Calculate the missing terms of the geometric sequence 2048,?,?,?,8
1 answer:
Answer: 2048, 512, 128, 32, 8
Step-by-step explanation:
Recognize 2048 is 2^11, as all hackers know
1024 is 2^10 :-). Also 8 is 2^3.
So this problem is exactly similar to filling in the geometric sequence starting at 10^11 = 100,000,000,000, with three intermediate values ending with 10^3 = 1000.
(100,000,000,000) = 10^11
1,000,000,000 = 10^9
10,000,000 = 10^7
100,000, = 10^5
(1,000) = 10^3
Or, it is exactly similar to filling in the arithmetic series 11, a, b, c, 3. That one is (11), 9, 7, 5, (3), where we subtract 2 each time.
The answer is (2048), 512, 128, 32, (8) where we divide by 2^2 each time. Or (2^11), 2^9, 2^7, 2^5, (2^3).
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Given:
The area model.
To find:
The area as a sum and area as a product.
Solution:
The four terms of the area model are .
The area as a sum is the sum of all the terms of given area model.
Area as a sum =
=
The area as a product is the factor form of sum of all the terms of given area model.
Area as a product =
=
=
Therefore, the area as a sum is and the area as a product is
.
Answer:
Step-by-step explanation:
The slope intercept form of a line is given as:
y = mx + c
Where m is the slope and c is the y-intercept
Let's rearrange the equation given in this form:
2x - 5y = -11
5y = 2x + 11
y = 2/5 x + 11/5
So the slope is 2/5
Slope of line that is perpendicular to this is the "negative reciprocal" of this slope. Which means the slope of perpendicular line would be -5/2
Thus, equation would become: y = -5/2x + c
Now we need to find c. For this we plug in 7 into x and 5 into y and solve for c [(7,5) is the point given]. Thus,
Thus, the equation of perpendicular line is:
First, we need to solve the first equation in order to see what the options need to be equivalent to. our first step to solving this is to distribute -3 through the parenthesis
y + 5 = -3x + 3
next, move the constant to the right side and change its sign
y = -3x + 3 - 5
calculate the difference
y = -3x - 2
since we cant find x, your final solution for y is y = -3x - 2, x ∈ R
now that we know the solution to that equation, we can now solve the options listed to see which ones are equivalent.
first is y = -3x - 2, which is very simple to solve because y has already been found. since we know y and there is no solution for x, our answer to this equation is y = -3x -2, x ∈ R. since this is the exact same answer as our first equation, we know that the A is equivalent to y + 5 = -3(x - 1)
the next equation is also already solved for y and has no x, so the answer to this equation is y = -4x - 5, x ∈ R. since this is does not have the same answer that <span>y + 5 = -3(x - 1) had</span>, option B is not equivalent.
our next equation is 3x + y = -2 does not provide y for us, so we must solve it.
first, you need to move the variable to the right side and change its sign
3x = -2 - y
now divide both sides of the equation by 3
x = - 2/3 = y/3
write all the numerators above their common denominators
x = - 2 + y/3
since we dont know what y is, our final solution is
x = -
, y ∈ R
since this answer does not match the answer we are looking for, option C is not equivalent.
finally, we must solve -4x + y = -5
the first step to solving this is to move the variable to the right side and change its sign
-4x = -5 - y
divide both sides of the equation by -4
x = 5/4 + y/4
now, write all the numerators above their common denominators
x = 5 + y/4
since we dont know what y is, our answer is x =
, y ∈ R
since this is also not equivalent to <span>y + 5 = -3(x - 1), our only answer is option A.
let me know if you have any further questions
:)</span>
y + 5 = -3x + 3
next, move the constant to the right side and change its sign
y = -3x + 3 - 5
calculate the difference
y = -3x - 2
since we cant find x, your final solution for y is y = -3x - 2, x ∈ R
now that we know the solution to that equation, we can now solve the options listed to see which ones are equivalent.
first is y = -3x - 2, which is very simple to solve because y has already been found. since we know y and there is no solution for x, our answer to this equation is y = -3x -2, x ∈ R. since this is the exact same answer as our first equation, we know that the A is equivalent to y + 5 = -3(x - 1)
the next equation is also already solved for y and has no x, so the answer to this equation is y = -4x - 5, x ∈ R. since this is does not have the same answer that <span>y + 5 = -3(x - 1) had</span>, option B is not equivalent.
our next equation is 3x + y = -2 does not provide y for us, so we must solve it.
first, you need to move the variable to the right side and change its sign
3x = -2 - y
now divide both sides of the equation by 3
x = - 2/3 = y/3
write all the numerators above their common denominators
x = - 2 + y/3
since we dont know what y is, our final solution is
x = -
since this answer does not match the answer we are looking for, option C is not equivalent.
finally, we must solve -4x + y = -5
the first step to solving this is to move the variable to the right side and change its sign
-4x = -5 - y
divide both sides of the equation by -4
x = 5/4 + y/4
now, write all the numerators above their common denominators
x = 5 + y/4
since we dont know what y is, our answer is x =
since this is also not equivalent to <span>y + 5 = -3(x - 1), our only answer is option A.
let me know if you have any further questions
:)</span>