Explanation

To find the sum:

(4x + 7y + 10z) + (−3x + 5y − 7z)

= (4x - 3x) + (7y + 5y) + (10z - 7z)

= x + 12y + 3

Explanation

2a³ - a³ = (2-1)a³ = 1a³ = a³

This is because when you subtract a³ from 2a³, you are essentially subtracting 1a³ from 2a³, leaving you with 1a³, which simplifies to a³.

Explanation

The formula for the difference of squares is 𝑎² − 𝑏² = (𝑎 − 𝑏)(𝑎 + 𝑏).

Explanation

Step 1: Recall the definition of a^0

Any non-zero number raised to the power of 0 is 1.

Step 2: Evaluate the options

𝑎/𝑎 = 1 (since any number divided by itself is 1, assuming 𝑎 ≠ 0)

𝑎^1−1 = 𝑎^0 = 1

Step 3: Determine the best answer

All the given options (𝑎/𝑎, 1, 𝑎^1−1) represent the value of 𝑎^0 correctly, assuming 𝑎 ≠ 0.

Explanation

Step 1: Substitute the values of a and b into the inequality

2 - a + 2 < b - 1

2 - 5 + 2 < 7 - 1

Step 2: Simplify both sides of the inequality

-1 < 6

Step 3: Determine the truth value of the inequality

Since -1 is less than 6, the inequality is true.

Explanation

First polynomial: 8x² + 10x - 25

Second polynomial: 5x² - 9x - 10

(8x² + 10x - 25) - (5x² - 9x - 10)

= 8x² + 10x - 25 - 5x² + 9x + 10

= 3x² + 19x - 15

Explanation

Given y = 3:

Step 1: Calculate y³.

y³ = 3³ = 27

Step 2: Calculate y³ - y.

y³ - y = 27 - 3 = 24

Step 3: Calculate y³(y³ - y).

y³(y³ - y) = 27 × 24

= 648

Explanation

To have infinite solutions, the two equations must be proportional, meaning:

(3x + 2y = 7)  

(6x + my = 14)

Compare coefficients:

- 6x / 3x = 2  

- 14 / 7 = 2  

→ So, m/2 must also be 2 → m = 4

Explanation

Given the equation 20 = 3x + 8:

Step 1: Subtract 8 from both sides.

20 - 8 = 3x

12 = 3x

Step 2: Divide both sides by 3.

x = 12 / 3

x = 4

Explanation

Given x = -1 and y = -3:

Let's evaluate the expression 5y² - 2(x² - 4xy) - 5y:

1. Calculate 5y² = 5(-3)² = 5(9) = 45

2. Calculate x² = (-1)² = 1

3. Calculate 4xy = 4(-1)(-3) = 12

4. Calculate x² - 4xy = 1 - 12 = -11

5. Calculate -2(x² - 4xy) = -2(-11) = 22

6. Calculate -5y = -5(-3) = 15

Now, combine the results:

5y² - 2(x² - 4xy) - 5y = 45 + 22 + 15

= 82