O ALGEBRAIC EQUATIONS AND INEQUALITIES
Solving a word problem with two unknowns using a linear equa...
Gabrielle is 10 years older than Mikhail. The sum of their ages is 110. What is Mikhail's age?

Mikhail is 50 years old.

Step-by-step explanation:

Let m represent how old Mikhail is.

110 = (m + 10) + m

Combine equal variables.

110 = 2m + 10

Get the variable alone by cancelling out the 10.

110 - 10 = 2m

Simplify.

100 = 2m

Divide.

m = 50

3. parallelogram

step-by-step explanation:

we turn each of our sides into direction vectors

ab=b-a=(3 - 7, 1 - 0) = (-4, 1)

bc=c-b=(1,6)

cd=d-c=(4,-1)

da=a-d=(-1,-6)

we see how the opposite sides have negated direction vectors; this is characteristic of a parallelogram.   we have congruent sides ab=cd and bc=da with unequal lengths because 1^2+6^2 is different from (-4)^2+1^2.   so it's not a square or a rhombus.  

we check the dot product of direction vectors of adjacent sides.   we have

ab dot bc = -4(1) + 1(6) = 2

that's not zero so the sides are not perpendicular.   we've ruled out rectangle.

the direction vectors indicate two pairs of congruent parallel sides, so we choose parallelogram over trapezoid.

6 meters

step-by-step explanation: