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12 days ago

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The sum of two polynomials is 8d5 – 3c3d2 + 5c2d3 – 4cd4 + 9. If one addend is 2d5 – c3d2 + 8cd4 + 1, what is the other addend?

The choices are: A. 6d5 – 2c3d2 + 5c2d3 – 12cd4 + 8 B. 6d5 – 4c3d2 + 3c2d3 – 4cd4 + 8 C. 6d5 – 4c3d2 + 5c2d3 – 12cd4 + 8 D. 6d5 – 2c3d2 – 3c2d3 – 4cd4 + 8

2 answers:

PIT_PIT [3.9K]12 days ago

5 0

Answer: The correct choice is A.

Step-by-step explanation: We have a polynomial that is the result of adding two other polynomials.

The resulting polynomial is: $8d^5-3c^3d^2+5c^2d^3-4cd^4+9$

One of the polynomials being summed is: $2d^5-c^3d^2+8cd^4+1$

Let us denote the other polynomial as 'x'

According to the problem statement:

$8d^5-3c^3d^2+5c^2d^3-4cd^4+9=x+(2d^5-c^3d^2+8cd^4+1)$

$x=8d^5-3c^3d^2+5c^2d^3-4cd^4+9-(2d^5-c^3d^2+8cd^4+1)$

Combining like terms in the equation provided results in:

$x=(8d^5-2d^5)+(-3c^3d^2+c^3d^2)+(5c^2d^3)+(-4cd^4-8cd^4)+(9-1)$

$x=6d^5-2c^3d^2+5c^2d^3-12cd^4+8$

The final answer, therefore, is option A.

Svet_ta [4.3K]12 days ago

3 0

Answer:

6d5 – 2c3d2 + 5c2d3 – 12cd4 + 8

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7 days ago

A small plane flies 760,320 yards in 2 hours. Use the formula d = rt, where d represents distance, r represents rate, and t repr

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Answer:

Refer to the explanation below.

Step-by-step explanation:

We start with a small aircraft that flies 760,320 yards within a duration of 2 hours.

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B)

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Thus, the aircraft speeds at 380,160 yards every hour.

C)

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To compute the speed in miles per hour, we apply dimensional analysis.

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$r=\frac{\text{380160 yards}}{\text{1 hour}}\cdot \frac{\text{1 mi}}{\text{1760 yards}}$

This eliminates yards:

$r=\frac{\text{380160}}{\text{1 hour}}\cdot \frac{\text{1 mi}}{\text{1760}}$

Now, multiply the values across:

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The final rate for the plane is 216 miles per hour.

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5 days ago

The sequence 6, 18, 54, 162, … shows the number of pushups Kendall did each week, starting

Svet_ta [4321]

a) The sequence is geometric.

b) The subsequent term is 486

c) The rule is: $a_n=6(3)^{n-1}$

The 20th term will be: a_{20}=6973568802

Step-by-step explanation:

The series 6, 18, 54, 162, ... depicts the number of push-ups Kendall performed each week, starting from her initial week of exercise.

Part a) Is this sequence arithmetic or geometric?

An arithmetic sequence has a constant difference between consecutive terms.

In the given series 6, 18, 54, 162,

18-6 = 12

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The differences are not constant, thus it isn’t arithmetic.

A geometric sequence maintains a constant ratio between consecutive terms.

In this series 6, 18, 54, 162,

18/6 = 3

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The ratios remain constant; therefore, the sequence is geometric.

The sequence in question is geometric.

Part b) How can you determine the next number in the series?

The next number can be calculated using the following formula:

$a_n=a(r)^{n-1}$

where a_n= nth term

a= first term

r= common ratio

The next number represents the 5th term of the sequence.

To find the 5th term:

$a_n=a(r)^{n-1}\\a_5=6(3)^{5-1}\\a_5=6(3)^4\\a_5=6*81\\a_5=486$

Thus, the next term in the sequence is 486

Part c) What is the rule for determining the 20th week? Calculate the 20th week.

The rule for determining the 20th week is:

$a_n=6(3)^{n-1}$

Here n=20

Calculating the 20th week

$a_n=6(3)^{n-1}\\a_{20}=6(3)^{20-1}\\a_(20)=6(3)^{19}\\a_{20}=6973568802$

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