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ziro4ka [17]
2 years ago
7

Write the equation of the circle centered at (3, 5) and tangent to x = -1. I need help pleasse

Mathematics
1 answer:
Annette [7]2 years ago
7 0

Answer:

(x - 3)² + (y - 5)² = 16

Step-by-step explanation:

the equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k ) are the coordinates of the centre and r the radius

given (h, k ) = (3, 5 ) we require to find r

r is the distance from the centre to a point on the circle

given x = - 1 is a tangent the r is the distance between the x- coordinates

r = | 3 - (- 1) | = | 3 + 1 | = | 4 | = 4

then equation of circle is

(x - 3)² + (y - 5)² = 4² , that is

(x - 3)² + (y - 5)² = 16

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Isabel found 54 coins at the bottom of her backpack. when she looked, she noticed they were only nickels and dimes. Isabel count
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She had 23 nickles and 31 dimes

Step-by-step explanation:

The given is:

  • Isabel found 54 coins at the bottom of her backpack
  • She noticed they were only nickels and dimes
  • Isabel counted the coins and they totaled $4.25

We need to find how many nickels and dimes she had

Assume that the number of nickels is x and the number of dimes is y

∵ Isabel had 54 coins

∵ The number of nickels is x

∵ The number of dimes is y

∴ x + y = 54 ⇒ (1)

∵ 1 nickle = 5 cents

∵ 1 dime = 10 cents

∵ The coins totaled $4.25

- Change the dollars to cents

∵ 1 dollar = 100 cents

∴ $4.25 = 4.25 × 100 = 425 cents

- Multiply the number of nickles by 5 and the number of dimes

  by 10, add the two products and equate the sum by 425

∴ 5x + 10y = 425 ⇒ (2)

Now we have a system of equations to solve it

Multiply equation (1) by -10 to eliminate y

∵ -10x - 10y = -540 ⇒ (3)

- Add equations (2) and (3)

∴ -5x = -155

- Divide both sides by -5

∴ x = 23

Substitute the value of x in equation (1) to find y

∵ 23 + y = 54

- Subtract 23 from both sides

∴ y = 31

She had 23 nickles and 31 dimes

Learn more:

You can learn more about the system of equations in brainly.com/question/6075514

#LearnwithBrainly

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