Question

2.

1. evaluate $-2x^2 + 4xy - y^2$, when $x = -2$ and $y = 4$.
2. find the amount to be repaid with a principal of $1000 borrowed at a simple interest rate of 8% for 2 years. use the formula $a = p(1 + rt)$.

equations, absolute value equations, inequalities, compound inequaliti

Explanation:

Problem 3: Evaluate \(-2x^{2}+4xy - y^{2}\), when \(x=-2\) and \(y = 4\)

Step 1: Substitute \(x=-2\) and \(y = 4\) into the expression

Substitute \(x=-2\) and \(y = 4\) into \(-2x^{2}+4xy - y^{2}\), we get:
\(-2\times(-2)^{2}+4\times(-2)\times4-4^{2}\)

Step 2: Calculate each term

First, calculate \((-2)^{2}=4\), so \(-2\times(-2)^{2}=-2\times4=-8\)
Second, calculate \(4\times(-2)\times4=-32\)
Third, calculate \(4^{2} = 16\), so \(-4^{2}=-16\)

Step 3: Sum up the terms

Add the three terms together: \(-8+(-32)+(-16)=-8 - 32-16=-56\)

Step 1: Identify the values of \(p\), \(r\) and \(t\)

We know that \(p = 1000\) (principal), \(r=8\%=0.08\) (interest rate), \(t = 2\) (time in years)

Step 2: Substitute the values into the formula

Substitute \(p = 1000\), \(r=0.08\) and \(t = 2\) into \(A=p(1+rt)\)
We get \(A=1000\times(1 + 0.08\times2)\)

Step 3: Calculate the value inside the parentheses

First, calculate \(0.08\times2 = 0.16\), then \(1+0.16 = 1.16\)

Step 4: Calculate the final amount

Multiply \(1000\) by \(1.16\): \(A=1000\times1.16 = 1160\)

Answer:

\(-56\)

Problem 4: Find the amount to be repaid with a principal of \(\$1000\) borrowed at a simple interest rate of \(8\%\) for \(2\) years. Use the formula \(A=p(1 + rt)\)