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3 years ago

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Pls helppppp ill give u brainliest

1 answer:

mafiozo [28]3 years ago

5 0

Answer:

1.) yuma

2.) Spanish

3.) 8th

4.) two years

5.) 8

6.) united

7.)aztec

8.) ?

9.) ?

10.) 1993

Step-by-step explanation:

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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

3 years ago

What is the smallest angle of rotational symmetry for a square? 45ş 90ş 180ş 360ş

vitfil [10]

Answer:

Step-by-step explanation:

i think 45 because a square could be broken up into 4s

6 0

3 years ago

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What is the slope-intercept form of the linear equation 2x + 3y = 6? Drag and drop the appropriate number, symbol, or variable t

aev [14]

Answer:

$y=-\frac{2}{3}x+2$

Step-by-step explanation:

y = -2/3 x + 2

5 0

3 years ago

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What is the area of a triangle whose base is 14 m and whose height is 22 m?

Ivanshal [37]

Base times height divided by 2 is the area. So 14 times 22 is 308 and divided by 2 is 154 so that is your answer. I hope this helps. Could I possibly get brainliest?

4 0

3 years ago

murzikaleks [220]

Answer:

7/9

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7 0

3 years ago

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