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PilotLPTM [1.2K]
3 years ago
12

What does the remainder theorem conclude given that f(x)/x+6 has a remainder of 14? Enter your answer by filling in the boxes.​

Mathematics
1 answer:
musickatia [10]3 years ago
6 0

Answer:

f(-6)=14

Step-by-step explanation:

According to the remainder theorem, if a function f(x) is divided by (x-a), then the remainder is defined by f(a).

It is given that \dfrac{f(x)}{x+6} has a remainder of 14.

Here, the function f(x) is divided by (x+6). So, on comparing (x+6) and (x-a), we get

a=-6

So, by remainder theorem, remainder of \dfrac{f(x)}{x+6} is f(-6).

Since the remainder is 14, therefore

f(-6)=14

Therefore, the answer for first blank is -6 and for second blank is 14, i.e., f(-6)=14.

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Please help me!!!!!!!!!!!!!!
OLga [1]

Answer:

  1. d, series and sequence diverge
  2. d, geometric/divergent
  3. c, e (geometric, |r|<1)

Step-by-step explanation:

<h3>1.</h3>

The sequence terms have a common difference of -5/8. That make it a non-trivial arithmetic sequence, so it diverges.

The series is the sum of terms of the sequence. Any non-trivial arithmetic series diverges.

(A "trivial" arithmetic series has a first term of 0 and a common difference of 0. It is the only kind of <em>arithmetic</em> series that doesn't diverge.)

__

<h3>2.</h3>

The terms of the series have a common ratio of -2. That makes it a geometric series. The ratio magnitude is greater than 1, so the series diverges.

__

<h3>3.</h3>

A sequence will converge only if the terms have a common difference of 0 or a common ratio with a magnitude less than 1. Of the offered choices, only C and E will converge:

  c. geometric, r = 3/5

  e. geometric, r = -1/6

_____

<em>Additional comment</em>

The convergence criteria stated for problem 3 applies only to arithmetic and geometric sequences. There are many other kinds of sequences that converge, but these are the kinds being considered in this problem set.

3 0
2 years ago
The concession stand sells hot dogs and soda during the pee-wee football games.John bought 6 hot dogs and 4 sodas and paid $6.70
Eva8 [605]

Answer: Hotdog cost $0.75

Price of soda = $0.55

Step-by-step explanation:

Let the price of hot dogs be x.

Let the price of sodas be y.

6x + 4y = 6.70 ...... i

4x + 3y = 4.65 ....... ii

Multiply equation i by 4

Multiply equation ii by 6

24x + 16y = 26.80 ........ iii

24x + 18y = 27.90 ......... iv

Subtract iii from iv

2y = 1.10

y = 1.10/2

y = $0.55

Price of soda = $0.55

From equation i,

6x + 4y = 6.70

6x + 4(0.55) = 6.70

6x + 2.20 = 6.70

6x = 6.70 - 2.20

6x = 4.50

x = 4.50/6

x = $0.75

Hotdog cost $0.75

7 0
3 years ago
What is the greatest common factor between 18 and 24?
klemol [59]

Answer: 6.

We found the factors and prime factorization of 18 and 24. The biggest common factor number is the GCF number.

4 0
4 years ago
Read 2 more answers
(please help i have 30 min left )
GenaCL600 [577]
The coefficient of -7x is -7, since -7 is the number being multiplied by x.

Similarly, the coefficient of 9/4y is 9/4, since it is the number being multiplied by y.



Please consider marking this answer as Brainliest to help me advance.
7 0
3 years ago
What is the sum of the opposite angles in a square
xxMikexx [17]

Answer: (The sides are therefore chords in the circle!) This conjecture give a relation between the opposite angles of such a quadrilateral. It says that these opposite angles are in fact supplements for each other. In other words, the sum of their measures is 180 degrees.



6 0
3 years ago
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