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3 years ago

10

What is the measure of XYZ?

1 answer:

boyakko [2]3 years ago

5 0

Answer:

a. An inscribed angle is 1/2 the intercepted arc. The intercepted arc is 68°. The measure of angle xyz is therefore 34°.

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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

The area of a rectangular wall of a barn is 85 square feet. Its length is 12 feet longer than the width. Find the length and wid

MaRussiya [10]

Answer:

Length = 17 feet, Width = 5 feet

Step-by-step explanation:

Given:

The area of a rectangular wall of a barn is 85 square feet.

Its length is 12 feet longer than the width.

Question asked:

Find the length and width of the wall of the barn.

Solution:

Let width of a rectangular wall of a barn = $x$

<u>As length is 12 feet longer than the width.</u>

Length of a rectangular wall of a barn = $12+x$

As we know:

$Area\ of\ rectangle=length\times breadth$

$85=(12+x)x\\\\85=12x+x^{2} \\$

Subtracting both sides by 85

$x^{2} +12x-85=0\\x^{2} +17x-5x-85=0\\Taking\ common\\x+(x+17)-5x(x+17)=0\\(x+17)(x-5)=0\\x+17=0, x-5=0\\x=-17,x=5$

As width can never be in negative, hence width of a rectangular wall of a barn = $x$ = 5 feet

Length of a rectangular wall of a barn = $12+x=12+5=17\ feet$

Therefore, length and width of the wall of the barn is 17 feet and 5 feet respectively.

4 0

3 years ago

What is the best estimate for this sum 1/8+1/6=The sum will be close to?

tamaranim1 [39]

The expression given is

$\frac{1}{8}+\frac{1}{6}$

The sum of the expression will be,

$\frac{1}{8}+\frac{1}{6}=\frac{6+8}{48}=\frac{14}{48}=\frac{7}{24}$

The sum will be

$\frac{7}{24}$

8 0

1 year ago

Juanito has a bag of marbles. In his bag he has 5 yellow marbles, 5 blue marbles, 3 red marbles, and 2 white marbles. What is th

lianna [129]

2/15

Step-by-step explanation:

yellow Marbles =5

blue marble =5

red marbles =3

white marbles =2

total marbles =15

p of white marbles= white marble/ total marble

so 2/15

in simplest from 7.5

3 0

2 years ago

Multiply 6.75x10^6 and 1.2x10^6 Keep the numbers written in scientific notation when you are solving the problem Show all of you

harkovskaia [24]

Answer:

8.1×10^12

Step-by-step explanation:

6.75×1.2=8.1 and power should be added 6+6=12 and answer is 8.1×10^12

4 0

2 years ago