answer:To solve the given system of inequalities, we proceed as follows: 1. For the first inequality, 12 - 4x > -8: [ begin{align*} 12 - 4x &> -8 12 + 8 &> 4x 20 &> 4x 5 &> x x &< 5 end{align*} ] 2. For the second inequality, x + 3 geq 5: [ begin{align*} x + 3 &geq 5 x &geq 5 - 3 x &geq 2 end{align*} ] Combining these results, we find that the solution set for x must satisfy both conditions: 2 leq x < 5. The integer solutions that satisfy these conditions are 2, 3, and 4. Thus, there are a total of 3 integer solutions. Therefore, the correct answer is boxed{C}.

answer:To determine which of the given options can be calculated using the formula for the difference of squares, we analyze each option step by step: **Option A: (-x+y)(x+y)** We observe that this expression is in the form of (a+b)(a-b), where a=x and b=-y. However, to align it more closely with the standard form, we rewrite it as: (-x+y)(x+y) = -(x+y)(x-y) This manipulation shows that Option A can indeed be expressed in a form that resembles the difference of squares, albeit with an additional negative sign which does not affect the fundamental structure for the difference of squares. **Option B: (-x+y)(x-y)** This option simplifies as follows: (-x+y)(x-y) = -(x-y)(x-y) = -(x-y)^2 Here, we see that the expression results in the square of (x-y), negated. This is not a difference of squares but rather a square of a binomial. **Option C: (x+2)(2+x)** This simplifies to: (x+2)(2+x) = (x+2)^2 This expression is a perfect square, not a difference of squares. **Option D: (2x+3)(3x-2)** This expression does not fit the form (a+b)(a-b) directly and cannot be easily manipulated into the difference of squares formula. It involves two terms with different coefficients and does not simplify to a form that directly applies the difference of squares formula. Therefore, based on the analysis: - Option A can be manipulated into a form that resembles the difference of squares. - Options B, C, and D do not align with the formula for the difference of squares in their given forms. Hence, the correct answer is: boxed{A}

answer:To solve the equation, start by isolating (2^x): [ 5(2^x) = 320 ] Divide both sides by 5: [ 2^x = frac{320}{5} ] [ 2^x = 64 ] Since (64 = 2^6) (because (2 times 2 times 2 times 2 times 2 times 2 = 64)), we set the exponent of 2 equal to 6: [ x = boxed{6} ]

answer:1. **Identify the average population**: The average population per city is indicated by a horizontal dashed line on the bar chart, positioned between 3,200 and 3,600. Calculate the average by taking the midpoint: [ frac{3,200 + 3,600}{2} = 3,400 ] 2. **Calculate the total population**: There are 25 cities in the Metropolitan Area of Jackson. Using the average population per city calculated above: [ 25 times 3,400 = 85,000 ] 3. **Conclusion**: The total population of all 25 cities in the Metropolitan Area of Jackson is 85,000. The final answer is boxed{textbf{(C) }85{,}000}