Which ratios are equal to cos(B)? Choose the TWO ratios that apply.

Solving Rational Functions Hello I'm posting again because I really need help on this any help is appreciated!!

Greeley [361]

Answer:

x = √17 and x = -√17

Step-by-step explanation:

We have the equation:

$\frac{3}{x + 4} - \frac{1}{x + 3} = \frac{x + 9}{(x^2 + 7x + 12)}$

To solve this we need to remove the denominators.

Then we can first multiply both sides by (x + 4) to get:

$\frac{3*(x + 4)}{x + 4} - \frac{(x + 4)}{x + 3} = \frac{(x + 9)*(x + 4)}{(x^2 + 7x + 12)}$

$3 - \frac{(x + 4)}{x + 3} = \frac{(x + 9)*(x + 4)}{(x^2 + 7x + 12)}$

Now we can multiply both sides by (x + 3)

$3*(x + 3) - \frac{(x + 4)*(x+3)}{x + 3} = \frac{(x + 9)*(x + 4)*(x+3)}{(x^2 + 7x + 12)}$

$3*(x + 3) - (x + 4) = \frac{(x + 9)*(x + 4)*(x+3)}{(x^2 + 7x + 12)}$

$(2*x + 5) = \frac{(x + 9)*(x + 4)*(x+3)}{(x^2 + 7x + 12)}$

Now we can multiply both sides by (x^2 + 7*x + 12)

$(2*x + 5)*(x^2 + 7x + 12) = \frac{(x + 9)*(x + 4)*(x+3)}{(x^2 + 7x + 12)}*(x^2 + 7x + 12)$

$(2*x + 5)*(x^2 + 7x + 12) = (x + 9)*(x + 4)*(x+3)$

Now we need to solve this:

we will get

$2*x^3 + 19*x^2 + 59*x + 60 = (x^2 + 13*x + 3)*(x + 3)$

$2*x^3 + 19*x^2 + 59*x + 60 = x^3 + 16*x^2 + 42*x + 9$

Then we get:

$2*x^3 + 19*x^2 + 59*x + 60 - ( x^3 + 16*x^2 + 42*x + 9) = 0$

$x^3 + 3x^2 + 17*x + 51 = 0$

So now we only need to solve this.

We can see that the constant is 51.

Then one root will be a factor of 51.

The factors of -51 are:

-3 and -17

Let's try -3

p( -3) = (-3)^3 + 3*(-3)^2 + +17*(-3) + 51 = 0

Then x = -3 is one solution of the equation.

But if we look at the original equation, x = -3 will lead to a zero in one denominator, then this solution can be ignored.

This means that we can take a factor (x + 3) out, so we can rewrite our equation as:

$x^3 + 3x^2 + 17*x + 51 = (x + 3)*(x^2 + 17) = 0$

The other two solutions are when the other term is equal to zero.

Then the other two solutions are given by:

x = ±√17

And neither of these have problems in the denominators, so we can conclude that the solutions are:

x = √17 and x = -√17

6 0

3 years ago

WILL MARK BRAINLIEST ONLY HAVE 10 MINUTES AND DOUBLE POINTS

allochka39001 [22]

Hey there!

They are both correct, and their expressions are equivalent.'

9(S + T) + 45 = 9S + 9T + 45

Have a terrificly amazing day!

8 0

3 years ago

If one 1.5 cups is 12 fluid ounces, how many fluid ounces do I have if I

Alchen [17]

Answer:

120

Step-by-step explanation:

15/1.5=10

10 x 12=120

7 0

2 years ago

Read 2 more answers

Which expression defines the given series for seven terms?<br><br> 15 + 19 + 23 + . . .

dolphi86 [110]

The expression defines the given series for seven terms, i don't understand the question but i do know the sum which you should know to

15 + 19 + 23 = 57

Sorry

5 0

3 years ago

Read 2 more answers

I can not figure these type of problems out. I have multiple, and if I can understand how to do the problem once then I can fini

sladkih [1.3K]

The question has to do with scientific notation

<h3>What is scientific notation?</h3>

Scientific notation is the expression of a number in the form a × 10ⁿ where 1 ≤ a ≤ 10 and n is an integer.

<h3>How to simplify the expression?</h3>

Now to simplify the expression (9 × 10⁻¹³) - (6.3 × 10⁻¹⁵) both number have to have the same exponent to the power of 10.

So, re-writing, we have

(9 × 10⁻¹³) - (6.3 × 10⁻¹⁵) = (9 × 10⁻¹³) - (6.3 × 10⁻¹³ × 10⁻²)

= (9 × 10⁻¹³) - (6.3 × 10⁻² × 10⁻¹³ )

= (9 × 10⁻¹³) - (0.063 × 10⁻¹³ )

= (9 - 0.063) × 10⁻¹³ )

= 8.937 × 10⁻¹³

So, simplifying the expression (9 × 10⁻¹³) - (6.3 × 10⁻¹⁵) = 8.937 × 10⁻¹³

Learn more about scientific notation here:

brainly.com/question/28007630

#SPJ1

3 0

1 year ago