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3 years ago

7

Graph the solution set of the system of inequalities or indicate that the system has no solution.

1 answer:

alina1380 [7]3 years ago

7 0

The graph is the intersection of the interior of a circle with a half-plane.

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<img src="https://tex.z-dn.net/?f=y%20%3D%20%20%5Cfrac%7B2%7D%7Bx%20-%201%7D%20%20%2B%201" id="TexFormula1" title="y = \frac{2}

Dmitriy789 [7]

Answer:

x = $\frac{y+1}{y-1}$

Step-by-step explanation:

4 0

3 years ago

Let f(x)=x2+6x−16 . Enter the x-intercepts of the quadratic function in the boxes. and

gizmo_the_mogwai [7]

Answer:

x = - 8, x = 2

Step-by-step explanation:

Given

f(x) = x² + 6x - 16

To find the x- intercepts equate f(x) to zero, that is

x² + 6x - 16 = 0 ← in standard form

(x + 8)(x - 2) = 0 ← in factored form

Equate each factor to zero and solve for x

x + 8 = 0 ⇒ x = - 8

x - 2 = 0 ⇒ x = 2

8 0

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

6 0

2 years ago

What is the image point of (1, 4) after a translation left 5 units and down 3 units?

beks73 [17]

Answer:

(-4,1)

Step-by-step explanation:

for x you do:

1 - 5 = -4

for y you do:

4 - 3 = 1

so it is (-4,1)

8 0

3 years ago

Help me pls it is geometry

Gekata [30.6K]

Answer:

m < b = 76

Step-by-step explanation:

Because b is directly across from the 76 degree angle, that makes them vertical angles, which means they are the same degree I believe.

5 0

2 years ago

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