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mihalych1998 [28]
3 years ago
8

Given that the center of a circle is C(-10,-7) and the point S(4,4) lies on the circle's edge calculate the circle's radius to t

wo decimal places
Mathematics
1 answer:
fredd [130]3 years ago
8 0

Answer:

r\approx 17.80

Step-by-step explanation:

<u>Equation of the Circle</u>

A circle can be completely defined knowing its center and radius. The radius is the distance from the center to any point in its edge. Since we know the center of the circle is (-10,-7) and one point in its edge is (4,4), we calculate the distance between those points:

r=\sqrt{(4-(-10))^2+(4-(-7))^2}

r=\sqrt{14^2+11^2}

r=\sqrt{196+121}=\sqrt{317}

\boxed{r\approx 17.80}

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Sterre charges $ 3 5 $35dollar sign, 35 to file tax returns, but files for free if she only needs the easiest form. Then she don
blagie [28]

Given:

  • $35 is charged per form, but $0 if only the easiest form is filed.
  • $2 donated for every single tax return filed (since it is not explicitly mentioned otherwise, I will assume she donates $2 whether she charges $35 or does it for free)
  • Total amount charged for the full year = $7245
  • Total amount donated for the full year = $1242

To Find: The number of forms for which Sterre charged $35 and the number of forms Sterre did it for free.

Concept:

We can make use of the Unitary Method here. <u>Given the number of units in a group, the Unitary Method can be used to find the value of a single unit or and individual unit when we are given the value for a group.</u>

So,

<u>Value of Single Unit = Value of Entire Group of Units ÷ Number of Units in the Group</u>


Explanation & Calculation:

We are given that Sterre charged $7245 for the full year. Taking each Unit as the $35 type of form, and value of each Unit would be the amount that Sterre charges per form which is obviously $35, we can find the number of $35 forms using the expression written above.

So, putting in the values into the expression,

$35 = $7245 ÷ number of $35 forms

Therefore, number of $35 forms = $7245 ÷ $35

Using simple division, number of $35 forms = 207

Next, we are given Sterre donated $1242 in the full year and she donates $2 for every form (whether it is the $35 form or the free form).

If this time, we define each Unit as being each form (both $35 form and free form), value of each unit we define as the $2 donation money, we see that the value of the full group of units is $1242.

So, putting the values into the expression,

$2 = $1242 ÷ total number of forms

Therefore, total number of forms = $1242 ÷ $2

Using simple division, total number of forms = 621


Conclusion:

Sterre has filed <u>a total of 621 tax returns</u> (both charged and for free).

Of these 621 returns filed, <u>for 207 forms, Sterre charged $35</u>.

The number of returns Sterre filed for free (that is, the easiest forms) is

Total number of forms - Chargeable forms = 621 - 207 = 414

Thus, Sterre filed <u>414 tax returns for free</u>.


8 0
3 years ago
Do 8feet + 10feet + 12feet make a right triangle
bija089 [108]

9514 1404 393

Answer:

 no

Step-by-step explanation:

If triangle side lengths are an arithmetic sequence (have a common difference), they must have the ratios 3:4:5 to make a right triangle. Here, the ratios of the side lengths are 4:5:6, so will not be a right triangle.

4 0
3 years ago
Math problem need help plz
alexira [117]

Answer:

angle LXZ is 121°

Step-by-step explanation:

Since the sum of same side interior angles equals 180 you just subtract the angle you're given from 180 (180°-59°=121°)

6 0
3 years ago
How do I solve The sum of a number and 3 is subtracted from 10 the result is 5
meriva

State the given in the question

Given that the sum of a number and 3 is subtracted from, the result is 5

State what is to be found in the question

We are to find the number. In other to achieve this, we would follow the steps below:

Step 1: Represent the number with an unknown

Let x represent the number

Step 2: Interpret the given statement mathematically

If x is the number, then the sum of the number and 3 would be

x+3

Then the sum of a number and 3 subtracted from 10 would be

10-(x+3)

Finally, when the sum of a number and 3 subtracted from 10, the result is 5, would be

10-(x+3)=5

Step 3: Solve for x in the mathematical interpretation of the given statement

The value of x is as calculated as shown below:

\begin{gathered} 10-(x+3)=5 \\ \text{Open the bracket or the parenthesis} \\ 10-x-3=5 \\ \text{collect like terms} \\ 10-3-5=x \\ 7-5=x \\ 2=x \\ \text{Therefore:} \\ x=2 \end{gathered}

Hence, the number is 5

4 0
1 year ago
There are 3 3/4 pounds of bricks in a bag. Each brick weighs 5/8 of a pound. How many bricks are in the bag.
Bess [88]

Answer: There are 6 bricks in the bag.

Step-by-step explanation:

Convert from mixed number to decimal number. To do it, divide the numerator of the fraction by the denominator and add the result to the whole number part. Then:

3\frac{3}{4}\ lb=(3+0.75)\ lb=3.75\ lb

Convert from fraction to decimal number. To do it you need to divide the numerator by the denominator. Then, you get:

\frac{5}{8}lb=0.625\ lb

Let be "x" the number of bricks in the bag<em>.</em>

<em> </em>Based on the information given in the exercise, you can set up the following proportion:

\frac{1}{0.625}=\frac{x}{3.75}

Finally, you must solve for "x" in order to find its value. This is:

(3.75)(\frac{1}{0.625})=x\\\\x=6

8 0
3 years ago
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