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3 years ago

Log base 6 (2x+1) = log base 6 (x-3) + log base 6 (x+5)

Mathematics

1 answer:

spin [16.1K]3 years ago

8 0

We assume you want to find values of x that make the expression true.

Use the rules of logarithms to rewrite as a single log. Then take the antilog and solve the resulting quadratic.

$\log_{6}(2x+1)=\log_{6}(x-3)+\log_{6}(x+5)=\log_{6}((x-3)(x+5))\\\\2x+1=(x-3)(x+5)=x^{2}+2x-15\\\\0=x^{2}-16=(x-4)(x+4)$

The term $\log_{6}(x-3)$ is only defined for x > 3, so the only solution to this equation is x = 4.

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Find the zeros from the factored form Quadratic Equation y=-x(x-3) ( ,0) & ( ,0)

tangare [24]

Answer:

(0, 0) and (3, 0)

Step-by-step explanation:

Zeros of any equation means, value of variable x at y = 0.

Given quadratic equation is,

y = -x(x - 3)

For y = 0,

-x(x - 3) = 0

x = 0

And (x - 3) = 0

x = 3

Therefore, x-intercepts of the given quadratic equation will be,

x = 0, 3

Points showing the x-intercepts will be,

(0, 0) and (3, 0)

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3 years ago

Which set of ordered pairs represents a function? (1 point) {(0, 1), (1, 3), (1, 5), (2, 8)} {(0, 0), (1, 2), (2, 6), (2, 8)} {(

Aleonysh [2.5K]

Answer:

{(0, 2), (1, 4), (2, 6), (3, 6)}

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

Find+the+positive+value+for+α+if+the+radius+of+the+circle+3x^2+3y-6αx+12y-3α=0+is+4

Alik [6]

Answer:

$\alpha=3$

Step-by-step explanation:

<u>Equation of a Circle</u>

A circle of radius r and centered on the point (h,k) can be expressed by the equation

$(x-h)^2+(y-k)^2=r^2$

We are given the equation of a circle as

$3x^2+3y^2-6\alpha x+12y-3\alpha=0$

Note we have corrected it by adding the square to the y. Simplify by 3

$x^2+y^2-2\alpha x+4y-\alpha=0$

Complete squares and rearrange:

$x^2-2\alpha x+y^2+4y=\alpha$

$x^2-2\alpha x+\alpha^2+y^2+4y+4=\alpha+\alpha^2+4$

$(x-\alpha)^2+(y+2)^2=r^2$

We can see that, if r=4, then

$\alpha+\alpha^2+4=16$

Or, equivalently

$\alpha^2+\alpha-12=0$

There are two solutions for $\alpha$ :

$\alpha=-4,\ \alpha=3$

Keeping the positive solution, as required:

$\boxed{\alpha=3}$

8 0

3 years ago

Can I get help with this math question plz thx

lidiya [134]

Answer:

1/5.

Step-by-step explanation:

There are 5 sections. 2 green 1 yellow, and one red. There is only one yellow and red, so to land on yellow red the answer would be 1/5, if you wanted to land on a green, therefore the answer would be 2/5. :>

3 0

3 years ago

Read 2 more answers

Which rule represent the reduction of a figure?

vazorg [7]

Answer:

Correct option: second one

Step-by-step explanation:

Let's check each option to find the correct one.

First option: x and y increase by 2.3 times, so the figure expands. So this is not the correct option.

Second option: x and y decrease 0.52 times, so the figure is reduced. So this is the correct option.

Third option: x and y are translated by 1/3 of their position, so the figure is not reduced.

Fourth option: x and y increase by 7/2 times, so the figure expands. So this is not the correct option.

Correct option: second one

5 0

3 years ago