Answer:
<em>a) x = -2+√3 and -2-√3</em>
<em>b) x = -1 + 2√3/3 and -1 - 2√3/3</em>
<em>c) x = 3.185 and 0.315</em>
Step-by-step explanation:
To solve the following quadratic equation, we will use the general formula
x = -b±√b²-4ac/2a
a) x²+4x+1 = 0
a = 1, b = 4 and c = 1
Substitute into the formula
x = -4±√4²-4(1)(1)/2(1)
x = -4±√16-4/2
x = -4±√12/2
x = -4±2√3/2
x = (-4+2√3)/2 and (-4-2√3)/2
<em>x = -2+√3 and -2-√3</em>
b) 3x²+6x-1 = 0
a = 3, b = 6 and c = -1
Substitute into the formula
x = -6±√6²-4(3)(-1)/2(3)
x = -6±√36+12/6
x = -6±√48/6
x = -6±4√3/6
x = (-6+4√3)/6 and (-6-4√3)/6
<em>x = -1 + 2√3/3 and -1 - 2√3/3</em>
<em></em>
c) 2x² - 7x + 2 = 0
a = 2, b = -7 and c = 2
x = -(-7)±√(-7)²-4(2)(2)/2(2)
x = 7±√49-16/4
x =7±√33/4
x = 7±5.74/4
x = 7+5.74/4 and 7-5.74/4
x = 12.74/4 and 1.26/4
<em>x = 3.185 and 0.315</em>
<em></em>
5√7 + 12√6 - 10√7 - 5√6
Write it like this:
(12√6 - 5√6) + (5√7 - 10√7),
as the 12 and 5 are both being multiplied by √6, they can be added or subtracted and its the same with 5 and 10, so it becomes:
7√6 - 5√7
You should leave it like this.
Answer:
About 75 degrees
Step-by-step explanation:
Let's call the point between C and B D. Using the Pythagorean Theorem, you know that CD is 
cm, meaning that BC has length 
cm. Additionally, we know that AB has length 
. Using the law of cosines:
Hope this helps!
Answer:
f(x) = -|x -2| +1
Step-by-step explanation:
The transformation ...
g(x) = f(x -h) +k
translates the function f(x) so that the point on its graph (0, f(0)) is moved to the location (h, k) on the graph of g(x).
The vertex of the "upside down" absolute value function f(x) = -|x| is (0, 0). In your graph, that point has been moved to (h, k) = (2, 1). So, the transformed function is ...
f(x) = -|x -2| +1 . . . . matches the last choice
