Question

The perimeter of triangle ABC is given by the expression 3x2 - 7x + 2.

Answer 1

Answer:

Perimeter of ABC = AB + BC+AC. Replace letters with equations.

3x^2-7x+2 = 2x^2-10x+6 + x^2-x-4 + AC = 3x^2-11x+2 + AC.

AC = 4x;

Answer 2

Question 1:

For this case we must simplify the following expression:

$(6k-k ^ 2 + 6) - (5 + 7k + 6k ^ 2) - (1 + 3k ^ 2-4k)$

We eliminate the parentheses taking into account that:

$- * + = -\\- * - = +\\6k-k ^ 2 + 6-5-7k-6k ^ 2-1-3k ^ 2 + 4k =$

We group similar terms:

$-k ^ 2-6k ^ 2-3k ^ 2 + 6k-7k + 4k + 6-5-1 =$

We take into account that:

Same signs add up and the same sign is placed

Different signs are subtracted and the major sign is placed

$-10k ^ 2 + 3k + 0 =\\-10k ^ 2 + 3k$

Answer:

$-10k ^ 2 + 3k$

Question 2:

For this case we must simplify the following expression:

$(5a^4-2a^2-6a^3)+(2a-3a^3-a^4)-(7a+6a^4-5a^3)$

We eliminate the parentheses taking into account that:

$- * + = -\\- * - = +\\5a^4-2a^2-6a^3+2a-3a^3-a^4-7a-6a^4+5a^3=$

We group similar terms:

$5a^4-a^4-6a^4-6a^3-3a^3+5a^3-2a^2+2a-7a=$

We take into account that:

Same signs add up and the same sign is placed

Different signs are subtracted and the major sign is placed

$-2a ^ 4-4a ^ 3-2a ^ 2-5a$

Answer:

$-2a ^ 4-4a ^ 3-2a ^ 2-5a$

Question 3:

For this case we must simplify the following expression:

$(3k ^ 4 + k ^ 2-5 + 3k) + (1-5k + 4k ^ 4-8k ^ 3) + (5 + k ^ 2-3k ^ 4 + 3k)$

We eliminate the parentheses taking into account that:

$- * + = -\\- * - = +\\3k ^ 4 + k ^ 2-5 + 3k + 1-5k + 4k ^ 4-8k ^ 3 + 5 + k ^ 2-3k ^ 4 + 3k =$

We group similar terms:

$3k ^ 4 + 4k ^ 4-3k ^ 4-8k ^ 3 + k ^ 2 + k ^ 2 + 3k-5k + 3k-5 + 1 + 5 =$

We take into account that:

Same signs add up and the same sign is placed

Different signs are subtracted and the major sign is placed

$4k ^ 4-8k ^ 3 + 2k ^ 2 + k + 1$

ANswer:

$4k ^ 4-8k ^ 3 + 2k ^ 2 + k + 1$

Question 4:

For this case we must simplify the following expression:

$(4v-7-7v ^ 2-5v ^ 4) + (2v ^ 3-4 + 2v-8v ^ 2) + (8v-6v ^ 3-1 + 4v ^ 2)$

We eliminate the parentheses taking into account that:

$- * + = -\\- * - = +\\4v-7-7v ^ 2-5v ^ 4 + 2v ^ 3-4 + 2v-8v ^ 2 + 8v-6v ^ 3-1 + 4v ^ 2 =$

We group similar terms:

$-5v ^ 4 + 2v ^ 3-6v ^ 3-7v ^ 2-8v ^ 2 + 4v ^ 2 + 4v + 2v + 8v-7-4-1 =$

We take into account that:

Same signs add up and the same sign is placed

Different signs are subtracted and the major sign is placed

$-5v ^ 4-4v ^ 3-11v ^ 2 + 14v-12$

Answer:

$-5v ^ 4-4v ^ 3-11v ^ 2 + 14v-12$

Question 5:

For this case we have that by definition, the perimeter of the triangle will be given by the sum of its sides. That is to say:

$3x ^ 2-7x + 2 = (2x ^ 2-10x + 6) + (x ^ 2-x-4) + AC$

We simplify the right side of the equation:

$3x ^ 2-7x + 2 = 2x ^ 2-10x + 6 + x ^ 2-x-4 + AC\\3x ^ 2-7x + 2 = 3x ^ 2-11x + 4 + AC$

We cleared AC:

$AC = 3x ^ 2-7x + 2- (3x ^ 2-11x + 4)\\- * + = -\\- * - = +\\AC = 3x ^ 2-7x + 2-3x ^ 2 + 11x-4\\AC = 4x-2$

Answer:

$AC = 4x-2$