Answer:
(see below)
Step-by-step explanation:
First, to make it easier for yourself, "flip" the triangles so that they "match." To see what I'm talking about, refer to IMAGE.A.
Now that you can tell that the congruent side and angles are corresponding, you have to prove them congruent.
There is one side and two angles, so it's AAS or SAA.
C= number of children tickets
a= number of adult tickets
In the equation, $9.50 per ticket must be multiplied by each c and a in order to calculate the total.
($9.50 * c) + ($9.50 * a)
since each term has $9.50 in it, we can pull out the common $9.50 in each
$9.50(c + a)
this expression now means that we must multiply $9.50 by c and then multiply $9.50 by a (using the distributive property)
ANSWER: $9.50(c + a) - the second choice down
Hope this helps! :)
Answer:
x = -2i and x = 2i
x = 3 and x = - 3
Step-by-step explanation:
x^4 - 5x^2 - 36 = 0
let u = x^2 and substitute
we have:
u^2 - 5u - 36 = 0
(u - 9)(u + 4) = 0
u = 9 and u = - 4
substitute back for u
x^2 = 9
x = 3 and x = - 3
x^2 = -4 -- i am going to assume you've learned imaginary numbers; otherwise, you cannot take the square root of a negative number.
x = -2i and x = 2i
By definition of tangent,
tan(<em>x</em>) = sin(<em>x</em>) / cos(<em>x</em>)
so if tan(<em>x</em>) < 0, and we're given cos(<em>x</em>) = -1/4 < 0, then it follows that sin(<em>x</em>) > 0.
Recall the Pythagorean identity:
cos²(<em>x</em>) + sin²(<em>x</em>) = 1 → sin(<em>x</em>) = + √(1 - cos²(<em>x</em>))
Then
sin(<em>x</em>) = √(1 - (-1/4)²) = √(15/16) = √(15)/4
Recall the double angle identity:
sin(2<em>x</em>) = 2 sin(<em>x</em>) cos(<em>x</em>)
Then
sin(2<em>x</em>) = 2 • √(15)/4 • (-1/4) = -2√(15)/16 = -√(15)/8
