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3 years ago

10

As i turned out, avery spent 5 hours per day driving and drove a total of 5565 miles. what was his average speed for the hours h

e drove?

1 answer:

soldi70 [24.7K]3 years ago

6 0

He drove 1113 per hour.

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Show work please<br> \sqrt(x+12)-\sqrt(2x+1)=1

Nesterboy [21]

Answer:

$x=4$

Step-by-step explanation:

Given $\displaystyle\\\sqrt{x+12}-\sqrt{2x+1}=1$ , start by squaring both sides to work towards isolating $x$ :

$\displaystyle\\\left(\sqrt{x+12}-\sqrt{2x+1}\right)^2=\left(1\right)^2$

Recall $(a-b)^2=a^2-2ab+b^2$ and $\sqrt{a}\cdot \sqrt{b}=\sqrt{a\cdot b}$ :

$\displaystyle\\\left(\sqrt{x+12}-\sqrt{2x+1}\right)^2=\left(1\right)^2\\\implies x+12-2\sqrt{(x+12)(2x+1)}+2x+1=1$

Isolate the radical:

$\displaystyle\\x+12-2\sqrt{(x+12)(2x+1)}+2x+1=1\\\implies -2\sqrt{(x+12)(2x+1)}=-3x-12\\\implies \sqrt{(x+12)(2x+1)}=\frac{-3x-12}{-2}$

Square both sides:

$\displaystyle\\(x+12)(2x+1)=\left(\frac{-3x-12}{-2}\right)^2$

Expand using FOIL and $(a+b)^2=a^2+2ab+b^2$ :

$\displaystyle\\2x^2+25x+12=\frac{9}{4}x^2+18x+36$

Move everything to one side to get a quadratic:

$\displaystyle-\frac{1}{4}x^2+7x-24=0$

Solving using the quadratic formula:

A quadratic in $ax^2+bx+c$ has real solutions $\displaystyle x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$ . In $\displaystyle-\frac{1}{4}x^2+7x-24$ , assign values:

$\displaystyle \\a=-\frac{1}{4}\\b=7\\c=-24$

Solving yields:

$\displaystyle\\x=\frac{-7\pm \sqrt{7^2-4\left(-\frac{1}{4}\right)\left(-24\right)}}{2\left(-\frac{1}{4}\right)}\\\\x=\frac{-7\pm \sqrt{25}}{-\frac{1}{2}}\\\\\begin{cases}x=\frac{-7+5}{-0.5}=\frac{-2}{-0.5}=\boxed{4}\\x=\frac{-7-5}{-0.5}=\frac{-12}{-0.5}=24 \:(\text{Extraneous})\end{cases}$

Only $x=4$ works when plugged in the original equation. Therefore, $x=24$ is extraneous and the only solution is $\boxed{x=4}$

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2 years ago

A car dealership paid $12,800 for a car. They mark up the price by 20%

ch4aika [34]

Answer:

$15,360

Step-by-step explanation:

To find the retail price, multiply 12,800 by 1.2

12,800(1.2)

= 15,360

So, the retail price is $15,360

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3 years ago

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Is 4/2 + 5/2 a rational or irrational number

sesenic [268]

As both 4/2 and 5/2 are rational Numbers and Sum of rationals is a Rational Number.
Therefore, 9/2 is a Rational Number.

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3 years ago

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How many cups are in 25 gallons

dmitriy555 [2]

There are 400 cups in 25 Gallons !!!

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3 years ago

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Rewrite the expression as a multiple of a sum of two numbers with no common factor 15+24 _____

nata0808 [166]

<span>To rewrite the expression as a multiple of a sum of two numbers with no common factor, we're supposed to find the greatest common factor between the terms and factor it out. </span>We can see that both 15 and 24 are divisible by 3. So let's factor the 3 out. Since the 3 goes into 15 five times and into 24 eight times, the expression can be rewritten like this.

15 + 24 = 3(5 + 8)

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3 years ago