The equation of a circle is ​ (x−2)^2+(y−16)^2=169 ​ . What is the circle's radius?

Arithmetic is the answer

Answer:  13

Step-by-step explanation:

Given : The equation [tex]d=\dfrac{1}{2}n(n-3)[/tex] gives the number of diagonals d for polygon with n sides.

To find the number of sides n for a polygon that has 65 diagonals, we substitute the value of d= 65 in the given equation, we get

[tex]65=\dfrac{1}{2}n(n-3)[/tex]

Multiply 2 on both sides , we get

[tex]n(n-3)=130\\\\\Rightarrow\ n^2-3n-130=0\\\\\Rightarrow\ n^2-13n+10n-130=0\\\\\Rightarrow\ n(n-13)+10(n-13)=0\\\\\Rightarrow\ (n-13)(n+10)=0\\\\\Rightarrow\ n= -10\ or\ n= 13[/tex]

But number of sides cannot be negative, so the number of sides n for a polygon that has 65 diagonals = 13

Answer:

[tex]\frac{(x-7)}{(x-5)}[/tex]

option D is correct

Step-by-step explanation:

[tex]\frac{(x-7)(x+1)}{(x+1)(x-5)}[/tex]

In an rational expression , if we have same factors at the top and bottom  then we cancel it out

In our given rational expression we have x+1  at the top and  bottom

so we cancel out x+1

After cancelling out x+1, we are left with

[tex]\frac{(x-7)}{(x-5)}[/tex]

option D is correct

A person needing a car for a few weeks while visiting family out of state would most likely choose A. Car rental for its short-term flexibility and convenience.

Car rental is the ideal choice for short-term car needs while visiting family out of state.

It offers flexibility in terms of duration, allowing individuals to rent vehicles for specific periods, such as a few weeks, without the commitment of ownership or long-term contracts.

With a wide range of vehicle options and rental locations available, car rental services provide convenience and accessibility.

Additionally, rental agreements typically include insurance coverage and roadside assistance, offering peace of mind to travelers during their stay.

Overall, car rental meets the temporary transportation needs of visitors efficiently and effectively.

Complete Question:

A person needing a car for a few weeks while visiting family out of state would most likely choose which of the following?

A. Car rental

B. Car share

C. Carpool

D. Car lease

Data that is collected can be either categorical or numerical data.Categorical variables represent types of data which may be divided into groups.

December is the twelfth and last month of the year .The word December is a  categorical discrete data which is also known as qualitative, because it is a name instead of a number.Among the options given December is a month of a year.

The month of the year is December is a categorical data .

Answer:

A. 12 square units.

Step-by-step explanation:

We have been given graph of a triangle and we are asked to find the area of our given triangle.

Since we know that area of a triangle is half the product of height of triangle and base of the triangle.

[tex]\text{Area of triangle}=\frac{1}{2}*\text{Base*Height}[/tex]

We can see that MN is base of our triangle and LM is height of triangle, so let us find lengths of MN and LM using distance formula.

[tex]\text{Distance}=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

[tex]\text{Distance between point M and N}=\sqrt{(3--1)^2+(-4--4)^2}[/tex]

[tex]\text{Distance between point M and N}=\sqrt{(3+1)^2+(-4+4)^2}[/tex]

[tex]\text{Distance between point M and N}=\sqrt{(4)^2+(0)^2}[/tex]

[tex]\text{Distance between point M and N}=4[/tex]

[tex]\text{Distance between point L and M}=\sqrt{(-1--1)^2+(-4-2)^2}[/tex]  

[tex]\text{Distance between point L and M}=\sqrt{(-1+1)^2+(-6)^2}[/tex]  

[tex]\text{Distance between point L and M}=\sqrt{0+36}[/tex]  

[tex]\text{Distance between point L and M}=6[/tex]  

Now let us substitute our side lengths is area formula.

