G The background of a printed company logo is in the shape of an ellipse with height 20 inches and width 24 inches. Find an equation for the ellipse and use it to find the vertical width, in inches, of the logo background at a distance of 3 inches horizontally from the center.

Equation is x^2/576+y^2/400=1

Vertical height is 19.84inches

Step-by-step explanation:

The equation of an ellipse with horizontal major axis with center at (0,0) is x^2/a^2+y^2/b^2=1

From the question, a=24 and b=20

Therefore the equation of the ellipse = x^2/24^2+y^2/20^2=1

= x^2/576+y^2/400=1

To calculate vertical height y:

y^2/400=1- x^2/576

y^2=(1- x^2/576)*400

y=20√(1- x^2/576)

At x=3 inches from the centre

y=20√1-0.0156

y=20*0.9922

y=19.84inches

boxplot e is the answer

so firstly, we need to isolate the y variables to be able to solve these inequalities. firstly, add 0.5x on both sides of the first inequality and subtract 1.5x on both sides of the second inequality:

now since the slope is positive for the first inequality, this means that the line going upwards belongs to the first inequality, and the line going downwards belongs to the second inequality.

next, since y ≥ in the first inequality, this means that the shaded region will be above the first inequality's line, thus shading regions a and b.

next, since y ≤ in the second inequality, this means that the shaded region is going to be below this line, thus shading regions a and c.

since both lines shade region a, this means that region a is the solution.

step-by-step explanation:

mark brainliest!