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3 years ago

12

Simplify the expression: ( X + 5)( X-7)

2 answers:

Hitman42 [59]3 years ago

7 0

(x + 5)(x - 7)
x(x - 7) + 5(x - 7)
x(x) - x(7) + 5(x) - 5(7)
x² - 7x + 5x - 35
x² - 2x - 35

Igoryamba3 years ago

3 0

Answer is in the photo UwU

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Julie's city had a parade last weekend. Of the residents in Julie's city, 90,000 came to the parade and 10,000 did not. What per

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90% of people did come

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The temperature in the late afternoon was -7.5° it dropped 5° by early evening and then dropped another 85° by midnight what was

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Step-by-step explanation:

i think you missed a decimal place for 8.5°

when temperatures drop it means minus

so

-7.5-5-8.5= -21°

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Write an exponential expression showing organism B’d increase in population over the same 8 days

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Step-by-step explanation:

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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

A carnival is being set up in your hometown. From experience, the carnival organizer knows that the amount of money he will brin

pentagon [3]

Answer:

$6,200

Step-by-step explanation:

The question is to find the expected value.

We know the expected value of a scenario is the sum of the products of each probability of event and its profit or loss.

There are 3 probabilities in the scenario:

Rainy: 20% = 20/100 = 0.2

Sunny: 50% = 50/100 = 0.5

Cloudy: Rest, which is 100 - (50+20) = 100 - 70 = 30% = 30/100 = 0.3

Now, the gain and loss is:

Rainy: Lose 5000 means -5000

Cloudy: Gain 4000 means +4000

Sunny: Gain 12,000 means +12,000

Now, the expected value is:

Expected Value = (0.2)(-5000) + (0.5)(12000) + (0.3)(4000) = $6,200

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3 years ago