The shape abcd is made from a rectangle ancd and the right-angled triangle nbc. anb is a straight line. an=9cm, nb=5cm. the area of rectangle ancd is 36cm squared. work out the area of shale abcd.

46 cm²

Step-by-step explanation:

Given: ANB is a straight line

          AN= 9 cm

          NB= 5 cm

          Are of rectangle( ANCD)= 36 cm²

Now finding the length of rectangle ANCD.

Lets assume the length of rectangle be "l"

Area of rectangle=

⇒

dividing both side by 9 cm.

∴

Hence, NC= 4 cm

Next, finding the area of triangle ΔNBC

Area of triangle=

⇒ Δ NBC=

∴Δ NBC= 10 cm²

We know, the area of ANCD= 36 cm²

∴ Area of ABCD= Area of rectangle+area of triangle

⇒Area of ABCD= 36+10

∴ Area of ABCD= 46 cm²

(a) {a₁, a₁r, a₁r², … a₁rⁿ⁻¹, …}

(b) $59 398

step-by-step explanation:

(a) the annual sequence of profits

aₙ = a₁rⁿ⁻¹

the model for the sequence of profits is {a₁, a₁r, a₁r², … a₁rⁿ⁻¹, …} .

(b) profit after 15 yr

  a₁ = $ 30 000

  r = 1.05

a₁₅ = 30 000 × 1.05¹⁴

a₁₅ = 30 000 × 1.979 93

a₁₅ = $59 398

the profit in year 15 will be $59 398.