Explanation

• Sum of two numbers: $-3 + (-5) = -8$
  

• Product: $(-3) times (-5) = +15$
  

Let’s now write an algebraic expression where the sum is $-8$and the product is $+15$.

This is a quadratic expression of the form:

$$x^2 + 8x + 15$$

Explanation

$$(44x+35y)+(34x-25y)$$

$$=(44x+34x)+(35y-25y)$$

$$=78x+10y$$

Explanation

Step 1: Multiply the coefficients

$$-5\times 10=-50$$

Step 2: Multiply the variables

• $x cdot x = x^2$
  

• $y cdot y = y^2$
  

• $z cdot 1 = z$
  

• $a$ appears once

• $b$ appears once

Step 3: Combine all parts

$$-50abx^2y^2z$$

Explanation

To solve the equation:

$$x^2 + 16 = 0$$

Step 1: Isolate x^2

$$x^2 = -16$$

Step 2: Take the square root of both sides

$$x = pm sqrt{-16}$$

Since $sqrt{-16}$

involves the square root of a negative number, we use imaginary numbers:

$$x = pm 4i$$x=±4i

Explanation

Combine terms: (2x/24) + (x/24) = 0 → (3x/24) = 0

Multiply both sides by 24: 3x = 0 → x = 0

Explanation

Given: a/b = 3/5 ... (1)

When 2 is added to both numbers, the ratio becomes 2/3, so we can write:

(a+2)/(b+2) = 2/3 ... (2)

Cross-multiplying (2), we get:

3(a+2) = 2(b+2)

Expanding and simplifying, we get:

3a + 6 = 2b + 4

Subtracting 6 from both sides gives:

3a = 2b - 2

Now, substituting (1) in the above equation, we get:

3(3/5)b = 2b - 2

Multiplying both sides by 5, we get:

9b = 10b - 10

Subtracting 10b from both sides gives:

-b = -10

Dividing both sides by -1, we get:

b = 10

So, the correct answer is: 10

Explanation

Given the equation x² - 3x - 4 = 0:

Step 1: Factor the quadratic equation

x² - 3x - 4 = (x - 4)(x + 1) = 0

Step 2: Solve for x

x - 4 = 0 or x + 1 = 0

x = 4 or x = -1

Explanation

Like terms: 2x² + 3x² = (2 + 3)x²

Result = 5x²

Explanation

Let's break it down:

A = x% of y = (x/100)y = xy/100

B = y% of x = (y/100)x = yx/100

Since xy = yx, A = B.

Explanation

The factors of -4 that add up to -3 are -4 and +1.

So, x² - 3x - 4 = (x - 4)(x + 1).