Write an equation of the circle with center (5, 2) and diameter 12.


Answer 1


(x-5)^2 + (x-2)^2 = 6^(2)

Step-by-step explanation:

Standard equation of a circle is

(x-x_(0))^2-(y-y_(0))^2 = r^2\nr=(1)/(2)d

As the radius is half of the diameter we can divide 12 by 2 to get a radius, then we can input values into this equation.

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Which figure must be a trapezoid? A.
a quadrilateral with no congruent angles

a quadrilateral with no congruent sides

a quadrilateral with no right angles

a quadrilateral with exactly one pair of parallel sides


DA trapezoid is a quadrilateral that has one pair of parallel sides. 
A trapezoid is a quadrilateral meaning it has four sides, and it also has one pair of parallel line meaning the lines will never touch so the answer is D.

A group of students wish to go bowling. There is a flat rate of $5 per student for shoe rental. It then costs $2.50 pergame up to 2 games total and then the cost is $2.00 per game after the first 2. If 6 students went, each rented shoes
and each rolled 3 games;
1. create a step function equation to calculate the cost per student per game
2. graph your step function
3. determine the total cost for this bowling outing



  1. c(g)=\left\{\begin{array}{lcl}(5)/(\lceil g\rceil)+2.5&\text{for}&0<g \le 2\n\n(6)/(\lceil g\rceil)+2&\text{for}&g>2\end{array}\right.
  2. see below
  3. $72

Step-by-step explanation:

1. Since the function is supposed to give cost per game, it will be the stated cost per game (2.50 or 2.00) in addition to the quotient of the fixed cost and the number of games. For more than 2 games, the "fixed cost" is essentially the $5 shoe cost plus the premium on the first two games, an additional dollar.

For graphing purposes, we choose to use the "ceiling" function, so that any fractional game is charged at the price for the next higher integer number of games.

The "cost per game" function can be written as ...

  c(g)=\left\{\begin{array}{lcl}(5)/(\lceil g\rceil)+2.5&\text{for}&0<g \le 2\n\n(6)/(\lceil g\rceil)+2&\text{for}&g>2\end{array}\right.


2. The graph is shown in the attachment.


3. The cost per game for 3 games is c(3) = 6/3+2 = 4, so the cost for 3 games for 1 student is 3·4 = 12. The cost for 6 students is then 6·12 = 72 dollars.

Convert the decimal 0.6333… to a fraction and classify it as either rational or irrational.A. 57⁄9, irrational
B. 57⁄90, rational
C. 63⁄90, rational
D. 63⁄99, rational


answer B

We assume        x=  0.6333

100x = 63.3333

  10x=  6.333  33               (subtract it )


 90x = 57 ( divide by 90 on both sides)

So x= (57)/(90)

Answer : (57)/(90)

When we can write a number in fraction form then it is a rational number.

We converted the  decimal number into a fraction so it is rational

The answer is B. 57/90, rational.

Jan is using toothpicks to create patterns as shown below.Figure 1
Figure 2
Figure 3
based on the pattern, how many toothpicks will Jan use in figure 20?


Where Jan is using toothpicks to create patterns as shown below, He will need 79 toothpicks to complete figure 16. This is an arithmetic progression problem.

How to derive the Number of Toothpicks required for the 20th diagram

As indicated above, the given sequence is an arithmeticprogression.

It is also to be noted that each figure increases with a number of 4 toothpicks.

Thus, to find how many toothpicks will be required at the 20th figure, we need to use the following formula:

The nth term of an arithmetic sequence is given by the formula:

\[a_n = a_1 + (n-1)d\]

For this sequence:

\(a_1 = 3\),

\(d = 4\),

\(n = 20\).

\[a_(20) = 3 + (20-1) * 4\]

\[a_(20) = 3 + 19 * 4\]

\[a_(20) = 3 + 76\]

\[a_(20) = 79\]

Learn more about arithmetic progression at:



Full Question:

Although part of your question is missing, you might be referring to this full question:

Jan is using toothpicks to create patterns as shown below. Based on the pattern, how many toothpicks will Jan use in Figure 16?
See attached.




They are adding 2 triangles to each figure, you could do it the LONG way by adding 2 to each figure or use an explicit rule

Hope it helps!

A population of 100 mice increases by 50% how many miles would there be after the population growth?


150!! 50% of 100 is 50 so you add that to the original 100!

Esteban has a big jar of change in his room. He has 600 coins total, and 240of them are pennies.
What percentage of the coins are pennies?


You just have to divide 240 by 600 and then multiply that by 100. So it will be 40%