Answer:
D
Step-by-step explanation:
Let's draw a picture (see attachment).
We know that since our point is (-5, -12), it must pass in the third quadrant. Now, if we drop a perpendicular line from the point (-5, -12) to the x-axis, we have a right triangle. Notice that we already know the two leg lengths of this: -5 and -12.
Cosine is adjacent / hypotenuse. Here, the adjacent side to the angle θ is -5. We need to find the hypotenuse, which we can do so by using the Pythagorean Theorem:
c² = a² + b²
c² = (-5)² + (-12)²
c² = 25 + 144 = 169
c = 13
So, the hypotenuse is 13. Now, plug these values in:
cos(θ) = adjacent / hypotenuse = -5/13
The answer is D.
Answer: 2x![y^{2}](https://tex.z-dn.net/?f=y%5E%7B2%7D)
Step-by-step explanation:
6x2y2 - 8xy2 + 10xy3
- 3 ,2 , x, x, y, y - 2xyy
= 4, 2 , x, y , y- 2xyy
10x
= 5, 2, x ,y ,y, y - 2xyy
Answer:
110
Step-by-step explanation:
![30 + 25 \\ = 55 \times 2 \\ = 110](https://tex.z-dn.net/?f=30%20%2B%2025%20%5C%5C%20%20%3D%2055%20%5Ctimes%202%20%5C%5C%20%20%3D%20110)
Answer:
Step-by-step explanation:
<u>Coordinates of points</u>
i) lies on x- axis with abscissa - 3
- If it lies on x- axis, it has zero y-coordinate
- It is (-3, 0)
ii) lies on y-axis with ordinate 5
- It lies on y-axis, it has zero x-coordinate
- It is (0, 5)
Answer:
40 feet
Step-by-step explanation:
Required:
Find the length of Samson's shadow
The question can be illustrated with the attached figure where Samson's shadow is represented with x.
To solve for x, we make use of the following equivalent ratios:
![18.75 : 120 = 6.25 : x](https://tex.z-dn.net/?f=18.75%20%3A%20120%20%3D%206.25%20%3A%20x)
Convert to fraction
![\frac{18.75}{120} = \frac{6.25}{x}](https://tex.z-dn.net/?f=%5Cfrac%7B18.75%7D%7B120%7D%20%3D%20%5Cfrac%7B6.25%7D%7Bx%7D)
Cross Multiply
![18.75 * x = 120 * 6.25](https://tex.z-dn.net/?f=18.75%20%2A%20x%20%3D%20120%20%2A%206.25)
![18.75 * x = 750](https://tex.z-dn.net/?f=18.75%20%2A%20x%20%3D%20750)
Make x the subject
![x =\frac{750}{18.75}](https://tex.z-dn.net/?f=x%20%3D%5Cfrac%7B750%7D%7B18.75%7D)
![x =40](https://tex.z-dn.net/?f=x%20%3D40)
<em>Hence, Samson's shadow is 40ft</em>