On a map of North Carolina, the distance between Raleigh and Charlotte is 3 1/4 inches. The scale on the map is 1 inch = 40 miles. What is the actual distance?

130 miles

Step-by-step explanation:

A scale drawing is a reduced form in terms of dimensions of an original image / building / object

the scale drawing is usually reduced at a constant dimension

scale of the drawing = original dimensions / dimensions of the scale drawing

Actual distance = 31/4 x 40

convert 31/4 to an improper fraction

to convert to improper fraction, take the following steps :  

1.Multiply the whole number  by the denominator

2.Add the numerator to the answer gotten in the previous step

3.divide the number gotten in the previous step by the denominator  

13/4 x 40 = 130 miles

answer is 8x+24

area of vanessa's patio = length × width

given, length = (3x² + 5x + 10)

width = (x² - 3x - 1)

area of vanessa's patio = (3x² + 5x + 10)(x² - 3x - 1)

= 3x²(x² - 3x - 1) + 5x(x² - 3x - 1) + 10(x² - 3x - 1)

= 3x⁴ - 9x³ - 3x² + 5x³ - 15x² - 5x + 10x² - 30x - 10

= 3x⁴ - 4x³ - 8x² - 35x - 10

hence, expression of vanessa's patio = (3x⁴ - 4x³ - 8x² - 35x - 10)