Sum of 3x^3+8,2x^2+5x and x^3+2x^2-3x-3

4x^3 + 4x^2 + 2x + 5

Step-by-step explanation:

To add expressions where many different variables are used, be sure to remember like terms. Like terms are terms which have the same variable bases and exponents. For instance a and b are different bases but ab and ab are the same. a^2b and ab^2 are different bases while a^2b^2 and a^2b^2 are the same. Both the variable and the exponents must be the same.

In this expression, there is 1 variable with three types of exponents. x^3, x^2, and x should be combined only with the same type.

3x^3+8 + 2x^2+5x + x^3+2x^2-3x-3

The simplified expression is 4x^3 + 4x^2 + 2x + 5

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.

total amount of money that he should pay if he has not used his duty free exemption is $98

step-by-step explanation:

given a united states citizen returning to the states declares the following items at the customs office: 3 shirts at $8.50 each 2 dresses at $27.50 each 1 pair of gold cuff links at $17.50 per pair. we have to find how much he pay

cost of 3 shirts if one cost at $8.50 is

cost of 2 dresses if one cost at $27.50 is  

cost of 1 pair of gold cuff at $17.50

so, total amount of money that he should pay if he has not used his duty free exemption is   $25.5+$55+$17.50=$98