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Alborosie
3 years ago
13

What is the equation of the circle passing through the point (6,5) and centered at (3.-4)?

Mathematics
1 answer:
Pavlova-9 [17]3 years ago
3 0

Answer:

(x - 3)² + (y + 4)² = 90 or [3√10)²

Step-by-step explanation:

We need to calculate the radius of this circle.  To do this we calculate the distance from the center (3, -4) to the point (6, 5).  

As we move from (3, -4) to (6, 5), x (the run) increases by 3 and y (the run) increases by 9.  Thus, the distance between these points, according to the Pythagorean Theorem, is

r = √[3² + 9²], or r = √90, or r = 3√10.

Using the standard equation of the circle, (x - h)² + (y - k)² = r², we obtain

(x - 3)² + (y + 4)² = 90 or [3√10)²

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Eggs are sold in boxes. A small box holds 6 eggs.A large box holds 12 eggs.Hina buys x small boxes of eggs.Hina also buys 4 less
yuradex [85]

Answer:

a) 12x - 48 or 6(2x - 8)

b) 18x - 48 or 6(3x - 8)

Step-by-step explanation:

A small box holds 6 eggs

A large box holds 12 eggs.

Hina buys x small box of eggs

Hina also buys (x-4) large box of eggs

a) Total number of eggs in the large box by Hina = (x-4)12

= 12x - 48

= 6(2x - 8)

b) Total number of eggs bought by Hina = (x) 6 + (x-4)12

= 6x + 12x - 48

= 18x - 48

= 6(3x - 8)

8 0
3 years ago
Istg if yall don't help me on this question <br> im not tryna fail
Ivanshal [37]

Answer:

eq.1 is x + y = 24

eq.2 is x - y =2

part c is

13 + 11= 24

and

13 - 11 =2

4 0
3 years ago
How does mathematics connect to the everyday life of an individual?
mr_godi [17]

Answer:

Math is considered to be a part in everyones life, for example, you use math to throw a ball, like the force you use, or the height of the ball. Math is an important concept, and is lingering in our everyday lives, but the reason we take math is to find out of its exsitence, and use it for engineering, etc.

Step-by-step explanation:

5 0
2 years ago
If CE bisects ZBCD and if m ZBCE = 3x - 6
horrorfan [7]

Answer:

m∠BCD = 90°

∠BCD is a right angle

Step-by-step explanation:

<em>If a ray bisects an angle, that means it divides the angle into two equal parts in measure</em>

∵ Ray CE bisects ∠BCD

→ Means divide it into two angles BCE and ECD which equal in measures

∴ m∠BCE = m∠ECD = \frac{1}{2} m∠BCD

∵ m∠BCE = 3x - 6

∵ m∠ECD = 2x + 11

→ Equate them to find x

∴ 3x - 6 = 2x + 11

→ Add 6 to both sides

∵ 3x - 6 + 6 = 2x + 11 + 6

∴ 3x = 2x + 17

→ Subtract 2x from both sides

∵ 3x - 2x = 2x - 2x + 17

∴ x = 17

∵ m∠BCE =  \frac{1}{2} m∠BCD

→ Substitute x in the measure of ∠BCE to find it, then use it to

   find m∠BCD

∵ m∠BCE = 3(17) - 6 = 51 - 6

∴  m∠BCE = 45°

∵ 45 = \frac{1}{2} m∠BCD

→ Multiply both sides by 2

∴ 90 = m∠BCD

∴ m∠BCD = 90°

→ The measure of the acute angle is less than 90°, the measure of

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   right angle is 90°

∴ ∠BCD is a right angle

6 0
3 years ago
Mary invests £12000 in a savings account. The account pays 1. 5% compound interest per year. Work out the value of her investmen
mestny [16]

Answer:

The value of Mary's investment after two years = £12362.7

Step-by-step explanation:P = Principal / initial amountR = rate of interest per cent per yearT = number of yearsA = final amount at the end of T yearsThen:A = P*(1 + R/100)^2In our example:P = £12000R = 1.5 per cent per yearT = 2 yearsThus:A = 12000*(1 + 1.5/100)^2   = 12000*(1 + 0.015)^2   = 12000*(1.015)^2    = 12000*(1.030225)    = 12362.7Value of investment after two years = £12362.7

4 0
2 years ago
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