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3 years ago

What is the soulution of the equation 3(2x+5)=3x+4

Mathematics

2 answers:

lakkis [162]3 years ago

8 0

x=- $\frac{11}{3}$

x=-3.666666666666666666666666666666666666666666666

mel-nik [20]3 years ago

8 0

Answer:

x=-11/3

Step-by-step explanation:

Given equation is 3(2x+5)=3x+4

Multiplying 3 into the equation we get

6x+15=3x+4

Adding (-3x) and (-15) to both sides of equation

6x+15+(-3x)+(-4)=3x+4+(-3x)+(-15)

Simplifying

6x+15-3x-15=3x+4-3x-15

6x-3x+15-15=3x-3x+4-15

we know that +15-15=0 and 3x-3x=0

3x+0=0-11

3x=-11

dividing by 3 to both sides of equation we get

3x/3=-11/3

x=-11/3 which is the answer.

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3 years ago

R=-6 and t=3. what is 12-t | 3r-2 |

SVEN [57.7K]

12 - t|3r - 2|

r = -6; t = 3

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3 years ago

WILL MARK BRAINLIEST <br><br> what is the domain of (f/g) (x)?

tatyana61 [14]

Given that $f(x) = \sqrt{7-x}$ and $g(x) = \sqrt{x + 2}$ , we can say the following:

$\Bigg(\dfrac{f}{g}\Bigg)(x) = \dfrac{f (x)}{g(x)} = \dfrac{\sqrt{7 - x}}{\sqrt{x+2}}$

Now, remember what happens if we have a negative square root: it becomes an imaginary number. We don't want this, so we want to make sure whatever is under a square root is greater than 0 (given we are talking about real numbers only).

Thus, let's set what is under both square roots to be greater than 0:

$\sqrt{7 - x} \Rightarrow 7 - x \geq 0 \Rightarrow x \leq 7$

$\sqrt{x + 2} \Rightarrow x + 2 \geq 0 \Rightarrow x \geq -2$

Since both of the square roots are in the same function, we want to take the union of the domains of the individual square roots to find the domain of the overall function.

$x \leq 7 \,\,\cup x \geq -2 = \boxed{-2 \leq x \leq 7}$

Now, let's look back at the function entirely, which is:

$\Bigg( \dfrac{f}{g} \Bigg)(x) = \dfrac{\sqrt{7 - x}}{\sqrt{x+2}}$

Since $\sqrt{x + 2}$ is on the bottom of the fraction, we must say that $\sqrt{x + 2} \neq 0$ , since the denominator can't equal 0. Thus, we must exclude $\sqrt{x + 2} = 0 \Rightarrow x + 2 = 0 \Rightarrow x = -2$ from the domain.

Thus, our answer is Choice C, or $\boxed{ \{ x | -2 < x \leq 7 \}}$ .

<em>If you are wondering why the choices begin with the $x |$ symbol, it is because this is a way of representing that $x$ lies within a particular set.</em>