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igor_vitrenko [27]

3 years ago

6

Question 7 of 12. Step 1 of 1

1 answer:

Ostrovityanka [42]3 years ago

5 0

Answer:

97

Step-by-step explanation:

Sorry for messy working out

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Solve:<br><br> a.x3+x2-8x - 12x+2<br> b. x3-4x2-3x + 18x-3<br> c. x2 + 4x + 4<br> d. x2 - 6x + 9

NeTakaya

<h2>Steps:</h2>

So firstly, this function is asking us to divide f(x) by g(x) so let's set that up as such:

$(\frac{f}{g})(x)=\frac{x^2-x-6}{1}\div \frac{x-3}{x+2}$

Next, remember that <u>dividing by a number is the same as multiplying by its reciprocal.</u> To find the reciprocal of a number, flip the numerator and denominator around. With this info, flip the second fraction to it's reciprocal and change the sign to multiplication:

$(\frac{f}{g})(x)=\frac{x^2-x-6}{1}\times \frac{x+2}{x-3}$

Next, we are going to factor x² - x - 6. Firstly, what two terms have a product of -6x² and a sum of -x? That would be -3x and 2x. Replace -x with 2x - 3x:

$(\frac{f}{g})(x)=\frac{x^2+2x-3x-6}{1}\times \frac{x+2}{x-3}$

Next, factor x² + 2x and -3x - 6 separately. Make sure that they have the same quantity on the inside of the parentheses:

$(\frac{f}{g})(x)=\frac{x(x+2)-3(x+2)}{1}\times \frac{x+2}{x-3}$

Now you can rewrite it as:

$(\frac{f}{g})(x)=\frac{(x-3)(x+2)}{1}\times \frac{x+2}{x-3}$

Next, multiply:

$(\frac{f}{g})(x)=\frac{(x-3)(x+2)^2}{x-3}$

Next, divide:

$(\frac{f}{g})(x)=(x+2)^2$

And lastly, simplify:

A good tip: $(x+y)^2=x^2+2xy+y^2$

$(\frac{f}{g})(x)=x^2+4x+4$

<h2>Answer:</h2>

<u>The correct option is C. x² + 4x + 4.</u>

7 0

3 years ago

Twice the difference of a number and 16 is the same as three times a number less than 18

Maksim231197 [3]

Answer:

Step-by-step explanation:

Let x be the "number."

"twice the difference of a number and 16" can be written as:

2(x-16)

"is the same as three times a number less than 18" can be written as:

= 3(x<18)

I wonder if this was meant to say "is the same as three times a number less 18," instead of "less than 18." If so, we would have:

=3(x-18)

1. Using the sentence as written: 2(x-16) = 3(x<18)

2. Using the sentence as amended: 2(x-16) = =3(x-18)

Going with this interpretation:

2(x-16) = 3(x-18)

2x - 32 = 3x - 54

x = 22

4 0

2 years ago

What is the value of 3x^2 + 5x + 25 when x = 3

Leno4ka [110]

Answer: 121

Step-by-step explanation:

6 0

2 years ago

Read 2 more answers

Help please asap with this

Allushta [10]

Use photo math app it will help you

The second one 1.7 = 17/10
-0.048 = -6/125
98% = 98/100= 49/50

5 0

2 years ago

The diagram shows several planes, lines, and points.

zhannawk [14.2K]

I think the answer is C...

7 0

3 years ago

Read 2 more answers