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ANSWER

EXPLANATION

The given triangle has a right angle.

The side opposite to the 45° angle is 7 units.

To find angle x, we use the tangent ratio.

Recall the mnemonics TOA, which means,

To find y, we use the sine ratio, which means

see explanation

Step-by-step explanation:

Using the trig. ratios in the right triangle and

tan45° = 1, sin45° = , then

tan45° = =

Multiply both sides by x

x × 1 = 7 ⇒ x = 7

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sin45° = =

Multiply both sides by y

y × sin45° = 7 ( divide both sides by sin 45° )

y = 7 / sin45° = 7 / 1/ = 7

b

step-by-step explanation:

the equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (0, 4) and (x₂, y₂ ) = (3, - 5) ← 2 points on the line

m = = = - 3

with m = - 3 and (a, b) = (3, - 5), then

y - (- 5) = - 3(x - 3), that is

y + 5 = - 3(x - 3) → b