Answer:
r = 2
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
Given
x² + y² + 4x - 2y = - 1 ← rearrange the x and y terms together
x² + 4x + y² - 2y = - 1
Using the method of completing the square
add ( half the coefficient of the x/ y terms )² to both sides
x² + 2(2)x + 4 + y² + 2(- 1)y + 1 = - 1 + 4 + 1
(x + 2)² + (y - 1)² = 4 ← in standard form
with r² = 4 ⇒ r = = 2
<em>Answer</em><em>:</em>
<em>m</em><em><</em><em>DAC</em><em>=</em><em>6</em><em>0</em><em>°</em>
<em>Sol</em><em>ution</em><em>,</em>
<em>m</em><em><</em><em>BAC</em><em>=</em><em>3</em><em>0</em><em>°</em>
<em>let</em><em> </em><em>m</em><em><</em><em>DAC</em><em> </em><em>be</em><em> </em><em>X</em>
<em>Now</em><em>,</em>
<em></em>
<em>hope</em><em> </em><em>this</em><em> </em><em>helps</em><em>.</em><em>.</em>
<em>Good</em><em> </em><em>luck</em><em> on</em><em> your</em><em> assignment</em><em>.</em><em>.</em>
Answer:
f(x) = x^3 + 4x^2 - 7x - 28
Step-by-step explanation:
If the roots of this cubic function are Square root of seven, -Square root of seven, -4, then the factors must be (x^2 - 7)(x + 4).
Multiplying this out, we get f(x) = x^3 + 4x^2 - 7x - 28.
Note: Please use " ^ " to indicate exponentiation.
Answer: Angles 4 and 5
Step-by-step explanation:
Supplementary angles are angles that add up to 180. The only angle pairs the add up to 180 (you can tell by seeing if two angles are the only two on a straight line) are angles 4 and 5, and angles 3 and 4. Angles 3 and 4 isn’t an option, so it’s 4 and 5.
Answer:
5/6
Step-by-step explanation:
Suppose x = 0.83 (3 repeating).
Multiply both sides by 10:
10x = 8.3 (repeating 3)
Now, multiply both sides by 10 again:
100x = 83.3 (repeating 3)
So, we have:
100x = 83.3 (repeating 3)
10x = 8.3 (repeating 3)
We see that if we subtract these two equations, the repeating 3s cancel out, and we're left with:
100x - 10x = 83 - 8
90x = 75
x = 75/90 = 5/6
Thus, the answer is 5/6.
Hope this helps!