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[Quick Answer Needed] Which of the following shows the extraneous solution to the logarithmic equation?

Nitella [24]

Answer:

C

Step-by-step explanation:

Given the logarithmic equation

$\log_4x+\log_4(x-3)=\log_4(-7x+21)$

First, notice that

$x>0\\ \\x-3>0\Rightarrow x>3\\ \\-7x+21>0\Rightarrow 7x$

So, there is no possible solutions, all possible solutions will be extraneous.

Solve the equation:

$\log_4x+\log_4(x-3)=\log_4x(x-3),$

then

$\log_4x(x-3)=\log_4(-7x+21)\\ \\x(x-3)=-7x+21\\ \\x^2-3x+7x-21=0\\ \\x^2+4x-21=0\\ \\D=4^2-4\cdot 1\cdot (-21)=16+84=100\\ \\x_{1,2}=\dfrac{-4\pm 10}{2}=-7,\ 3$

Hence, $x=3$ and $x=-7$ are extraneous solutions

6 0

3 years ago

A triangle with a 135° angle

GuDViN [60]

Answer:

The 135 external angle means its corresponding internal angle is (180–135) 45 degrees. The other internal angle of 65 plus the 45 is 110 degrees. Since the sum of degrees in the angles in a triangle is 180, the other interior angle is (180–110), or 70 degrees.

Step-by-step explanation:

6 0

3 years ago

State the value of the discriminant of -6x^2 +2x + 3 = 0

Dmitry [639]

Answer:

76

Step-by-step explanation:

recall that for a quadratic equation in the form

ax² + bx + c = 0, the discriminant is given by

discriminant, D = b²- 4ac

we are given the following:

-6x² + 2x + 3 = 0,

comparing this with the general equation above, it is clear that,

a = -6, b = 2 and c = 3,

substituting these into our equation for discriminant:

D = b²- 4ac

= 2² - 4(-6)(3)

= 4 + 72

= 76

4 0

3 years ago

Distributive property to expand -1/6(5x-12)

castortr0y [4]

Answer:

-5/6x+2

Step-by-step explanation:

hope that helps

3 0

3 years ago

Veronica has been saving dimes and quarters she has 110 coins in all and the total value is 18.50 how many dimes and quarters do

Lady_Fox [76]

This problem can be solved by the chicken rabbits method or you can just do simple algebra.

I.) Chicken and rabbits method

First assume all 110 coins are dimes and none are quarters.

We will have a total value of 11 dollars

Now for each dime we switch out for a quarter, we adds 15 cents to the total value.

18.50-11=7.50 dollars

There are 750/15=50 group of 15 cents in the 7 dollars and 50 cents.

This also meant that we need to switch out 50 dimes for 50 quarters.

So we have 50 quarters.

That first method is very good and very quick once you get the hang of it, now I'm going to show you the algebraic way to solve this.

Let's say there are x dimes and y quarters.

Set up equation

x+y=110

10x+25y=1850

Now solve multiply first equation by 10

10x+10y=1100

subtract

15y=750

y=50

Now we set the numbers of quarters to y so the answer is 50 quarters.

I personally recommend using algebra whenever you can because the practice is very important and you will eventually get really fast at setting up and solving equations. The first method is faster in this case but the second is more generalize, hope it helps.

6 0

3 years ago