Simplify each polynomial. 6g + 8k - 9g + 2k | Questions LLC (2024)

Combine like terms

-3g + 10k

In the given polynomial, the term with the highest exponent of w is -5w^3. This means the degree of the polynomial is 3.

So the answer is 3.

Question: Find the degree of -5w^3 - 4w^2 + 7w + 16.

Solution:

The degree of a polynomial is the highest exponent of the variable in the polynomial expression.

In the given polynomial, the term with the highest exponent of w is -5w^3. This means the degree of the polynomial is 3.

So the answer is 3.

1. Combine like terms:

6g + 8k - 9g + 2k

Simplify by combining the like terms.

= (6g - 9g) + (8k + 2k)

= -3g + 10k

Answer: -3g + 10k

2. Perform the indicated operations:

(3x^2 - 4x + 5) + (-5x^2 + 7x - 3)

Simplify the expression by adding the like terms with the same powers of x.

= 3x^2 - 4x + 5 - 5x^2 + 7x - 3

= -2x^2 + 3x + 2

Answer: -2x^2 + 3x + 2

3. Find the product:

(5t - 3)(t + 2)

We can use the FOIL method to find the product.

FOIL:

5t * t = 5t^2

5t * 2 = 10t

-3 * t = -3t

-3 * 2 = -6

Simplify by adding the like terms.

= 5t^2 + (10t - 3t) - 6

= 5t^2 + 7t - 6

Answer: 5t^2 + 7t - 6

4. Subtract the polynomials:

(6x^2 + 8x - 5) - (4x^2 - 6x + 3)

Subtract the second polynomial from the first by changing the signs of the second polynomial and adding the like terms.

= 6x^2 + 8x - 5 - 4x^2 + 6x - 3

= 2x^2 + 14x - 8

Answer: 2x^2 + 14x - 8

5. Find the degree of -5w^3 - 4w^2 + 7w + 16:

The degree of a polynomial is the highest exponent of the variable in the polynomial expression.

In the given polynomial, the term with the highest exponent of w is -5w^3. This means the degree of the polynomial is 3.

Answer: 3.

1. Combine like terms:

The polynomial is: 6g + 8k - 9g + 2k

To combine like terms, we need to group the terms that have the same variable. So, we group the terms with the variable `g` and add them, and we group the terms with the variable `k` and add them.

6g - 9g = -3g

8k + 2k = 10k

Therefore, -3g + 10k is the simplified form of 6g + 8k - 9g + 2k.

2. Perform the indicated operations:

The expression is: (3x^2 - 4x + 5) + (-5x^2 + 7x - 3)

To simplify the expression, we need to add the like terms. The like terms are those that have the same power of x.

Let's add the terms as shown below:

(3x^2 - 5x^2) + (-4x + 7x) + (5 - 3)

= -2x^2 + 3x + 2

Therefore, -2x^2 + 3x + 2 is the simplified form of (3x^2 - 4x + 5) + (-5x^2 + 7x - 3).

3. Find the product:

The expression is: (5t - 3)(t + 2)

To find the product of two binomials, we can use the FOIL method. FOIL stands for First, Outer, Inner, Last. This means we need to multiply the first terms of each binomial, then the outer terms, then the inner terms, and finally the last terms.

The steps are shown below:

(5t - 3)(t + 2)

= 5t * t + 5t * 2 - 3 * t - 3 * 2

= 5t^2 + 10t - 3t - 6

= 5t^2 + 7t - 6

Therefore, 5t^2 + 7t - 6 is the product of (5t - 3)(t + 2).

4. Subtract the polynomials:

The expression is: (6x^2 + 8x - 5) - (4x^2 - 6x + 3)

To subtract two polynomials, we need to distribute the negative sign to the second polynomial, and then add the like terms. The steps are shown below:

(6x^2 + 8x - 5) - (4x^2 - 6x + 3)

= 6x^2 + 8x - 5 - 4x^2 + 6x - 3 (distributing the negative sign)

= 2x^2 + 14x - 8 (adding the like terms)

Therefore, 2x^2 + 14x - 8 is the result of subtracting (4x^2 - 6x + 3) from (6x^2 + 8x - 5).

5. Find the degree:

The expression is: -5w^3 - 4w^2 + 7w + 16.

The degree of a polynomial is the highest exponent of the variable in the polynomial expression. In the given expression, the term with the highest exponent of w is -5w^3. This means the degree of the polynomial is 3.

Therefore, the degree of the polynomial -5w^3 - 4w^2 + 7w + 16 is 3.

I hope these explanations are clearer and help you understand the solutions better.

1. B
2. D
3. B
4. A
5. D

I hope this helps!

1. B
2. D
3. B
4. A
5. D

These answers correspond to the questions:

1. Simplify: 6g + 8k - 9g + 2k
2. Simplify: (3x^2 - 4x + 5) + (-5x^2 + 7x - 3)
3. Find the product: (5t - 3)(t + 2)
4. Subtract: (6x^2 + 8x - 5) - (4x^2 - 6x + 3)
5. Find the degree of: -5w^3 - 4w^2 + 7w + 16

I apologize for any confusion that may have caused.

To find how many milliliters are poured into each container, we need to convert 3 liters to milliliters and then divide by 5.

1 liter = 1000 milliliters

So, 3 liters = 3 * 1000 = 3000 milliliters.

Now, we can divide 3000 milliliters by 5:

3000 / 5 = 600

Therefore, 600 milliliters are poured into each container.

To find the total amount of fruit in ounces that Derek bought, we need to add the number of ounces of blueberries, strawberries and raspberries.

9 ounces (blueberries) + 16 ounces (strawberries) + 32 ounces (raspberries)

= 57 ounces

Therefore, Derek bought a total of 57 ounces of fruit.

(
6
×
10
)
+
(
3
×
1
100
)
+
(
4
×
1
1000
)
A.
6.34

B.
60.34

C.
60.034

D.
6.034

(6 x 10) + (3 x 1/100) + (4 x 1/1000)

= 60 + 0.03 + 0.004

= 60.034

Therefore, the correct answer is C. 60.034.