![\bf sin(x)[csc(x)-sin(x)]~~=~~cos^2(x) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ sin(x)\left[\cfrac{1}{sin(x)}-\cfrac{sin(x)}{1} \right]\implies \underline{sin(x)}\left[\cfrac{1-sin^2(x)}{\underline{sin(x)}} \right] \\\\\\ 1-sin^2(x)\implies cos^2(x)](https://tex.z-dn.net/?f=%5Cbf%20sin%28x%29%5Bcsc%28x%29-sin%28x%29%5D~~%3D~~cos%5E2%28x%29%20%5C%5C%5C%5C%5B-0.35em%5D%20%5Crule%7B34em%7D%7B0.25pt%7D%5C%5C%5C%5C%20sin%28x%29%5Cleft%5B%5Ccfrac%7B1%7D%7Bsin%28x%29%7D-%5Ccfrac%7Bsin%28x%29%7D%7B1%7D%20%5Cright%5D%5Cimplies%20%5Cunderline%7Bsin%28x%29%7D%5Cleft%5B%5Ccfrac%7B1-sin%5E2%28x%29%7D%7B%5Cunderline%7Bsin%28x%29%7D%7D%20%5Cright%5D%20%5C%5C%5C%5C%5C%5C%201-sin%5E2%28x%29%5Cimplies%20cos%5E2%28x%29)
recall again, sin²(θ) + cos²(θ) = 1.
Answer:
- a rotation, followed by a translation
- a translation, followed by two reflections
Step-by-step explanation:
The rigid motions are the transformations that produce congruent images.
There are three main kinds of rigid motions :
- Reflections : Flips a figure across a line of reflection.
- Rotations : Rotates a figure about some degrees around a center point.
- Translations : Moves figure on a plane about some distance in a certain direction.
But dilation is not a rigid transformation because it may change the size of the image. It is usually used to shrink or enlarge a shape.
So, the options having dilation and term "stretch" cannot produce congruent figures.
Hence, the correct options are :
- a rotation, followed by a translation
- a translation, followed by two reflections
Answer:
Step-by-step explanation:
13) x⁴-12x² +36
(a-b)² = a²-2ab+b²
a = x² ; b = 6
(x²)² - 2 * x² * 6 + 6² = (x² - 6)²
14) w⁴- 14w² - 32 = w⁴+ 2w² - 16w² - 32 = w² (w² + 2) - 16 (w²+2)
= (w² + 2) (w² -16 )
15) k³ + 7k² - 44k = k ( k² + 7k -44) = k ( k+11 ) ( k-4 )
16) 2a³ +28a²+96a =2a(a²+14a+48) = 2a(a+6)(a+8)
17) -x³ +4x² +21x = (-x) ( x² - 4x - 21) = (-x)(x-7)(x+3)
18) m⁶ - 7m⁴ -18m² = m² ( m⁴-7m²-18) = m² (m²-9)(m²+9)
= m² (m+1) (m-1)(m²+9)
19) 9y⁶ +6y⁴ + y²= y² ( 9y⁴+6y²+1) = y² (3y²+1)²
20) 8c⁴+10c² -3 = (4c +1)(2c-3)
Answer: (C)The square root of terms separated by addition and subtraction cannot be calculated individually.
Step-by-step explanation:
