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3 years ago

12

Select the correct difference. -3z 5 - (-7z 5) -10z5 -4z5 4z5 4z

2 answers:

bezimeni [28]3 years ago

8 0

-10z5 is the answer.

Alinara [238K]3 years ago

3 0

<span>-10z5 is the answer. </span>

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

6 0

2 years ago

Which of the following systems of inequalities has no solution?

RSB [31]

Answer:

The third one

Step-by-step explanation:

y=>x+1

y=<x-1

removing y

x-1 => x+1

removing x

we have no solution

6 0

2 years ago

Read 2 more answers

What is this pls help me 1/3 times 3/7

alex41 [277]

Answer:

2/21

Step-by-step explanation:

2/21 is the answer...........that is the fraction......

x+1/3=3/7

x=3/7-1/3

LCM=21

x=9/21-7/21

x=2/21

7 0

2 years ago

Melissa Silva borrowed $6,300 from the bank. If she has already repaid

melamori03 [73]

The remaining balance would be $3,600.

$6,300/7 = 900 x 3 = $2,700
$6,300 - $2,700 = $3,600

8 0

2 years ago

1. Write the equation of the line best fit

navik [9.2K]

Hmmmm interesting I really don’t know but

7 0

2 years ago