Answer:
2 to the power of one sixth
Step-by-step explanation:
Assuming you don't already know this, any type of root can be expressed as an exponent. Generally speaking:
![\sqrt[n]{x} = {x}^{ \frac{1}{n} }](https://tex.z-dn.net/?f=%20%5Csqrt%5Bn%5D%7Bx%7D%20%20%3D%20%20%7Bx%7D%5E%7B%20%5Cfrac%7B1%7D%7Bn%7D%20%7D%20)
So you can rewrite the given fraction as
and then reduce as you normally would. That is, if the bases of the numerator and denominator are the same, then you can subtract the denominator's exponent from the numerator's exponent like so:
Since
the answer is
![{2}^{ \frac{1}{6} } \: or \: \sqrt[6]{2}](https://tex.z-dn.net/?f=%20%7B2%7D%5E%7B%20%5Cfrac%7B1%7D%7B6%7D%20%7D%20%20%5C%3A%20or%20%5C%3A%20%20%5Csqrt%5B6%5D%7B2%7D%20)
Answer:
the common ratio is either 2 or -2.
the sum of the first 7 terms is then either 765 or 255
Step-by-step explanation:
a geometric sequence or series of progression (these are the most common names for the same thing) means that every new term of the sequence is created by multiplying the previous term by a constant factor which is called the common ratio.
so,
a1
a2 = a1×f
a3 = a2×f = a1×f²
a4 = a3×f = a1×f³
the problem description here tells us
a3 = 4×a1
and from above we know a3 = a1×f².
so, f² = 4
and therefore the common ratio = f = 2 or -2 (we need to keep that in mind).
again, the problem description tells us
a2 + a4 = 30
a1×f + a1×f³ = 30
for f = 2
a1×2 + a1×2³ = 30
2a1 + 8a1 = 30
10a1 = 30
a1 = 3
for f = -2
a1×-2 + a1×(-2)³ = 30
-10a1 = 30
a1 = -3
the sum of the first n terms of a geometric sequence is
sn = a1×(1 - f^(n+1))/(1-f) for f <>1
so, for f = 2
s7 = 3×(1 - 2⁸)/(1-2) = 3×-255/-1 = 3×255 = 765
for f = -2
s7 = -3×(1 - (-2)⁸)/(1 - -2) = -3×(1-256)/3 = -3×-255/3 =
= -1×-255 = 255
You might have made an error the first time you solved for x. I got x = -0.5.
When you have your log base 4, the way you cancel that out is by making 4 the base on both sides, so you get 4^(log4) to reduce to 1, and you're left with:
2x + 3 = 4^(1/2) ... Simplify
2x + 3 = 2
2x = -1
x = -1/2
If you plug that back in, everything checks out. Maybe double check your use of logarithm/exponent properties?
Answer:
d
Step-by-step explanation:
formula for area of a triangle is base * width * 1/2
Answer:
m<1 = 140
Step-by-step explanation:
m<1 = 140 because of alternate interior angles
