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2 years ago

I’m confused on this

Mathematics

2 answers:

dexar [7]2 years ago

4 0

$\huge\boxed{x=25}$

The mistake is in Step 1. The solver should have also squared $9$ when squaring the other side of the equation.

<h3>Correctly solving</h3>

$\begin{aligned}\sqrt{3x+6}&=9\\(\sqrt{3x+6})^2&=9^2\\3x+6&=81\\3x+6-6&=81-6\\3x&=75\\\frac{3x}{3}&=\frac{75}{3}\\x&=25\end{aligned}$

goldfiish [28.3K]2 years ago

3 0

Answer:

x = 25

Step-by-step explanation:

The mistake here is the squaring. When you square one side, you have to do the same on the other side:

$\sqrt{3x+6}$ = 9

$(\sqrt{3x+6}) ^{2}$ = $9^{2}$

3x + 6 = 81

3x = 75

x = 25

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Solve for x: 4 over x plus 4 over quantity x squared minus 9 equals 3 over quantity x minus 3. (2 points) Select one: a. x = -4

Kay [80]

Answer:

Step-by-step explanation:

$\dfrac{4}{x}+\dfrac{4}{x^2-9}=\dfrac{3}{x-3}$

Domain:

$x\neq0\ \wedge\ x^2-9\neq0\ \wedge\ x-3\neq0\\\\x\neq0\ \wedge\ x\neq\pm3$

solution:

$\dfrac{4}{x}+\dfrac{4}{x^2-3^2}=\dfrac{3}{x-3}$

use <em>(a - b)(a + b) = a² - b²</em>

$\dfrac{4}{x}+\dfrac{4}{(x-3)(x+3)}=\dfrac{3}{x-3}$

multiply both sides by (x - 3) ≠ 0

$\dfrac{4(x-3)}{x}+\dfrac{4(x-3)}{(x-3)(x+3)}=\dfrac{3(x-3)}{x-3}$

cancel (x - 3)

$\dfrac{4(x-3)}{x}+\dfrac{4}{x+3}=3$

subtract $\frac{4(x-3)}{x}$ from both sides

$\dfrac{4}{x+3}=3-\dfrac{4(x-3)}{x}\\\\\dfrac{4}{x+3}=\dfrac{3x}{x}-\dfrac{(4)(x)+(4)(-3)}{x}\\\\\dfrac{4}{x+3}=\dfrac{3x-\bigg(4x-12\bigg)}{x}\\\\\dfrac{4}{x+3}=\dfrac{3x-4x-(-12)}{x}\\\\\dfrac{4}{x+3}=\dfrac{-x+12}{x}$

cross multiply

$(4)(x)=(x+3)(-x+12)$

use FOIL

$4x=(x)(-x)+(x)(12)+(3)(-x)+(3)(12)\\\\4x=-x^2+12x-3x+36$

subtract 4x from both sides

$0=-x^2+12x-3x+36-4x$

combine like terms

$0=-x^2+(12x-3x-4x)+36\\\\0=-x^2+5x+36$

change the signs

$x^2-5x-36=0\\\\x^2-9x+4x-36=0\\\\x(x-9)+4(x-9)=0\\\\(x-9)(x+4)=0$

The product is 0 if one of the factors is 0. Therefore:

$x-9=0\ \vee\ x+4=0$

$x-9=0$ <em>add 9 to both sides</em>

$x=9\in D$

$x+4=0$ <em>subtract 4 from both sides</em>

$x=-4\in D$

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3 years ago

The angle between two vectors ⃗ = 2⃗ − ⃗ and ⃗⃗ = ⃗ − 3⃗ is

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Answer:

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3 years ago

What's 12748 rounded to the nearest thousand

FinnZ [79.3K]

12748 rounded to the nearest thousand is 13000

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3 years ago

KonstantinChe [14]

<h2> QUESTION # 1</h2>

Answer:

Total distance = 21 units (meters)

The average speed = 7 meter per second.

Step-by-step explanation:

To Determine:

If the whole run took the bug 3 seconds, what was its average speed?

Information Fetching and Solution Steps:

A beetle was running along a number line.

The beetle ran from 4 to 25.

Let suppose each unit on a number line represents 1 meter.

As the beetle ran from 4 to 25, so

the distance covered by beetle is:

25 - 4 = 21 units. i.e. 21 meters

As the average speed can be determined by dividing the total distance by the total time, so

The average speed = total distance / total time

Total distance = 21 units (meters)

Total time = 3 seconds

The average speed = total distance / total time

= 21/3

= 7 meter per second

Therefore, the average speed = 7 meter per second.

<h2> QUESTION # 2</h2>

Answer:

Total distance = 54 units (meters)

The average speed = 6 meter per second.

Step-by-step explanation:

To Determine:

If the whole run took the bug 9 seconds, what was its average speed?

Information Fetching and Solution Steps:

A beetle was running along a number line.

The beetle ran from 24 to 78.

Let suppose each unit on a number line represents 1 meter.

As the beetle ran from 24 to 78, so

the distance covered by beetle is:

78 - 24 = 54 units. i.e. 54 meters

As the average speed can be determined by dividing the total distance by the total time, so

The average speed = total distance / total time

Total distance = 54 units (meters)

Total time = 9 seconds

The average speed = total distance / total time

= 54/9

= 6 meter per second

Therefore, the average speed = 6 meter per second.

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3 years ago

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olga_2 [115]

Answer:

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Step-by-step explanation:

0.006 = 6 × 10^-3

3.08 = 3.08 × 10^0 (10^0 is equal to 1)

(6 × 10^-3) × (3.08 × 10^0) = 18.48 × 10^-3 = 1.848 × 10^-2

8 0

2 years ago