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

1.4

2.3

step-by-step explanation:

the formula for the constant of variation is

y= kx

divide each side by x

y/x =kx/x

y/x =k

we know a and y

1.   y/x = k

4/1 =4

check the other values to make sure they are the same

8/2 = 4   12/3 =4   and 16/4 =4  

the constant of variation is 4

2.   y/x = k

3/1 =3

check the other values to make sure they are the same

6/2 = 3   9/3 =3   and 12/4 =3  

the constant of variation is 3

∠lno ≅ ∠lnm

∠oln ≅ ∠mln

step-by-step explanation:

given   that triangle lno is congruent to triangle lnm.

we have to fill up the blanks in the given question.

according to above order of congruency   kept in mind we can say that

∠lno ≅ ∠lnm

∠oln ≅ ∠mln

ln ≅ ln due to common in both.

hence, by sas congruency,

the side angle side rule   states that if two sides and the included angle of one triangle are congruent to another triangle, then these two triangles are congruent.