A triangular bandana has an area of 34 square inches. The height of the triangle is 8 1/2 inches. Enter and solve an equation to find the length of the base of the triangle. Use b to represent the length of the base.

8 inches

Step-by-step explanation:

Use the formula for area of a triangle:

A = bh/2

"A" for area

"b" for base

"h" for height

What we know:

A = 34in²

h = 8 1/2 in

Substitute the known values into the formula

A = bh/2

(34in²) = b(8 1/2 in)/2

Isolate "b" to solve for the length of the base

(34in²) * 2 = b(8 1/2 in)/2 * 2              Multiply both sides by 2.

(68in²) = b(8 1/2 in)              

(68in²)/(8 1/2 in) = b(8 1/2 in)/(8 1/2 in)      Divide both sides by (8 2/1 in)

(68in²)/(8 1/2 in) = b         Simplify and move variable to left

b = (68in²)/(8 1/2 in)

How to divide a mixed fraction:

           Convert to improper fraction

          Reformat division

          Flip the second fraction

           Combine into numerator

             Length of base

Therefore the base is 8 inches.

linearly: 8560 bacteria

exponentially: approximately 75233 bacteria

step-by-step explanation:

assuming it is not exponential (we would have some really complicated logarithms), let's say it is linear. then, after 5 hours, it increased by 1200 bacteria, so every hour it increases by 240 bacteria. this means that after 19 hours, we get 19 * 240 + 4000 bacteria or 3800 + 760 + 4000 = 7800 + 760 = 8560 bacteria.

because it says round your answer, i will do this exponentially (with a calculator, of course). first, we need to find how much it multiplies by every hour, by taking the 5th root of 52/40 or 13/10. this is approximately 0.167. we still need to add 1 to this, because we are multiplying by that number, not adding that amount of the number. now, we just calculate 4000 * (1.167)^19. use a calculator to get approximately 75232.6, or 75233.