10. the measures of the bases of a
trapezoid are x2 – 19 and 10. the
measure of the midsegment is 8.
find the value of x.

The value of x is 2 .

Step-by-step explanation:

Given as :

The area of Trapezoid = x² unit²

The measure of base 1 = = - 19 unit

The measure of base 2 = = 10 unit

The height of the mid segment = 8 unit

Now, From the Area of Trapezoid

i.e Area = × (sum of opposite base) × height

Or, x² = × (19 + 10) × 8

Or,  x² = × (29)

Or, x² = 4 × (29)

Or,  x² = 116

∴ x =

I.e x = 2

Hence, The value of x is 2 . Answer

answer: integers are just whole numbers: positive, negative, and zero.

i = {-∞, -2, -1, 0, 1, 2, 3, ∞}

let x = 1st integer

let y = 2nd integer

x = 3y + 17   {equation 1}

xy = -24         {equation 2}

substitute 3y+17 in place of x n equation 2

and solve for y.

(3y+17)y = -24

3y2 + 17y = -24

3y2 + 17y + 24 = 0

from quadratic equation:

y = [-17±√(172-4(3)(24))]/(2(3))

y = (-17 ±√1)/6

y = (-17+1)/6   or     y = (-17-1)/6

y = -16/6           or     y = -18/6

y = -2 2/3         or   y = -3

since we are dealing with

y = -3

x = 3y+17 = -9+17 = 8

the integers are -3, 8

step-by-step explanation: