Paul has a piece of wood that is 4 yards long. he know that there is 12 inces in 1 foot and 3 feet in 1 yard if there is no wood left over, how many 6inch pieces can paul cut from the length of wood

24 pieces

Step-by-step explanation:

You have to first convert the 4 yards into feet. To do this, you set up a simple equation.

4yrds         1yrd

 ?             3 ft

We know 1 yard = 3 ft, so we make it a ratio. On the top, 1yrd times 4 equals 4 yrds. Therefore, 3 ft times 4 equals 12 feet. (what you do on the top you do on and bottom, and in this case, we multiplyed 4.)

Now we know that 4yrds = 12ft

We now have to convert 12ft into inches. To do this, we set up another equation.

12ft       1ft

 ?          12in

We know 1 foot = 12 inches, so we make it a ratio. On the top, 1ft times 12 equals 12ft. Therefore, 12in times 12 equals 144 inches. (what you do on the top you do on and bottom, and in this case, we multiplyed 12.)      

Now we know the wood is 144 inches. All there is left to do is divide that by 6 inches to find out how many 6 inch pieces we will have!

144 divided by 6 equals 24, therefore, there are 24 pieces of 6 inch wood.

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17

step-by-step explanation:

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)