Answer:
r = √13
Step-by-step explanation:
Starting with x^2+y^2+6x-2y+3, group like terms, first x terms and then y terms: x^2 + 6x + y^2 -2y = 3. Please note that there has to be an " = " sign in this equation, and that I have taken the liberty of replacing " +3" with " = 3 ."
We need to "complete the square" of x^2 + 6x. I'll just jump in and do it: Take half of the coefficient of the x term and square it; add, and then subtract, this square from x^2 + 6x: x^2 + 6x + 3^2 - 3^2. Then do the same for y^2 - 2y: y^2 - 2y + 1^2 - 1^2.
Now re-write the perfect square x^2 + 6x + 9 by (x + 3)^2. Then we have x^2 + 6x + 9 - 9; also y^2 - 1y + 1 - 1. Making these replacements:
(x + 3)^2 - 9 + (y - 1)^2 -1 = 3. Move the constants -9 and -1 to the other side of the equation: (x + 3)^2 + (y - 1)^2 = 3 + 9 + 1 = 13
Then the original equation now looks like (x + 3)^2 + (y - 1)^2 = 13, and this 13 is the square of the radius, r: r^2 = 13, so that the radius is r = √13.
<h3>
Answer: Choice A</h3><h3>
9.80h+10 = 88.40</h3>
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Work Shown:
- h = number of hours worked.
- 9.80h = amount of money earned after working h number of hours (ignoring the meal bonus).
- 9.80h+10 = total amount of money earned after adding on the meal bonus.
- 9.80h+10 = 88.40 is the equation we use since the total 9.80h+10 is the same as the total she earned 88.40 dollars.
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Extra info (optional section)
If you want to solve for h, then you could follow these steps.
9.80h+10 = 88.40
9.80h = 88.40-10 ... subtract 10 from both sides
9.80h = 78.40
h = 78.40/9.80 .... divide both sides by 9.80
h = 8
Valerie worked 8 hours on Friday.
As a check,
9.80h + 10 = 88.40
9.80*8 + 10 = 88.40
78.40 + 10 = 88.40
88.40 = 88.40
The answer is confirmed.
<h3>The number of beads lina has is 31</h3><h3>
Laura made a mistake by adding the constant 7 and variable 4b</h3>
<em><u>Solution:</u></em>
Given that,
Laura wrote and solved the following expression to find the total number of beads Lina has
There are 6 beads in each packet
7+4b = 11b
= 11(6)
=66
From given,
Lina has a total of 7 + 4b beads
Given that, There are 6 beads in each packet
Substitute b = 6
7 + 4(6)
Simplify
7 + 24
Add
31
Thus, she has a total of 31 beads and not 66 beads
Laura made a mistake by adding the constant 7 and variable 4b
But a constant and variable cannot be added
Answer: the length of the ladder is 40 meters.
Step-by-step explanation:
The ladder forms a right angle triangle with the wall and the ground.
The length of the ladder represents the hypotenuse of the right angle triangle.
The distance of the base of the ladder due west of the burning building represents the adjacent side of the right angle triangle.
To determine the length of the ladder, h, we would apply the cosine trigonometric ratio. It is expressed as
Cos θ = adjacent side/hypotenuse. Therefore,
Cos 51 = 25/h
h = 25/Cos 51 = 25/0.6293
h = 40 meters to the nearest meter.
Domain: 1 2 3 4 5 6 range: -1 0 1 2 3 6
