Answer:
-3
Step-by-step explanation:
Answers:
x = -8/5 or x = 8/5
Sum of the first ten terms where all terms are positive = 4092
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Explanation:
r = common ratio
- first term = 4
- second term = (first term)*(common ratio) = 4r
- third term = (second term)*(common ratio) = (4r)*r = 4r^2
The first three terms are: 4, 4r, 4r^2
We're given that the sequence is: 4, 5x, 16
Therefore, we have these two equations
Solve the second equation for r and you should find that r = -2 or r = 2 are the only possible solutions. If r = -2, then 5x = 4r solves to x = -8/5. If r = 2, then 5x = 4r solves to x = 8/5.
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To find the sum of the first n terms, we use this geometric series formula
Sn = a*(1 - r^n)/(1 - r)
We have
- a = 4 = first term
- r = 2, since we want all the terms to be positive
- n = 10 = number of terms to sum up
So,
Sn = a*(1 - r^n)/(1 - r)
S10 = 4*(1 - 2^10)/(1 - 2)
S10 = 4*(1 - 1024)/(-1)
S10 = 4*(-1023)/(-1)
S10 = 4092
Answer: 16 ounces : 1 pound
Answer:
1/4
Step-by-step explanation:
its bigger
Answer:
j² - 5j²k - 2
Step-by-step explanation:
3j² - j²k - 6 - 4j²k - 2j² + 4
To simplify this polynomial, we can collect like terms. A term is number(s) or variable(s) that are grouped together by multiplication. <u>Like terms have the same variable and exponent</u>.
We have three groups of like terms:
The j-squares (j²), the j-squared k (j²k) and the constants (no variable).
Remember to include the negatives!
The j-squares are: 3j² ; -2j²
The j-squares k are: - j²k ; - 4j²k
The constants are: - 6 ; 4
Simplify:
3j² - j²k - 6 - 4j²k - 2j² + 4
Rearrange the polynomial by like terms
= (- j²k - 4j²k) + (3j² - 2j²) + (- 6 + 4)
Add or subtract the like terms
= (-5j²k) + (j²) + (-2)
Remove brackets and rearrange so the negative is not first
= j² + - 5j²k + - 2
Simplify where two signs are together. Adding a negative is subtraction.
= j² - 5j²k - 2 Simplified
