Can someone help me with my math homework

Mathematics

1 answer:

Roman55 [17]3 years ago

7 0

Answer:

1.y= -2x+3 slope -2

2. y= -4/5x-6 slope -4/5

3. y= 1/3x=4 slope 1/3

4. y= x+8 slope 1

5. y= 4x slope 4

6. y= 3/2x+7 slope 3/2

7. y= 3/2x+5 slope 3/2

8. y= -1/5x-3 slope -1/5

Step-by-step explanation:

move variable to the right

change the signs

divide both sides

reorder the terms

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Question 15

We can search x such that:

$x^2-4x+4=2x-5\\\\\text{*** subtract 2x-5 from both sides ***}\\ \\x^2-4x-2x+4+5=0\\ \\\text{*** simplify ***}\\ \\x^2-6x+9=0 \\ \\\text{*** we can notice a perfect square ***}\\ \\x^2 -2\cdot x \cdot 3 + 3^2=(x-3)^2=0\\\\\text{*** taking the root ***}\\\\x-3=0\\\\\large \boxed{\sf \ \ x=3 \ \ }$

There is 1 solution.

Question 16

Again, we search x such that:

$x^2-8x+15=2x-6\\\\\text{*** subtract 2x-6 from both sides ***}\\\\x^2-8x-2x+15+6=0\\\\\text{*** simplify ***}\\\\x^2-10x+21=0 \\ \\\text{*** we are looking for two roots where the sum is 10 and the product is 21 = 7 x 3 ***} \\\\x^2-7x-3x+21=x(x-7)-3(x-7)=(x-3)(x-7)=0\\\\\large \boxed{\sf \ \ x= 3 \ or \ x =7 \ \ }$ There are two solutions.