Jay just bought a new 75" television for his apartment. The opening in the entertainment center (where the tv will be placed) is only 70 inches by 35 inches. If the newer television has an aspect ratio of 16:9, will the new tv fit in the old entertainment center? Justify your answer by finding the width and height of the new television.

Width of the new tv= 65.44 inches

Height of the new tv = 36.41 inches

If the newer television has an aspect ratio of 16:9, will the new tv fit in the old entertainment center?

Since the old entertainment set has a dimension of 70 inches by 35 inches

,new TV set, has dimension of 65.44 inches by 36.81 inches, the new TV may not be able to fit into the old entertainment set properly because it is 1.81 inches higher than the entertainment set.

Step-by-step explanation:

The newer TV set has an aspect ratio of 16: 9 and it is 75 inches

We are going to make use of Pythagoras theorem

= Width² + Height ² = Size of TV²

Width = 16x

Height = 9x

75² = (16x)² + (9x)²

5625 = 256x² + 81x²

5625 = 337x²

x² = 5625/337

x² = 16.691394659

x = √16.691394659

x = 4.0855103303

Approximately = 4.09

Hence, we can find the width and height of the new TV

Width = 16x

Width = 16 × 4.09

Width = 65.44 inches

Height = 9x

Height = 9 × 4.09

Height = 36.81 inches

Hence, the dimensions of the new TV set = 65.44 inches by 36.81 inches

If the newer television has an aspect ratio of 16:9, will the new tv fit in the old entertainment center?

Since the old entertainment set has a dimension of 70 inches by 35 inches

,new TV set, has dimension of 65.44 inches by 36.81 inches, the new TV may not be able to fit into the old entertainment set properly because it is 1.81 inches higher than the entertainment set.

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