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-Dominant- [34]

3 years ago

7

a system of equations is shown below:x y = 32x −y = 6the x-coordinate of the solution to this system of equations is

1 answer:

Salsk061 [2.6K]3 years ago

5 0

X + y = 32 . . . . . . . . (1)
x - y = 6 . . . . . . . . (2)
(1) + (2): 2x = 38
x = 19

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Please Help!!!<br> I know the answer but need work.

hammer [34]

How do you know the answer if you don't have the work?

2/3(x+1/8) =1/6(x)
2/3×x+2/3×1/8=1/6(x)
2/3(x)+1/12=1/6(x)
2/3(x)-2/3(x)+1/12=1/6(x)-2/3(x)
1/12=1/6(x)-2/3(x)
1/12=1/6(x)-4/6(x)
1/12=-3/6(x)
1/12÷-3/6=-3/6(x)÷-3/6
-1/6=x

3 0

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

6 0

2 years ago

Write the ratio 21 inches to 9 free as a fraction in simplest form

saveliy_v [14]

Answer: 7/3

Step-by-step explanation:

21/9

7/3 is the fraction in simplest form

4 0

3 years ago

The figure below shows a line graph and two shaded triangles that are similar:

VLD [36.1K]

Every time the y-value decreases by 1, the x-value increases by 2, so the slope is -1/2 throughout the line.

4 0

3 years ago

Read 2 more answers

Write a quadratic function in vertex form whose graph has the vertex (−5, −1) and passes through the point (−2, 2)

denis23 [38]

This is your perfect answer

3 0

2 years ago