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3 years ago

What is true about the sum of two polynomials?

Mathematics

1 answer:

zhannawk [14.2K]3 years ago

4 0

Answer:

The sum is a binomial of degree 3.

Step-by-step explanation:

You are adding two binomials. Each binomial has two terms.

The terms 6s^2t and 4s^2t are like terms and combine to give the sum 10s^2t.

The terms -2st^2 and -3st^2 are like terms and combine to give the sum -5st^2.

The sum of the binomials is the binomial 10s^2t - 5st^2.

Since each original binomial is of degree 3, the sum is also of degree 3.

Answer: The sum is a binomial of degree 3.

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A triangle has one side length of 12 inches and another of 8 inches. Describe all possible lengths of the third side. Show and e

katrin [286]

Answer:

The third side must be smaller than 20 inches and greater than 4 inches

$4$

Step-by-step explanation:

Let a, b and c be the lengths of triangle's sides. Then

$a+b>c\\ \\a+c>b\\ \\b+c>a$

Use this rule in your case. So, if a=12 and b=8, then

$12+8>c\\ \\12+c>8\\ \\8+c>12$

Hence, you get

$c-4\\ \\c>4$

From these inequalities, you can state that

$4$

So, c must be smaller than 20 inches and greater than 4 inches.

5 0

3 years ago

Read 2 more answers

Determine whether the sequence converges or diverges. If it converges, give the limit.

vaieri [72.5K]

Answer:

The given series converges and $\lim_{n \to \infty} a_n =0$

Step-by-step explanation:

Given is 108, -18, 3,...

It is an alternate series. An alternate series is convergent if:

1. The series is decreasing.

2. If the last term (n-th term) of series converges to 0.

<u>Since each next term is less than its preceding term, so it is decreasing.</u>

First term, a = 108

Second term = -18

Common ratio, r = -18/108 = -1/6

General term, aₙ = a*rⁿ = 108*(-1/6)ⁿ

<u>When n increases to infinity, the exponent term will decreases to zero, and last term (n-th term) will converge to 0 as well.</u>

Hence, the given series converges.

Now limit will be: $\lim_{n \to \infty} a_n$

$\lim_{n \to \infty} 108*(-1/6)^n \\= 108*(-1/6)^\infty \\= 108*(1/\infty) \\= 108*0 \\= 0$

Hence, $\lim_{n \to \infty} a_n =0$

7 0

3 years ago

Solve for x: 2x + 3 + (-1) = x + 5

faust18 [17]

Answer:

x=3

Step-by-step explanation:

2x-x=5-3+1

x=3

I think that's it

5 0

3 years ago

David needs 36 gallons of punch for a party and has two different coolers to carry it in. the bigger cooler is 5 times as large

serg [7]

The little cooler can contain = 6 gallons.

The large cooler can contain is = 30 gallons.

<h3>What is volume surface area?</h3>

Any particular object's surface area is the space that the object's surface takes up. Volume, however, refers to the quantity of space a thing has. Different shapes and sizes exist in geometry, including spheres, cubes, cuboid shapes, cones, and cylinders, among others. Both the surface area and the volume are unique to each shape.

<h3>According to the given information:</h3>

The number of gallons that a small cooler can hold is: x gallons.

and a larger cooler can hold: 5x the number of gallons.

(Because it was noted:

In comparison to the smaller cooler, the larger cooler is five times bigger.

Additionally, a party requires 36 gallons of punch in total.

The result is:

x+5x=36

i.e. 6x=36

Divide both sides by 6, and the result is:

x=6

In light of this, the little cooler can contain 6 gallons.

and how many gallons the large cooler can contain is: 5 x 6 = 30 gallons.

To know more about volume surface area visit:

brainly.com/question/12446369

#SPJ4

6 0

1 year ago

What 9 intergers are between -3.5 and 5.5

laila [671]

3.5 3.4 3.3 3.2 3.1 3 -5.5 -1 -2

6 0

3 years ago