Is it possible to draw three points that are noncoplanar? Explain.

1 answer:

6 0

No, it is not possible to draw three points that are noncoplanar. This is because when you draw these points they will form a single plane which means they are coplanar. This is the same with two points forming a line therefore the points are colinear.

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Jason earned a total of $15900 from two part-time jobs. If he earned 3700 more from one job than the other , how much did he ear

KiRa [710]

Let's call job one x.

Job two can be y.

Jason earned $3,700 more from job y than x. Therefore y = x + 3700

From the two jobs, Jason earned $15,900. This can be written as x + y = 15900.

Now substitute y for x + 3700:

x + x + 3700 = 15900

2x + 3700 = 15900

Subtract 3700 from both sides:

2x = 12200

Divide both sides by 2:

x = 6100

Take the original equation x + y = 15900 and substitute x with 6100:

6100 + y = 15900

y = 9800

Job one (x) paid Jason $6,100.

Job two (y) paid Jason $9,800.

6 0

3 years ago

(20 points)Solve the equation cos x = sin (x + 22)

Law Incorporation [45]

Answer:

$\bold{x = 34^\circ}$

Step-by-step explanation:

Given:

$cos x = sin (x + 22^\circ)$

To solve:

The given equation.

Solution:

First of all, let us consider an important property of sine and cosine.

$sin(90^\circ-\theta )=cos\theta$

$cos(90^\circ-\theta )=sin\theta$

We can apply above property to solve for $x$ as per given equation.

$cos x = sin (x + 22^\circ)$

Changing $cosx$ to sine form:

$cosx=sin(90^\circ-x)$

$cosx=sin(90^\circ-x) = sin(x+22^\circ)$

$\therefore 90^\circ-x=x+22^\circ\\\Rightarrow 90^\circ-22^\circ=x+x\\\Rightarrow 2x=68^\circ\\\Rightarrow \bold{x = 34^\circ}$

So, solution to the equation $cos x = sin (x + 22^\circ)$ is:

$\bold{x = 34^\circ}$

7 0

3 years ago

Built in 2011, the capital gate tower is 150 meters tall (measured vertically from the ground) and makes a 72 degree angle with

Softa [21]

Answer:

Step-by-step explanation:

You can create a right triangle out of this information and then use right triangle trig to solve.

We are given the height of the triangle as the height of the tower which is 150m.

We are given the angle of inclination as the degree the tower makes with the ground which is 72.

From the angle of 72 degrees, which is also known as the reference angle, we have the side across from it (the height) and we are looking for the side adjacent to it (how far from the base of the tower the keys will land). Side opposite the reference angle over side adjacent to the reference angle is the tangent ratio:

$tan(72)=\frac{150}{x}$ and, solving for x,