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2 years ago

Hudson was working on the problem 1/8y=4 He thought he should multiply bolth sides of the equation by 8 to get 32.

Mathematics

1 answer:

kaheart [24]2 years ago

7 0

Answer: Use the given functions to set up and simplify

32. 1/8y = 4He= y =32He8= y =32He32=y=32He

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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

All of the following are examples of composite numbers except which one?

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<span>All of the following are examples of composite numbers except which one?

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What is an efficient way to study for a test/exam

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Take 2 hours out of your day to look over notes/ work on problems, tutoring also helps. Put yourself in a room that's silent thay way no distractions also make sure you take 5 minutes breaks so your brain doesn't overheat

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Which step is not necessary when solving this system of equations by graphing? 3x-y=4 x+y= -4

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Answer: The answer is C: determine the shaded area for each line.

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-3x^{2}-21x-54 what are the zeros? (Solutions)

Irina-Kira [14]

The only way to solve if it is equal to something
assuming that the teacher wanted you to make it equal to zero do
0=-3x^2-21x-54

remember if we can do
xy=0 then assume x and y=0

so factor

0=-3x^2-21x-54
undistribute the -3
0=-3(x^2+7x+18)
remember 0 times anything=0 so
x^2+7x+18 must equal zero
use quadratice formula which is

if you have
ax^2+bx+c=0 then
x= $\frac{-b+/- \sqrt{b^{2}-4ac} }{2a}$

x^2+7x+18
a=1
b=7
c=18

x= $\frac{-7+/- \sqrt{7^{2}-4(1)(18)} }{2(1)}$
x= $\frac{-7+/- \sqrt{49-72} }{2}$
x= $\frac{-7+/- \sqrt{-23} }{2}$
i=√-1
x= $\frac{-7+/- i\sqrt{23} }{2}$

the zerose would be
x= $\frac{-7+ i\sqrt{23} }{2}$ or $\frac{-7- i\sqrt{23} }{2}$

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2 years ago