Given right triangle ABC with altitude BD drawn to hypotenuse AC. If AB = 3 and AC = 9, what is the length of AD? (Note: the figure is not drawn to scale.)

The length of AD is 1 unit

Step-by-step explanation:

Let us solve the question

In Δ ABC

∵ ∠B is a right angle

∵ BD is perpendicular to the hypotenuse AC

∴ (AB)² = AD × AC ⇒ rule

∵ AB = 3 units

∵ AC = 9 units

∵ AD = x

→ Substitute them in the rule above

∴ (3)² = x × 9

∴ 9 = 9x

→ Divide both sides by 9

∵ =

∴ 1 = x

∴ The length of AD is 1 unit

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

see explanation

step-by-step explanation:

a

(6r + 7) + (13 + 7r) ( remove brackets and collect like terms )

= 6r + 7 + 13 + 7r

= 13r + 20

b

remove brackets and collect like terms

13 - r - 1 + r

= 12 - r

c

remove brackets and collect like terms

= - 8 - r + 2r - 4

= - 12 + r

d

remove brackets and collect like terms

= 7r - - - 6r

[-   - = - - = - ]

= r -