9514 1404 393
Answer:
D'(2, -1)
Step-by-step explanation:
Dilation about the origin by factor k multiplies each coordinate by that factor:
(x, y) ⇒ (kx, ky)
For k = 1/3, this is ...
(x, y) ⇒ (x/3, y/3)
D(6, -3) ⇒ D'(6/3, -3/3) = D'(2, -1)
Answer:
JK = 20
Step-by-step explanation:
Angle Bisector Theorem: an angle bisector of a triangle divide the opposite side into two segments that are proportional to the other two sides of the triangle
LK / JK = LM / JM
(45 - JK) / JK = 75 / 60 = 5 / 4
5 JK = 4 (45 - JK)
5 JK = 180 - 4 JK
9 JK = 180
JK = 20
Answer:
it is used to subtract 10 from both sides
Answer:
(- 2, 1 ) and (1, 4 )
Step-by-step explanation:
Given the 2 equations
y = - x² + 5 → (1)
- x + y = 3 → (2)
Rearrange (2) expressing y in terms of x by adding x to both sides
y = x + 3 → (3)
Substitute y = x + 3 into (1)
x + 3 = - x² + 5 ( subtract - x² + 5 from both sides )
x² + x - 2 = 0 ← in standard form
(x + 2)(x - 1) = 0 ← in factored form
Equate each factor to zero and solve for x
x + 2 = 0 ⇒ x = - 2
x - 1 = 0 ⇒ x = 1
Substitute these values into (3) for corresponding values of y
x = - 2 : y = - 2 + 3 = 1 ⇒ (- 2, 1 )
x = 1 : y = 1 + 3 = 4 ⇒ (1, 4 )
divide the base by the sin of the opposite angle
base = 2
opposite angle = 30 degrees
2/sin(30) = 4
x = 4
