(x + 5)2 + (y - 7)2 = 36, its radius is

Answers

Answer 1

Answer: The answer would be 6

Steps: The equation of a circle is (x – h)² + (y – k)² = r²; since we are trying to find the radius we are going to focus on the r². Now if you look the equation has the 36 filled in as the r² so r² = 36; we now have to isolate the r to get the radius, how do we get the radius? We Square root the r² and 36. After we get r = 6, The radius is 6 units

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What 3 consecutive numbers add up to 237?

Answers

let three consecutive numbers be a-1 , a ,a+1

sum of above (a-1)+(a)+(a+1) = 237
3a = 237
a = 79

therefore three numbers are = 78, 79,80

Take the three consecutive numbers as x, x+1 and x+2. These three have to add up to 237 so we get the equation:

x + (x+1) + (x+2) = 237
3x + 3 = 237
3x = 234
x = 234 / 3 = 78

Therefore the numbers are x (78), x+1 (79) and x+2 (80)

1. Refer to the triangle below. If a = 3 and b = 6, A. Find the exact length of c in unsimplified radical form B. Find the exact length of c in simplified radical form C. Find c to the nearest hundredth

Answers

I'm assuming that the triangle is a right triangle wherein the Pythagorean theorem is applicable.

a² + b² = c²

c = √a²+b²
c = √3² + 6²
c = √9 + 36
c = √45 unsimplified radical form
c = √9 * 5
c = 3 √5 simplified radical form
c = 3 * 2.24
c = 6.71 value of c to the nearest hundredth

In an equation or inequality, you want to get the variable.

Answers

To solve for [variable] in the equation [equation], apply inverse operations to isolate [variable]. For inequalities, follow the same steps, but note the direction of the inequality sign to find valid values.

To solve for a variable in an equation, one must follow a systematic process. First, identify the equation's form, whether linear, quadratic, or another type. Then, apply appropriate operations to isolate the variable. For example, in linear equations, perform addition, subtraction, multiplication, or division to isolate the variable on one side of the equation. For quadratic equations, use factoring, completing the square, or the quadratic formula.

When dealing with inequalities, the same principles apply, but one must also consider the direction of the inequality sign (>, <, ≥, ≤). When multiplying or dividing by a negative number, the inequality sign must be reversed.

In both cases, it's crucial to perform the same operation on both sides of the equation or inequality to maintain balance and equivalence. Lastly, check the solution by substituting it back into the original equation or inequality to ensure its validity.

This systematic approach ensures that we can accurately solve for variables in equations and find the values that satisfy inequalities while maintaining mathematical integrity.

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Complete question below:

"How do you solve for [variable] in the equation [equation]?""What are the steps to find the values of [variable] that satisfy the inequality [inequality]?"

What you want to do is get the variable x on the left side by itself (just like you would if this were an equation). Be sure to perform the same operations on both sides of the inequality until x is all by itself on the left side.

Solve the absolute value equation. |3x-4|=5

Answers

Absolute values are a way of finding a distant from zero, which means there will be 2 answers; one will be positive, and the other will be negative.

$|3x-4|=5 and |3x-4|=—5$ Because you need 2 answers, you have to make 5 positive and negative.

Another way to write this equation would be...
5=|3x-4|=—5

Now lets continue...
5=3x-4=—5

Add 4 to both sides...
9=3x=—1

Now divide by 3...
3=x= $- (1)/(3)$

So the solution is...
X={ $-(1)/(3)$ , 3}

12 less than one-eleventh of some number, w"

Answers

The required number is 132.

It is required to find the number.

What is arithmetic?

Arithmetic is the branch of mathematics that deals with the study of numbers using various operations on them. Basic operations of math are addition, subtraction, multiplication and division. These operations are denoted by the given symbols.

Given:

According to given question we have,

Let the number be x.

1/11w - 12

1/11w-12=0

Add 12 both sides we get,

1/11w-12+12=0+12

1/11w=12

w = 132

Therefore, the required number is 132.

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