Help on 3 5 and 7 please

. What is the value of x? rectangle with length 45 feet, width x feet, and diagonal 53 feet

allsm [11]

a^2 + b^2 = c^2

45^2 + X^2 = 53^2

2025 + x^2 = 2809

x^2 = 784

sqrt(784) = 28 feet

6 0

3 years ago

Most television showsUse 13 minutes of every hour for commercials leaving the remaining 47 minutes for the actual show. One popu

babunello [35]

Answer:

Step-by-step explanation:née

6 0

2 years ago

You are about to list your house as For Sale By Owner. Suppose you need to allow

lions [1.4K]

Answer:

(c) $95,400

Step-by-step explanation:

You want the listing price of your house such that you can clear $92,500 after paying a 3% commission to the buyer's realtor.

<h3>Setup</h3>

The buyer's agent will receive 3% of the sale price (P), so you receive that amount less. You want your share to be $92,500.

(1 -3%)P = 92,500

<h3>Solution</h3>

Dividing by the coefficient of P, we get ...

P = 92,500/0.97 ≈ 95,361

We are asked to round this value to the nearest $100. That makes the listing price ...

$95,400 . . . . listing price

__

<em>Additional comment</em>

You can estimate the listing price by adding 3% of 92500 to that value, and you can estimate the added amount as 3%×90,000 = 2700. That is, you know the listing price needs to be slightly higher than ...

92500 +2700 = 95,200

Only one of the answer choices is above that value and <em>rounded to the nearest $100</em>. (You can eliminate the first two choices, because they are not properly rounded.)

4 0

1 year 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

Why is -a² is always negative (a ≠ 0) and why is (-a)² is always positive?

hjlf

$-a^2=(-1)\cdot a\cdot a$

Regardless of the sign of $a$ , we have $a\cdot a=a^2\ge0$ (never negative). But multiplying by -1 makes it negative.

On the other hand,

$(-a)^2=((-1)\cdot a)^2=(-1)^2\cdot a^2=1\cdot a^2=a^2$

which can never be negative for real $a$ .

6 0

2 years ago