Answer:
Step-by-step explanation:
The recursive rule is given by;
a = r .an-1 where n is the number of terms.
Given the sequence: -64, -16, -4 , -1, ....
This sequence is a geometric sequence with common ratio (r) = 1/4
Here, first term a1 = -64
Since,
\frac{-16}{-64} = \frac{1}{4}
\frac{-4}{-16} = \frac{1}{4} and so on....
The recursive rule for this sequence is;
an = 1/4*an-1
Answer:
x <= 0 or 1 = < x <= 5.
Step-by-step explanation:
First we find the critical points:
x(x - 1)(x - 5) = 0
gives x = 0, x = 1 and x = 5.
Construct a Table of values:
<u> x < 0 </u> <u>x = 0 </u> 0<u>< x < 1</u> <u>1 =< x <= 5</u> <u>x = 5</u>
x <0 0 >0 <0 0
x - 1 <0 -1 >0 <0 0
x - 5 < 0 0 > 0 <0 0
x(x-1)(x-5) < 0 0 >0 <0 0
So the answers are x =< 0 or 1 =< x <= 5.
Answer:
70
Step-by-step explanation:
= First term = 
= Common difference = 
= Number of terms = 20
Sum of arithmetic progression is given by
![S=\dfrac{n}{2}[2a_1+(n-1)d]\\\Rightarrow S=\dfrac{20}{2}\times (2\times \dfrac{1}{3}+(20-1)\dfrac{1}{3})\\\Rightarrow S=70](https://tex.z-dn.net/?f=S%3D%5Cdfrac%7Bn%7D%7B2%7D%5B2a_1%2B%28n-1%29d%5D%5C%5C%5CRightarrow%20S%3D%5Cdfrac%7B20%7D%7B2%7D%5Ctimes%20%282%5Ctimes%20%5Cdfrac%7B1%7D%7B3%7D%2B%2820-1%29%5Cdfrac%7B1%7D%7B3%7D%29%5C%5C%5CRightarrow%20S%3D70)
The sum of the first 20 terms of the arithmetic sequence is 70.
answer
D 2
factor
factor the equation 
into (x + a) and (x + b) so that a + b = -2 and a * b = -8
the two numbers that meet these conditions are a = -4 and b = 2
find solutions
set both (x - 4) and (x + 2) equal to zero to find your solutions
x - 4 = 0
x = 4
x + 2 = 0
x = -2
add solutions
since the two solutions are x = 4 and x = -2, add them together to get your final answer
4 + (-2) = 2
Answer: x = 9 (choice D)
Assuming this is a geometric kite, then this means that triangle ABD is a reflection over the line BD to get triangle BCD. Furthermore, this points to AB and BC being the same length
AB = BC
3x - 5 = 22 .... substitution
3x - 5+5 = 22+5 .... add 5 to both sides
3x = 27
3x/3 = 27/3 ..... divide both sides by 3
x = 9
