Answer:
<em>x = 1 and -2</em>
<em>Sum of the first ten terms = 1,398,100</em>
Step-by-step explanation:
Given the geometric progression 2x+2, 16, 64x...
Since they are in GP, their common ratio is expressed as;
16/2x+2 = 64x/16
16/2(x+1) = 4x
8/x+1 = 4x
Cross multiply
4x(x+1) = 8
4x²+4x = 8
4x²+4x - 8 = 0
divide through by 4
x²+x - 2 = 0
Factorize
x²+2x-x- 2 = 0
x(x+2)-1(x+2) = 0
(x-1)(x+2) = 0
x = 1 and -2
Hence the values of x are 1 and -2
Get the common ratio;
r = 16/2x+2
Since x = 1
r = 16/2(1)+2
r = 16/4
r = 4
Sum of the first n terms is expressed as;
Sn = a(rⁿ-1)/r-1
a = 2x+2
a = 2(1)+2
a = 4
Substitute;
S10 = 4(4^10 - 1)/4 - 1
S10 = 4(1,048,576-1)/3
S10 = 4,194,300/3
S10 = 1,398,100
Hence the sum of the first ten terms is 1,398,100
The area of a rectangle can be directly calculated using
the formula:
A = l * w
Where l is the length or the depth while w is the width
Therefore,
A = 50 feet * 100 feet
<span>A = 5000 square feet</span>
Answer:
• Gayle: 14
• Crystal: 3
Step-by-step explanation:
Let g represent the number of paperclips Gayle has. Then 42/g is the number Crystal has. The relationship between the two numbers is said to be ...
g - (42/g) = 11
Multiplying by g gives ...
g^2 -42 = 11g
g^2 -11g -42 = 0 . . . . subtract 11 g to put into standard form
To factor this, you are looking for two factors of -42 that sum to -11.
-42 = -42·1 = -21·2 = -14·3 = -7·6
You can see that -14 and 3 sum to -11, so the factoring is ...
(g -14)(g +3) = 0
g = 14 . . . . . . . . . . makes the product zero. (The g=-3 solution is extraneous.)
Gayle has 14 paperclips and Crystal has 3.
Answer:
Step-by-step explanation:
Hope this helps u!!
