Solve for x 3 (x- 4) = 44 - 5x A: 4 B: 5 C: 6 D: 7

In a parallelogram, if the measure of y is 32 degrees what is the measure of w

alekssr [168]

Talking about a parallelogram, we know that:
opposite sides and angles are congruent
in the picture below:
∠A = ∠C
AD = BC
if one angle is right, then the rest are right as well (making it a rectangle/square)
The consecutive angles are supplementary (meaning they add up to 180)
A + D = 180°

If y and w are consecutive angles, then
w = 180 - 32
=148°
If they are opposite angles, w = 32° (congruent angles)

8 0

3 years ago

Find sin theta if theta is an angle in standard position and the point with coordinates (3, -4) lies on the terminal side of an

alisha [4.7K]

Answer:

$\sin \theta=-\frac{4}{5}$

Step-by-step explanation:

Given:

Angle is in standard position which means the starting ray is at the origin. The terminal side has coordinates (3, -4).

So, the 'x' value is 3 and 'y' value id -4.

Using Pythagoras Theorem, we find the hypotenuse.

Hypotenuse = $\sqrt{3^2+(-4)^2}=\sqrt{9+16}=\sqrt{25}=5$

Now, using the sine ratio for the angle, we have

$\sin \theta=\frac{Opposite}{Hypotenuse}\\\sin \theta=\frac{-4}{5}\\\sin \theta=-\frac{4}{5}$

Therefore, the value of $\sin \theta$ is $-\frac{4}{5}$ .

The value is negative as the point (3, -4) lies in the fourth quadrant and sine ratio is negative in the fourth quadrant,

4 0

3 years ago

line segment with one endpoint at (2,5) is divided in the ratio 4:5 by the point (10,1). which coordinates could represent the o

rodikova [14]

Answer:

(20,-4)

Step-by-step explanation:

We are given;

One end point as (2,5)

Point of division as (10,1)

The ratio of division as 4:5

We are required to calculate the other endpoint.

Assuming the other endpoint is (x,y)

Using the ratio theorem

If the unknown endpoint is the last point on the line segment;

Then;

$\left[\begin{array}{ccc}10\\1\end{array}\right]$ = $\frac{4}{5} \left[\begin{array}{ccc}x\\y\end{array}\right]$ + $\frac{5}{9}\left[\begin{array}{ccc}2\\5\end{array}\right]$