answer:To solve the system, we can use the method of substitution or elimination. Here, we'll use elimination by multiplying the second equation by 3 to make the coefficient of ( y ) equal in both equations: begin{align*} 15x + 21y &= 4 12x + 12y &= -42 quad text{(After multiplying by 3)} end{align*} Now, subtract the second equation from the first to eliminate ( y ): begin{align*} (15x + 21y) - (12x + 12y) &= 4 - (-42) 15x + 21y - 12x - 12y &= 4 + 42 3x + 9y &= 46 end{align*} Divide the entire equation by 3 to simplify: begin{align*} x + 3y &= frac{46}{3} x &= frac{46}{3} - 3y end{align*} Now, substitute this expression for ( x ) back into the second equation: begin{align*} 4left(frac{46}{3} - 3yright) + 4y &= -14 frac{184}{3} - 12y + 4y &= -14 frac{184}{3} - 8y &= -14 end{align*} Multiply through by 3 to clear the fraction: begin{align*} 184 - 24y &= -42 -24y &= -42 - 184 -24y &= -226 end{align*} Divide both sides by -24: begin{align*} y &= frac{-226}{-24} y &= frac{113}{12} end{align*} Now, substitute ( y ) back into the equation ( x = frac{46}{3} - 3y ): begin{align*} x &= frac{46}{3} - 3left(frac{113}{12}right) x &= frac{46}{3} - frac{339}{12} x &= frac{46 cdot 4}{3 cdot 4} - frac{339}{12} x &= frac{184}{12} - frac{339}{12} x &= frac{-155}{12} end{align*} The solution to the system is ( x = -frac{155}{12} ) and ( y = frac{113}{12} ). However, there seems to be an error in the provided answer. The correct values are: [ x = -frac{155}{12}, quad y = frac{113}{12} ]

answer:The FOIL method is a technique used to multiply two binomials. It can also be used to factor a binomial expression. Here's how to use the FOIL method to factor a binomial expression: 1. **Identify the two factors:** Let's say we have a binomial expression (a + b)(c + d). These are the two factors we need to multiply. 2. **Write out the FOIL acronym:** FOIL stands for First, Outer, Inner, Last. This represents the four terms that will be created when we multiply the two binomials. 3. **Multiply the First terms:** Multiply the first terms of each binomial, which are a and c in this example. This gives us ac. 4. **Multiply the Outer terms:** Multiply the outer terms of each binomial, which are a and d in this example. This gives us ad. 5. **Multiply the Inner terms:** Multiply the inner terms of each binomial, which are b and c in this example. This gives us bc. 6. **Multiply the Last terms:** Multiply the last terms of each binomial, which are b and d in this example. This gives us bd. 7. **Combine like terms:** Combine the four terms we obtained in steps 3-6. In this example, we have ac + ad + bc + bd. 8. **Factor the expression:** Look for common factors among the terms. In this example, we can factor out a common factor of (a + b) from the first two terms and a common factor of (c + d) from the last two terms. This gives us (a + b)(c + d). Therefore, the factors of the binomial expression (a + b)(c + d) are (a + b) and (c + d).

answer:** Given Data: {eq}n = 9 {/eq} {eq}SS = 72 {/eq} To find the sample variance for a sample: begin{align*} s^2 &= frac{SS}{n -1} [0.3cm] &= frac{72}{9-1} [0.3cm] &= frac{72}{8} [0.3cm] therefore Var(x) &= 9 end{align*} Hence, the sample variance for a sample is {eq}color{blue}{s^2=9.} {/eq} Let us find the estimated standard error for a sample: begin{align*} sM &= sqrt{frac{s^2}{n}} [0.3cm] &= sqrt{frac{9}{9}} [0.3cm] &= sqrt{1} [0.3cm] therefore sM &= 1 end{align*} Hence, the standard error for a sample is {eq}color{blue}{1} {/eq}. Therefore, the correct answer is {eq}color{blue}{b} {/eq}.

answer:Locke's political ideas were highly influential in the development of modern democracy. His emphasis on individual rights and limited government helped shape the American Revolution and the founding of the United States. English philosopher John Locke defended two key political ideas: 1. **Natural Rights:** Locke argued that all humans are born with certain fundamental rights, such as the right to life, liberty, and property. These rights are inherent and cannot be taken away by any government or authority. 2. **Social Contract:** Locke believed that governments are formed through a social contract between the people and the rulers. This contract is based on the consent of the governed, and it outlines the rights and responsibilities of both parties. If the government violates the terms of the contract, the people have the right to alter or abolish it.