A rectangle measures 13 cm by 5 cm what is its area

Write the expression in complete factored form 3p^2(q+3)-4(q+3)

Tresset [83]

If you factored this the outcome would be,

(q+3)(3p^2-4)

6 0

3 years ago

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

Lola used 2 1/2 ink cartridges while her friends used 1 3/4 ink cartridges. How many more ink cartridges did Lola use than her f

iVinArrow [24]

Answer:

Lola used 3/4 more ink cartridges than her friends

Step-by-step explanation:

6 0

3 years ago

i don't know what to do ok so I like a guy an his freind like me an I blew up in his friends face an now they don't talk respond

almond37 [142]

Answer:

well if you liked them back then you should tell them that you are really sorry. and start hanging out with them again. (it should work)

i really hope this helps you with your problem and all!!! HAVE A NICE DAY!!!

8 0

3 years ago

Read 2 more answers

At Silver Gym, membership is $35 per month, and personal training sessions are $30 each. At Fit Factor,

Vanyuwa [196]

Answer:

5 sessions each

Step-by-step explanation:

Let the personal training sessions be x.

Then at Silver Gym Sarah would spend:

35 + 30x

And at Fit Factor she would spend:

85 + 20x

Since total costs are same, the amounts will be equal:

35+30x = 85 + 20x
30x - 20x = 85 - 35
10 x = 50
x= 50/10
x= 5

So Sarah would buy 5 training sessions for each of the gyms.

And she would spend $185 at each.

3 0

3 years ago