[tex]\text{Area of triangle LMN}=\frac{1}{2}*4*6[/tex]

[tex]\text{Area of triangle LMN}=2*6[/tex]

[tex]\text{Area of triangle LMN}=12[/tex]

Therefore, area of triangle LMN is 12 square units and option A is the correct choice.

The range of the function (eˣ)/(eˣ+c) is the closed interval [0,1].

The range of the function f(x) = (eˣ)/(eˣ+c) can be determined by analyzing the behavior of the function as x approaches positive and negative infinity. When x tends to positive infinity, the term eˣ grows much faster than c, so the denominator approaches infinity. Therefore, the function approaches 1 as x tends to infinity.

Similarly, when x tends to negative infinity, the term eˣ approaches 0 much faster than c, so the denominator becomes negligible. As a result, the function approaches 0 when x tends to negative infinity.

Since the function approaches 0 at negative infinity and approaches 1 at positive infinity, the range of the function is the closed interval [0,1].

Answer:

Step-by-step explanation:

No time because the wall is already built

Answer:

The answer is C

Step-by-step explanation:

Boy likes mayonnaise:  

12

(12 + 18 + 5)

=  

12 /35

= 0.3429 ≈ 34%

Girl likes mayonnaise:  

14

(14 + 13 + 15)

=  

14 /42

= 0.3333 ≈ 33%

thus,

boys (34 of 100) > girls (33 of 100)

Answer:

n + 4

Or 20

Step-by-step explanation:

Depends on how you see it the answer could be n´+4 since that´s how the function is working, and almost all of the time the independent clauses are actually independent and do not follow any progression.

But if there is a progression in the input, we can see that they are adding up uneven numbers to the input, so first we added 3, then we added 5, and last we should add 7: so the input would be 7+9= 16, the input in the forth spot should be 17, and the output should be 20.

To find similarity ratio a:b

We take the sides and make a proportion

[tex]\frac{height \ of \ smaller \ cone}{height \ of \ larger \ cone} = \frac{radius \ of \ smaller \ cone}{radius \ of \ larger \ cone}[/tex]

[tex]\frac{9}{15} = \frac{6}{10}[/tex]

[tex]\frac{3}{5} = \frac{3}{5}[/tex]

So the ratio a:b is 3:5

Degree and number of terms in each polynomial expression are as follow,

" Expression is defined as the relation between two or more variables or numbers are represented using mathematical operation."

According to the question,

Given polynomial expression,

Simplify the given expression we get,

[tex]4x + 6x^{3} -10x^{2}\\\\= 6x^{3} -10x^{2} +4x[/tex]

Degree of the polynomial expression : [tex]3[/tex]

Number of terms : [tex]3[/tex]

2. [tex](-3x^{4} +5x^{3} -12) + (7x^{3} -x^{5} +6)[/tex]

Simplify the given expression we get,

[tex]-3x^{4} +12x^{3} -6 -x^{5} \\\\= -x^{5} -3x^{4} +12x^{3} -6[/tex]

Degree of the polynomial expression : [tex]5[/tex]

Number of terms : [tex]4[/tex]

3. [tex](3x^{2} -3)(3x^{2} +3)[/tex]

Simplify the given expression we get,

[tex]9x^{4} -9[/tex]

Degree of the polynomial expression : [tex]4[/tex]

Number of terms : [tex]2[/tex]

Hence, degree and number of terms in each polynomial expression are as follow,

Learn more about expression here

brainly.com/question/14083225

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Answer:

40

Step-by-step explanation:

So she has 12 cucumbers to make 3 jars of pickles.

She uses 4 cucumbers to make each jar. (Based on the equation 12➗3 =4)

Shawtyyyy better be using those pickles on burgers and not eating it raw.

So she has 10 jars right? Right, and you know she used 4 pickles per jar, so

we can get the answer by the equation of 10 x 4 = 40

Have a great day shawtayyyyyy!