Need help on the #13-20.
13. What is the quotient of d − 2 ) d 4 − 6d 3 + d + 17
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A. d 3 − 4d 2 − 8d − 15 R −13
B. d 3 − 8d 2 + 16d − 31 R 79
C. d 3 − 4d 2 + 9d + 35
D. d 3 − 8d 2 + 17d − 17
14. What is the sum of the first 10 positive integers?
A. 50 C. 95
B. 55 D. 100
Examination
15. A bank account yields 7 percent interest, compounded annually. If you deposit $1,000 in the
account, what will the account balance be after 5 years?
A. $1070.00 C. $1402.55
B. $1350.00 D. $1700.00
16. The first two terms of an arithmetic sequence are a1 = 2 and a2 = 4. What is a10, the tenth
term?
A. 10 C. 19
B. 18 D. 20
17. Use the remainder theorem to determine the remainder when d 4 + 2d 2 + 5d – 10 is divided
by d + 4.
A. 42 C. 126
B. 106 D. 258
18. Which one of the following is a geometric sequence?
A. 2, –3, 9⁄2, −18⁄4
B. 0, 1, 2, 3, . . .
C. 8, 4, 2, 1, 1⁄2, 1⁄4, . . .
D. –7, 10, 23, 36, . . .
19. If y = 7.2 when x = 10, what is the value of x when y = 20? (y varies inversely as the square of x.)
A. 6 C. 14.4
B. 10 D. 20
20. Use the remainder theorem and the factor theorem to determine whether (c + 5) is a factor of
(c4 + 7c3 + 6c2 – 18c + 10).
A. The remainder is 0 and, therefore, (c + 5) is a factor of (c4 + 7c3 + 6c2 – 18c + 10).
B. The remainder is 0 and, therefore, (c + 5) isn’t a factor of (c4 + 7c3 + 6c2 – 18c + 10).
C. The remainder isn’t 0 and, therefore, (c + 5) is a factor of (c4 + 7c3 + 6c2 – 18c + 10).
D. The remainder isn’t 0 and, therefore, (c + 5) isn’t a factor of (c4 + 7c3 + 6c2 – 18c + 10).
72
Your question are unclear to me. Online "^" is used to indicate an exponent, e.g., x^2 = x squared. Also some of questions are lacking adequate data.
Lastly, we do not do your work for you. Once you have attempted to answer your questions, we will be happy to give you feedback on your work. Although it might require more time and effort, you will learn more if you do your own work. Isn't that why you go to school?
whats the answer to 17 i have the same question and I'm stuck on it and yes i get the question
13. To find the quotient of the given polynomial, we need to perform polynomial long division.
Step 1: Divide the first term of the dividend by the first term of the divisor. In this case, divide d^4 by d, which gives us d^3.
Step 2: Multiply the entire divisor by the quotient found in step 1. In this case, multiply (d - 2) by (d^3), which gives us d^4 - 2d^3.
Step 3: Subtract the result from step 2 from the dividend. In this case, subtract d^4 - 2d^3 from d^4 - 6d^3 + d + 17, which gives us 4d^3 + d + 17.
Step 4: Repeat steps 1-3 with the new dividend.
Following these steps, we continue to divide until all terms of the dividend have been accounted for. In this case, the quotient is d^3 - 4d^2 - 8d - 15, which corresponds to option A.
14. The sum of the first n positive integers can be found using the formula: Sn = (n/2)(a + l), where Sn is the sum, n is the number of terms, a is the first term, and l is the last term.
In this case, n = 10, a = 1, and l = 10.
Substituting these values in the formula: S10 = (10/2)(1 + 10) = 55. Therefore, the sum of the first 10 positive integers is 55, which corresponds to option B.
15. The formula to calculate compound interest is: A = P(1 + r/n)^(nt), where A is the final amount, P is the principal amount, r is the interest rate, n is the number of times compounded, and t is the time in years.
In this case, P = $1,000, r = 7%, n = 1 (compounded annually), and t = 5 years.
Substituting these values: A = 1000(1 + 0.07/1)^(1*5) = 1000(1.07)^5 ≈ $1402.55. Therefore, the account balance after 5 years is approximately $1402.55, which corresponds to option C.
16. To find the nth term of an arithmetic sequence, we use the formula: an = a1 + (n - 1)d, where an is the nth term, a1 is the first term, n is the term number, and d is the common difference.
In this case, a1 = 2 and a2 = 4. We need to find a10.
Using the formula: a10 = 2 + (10 - 1)(4 - 2) = 2 + 9(2) = 2 + 18 = 20. Therefore, the tenth term is 20, which corresponds to option D.
17. To find the remainder when a polynomial is divided by another polynomial, we can use the remainder theorem. According to the remainder theorem, the remainder when a polynomial P(x) is divided by (x - a) is equal to P(a).
In this case, we need to find the remainder when d^4 + 2d^2 + 5d - 10 is divided by d + 4.
Substituting d = -4 into the polynomial: (-4)^4 + 2(-4)^2 + 5(-4) - 10 = 16 + 32 - 20 - 10 = 18.
Therefore, the remainder when the polynomial is divided by d + 4 is 18, which corresponds to option B.
18. A geometric sequence is a sequence in which each term is found by multiplying the previous term by a constant called the common ratio.
Checking the options:
A. 2, -3, 9/2, -18/4: Not a geometric sequence as the ratio between terms is not constant.
B. 0, 1, 2, 3, ...: Not a geometric sequence as the difference between terms is not constant.
C. 8, 4, 2, 1, 1/2, 1/4, ...: Yes, this is a geometric sequence with a common ratio of 1/2.
D. -7, 10, 23, 36, ...: Not a geometric sequence as the difference between terms is not constant.
Therefore, option C is the geometric sequence.
19. The inverse variation between two variables x and y is defined as y = k/x, where k is a constant.
In this case, y = 7.2 when x = 10. To find the value of x when y = 20, we can use the inverse variation equation:
7.2 = k/10. Solving for k, we get k = 72.
Substituting this value into the inverse variation equation and solving for x:
20 = 72/x
x = 72/20
x = 3.6
Therefore, the value of x when y = 20 is 3.6, which corresponds to option A.
20. To determine whether (c + 5) is a factor of (c^4 + 7c^3 + 6c^2 - 18c + 10), we can use the remainder theorem and the factor theorem.
The remainder theorem states that if a polynomial P(x) is divided by (x - a), then the remainder is equal to P(a). The factor theorem states that if a polynomial P(x) has a factor (x - a), then P(a) = 0.
To check if (c + 5) is a factor, we need to determine the remainder when the polynomial is divided by (c + 5).
Substituting c = -5 into the polynomial: (-5)^4 + 7(-5)^3 + 6(-5)^2 - 18(-5) + 10 = 625 - 875 + 150 - 90 + 10 = -180.
Since the remainder is not equal to zero, we conclude that (c + 5) is not a factor of (c^4 + 7c^3 + 6c^2 - 18c + 10). Therefore, the correct answer is option B.