Answer:
Look below
Step-by-step explanation:
Given that CDB is 90 degrees, ACB is 90 degrees, and ACD is 60 degrees, we can determine that DCB = 90-60 = 30 degrees.
This means triangle BCD is a 30-60-90 (angle measures) right triangle
The proportions of the sides (from smallest to largest) is
x:x√3:2x
We are given that BC = 6 cm. This means...
2x=6
x=3
This means DB is 3 cm and CD is 3√3 cm
Using the linear pair theorem, we can find that Angle CDA is 90 degrees. This means ACD is also a 30-60-90 triangle.
x=3√3
x√3=9
2x=6√3
Now we need to find AB
AB = AD + DB
AB = 9 + 3
AB = 12 cm
<h3>
Answer: (x-2)(x+2)(x+3)(x+3)</h3>
This is the same as (x-2)(x+2)(x+3)^2. The order of the factors doesn't matter.
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Explanation:
x^2-4 factors to (x-2)(x+2) after using the difference of squares rule
x^2+6x+9 factors to (x+3)(x+3) after using the perfect square trinomial factoring rule
So overall, the original expression factors to (x-2)(x+2)(x+3)(x+3)
We can condense this into (x-2)(x+2)(x+3)^2 since (x+3)(x+3) is the same as (x+3)^2
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Side notes:
- Difference of squares rule is a^2 - b^2 = (a-b)(a+b)
- The perfect square trinomial factoring rule is a^2+2ab+b^2 = (a+b)^2
12/10 = 1 2/10 or 1 1/5
15/6 = 2 3/6 or 2 1/2.
To turn these fractions into mixed numbers you have to see how much times the denominator can go into the numerator and the amount of numbers left over. For 12/10, 10 can go into 12 1 time, so the whole number is 1. There is 2 numbers left over, so the numerator is 2 and you do not have to change the denominator. To simplify, divide the numerator and denominator by the highest number it can be divided to
Use our brains and what we know
f(x)=a(x-h)²+k
vetex is (h,k)
and a is te leading coefient
if directix is below the focus, then it opens up and a is positive
if directix is above focus, then it opens down and a is negaitve
vertex is in between directix and focus
so
(3,-1) and y=1
-1<1
so directix is above
a is negative
directly in between
distance from -1 to 1 is 2
2/2=1
1 above (3,-1) is (3,0)
vertex is (3,0)
y=a(x-3)²+0
y=a(x-3)²
the only option with a negative 'a' value is B
answer is B
