All categories

3 years ago

Find the value of x in the following figure. Show equations and work that lead to your answer.

Mathematics

2 answers:

irinina [24]3 years ago

5 0

Answer:

x = 7

Step-by-step explanation:

DedPeter [7]3 years ago

4 0

We're given a set of exterior angles for a polygon, here a quadrilateral. Exterior angles of any polygon add to 360 degrees.

46 + (12x + 37) + (12x - 2) + (20x - 29) = 360

44 x + 52 = 360

44 x = 308

x = 308/44 = 7

Check: The supplementary angles should add to 360 as well, they're the interior angles of a quadrilateral

(180-46) + (180 - (12(7) + 37)) + (180 - (12(7) - 2)) + (180 - (20(7) - 29)) = 360, good

Answer: 7

You might be interested in

What is the supplement angle of 100?

aleksley [76]

Answer:

An angle measuring 100 degrees would be supplementary to any angle measuring 80 degrees, but it cannot be called supplementary by itself. "Complementary" and "supplementary" are terms that describe the relationship between two angles. They are comparative words like "larger."

Step-by-step explanation:

5 0

3 years ago

Find the solution set of the inequality

Natalija [7]

Answer: x>- 7/3

Step-by-step explanation:

Solve for x by simplifying bot sides of the equation, then isolating the variable.

5 0

3 years ago

I need help with these two trigonometry problems.

Sloan [31]

Answer:

$B \approx 32.1\°; A \approx 39.0\°$

Step-by-step explanation:

Sine theorem: in any triangle, the ratio between a side and the sine of the opposite angle is constant

$\frac{sin\ \alpha}a = \frac{sin\ \beta}b =\frac{sin\ \gamma}c$

In our case, for the left triangle,

$\frac {sin\ 103\°}{11} =\frac{sin\ B} 6 \rightarrow sin\ B = \frac6{11} sin\ 103\°$

Time to grab a calculator and crunch numbers. Double check your calculator is in degrees and not in radians (plug in sin 30°, if you're getting 0.5 you're good) and you will get

$sin\ B \approx 0.53 \rightarrow B \approx 32.1\°$

Same difference with the right triangle. With the same calculations

$sin\ A = \frac{26}{41} sin 83\° \approx 0.68 \rightarrow A \approx 39.0\°$

5 0

2 years ago

If for two non-zero vectors a,b : ∣a+b∣=∣a−b∣ then angle between them is:______a. 0b. 45c. 60d. 90

Eddi Din [679]

Answer:

$90^\circ$

Step-by-step explanation:

Given two non zero vectors, $\vec a, \vec b$ .

Let the angle between the two vectors = $\theta$

Given that:

$|\vec a+\vec b|=|\vec a-\vec b|$

Let us have a look at the formula for magnitude of addition of two vectors:

$|\vec x+\vec y|=\sqrt{x^2+y^2+2xycos\theta}$

Where $\theta$ is the angle between the two vectors.

formula for magnitude of subtraction of two vectors:

$|\vec x-\vec y|=\sqrt{x^2+y^2-2xycos\theta}$

As per the given condition:

$\sqrt{a^2+b^2+2abcos\theta}=\sqrt{a^2+b^2-2abcos\theta}$

Squaring both sides:

$a^2+b^2+2abcos\theta=a^2+b^2-2abcos\theta\\\Rightarrow 2abcos\theta=-2abcos\theta\\\Rightarrow cos\theta = -cos\theta\\\Rightarrow 2cos\theta = 0\\\Rightarrow cos\theta = 0\\\Rightarrow \theta = 90^\circ$