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4 years ago

8

30 POINTS!

2 answers:

diamong [38]4 years ago

5 0

For this case we observe that both functions have the same behavior.
The cut point of f (x) with the y axis is:
(0, 4)
The cut point of g (x) with the y axis is:
(0, 2)
Therefore the transformation applied to g (x) is:
g (x) = f (x) - 2
Answer:
g (x) = f (x) - 2
option 2

lbvjy [14]4 years ago

3 0

The answer if g(x) = f(x) + 2.

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Marianna [84]

Answer:

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Step-by-step explanation:

a²+b²=c²

c will always be the hypotenuse

4²+7²=65² the opposite of ² is square root so

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3 years ago

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4 years ago

Convert binary into octal number system<br>(1011010)<br>(1010111)

stiv31 [10]

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3 years ago

Intersection point of Y=logx and y=1/2log(x+1)

GalinKa [24]

Answer:

The intersection is $(\frac{1+\sqrt{5}}{2},\log(\frac{1+\sqrt{5}}{2})$ .

The Problem:

What is the intersection point of $y=\log(x)$ and $y=\frac{1}{2}\log(x+1)$ ?

Step-by-step explanation:

To find the intersection of $y=\log(x)$ and $y=\frac{1}{2}\log(x+1)$ , we will need to find when they have a common point; when their $x$ and $y$ are the same.

Let's start with setting the $y$ 's equal to find those $x$ 's for which the $y$ 's are the same.

$\log(x)=\frac{1}{2}\log(x+1)$

By power rule:

$\log(x)=\log((x+1)^\frac{1}{2})$

Since $\log(u)=\log(v)$ implies $u=v$ :

$x=(x+1)^\frac{1}{2}$

Squaring both sides to get rid of the fraction exponent:

$x^2=x+1$

This is a quadratic equation.

Subtract $(x+1)$ on both sides:

$x^2-(x+1)=0$

$x^2-x-1=0$

Comparing this to $ax^2+bx+c=0$ we see the following:

$a=1$

$b=-1$

$c=-1$

Let's plug them into the quadratic formula:

$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

$x=\frac{1 \pm \sqrt{(-1)^2-4(1)(-1)}}{2(1)}$

$x=\frac{1 \pm \sqrt{1+4}}{2}$

$x=\frac{1 \pm \sqrt{5}}{2}$

So we have the solutions to the quadratic equation are:

$x=\frac{1+\sqrt{5}}{2}$ or $x=\frac{1-\sqrt{5}}{2}$ .

The second solution definitely gives at least one of the logarithm equation problems.

Example: $\log(x)$ has problems when $x \le 0$ and so the second solution is a problem.

So the $x$ where the equations intersect is at $x=\frac{1+\sqrt{5}}{2}$ .

Let's find the $y$ -coordinate.

You may use either equation.

I choose $y=\log(x)$ .

$y=\log(\frac{1+\sqrt{5}}{2})$

The intersection is $(\frac{1+\sqrt{5}}{2},\log(\frac{1+\sqrt{5}}{2})$ .

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3 years ago

Determine whether the two triangles are similar. PLEASE HELP!!

zvonat [6]

I think that it is C: PQR~XY by AA because there are only two angles that you are given ;the boxes represent 90, so each box has 90 and 62.

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4 years ago