= 8(1/2)+3

                                                                         = 4+3

                                                                         =7

so g(f(0)) is equal to 7

Hope this helps:)

Answer:

1

Step-by-step explanation:

y + z + 2

first you have to replace the variables with the numbers

This is your equation now.

-6 + 5 + 2

Now you just have to solve it.

-6 + 5 = -1 + 2 = 1

or

7 - 6 = 1

Answer: [tex]f^{-1}(x)=\sqrt{x+49}[/tex]

Step-by-step explanation:

To find the inverse of a function, you want to switch the x with y and y with x. After that, you solve for y.

y=x²-49                            [switch x with y and y with x]

x=y²-49                            [add both sides by 49]

x+49=y²                           [square root both sides]

[tex]y=\sqrt{x+49}[/tex]

Now, we know that [tex]f^{-1}(x)=\sqrt{x+49}[/tex].

Answer:

BD = 72

Step-by-step explanation:

C is the midpoint of BD.

Therefore,

BD = 2BC

13x - 6 = 2*6x

13x - 6 = 12x

13x - 12x = 6

x = 6

BD = 2*6X = 12*6= 72