Answer:
x = -1
x = 5
Step-by-step explanation:
Use pythagorean theorem: a² + b² = c²
x² + (2x + 2)² = (2x + 3)²
Since these are quantities, you'll have to make them into quadratic equations.
(2x + 2)(2x + 2) = 4x² + 4x + 4x + 4
(2x + 3)(2x + 3) = 4x² + 6x + 6x + 9
x² + 4x² + 4x + 4x + 4 = 4x² + 6x + 6x + 9
Combine like terms
5x² + 8x + 4 = 4x² + 12x + 9
Move one side to set the equation equal to 0
x² - 4x - 5 = 0
Solve
x² - 5x + x - 5 = 0
x(x - 5) + 1(x - 5) = 0
(x + 1)(x - 5) = 0
x = -1, 5
<em>We</em><em> </em><em>can</em><em> </em><em>check</em><em> </em><em>that</em><em> </em><em>these</em><em> </em><em>are</em><em> </em><em>correct</em><em> </em><em>by</em><em> </em><em>plugging</em><em> </em><em>them</em><em> </em><em>in</em><em> </em><em>for</em><em> </em><em>x</em><em> </em><em>and</em><em> </em><em>seeing</em><em> </em><em>if</em><em> </em><em>they</em><em> </em><em>are</em><em> </em><em>equal</em>
<em>For</em><em> </em><em>example</em>
<em>(</em><em>-1</em><em>)</em><em>²</em><em> </em><em>+</em><em> </em><em>(</em><em>2</em><em>(</em><em>-1</em><em>)</em><em> </em><em>+</em><em> </em><em>2</em><em>)</em><em>²</em><em> </em><em>=</em><em> </em><em>(</em><em>2</em><em>(</em><em>-1</em><em>)</em><em> </em><em>+</em><em> </em><em>3</em><em>)</em><em>²</em>
<em>1</em><em> </em><em>=</em><em> </em><em>1</em>
8 1/2 = 8 4/8, so…
8 4/8-2 5/8= 6 1/8
Final answer is…
6 1/8
Answer:
D, 576
Step-by-step explanation:
To find the volume of a rectangular prism, you simply need to multiply all of the side lengths together. 4*9*16=576, or answer choice D.
We need to convert the equation of the circle to standard form only then we can find the radius and the center of the circle.
From this equation we can write:
Center of the circle is (-1,1) and the radius of the circle is 4.
Answer:
![Interval: [-10.10]](https://tex.z-dn.net/?f=Interval%3A%20%5B-10.10%5D)
Step-by-step explanation:
Given
Set: -10 to 10
Required
Write as interval notation
We start by writing the given parameter as an inequality
The direct representation of 
and 
in interval representation of sets is 
and ![]](https://tex.z-dn.net/?f=%5D)
, which shows that the beginning and end of the interval are inclusive;
So, the above inequality in interval notation is:
