What is the solution set |x-3| >4

Mathematics

1 answer:

Umnica [9.8K]3 years ago

4 0

Answer:

$\begin{bmatrix}\mathrm{Solution:}\:&\:x7\:\\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:-1\right)\cup \left(7,\:\infty \:\right)\end{bmatrix}$

Step-by-step explanation:

apply the rule of absolute values: it means that x - 3 < - 4 or x - 3 > 4

solve each one:

x - 3 < -4 , x < -1

x - 3 > 4, x > 7

combine both answer sets

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Answer:

Choice A. 3.

Step-by-step explanation:

The triangle in question is a right triangle.

The length of the hypotenuse (the side opposite to the right angle) is given.
The measure of one of the acute angle is also given.

As a result, the length of both legs can be found directly using the sine function and the cosine function.

Let $\text{Opposite}$ denotes the length of the side opposite to the $30^{\circ}$ acute angle, and $\text{Adjacent}$ be the length of the side next to this $30^{\circ}$ acute angle.

$\displaystyle \begin{aligned}\text{Opposite} &= \text{Hypotenuse} \times \sin{30^{\circ}}\\ &=2\sqrt{3}\times \frac{1}{2} \\&= \sqrt{3}\end{aligned}$ .

Similarly,

$\displaystyle \begin{aligned}\text{Adjacent} &= \text{Hypotenuse} \times \cos{30^{\circ}}\\ &=2\sqrt{3}\times \frac{\sqrt{3}}{2} \\&= 3\end{aligned}$ .

The longer leg in this case is the one adjacent to the $30^{\circ}$ acute angle. The answer will be $3$ .

There's a shortcut to the answer. Notice that $\sin{30^{\circ}} < \cos{30^{\circ}}$ . The cosine of an acute angle is directly related to the adjacent leg. In other words, the leg adjacent to the $30^{\circ}$ angle will be the longer leg. There will be no need to find the length of the opposite leg.