Question

simplify each expression.

1. $4x + 5x$
2. $32y - 5y$
3. $4c^2 + 5c + 2c$
4. $5d^2 - 3d^2 + d$
5. $5f^2 + 2f + f^2$
6. $7x + 8x^2 - 3y$
7. $3(p + 9q - 2 + 9) + 14p$ 25. $6b + 6b^2 + 4b^3$
8. $2(a^2 + 2b + 2a^2) + b + 2c$
9. geometry write an expression for the perimeter of the given triangle. then evaluate the perimeter when $n$ is 1, 2, 3, 4, and 5.

$n$	1	2	3	4	5

(image of a triangle with sides $4n$, $6n$, $5n$)

Explanation:

Step1: Find the perimeter formula

The perimeter of a triangle is the sum of its three sides. The sides are \(4n\), \(5n\), and \(6n\). So the perimeter \(P = 4n + 5n + 6n\).
Combine like terms: \(4n+5n + 6n=(4 + 5+6)n=15n\).

Step2: Evaluate for \(n = 1\)

Substitute \(n = 1\) into \(P = 15n\): \(P=15\times1 = 15\).

Step3: Evaluate for \(n = 2\)

Substitute \(n = 2\) into \(P = 15n\): \(P=15\times2=30\).

Step4: Evaluate for \(n = 3\)

Substitute \(n = 3\) into \(P = 15n\): \(P=15\times3 = 45\).

Step5: Evaluate for \(n = 4\)

Substitute \(n = 4\) into \(P = 15n\): \(P=15\times4=60\).

Step6: Evaluate for \(n = 5\)

Substitute \(n = 5\) into \(P = 15n\): \(P=15\times5 = 75\).

Answer:

The expression for the perimeter is \(15n\). When \(n = 1\), perimeter is \(15\); \(n = 2\), perimeter is \(30\); \(n = 3\), perimeter is \(45\); \(n = 4\), perimeter is \(60\); \(n = 5\), perimeter is \(75\).