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2 years ago

Solve for x. Solve for x.

Mathematics

2 answers:

Nitella [24]2 years ago

4 0

Answer:

4√3

Step-by-step explanation:

This is a right triangle. When two sides are given in a right triangle, we need to use the Pythagorean Theorem to solve for the third side.

Pythagorean Theorem: a² + b² = c²

The a here is 11, while the b is x. The c is always the hypotenuse (the longest side), which is 13.

Now we substitute:

11² + x² = 13²

121 + x² = 169

-121 -121

x² = 48

√x² = √48

x = √48 <-- We can simplify that.

√48 = 12 * 4 = 3 * 4 * 4 = 4√3

Svetradugi [14.3K]2 years ago

4 0

Answer:

4*√3

Step-by-step explanation:

By Pythagoras Theorem,

11²+x²=13²

x²=169-121=48

x=4√3

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Consider the system of inequalities

$\left\{ \begin{array}{l} y\ge 2 \\ x\le 6 \\ y\le 3x+2 \\ y\le -x+10. \end{array}\right.$

1. Plot all lines that are determined by equalities (see attached diagram)

$\left\{ \begin{array}{l} y=2 \text{ (red line)} \\ x= 6 \text{ (blue line)}\\ y=3x+2 \text{ (green line)} \\ y= -x+10 \text{ (orange line)}. \end{array}\right.$

2. Determine which bounded part of the plane you should select:

$y\ge 2$ means that you should take points with y-coordinates greater than or equal to 2 (top part of the coordinate plane that was formed by the red line);
$x\le 6$ means that you should take points with x-coordinates less than or equal to 6 (left part of the coordinate plane that was formed by the blue line);
for $y\le 3x+2$ you can check where the origin is placed. Since $0\le 3\cdot 0+2$ , the origin belongs to the needed part and you have to take the right part of the coordinate plane that was formed by green line.
for $y\le -x+10$ you can check where the origin is placed. Since $0\le -1\cdot 0+10$ , the origin belongs to the needed part and you have to take the bottom part of the coordinate plane that was formed by orange line.