1) For her birthday, your grandmother wants you to replace her old, tube TV with a new, widescreen TV. Her current TV measures 42" and she would like her new TV to measure the same size. What are the dimensions of the new TV if the aspect ratio is 16:97

Both values are approximate, rounded to 3 decimal places.

Explanation:

I'm assuming you meant to say 16:9 instead of 16:97

The ratio 16:9 means that the horizontal width is 16x units and the height is 9x units. They form the ratio 16x:9x which reduces to 16:9

She wants the tv to be the same size as her old one, so the new tv will also have a diagonal of 42 inches (tv sizes are measured by the length of the diagonal).

Through the pythagorean theorem, we can say

a^2+b^2 = c^2

(16x)^2 + (9x)^2 = (42)^2

256x^2 + 81x^2 = 1764

337x^2 = 1764

x^2 = 1764/337

x^2 = 5.23442136498517 approximately

x = sqrt(5.23442136498517)

x = 2.28788578495194

x = 2.288

This means the dimensions would be

width = 16x = 16*2.288 = 36.608 inches

height = 9x = 9*2.288 = 20.592 inches

both are approximate

answer: a) (0,0), (1,1), (2,8), and (3,27).

step-by-step explanation:

0^3=0

1^3=1

2^3=8

3^3=27

in effect, the exponential equation for this would me y=3^x. each x-coordinate cubed is giving the y coordinate, so a is your answer : )

d, x=8

step-by-step explanation:

simplifying

4x + -5 = 2x + 11

reorder the terms:

-5 + 4x = 2x + 11

reorder the terms:

-5 + 4x = 11 + 2x

solving

-5 + 4x = 11 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-5 + 4x + -2x = 11 + 2x + -2x

combine like terms: 4x + -2x = 2x

-5 + 2x = 11 + 2x + -2x

combine like terms: 2x + -2x = 0

-5 + 2x = 11 + 0

-5 + 2x = 11

add '5' to each side of the equation.

-5 + 5 + 2x = 11 + 5

combine like terms: -5 + 5 = 0

0 + 2x = 11 + 5

2x = 11 + 5

combine like terms: 11 + 5 = 16

2x = 16

divide each side by '2'.