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2 years ago

The general form of the equation of a circle is x^2+y^2−4x−8y−5=0.

1 answer:

5 0

X² - 4x + y² - 8y = 5

Complete the square:
x² - 4x + (4) + y² - 8y + (16) = 5 + (4) + (16)
→ (x - 2)² + (y - 4)² = 25

Center: (2,4)
radius: √25 = 5

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Peter's salary is twice Anne's salary and half of David's salary. Then the average salary of Anne and David is _ of Peter's sala

satela [25.4K]

<h3><u>Answer:</u></h3>

Average of salary of Anne and David is 1.25 of Peter's Salary

<h3><u>Explanation:</u></h3>

In the question, relations between salaries of Peter, Anne, and David is given. From the given relations, we need to make few equations and calculate the average of Anne and David in terms of Peter's Salary.

Let us assume Peter's Salary as P.

Then we can calculate Anne's salary A = $\frac{P}{2}$ .

Also David's salary = D = $2 \times P$

Average of Anne's and David's salary = $\frac{A+D}{2}$

Average of Anne's and David's salary = $\frac{\frac{P}{2} + 2 \times P}{2}$

Average of Anne's and David's salary = $\frac{5 \times P}{4}$

Average = 1.25 \times P

6 0

2 years ago

The Japanese 5 yen coin has a hole in the middle. If the diameter of the coin is 22 mm and the diameter of the hole is 5 mm, how

Yanka [14]

Answer:

4.4mm

Step-by-step explanation:

Circumference of circle

2 Pi r

Diameter of coin = 22mm

Therefore the radius = 11mm

Therfroe the outer edge (circumference)

= 2 Pi r

= 2 x Pi x 11

=69.11mm

For the inner edge

Diameter = 5

Radius = 2.5

Therefroe inner edge (circumference)

= 2 Pi r

= 2 x Pi x 2.5

= 15.7mm

The difference is

69.11 - 15.7

=4.4mm

7 0

2 years ago

What is the change that occurs to the parent function f(x) = x^2 given the function f(x) = 2(x + 2)^2 + 1.

nikitadnepr [17]

Answer:

The graph is stretched by a factor of 2, moves 2 units to the left, and 1 unit up.

Step-by-step explanation:

The base of the quadratic function is

$f(x) = {x}^{2}$

We can transform this function to look narrower or wider.

Looking narrower is termed a stretch.

This happens when a>1

Looking wider is termed a compression.

This happens when 0<a<1

We can also

$g(x) = a {(x + h)}^{2} + k$

+h moves the parent graph to the left by h units

-h moves the parent graph to the left by h units.

+ k moves the parent function up by k units

- k moves the parent function down by k units.

The change that occurs to

$f(x) = {x}^{2}$

given

$f(x) = 2( {x + 2)}^{2} + 1$

is that, the graph is stretched by a factor of 2, moves 2 units to the left, and 1 unit up

Therefore the last choice is the correct answer.

3 0

3 years ago

determine the dimensions of a quadrilateral with a perimeter of 48 feet that will create the smallest area

Vsevolod [243]

A quadrilateral 24 ft long and 0 ft wide will have the smallest area.

4 0

3 years ago

K is the midpoint of JL. JK = 2x + 5 and JL = 50.

Sergeu [11.5K]

Steve set the equation equal to 50 which is the entire length of JL. instead he should've set the equation equal to 25, since it's half of 50 and would represent the midpoint. he should've said 2x + 5 = 25

8 0

2 years ago