POSSIBLE POINTS: 5 Taina found the area of a table in the shape of a trapezoid. The height of the trapezoid is 10 ft, base one is 6 ft and base two is 5 ft. Taina says the area of the figure
is 110 square foot inches. What mistake did Taina make? What is the actual answer?

9514 1404 393

Step-by-step explanation:

The formula for the area of a trapezoid is ...

  A = 1/2(b1 +b2)h

  A = (1/2)(6 ft +5 ft)(10 ft) = 55 ft²

The numerical value of the answer would be 110 if we "forgot" to multiply by 1/2.

The area units would be "square foot inches" if inch dimensions crept into the problem somewhere.

It looks like Taina made two mistakes:

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.

m∠a is 90°

m∠b is 40°