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jeka57 [31]
3 years ago
10

The diameter of a circle has endpoints P(–7, –10) and Q(3, 2).

Mathematics
1 answer:
7nadin3 [17]3 years ago
4 0

Answer:

Step-by-step explanation:

Since we are given the endpoints of the circle, the midpoint between the two endpoints will be the center of the circle. The formula for determining midpoint of a line is

Midpoint = 1/2(x1 + x2), 1/2(y1 + y2)

= 1/2(- 7 + 3), 1/2(- 10 + 2)

= (- 2, - 4)

The radius of the circle is the distance from the center to the endpoint. To determine the radius of the circle, we would apply The formula for determining the distance between two points on a straight line is expressed as

Distance = √(x2 - x1)² + (y2 - y1)²

Therefore,

Radius = √(- 2 - - 7)² + (- 4 - - 10)²

Radius = √5² + 6² = √61

A circle is the set of all points in a plane equidistant from a fixed point called the origin or center.

The center of the circle is (- 6, - 8)

The formula for determining the equation of a circle us expressed as

(x - h)² + (y - k)² = r²

Where

r represents the radius of the circle

h and k represents the x and y coordinates of the center of the circle. Comparing with the given points,

h = - 2 and k = - 4

Radius, r = √61

Substituting into the formula, it becomes

(x - h)² + (y - k)² = r²

(x - - 2)² + (y - - 4)² = √61²

(x + 2)² + (y + 4)² = 61

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Ernest borrowed $1000 from the bank. The interest rate is 30% and he borrowed it for 9 months. How much will he owe the bank?
Fudgin [204]

The total amount Ernest owes the bank after 9 months is $1,225.00

How many months of interest would be paid?

The fact the loan was taken for nine months means that the borrower, Ernest needs to pay interest for nine months, in other words, we would time-apportion the annual interest of 30% to determine the 9-month interest as shown below:

9-month interest rate=30%*9/12

9-month interest rate=22.50%

The amount Ernest is owing the bank is the principal borrowed plus the interest for  9 months as computed below:

total amount owed after 9 months=$1000*(1+22.50%)

total amount owed after 9 months=$1000*1.2250

total amount owed after 9 months=$1,225.00

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At the end of the summer a store marks down the outdoor furniture 8% a family bought 4 chairs in June at 35$ each then 2 more ch
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Answer:

$204.4

Step-by-step explanation:

The four chairs bought in June cost $35 each, all together $140. Then they bought 2 more chairs on sale for 8% off of $35 each or 92% of $35 which is $32.2 each, all together $64.4. Both buy's together would then equal $204.4

7 0
3 years ago
What is the slope of the line that passes through the points (-4,-4) and (9,4)
aleksandrvk [35]

Answer:

4-(-4)/9-(-4)

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1) Erica bought a car for $24,000. She had to add Pennsylvania's sales tax of 6%. The total price of the car is closest to?
Lina20 [59]
To find the car's total price, add the tax paid to the car's original price.

 

$32800 + $1968 = $34768

 

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What is 22.5% written as a fraction in simplest form?​
murzikaleks [220]

Answer:

9/40

Step-by-step explanation:

  • Write down the percent divided by 100 like this:

22.5/100

  • Multiply both top and bottom by 10 for every number after the decimal point:
  • As we have 1 digit after the decimal point, we multiply both numerator and denominator by 10, or, simply shift 1 decimal place to the right. So,

(22.5*10)(100*10)= 225/1000

  • Simplify (or reduce) the above fraction by dividing both numerator and denominator by the GCD (Greatest Common Divisor) between them. In this case, GCD(225,1000) = 25.

225 ÷ 25/ 1000÷25 = 9/40

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