Evan is making a table that will be created in the shape of the figure below. The table top is a triangle attached to a rectangle. To purchase the right amount of paint, he needs to know the area of the table top. He can only spend $10 on paint, which is enough to cover 150 ft2 of surface area. What is the maximum length of the base of the rectangle he can build? (3 points) An image of a compound shape made up of a rectangle and a triangle is shown. The length of the rectangle is labeled x and the width is labeled 6 feet. The base of the triangle is labeled 4 feet and the height is labeled 6 feet.

23 ft

Step-by-step explanation:

The surface area is known to be 150 square feet. Given the dimensions of this triangle ( 6 feet by 4 feet ) we can determine it's area, therefore calculating the area of this rectangle by subtracting the area of the triangle from the total surface area ( 150 square feet ). The amount of money on paint was there to mislead you, however it gave us the key point of being able to cover a maximum surface area of 150 square feet.

Surface Area = 150 ft²,

Area of Triangle = ( 6 4 ) / 2 = ( 24 ) / 2 = 12 ft²,

Area of Rectangle = Surface Area - Area of Triangle = 150 ft² -  12 ft²

= 138 ft²

Let x = length of the rectangle

138 ft² = x 6 ft,

x = 138 ft² / 6 ft = 23 ft - this is the maximum length of the base of the rectangle he can build.

dont know

step-by-step explanation:

the solution is x=1

step-by-step explanation:

we are given our   equation as

let's assume

left side function is

right side function is

now, we can draw graph

and then we can get intersection point

the intersection point will be solution

so, the solution is

x=1