Which algebraic rule describes the transformation? a) (x, y) → (x + 1, y − 3) b) (x, y) → (x + 3, y − 1) c) (x, y) → (x − 1, y + 3) d) (x, y) → (x − 3, y + 1)

B

Step-by-step explanation:

To get to to triangle Y'X'Z', you need to move triangle YXZ 3 units to the right (+3), and 1 unit down (-1). So (x+3,y-1)

b. x- 48 =120

step-by-step explanation:

m∠cdf = 43° , m∠gdf = 114°, m∠gde = 23°, m∠edh = 23° , m∠cdh = 157°

step-by-step explanation:

since, it is given that de bisects the angle gdh ⇒ de divides the angle gdh into two equal angles.

⇒ m∠gde = m∠edh

⇒ 8·x   - 1 = 6·x + 5

⇒ x = 3

so, m∠gde = 8·x - 1 = 23°

and m∠edh = 23°

now, it is given ∠cde is an straight angle so, m∠cde = 180°

⇒ m∠cdf + m∠fdg + m∠gde = 180°

⇒ 43° + m∠fdg + 23° = 180°

⇒ m∠fdg = 114°

again, m∠cde = m∠cdh + m∠edh = 180°

m∠cdh + 23° = 180°

⇒ m∠cdh = 157°