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3 years ago

Which equation does the graph below represent

Mathematics

1 answer:

____ [38]3 years ago

4 0

Answer: The answer is y=-3x

Step-by-step explanation: You can see in the picture that the line is going down which represents a negative slope so you can eliminate C and D. Now you are left with A and B. 1 unit up is equal to 3 so the rise over run is -3/1 and that translates to Y=-3x answer B

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Show work please \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

Determine the values of x when f(x)=40 for the function f(x)=2(x-3)^2-8

SpyIntel [72]

Answer:

x = 3 ± $\sqrt{24}$

x = 3 + $\sqrt{24}$ , x = 3 - $\sqrt{24}$

Step-by-step explanation:

given f(x) = 2(x - 3)^2 - 8, find when f(x) = 40

So, we plug in 40 for f(x) in the 1st equation and solve for x. (Aim to got x on its own)

40 = 2 (x - 3)^2 - 8

+ 8 + 8

-----------------------------

48 = 2 (x - 3)^2

/2 /2

-----------------------------

24 = (x - 3)^2

square root both sides

--------------------

$\sqrt{24}$ = x - 3

x = 3 ± $\sqrt{24}$

5 0

2 years ago

What is another word for translation? A.flip B.turn C.slide D.fall

stiv31 [10]

It's not a as flip is rotational, turn can also be rotational. I would go with slide as translation is a sideways motion

7 0

3 years ago

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kipiarov [429]

The slope of this line is -1 you find this by using the slip formula of y-y over x-x find two points on the line so I used points (-2,2) and (-1,1) plug them into the formula to get the slope of -1 hope this helps:)

6 0

2 years ago

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Write an equation where the left side is your power of 10 times n and the right side is the result of multiplying 0.1515... by t

Neko [114]

Answer:

$n10^x = 0.1515x$