What is the radius of the circle given by the equation below? x2 - 2x + y2 - 2y - 98 = 0?

Answers

Answer 1

Answer: Complete the square for the given equation
x² - 2x + ____ + y² - 2y + _____ = 98
x² - 2x + (1) + y² - 2y + (1) = 98 + (1) + (1)
(x - 1)² + (x - 1)² = 100
(x - 1)² + (x - 1)² = 10²

Now the equation is in the form (x - h)² + (y - k)² = r²

Radius = 10

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The sum of digits of a 3 digit number is 12. Three times the hundreds digit minus twice the tens digit is 5. If six time the units digit is added to four times the tens digit, the result is 50. Find the number.

Answers

so
xyz

x+y+z=12
3x-2y=5
6z+4y=50
so multiply 3x-2y=5 by 2
6x-4y=10
add to 6z+4y=50 and get
6x+6z+4y-4y=10+50
6x+6z=60
distribute
6(x+z)=6(10)
divide both sides by 6
x+z=10
subsitute 10 for x+z in the first equation
10+y=12
y=2
subsitute
3x-2(2)=5
3x-4=5
3x=9
x=3

x+z=10
3+z=10
z=7

x=3
y=2
z=7

number is
327

An angle measuring (870n)° is in standard position. For which value of n will the terminal side fall along the positive portion of the y-axis?n = 3
n = 4
n = 5
n = 6

Answers

Answer:

n = 3

Step-by-step explanation:

The terminal side of an angle fall along the positive portion of the y-axis,

If it can written in the form of (90°)a

Where a is any positive odd integer,

Here, the given angle is,

(870n)°,

For n = 3,

Our angle will be 2610°

Its terminal side fall along the positive portion of the y-axis,

If 2610° = (90°)a ⇒ a = 29 ( Positive odd integer )

Thus, for n = 3, the terminal side of the angle (870n)° falls along the positive portion of the y-axis,

For n = 4,

Our angle will be 3480°

Its terminal side fall along the positive portion of the y-axis,

If 3480° = (90°)a ⇒ a = 38.6667 ( Not possible )

Thus, for n = 4, the terminal side of the angle (870n)° does not fall along the positive portion of the y-axis

For n = 5,

Our angle will be 4350°

Its terminal side fall along the positive portion of the y-axis,

If 4350° = (90°)a ⇒ a = 48.333.. ( Not possible )

Thus, for n = 5, the terminal side of the angle (870n)° does not fall along the positive portion of the y-axis,

For n = 6,

Our angle will be 5220°

Its terminal side fall along the positive portion of the y-axis,

If 5220° = (90°)a ⇒ a = 58 ( Not possible )

Thus, for n = 6, the terminal side of the angle (870n)° does not fall along the positive portion of the y-axis.

The answer would be n=3

The total payroll for a baseball team is 2.38 x 10^9 dollars, and the total payroll for a football team is 2.7 x 10^11 dollars. How many more dollars is the football team's total payroll than the baseball team's total payroll? 0.32 x 10^9 dollars
2.6762 x 10^9 dollars
2.6762 x 10^11 dollars
3.2 x 10^11 dollars

Answers

To find out how many more dollars the football team's total payroll is compared to the baseball team's total payroll, we need to subtract the baseball team's total payroll from the football team's total payroll.

The baseball team's total payroll is given as 2.38 x 10^9 dollars.

The football team's total payroll is given as 2.7 x 10^11 dollars.

To subtract these numbers, we can simply subtract the coefficients (2.7 - 2.38) and keep the same exponent (10^11). This gives us 0.32 x 10^11 dollars.

However, it's important to note that 0.32 x 10^11 can be simplified. We can move the decimal point one place to the right, making the coefficient 3.2. Therefore, the football team's total payroll is 3.2 x 10^11 dollars more than the baseball team's total payroll.

So the correct answer is 3.2 x 10^11 dollars.

The difference between the payroll of football and baseball is 2.6762 × 10¹¹. Hence, option C is correct.

What is an equation?

Equations are logical assertions in mathematics that have two algebraic expressions on either side of an equals (=) sign. The expression on the left and the expression on the right is shown to be equal in reference to one another. LHS = RHS (left hand side = right hand side) appears in all mathematical equations. You can solve equations to determine the value of an unknown variable that represents an unknown quantity.

The payroll of the baseball team is 2.38 × 10⁹ and,

The payroll of the football team is 2.7 × 10¹¹.

So, the football team's payroll is more than the baseball team's payroll by,

$(2.7 \cdot 10^(11)) - (2.38 \cdot 10^(9))$

$=2.6762 \cdot 10^(11)$

Hence, the difference between the payroll of football and baseball is 2.6762 × 10¹¹. Hence, option C is correct.

To get more information about the equation:

brainly.com/question/33622350

A rectangle is dilated by a scale factor of n = 1. Which statement is true regarding the image of the dilation?

Answers

Well, you didn't bother to list the answer choices, so there's no way
I can help you pick the correct choice.

But I can tell you this: Any time a figure is dilated by a scale factor of 1,
the image is congruent to the original figure.

Answer:

It is a reduction because 0 < n < 1.

Step-by-step explanation:

Your portfolio has provided you with returns of 8.6 percent, 14.2 percent, -3.7 percent, and 12.0 percent over the past four years, respectively. what is the geometric average return for this period?

Answers

First you have to add all four of your numbers, 8.6+14.2+ -3.7+ 12=31.1. Then you divide your answer by 4, the number of numbers you added, and you get your answer of 7.775.

Simplify: (5) - (+8)

Answers

Answer:

-3

Step-by-step explanation:

hope it help

Answer:

Hello there!^^

Step-by-step explanation:

✰✰✰✰✰✰✰✰✰✰✰✰✰✰✰✰✰✰✰✰

Remove the parentheses

And than subtract the numbers

~~~~~~~~~~~~~~~~~~~~~~~~

→ 1. =5-8

→ 2. = -3

(You can also you a number line to solve this problem)

Answer: -3

Hence, your answer would be -3

By your fellow brainly user: xCherryxUwU

#Thanks!

✰✰✰✰✰✰✰✰✰✰✰✰✰✰✰✰✰✰✰✰

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