Emily wants to hang a painting in a gallery but the painting and frame must have an area of 31 square feet. the painting is 5 feet wide by 6 feet long. the frame must have an equal width of x on each side.

which quadratic equation represents the area of the painting and frame combined?

4x2 + 22x − 1 = 0

4x2 + 22x + 31 = 0

x2 + 11x − 1 = 0

x2 + 11x + 31 = 0

Marco has $38.43 dollars in his checking account. his checking account is linked to his amazon music account so he can buy music. the songs he purchases cost $1.29. part 1: write an expression to describe the amount of money in his checking account in relationship to the number of songs he purchases. part 2: describe what the variable represents in this situation.

Jose predicted that he would sell 48 umbrellas. he actually sold 72 umbrellas. what are the values of a and b in the table below? round to the nearest tenth if necessary

Acompany manufactures large valves, packed in boxes. a shipment consists of 1500 valves packed in 75 boxes. each box has the outer dimensions 1.2 x 0.8 x 1.6 m and the inner dimensions 1.19 x 0.79 x 1.59 m. the boxes are loaded on a vehicle (truck + trailer). the available capacity in the vehicle combination is 140 m3. each valve has a volume of 0.06 m3. - calculate the load factor on the box level (%). - calculate the load factor on the vehicle level (%). - calculate the overall load factor (%).