Answer:
We know that the equation of the circle in standard form is equal to <em>(x-h)² + (y-k)² = r²</em> where (h,k) is the center of the circle and r is the radius of the circle.
We have x² + y² + 8x + 22y + 37 = 0, let's get to the standard form :
1 - We first group terms with the same variable :
(x²+8x) + (y²+22y) + 37 = 0
2 - We then move the constant to the opposite side of the equation (don't forget to change the sign !)
(x²+8x) + (y²+22y) = - 37
3 - Do you recall the quadratic identities ? (a+b)² = a² + 2ab + b². Now that's what we are trying to find. We call this process <u><em>"completing the square"</em></u>.
x²+8x = (x²+8x + 4²) - 4² = (x+4)² - 4²
y²+22y = (y²+22y+11²)-11² = (y+11)²-11²
4 - We plug the new values inside our equation :
(x+4)² - 4² + (y+22)² - 11² = -37
(x+4)² + (y+22)² = -37+4²+11²
(x+4)²+(y+22)² = 100
5 - We re-write in standard form :
(x-(-4)²)² + (y - (-22))² = 10²
And now it is easy to identify h and k, h = -4 and k = - 22 and the radius r equal 10. You can now complete the sentence :)
Answer: THe Second answer is the correct one
Step-by-step explanation:
<span>An algebraic expression is an expression constructed from a number of constants and variables utilizing algebraic operations. These algebraic operations are addition, subtraction, multiplication, division, and exponentiation. A constant is constant, so its value is unchanged. A variable changes based on the value provided. In the provided example, 2x-1, there are two constants, "2" and "1", and one variable "x." The algebraic operations utilized are multiplication and subtraction. In order to evaluate the value of the algebraic expression, the given value for the variable must be substituted for the variable x, and then the algebraic operations executed to obtain the answer.
For instance, if you were told that the value of x in this case was 2, then you would substitute the value 2 for x and perform the described operations. Remember to follow the order of operations when evaluating an algebraic expression!
2x-1 for x=2
2(2) - 1
4 - 1
3 is the answer.
Remember, even though the multiplication operation is not explicitly stated, it is implied that a constant attached to a variable (termed a coefficient) is multiplied with the value of the variable.</span>
<u>Step-by-step explanation:</u>
(a) A natural number that is greater than 25 and less than 40
Natural Number : These are numbers starting from 1 or also sometimes from zero and are all positive ! A natural greater than 25 & less than 40 is 30 .
(b) An integer which is less than -5 and a multiple of 2
Integer : An integer is a whole number not a fraction including 0 . It can be positive or negative ! Integer less than -5 and a multiple of 2 is -6.
(c) A rational number between 1 and 2
Rational Number : A number which can be expressed in form of p/q where q is not equal to 0 . A rational number between 1 & 2 is 3/2 .
(d) An irrational number between 8 and 9.
Irrational Number: A real number which is not rational or can't be written in form of p/q . An irrational number between 8 & 9 is 
.
Group up the like terms and combine them
2x^2 and -7x^2 add up to -5x^2
6x and 2x add up to 8x
1 and -3 add up to -2
We end up with -5x^2 + 8x - 2
<h3>Answer: Choice B</h3>
