A bridge can hold at most 80,000 pounds. A tow truck weighing 7,000 pounds is broken down on the bridge. If the average car weights 2,800 pounds, how many cars can safety be on the bridge with the broken down tow truck.

26

Step-by-step explanation:

x = number of cars that an safety be on the bridge with the broken down tow truck.

The equation that can be used to determine the answer =

total weight the bridge can accommodate = total weight of truck + total weight of cars

total weight of cars = weight of a car x total number of cars

2800x

80,000 = 7000 + 2800x

collect like terms

80,000 - 7000 = 2800x

73,000 = 2800x

x = 73,000 / 2800

x = 26

step-by-step explanation:

equation

you are asked to write the equation

  expression = 0

using the given expression. when you do that, you have

  2x^2-2x-12 = 0

factoring

you can see that each of the coefficients is even, so a factor of 2 can be removed immediately.

  2(x^2 -x -6) = 0

if you multiply the binomials (x+a)(x+b), you get

  (x +a)(x +b) = x^2 +(a+b)x +ab

this tells you the coefficient of x is the sum of two factors of the constant term. here, that means -1 is the sum of two factors of -6. we want to know those factors so we can factor the trinomial.

  -6 = -1×6 = -2×3 = -3×2 = -6×1

the factor pair that sums to -1 is {-3, 2}, so our factorization is

  2(x -3)(x +2) = 0

solutions

the solutions to this equation are the values of x that make the product zero. a product is zero only when only of the factors of the product is zero. here, that means

  x - 3 = 0

  x = 3 . . . add 3 to both sides of the equation

or

  x +2 = 0

  x = -2 . . . add -2 to both sides of the equation

the solutions to the equation are x=3 or x=-2. both of these values of x satisfy the equation—they make it be true.

false

step-by-step explanation:

i looked it up