Witch answer choice represents a person running 90 calories by climbing 18 flights of stairs

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 $\boxed{x=4}$

4 0

2 years ago

A baby weighed 7.25 at birth. at the end of 8 month,the baby weighed 2 1/2 times its birth weight. how many pounds did the baby

Artyom0805 [142]

2 1/2 is in mixed fraction. So let's first make it into improper fraction.

(2*2 + 1) / 2 = 5/2

5/2 of 7.25 = (5*7.25) / 2 = 18.125

in short, 18.125 is the answer

4 0

3 years ago

Noriko multiplies 13 × 45.<br> Which of the following is NOT a partial product

LiRa [457]

Answer:

585

Step-by-step explanation:

7 0

2 years ago

Best explained and correct answer gets brainliest.

Zolol [24]

Your answer would be A because $4800 is your starting number and it increases 2% every year. How much is it in 20 years?

You use the formula ab^x
a is your starting number
b is the percentage
x is always the length of time

Since you are increasing and trying to get its worth larger than what it was before you use a number larger than one hundred percent in this case the number would be 1.02.

Y=4800(1.02)^20
Y=$7132.55

3 0

3 years ago

What’s the expression of this in simplest form

Ad libitum [116K]

Answer:

3/17

Step-by-step explanation:

3/4 divided by 4 1/4 is = to 3/4 divided by 17/4= 3/4 times 4/17 = 3/17

4 0

2 years ago

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