1. We we can split 4p into 9p - 5p, and now we have 3p² + 9p - 5p - 15 = 0. We can take out 3p from the first 2 terms and -5 from the last 2 terms. This gets us 3p (p + 3) -5 (p + 3) = 0. These two terms have (p + 3) as a common facor, so we can take that out as well, which give us (p + 3)(3p - 5) = ). Using Zero Product Property, p + 3 = 0 and 3p - 5 = 0, and when we solve each equation, we get p = -3, p= 5/3.

2. We will use the same process.

6x² + 14x - 3x - 7 = 0

2x (3x+7) - 1 (3x+7) = 0

(3x + 7)(2x - 1) = 0

3x + 7 = 0, 2x - 1 = 0

x = -7/3, x=1/2

Hope this helps!

4 0

3 years ago

A number is doubled, then decreased by 13.7. The result is greater than 125.28. What is the smallest integer that satisfies this

Elina [12.6K]

Answer:

x > 69.49

Step-by-step explanation:

Step 1: Write out equation

2x - 13.7 > 125.28

Step 2: Add 13.7 to both sides

2x > 138.98

Step 3: Isolate <em>x </em>by dividing both sides by 2

x > 69.49

So <em>x</em> has to be greater than 70 in order to fit into the question context.

8 0

4 years ago

If f(x) = -3x - 5 and g(x) = 4x - 2, find (f+ g)(x).

Stella [2.4K]

Answer:

$\boxed{\sf x - 7}$

Given:

f(x) = - 3x - 5

g(x) = 4x - 2

To Find:

(f + g)(x)

Step-by-step explanation:

$\sf (f + g)(x) = f(x) + g(x) \\ \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = - 3x - 5 + 4x - 2 \\ \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 4x - 3x - 5 - 2 \\ \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = x - 5 - 2 \\ \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = x - 7$

7 0

3 years ago