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sergey [27]
3 years ago
5

A circle has a center of (5,-5) and goes through (6,-2). What is the radius?

Mathematics
1 answer:
Fittoniya [83]3 years ago
6 0
Start with the equation of a circle whose center is at (h,k) and whose radius is r:

(x-h)^2 + (y-k)^2 = r^2

Substituting the given coordinates of the center:

(x-5)^2 + (y-[-5])^2 = r^2, or (x-5)^2 + (y+5)^2 = r^2

Substituding the given coordinates of a point (6,-2) on the circle:

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

Simplifying:

1^2 + 3^2 = r^2, or 1 + 9 = r^2, or 10= r^2.  Then r = sqrt(10).

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Solve the triangle<br> Solve sides
Montano1993 [528]

Answer:

Step-by-step explanation:

Triangle RST is a right angle triangle.

From the given right angle triangle

RT represents the hypotenuse of the right angle triangle.

With 26 degrees as the reference angle,

ST represents the adjacent side of the right angle triangle.

RS represents the opposite side of the right angle triangle.

1) To determine RS, we would apply trigonometric ratio

Sin θ = opposite side/hypotenuse Therefore,

Sin 26 = RS/9.1

RS = 9.1Sin26 = 9.1 × 0.4384

RS = 4.0

2) To determine ST, we would apply trigonometric ratio

Cos θ = adjacent side/hypotenuse Therefore,

Cos 26 = ST/9.1

ST = 9.1Cos26 = 9.1 × 0.8988

ST = 8.1

3) The sum of the angles in a triangle is 180 degrees. Therefore,

∠R + 26 + 90 = 180

∠R = 180 - (26 + 90)

∠R = 64 degrees

8 0
3 years ago
How do you expand -10(4-b)
katen-ka-za [31]

Answer:

<h2><u>=10b−40</u></h2><h2><u></u></h2>

Step-by-step explanation:

−10(4−b)

=(−10)(4+−b)

=(−10)(4)+(−10)(−b)

=−40+10b

<u>=10b−40</u>

5 0
2 years ago
Betsy started a business 2 years ago. She had 8 customers in the first year. She added 18
Tatiana [17]

Answer:

Betsy isn't correct. Betsy's calculations are wrong as she made her calculations by multiplying the base number of customers by 3 and then summing it all up for the 4 years under review instead of a continuous multiplication by 3.

26 × 3 × 4 is different from 26 × 3⁴

- If Betsy meets her target for the next 4 years, she will have 2106 customers in 4 years time.

Step-by-step explanation:

- Betsy started her business 2 years ago.

- In the first year, Betsy has 8 customers.

- In the second year, Betsy added 18 customers,

- So, her customers are now 8+18 = 26

- Betsy's goal is that in each of the next 4 years, she will have three times as many customers as the year before.

If the base number of customers is truly 26 this year,

Next year, Betsy would have 26 × 3 = 78 customers.

In 2 years, she would have 78 × 3 = 234

Thus indicating that in t years from now, the number of her customers will be

N(t) = N₀ × 3ᵗ

where

N(t) = number of customers t time from now

N₀ = number of customers at the moment = 26

t = number of years from now.

N(t) = 26 × 3ᵗ

In 4 years from now, Betsy will have

N(t=4) = 26 × 3⁴ = 2,106

So, it is evident that Betsy's calculations are wrong as she made her calculations by multiplying the base number of customers by 3 and then summing it all up for the 4 years under review instead of a continuous multiplication by 3.

26 × 3 × 4 is different from 26 × 3⁴

- If Betsy meets her target for the next 4 years, she will have 2106 customers in 4 years time.

Hope this Helps!!!

5 0
2 years ago
Alison has 1.60 worth of nickels and dimes in her coin pure. she has 11 more nickes than dimes
Jet001 [13]
There would be 7 dimes and 18 nickels
8 0
2 years ago
Jim is enclosing a rectangular garden with 170 feet of fencing. The length of the garden is 10 feet more than twice it's width,
Hunter-Best [27]

Answer: Area = 1500 feet^2

Step-by-step explanation:

Jim is enclosing a rectangular garden with 170 feet of fencing. This means the perimeter of the rectangular garden =170 feet

Let length = x

Let width = w

The length of the garden,x is 10 feet more than twice it's width, w. This means

x =10+2w---------1

Perimeter = 2x+2w =170---------2

Putting equation 1 in equation 2,

2(10+2w) +2w= 170

20 + 4w +2w = 170

6w = 170-20=150

w = 150/6

= 25feet

Put w=25 in equation 1

x =10 +2×25= 10+50=60 feet

Area = length × width = x×w

= 60×25=1500feet^2

5 0
3 years ago
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