Geometric proofs Can someone explain how to do number 1? It would really help

What's the answer to: ‎X + 9 = 18 - 2x?

ser-zykov [4K]

Remember you can do anything to an equation as long as you do it to both sides

x+9=18-2x
add 2x to both sides
2x+x+9=18+2x-2x
3x+9=18+0
3x+9=18
minus 9 both sides
3x+9-9=18-9
3x+0=9
3x=9
divide both sides by 3
(3x)/3=9/3
(3/3)x=3
1x=3
x=3

4 0

3 years ago

An observer on top of a 50-foot tall lighthouse sees a boat at a 7° angle of depression. To the nearest foot, how far is the boa

Yuri [45]

Answer:

407.22 foot is the boat from the base of the lighthouse

Step-by-step explanation:

Given the statement: An observer on top of a 50-foot tall lighthouse sees a boat at a 7° angle of depression.

Let x foot be the distance of the object(boat) from the base of the lighthouse

Angle of depression = $7^{\circ}$

$\angle CAB = \angle DCA = 7^{\circ}$ [Alternate angle]

In triangle CAB:

To find AB = x foot.

Using tangent ratio:

$\tan (\theta) = \frac{Opposite side}{Adjacent Base}$

$\tan (\angle CAB) = \frac{BC}{AB}$

Here, BC = 50 foot and $\angle CAB =7^{\circ}$

then;

$\tan (7^{\circ}) = \frac{50}{x}$

or

$x = \frac{50}{\tan 7^{\circ}}$

$x = \frac{50}{0.1227845609}$

Simplify:

AB = x = 407.217321 foot

Therefore, the boat from the base of the light house is, 407.22'

5 0

3 years ago

For which value of theta is cot (theta) undefined?

sattari [20]

The cotangent function is defined as the ratio between cosine and sine of a given angle, i.e.

$\cot(x) = \frac{\cos(x)}{\sin(x)}$

Since you can't have zero at the denominator, the cotangent function is not defined when the sine is zero.

Let's look at your option:

$\sin(90^\circ) = 1$ , so the cotangent is defined here

$\sin(180^\circ) = 0$ , so the cotangent is not defined here

$\sin(270^\circ) = -1$ , so the cotangent is defined here

$\sin(450^\circ) = \sin(360^\circ+90^\circ)=\sin(90^\circ) = 1$ , so the cotangent is defined here

6 0

3 years ago

Read 2 more answers

True or false: a pair of straight angles can also be adjacent angles

IrinaK [193]

Thank you for posting your question here at brainly. I hope the answer will help you. Feel free to ask more questions. the statement "a pair of straight angles can also be adjacent angles" is true

There are some special relationships between "pairs" of angles. Adjacent Angles are two angles that share a common vertex, a common side, and no common interior points. (They share a vertex and side, but do not overlap.) A Linear Pair is two adjacent angleswhose non-common sides form opposite rays.

7 0

3 years ago

Read 2 more answers

City

xxMikexx [17]

Answer:

The correct option is (B) 69.7%.

Step-by-step explanation:

The table provided represents the probabilities of a positive response to two government programs from citizens in eight cities.

The probabilities mentioned in the table are conditional probabilities, i.e. the probability of a positive response for program 1, given that the individual is from city x.

The probability a positive response for program 1 from an individual from Houston is 69.7%.

Then the conditional probability of a positive response for program 1, given that the individual is from Houston is 69.7%.

Thus, the correct option is (B).

7 0

3 years ago