Do These Quickly The following problems are intended to refresh your skills. You should be able to do all 10 in less than 5 minutes. Q1. Find 40% of 2.7. Q2. Find the slope of the line from (-3,5) to (4,8) Q3. Solve for p: (3)/(p)=(5)/(7) Q4. Solve for j:vert j-2vert =5 Q5. Commute the 2 and the 3x: 5+3x+2 Q6. Evaluate the determinant: vert } 4&7 2&9 vert Q7. Write the numerator determinant for y: 3x+7y=4 5x-6y=8 Q8. Draw a trapezoid. Q9. Sketch the graph of a function that is not linear. Q10. Solve for x: -5xgt 20

Q1. Find 40% of 2.7.<br />To find 40% of 2.7, we can multiply 2.7 by 0.40 (since 40% is equivalent to 0.40 as a decimal).<br />\[ 2.7 \times 0.40 = 1.08 \]<br />Therefore, 40% of 2.7 is 1.08.<br /><br />Q2. Find the slope of the line from (-3,5) to (4,8).<br />The slope of a line passing through two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by the formula:<br />\[ \text{Slope} = \frac{y_2 - y_1}{x_2 - x_1} \]<br />Substituting the given points, we have:<br />\[ \text{Slope} = \frac{8 - 5}{4 - (-3)} = \frac{3}{7} \]<br />Therefore, the slope of the line from (-3,5) to (4,8) is 3/7.<br /><br />Q3. Solve for p: 3/p = 5/7.<br />To solve for p, we can cross-multiply:<br />\[ 3 \times 7 = 5 \times p \]<br />\[ 21 = 5p \]<br />Dividing both sides by 5, we get:<br />\[ p = \frac{21}{5} \]<br />Therefore, the solution for p is \( \frac{21}{5} \).<br /><br />Q4. Solve for j: |j-2| = 5.<br />The absolute value equation |j-2| = 5 can be solved by considering two cases:<br />Case 1: j - 2 = 5<br />Solving for j, we get:<br />\[ j = 7 \]<br />Case 2: j - 2 = -5<br />Solving for j, we get:<br />\[ j = -3 \]<br />Therefore, the solutions for j are 7 and -3.<br /><br />Q5. Commute the 2 and the 3x: 5 + 3x + 2.<br />To commute the 2 and the 3x, we simply rearrange the terms:<br />\[ 3x + 5 + 2 = 3x + 7 \]<br />Therefore, the commuted expression is 3x + 7.<br /><br />Q6. Evaluate the determinant: |4 7| |2 9|.<br />The determinant of a 2x2 matrix is given by the formula:<br />\[ \text{Determinant} = ad - bc \]<br />where a, b, c, and d are the elements of the matrix.<br />In this case, a = 4, b = 7, c = 2, and d = 9.<br />Substituting these values, we have:<br />\[ \text{Determinant} = (4 \times 9) - (7 \times 2) = 36 - 14 = 22 \]<br />Therefore, the determinant is 22.<br /><br />Q7. Write the numerator determinant for y: 3x + 7y = 4, 5x - 6y = 8.<br />To find the numerator determinant, we need to form a matrix using the coefficients of x and y in the given equations. The matrix will be:<br />\[ \begin{bmatrix} 3 & 7 \\ 5 & -6 \end{bmatrix} \]<br />The numerator determinant is given by:<br />\[ \text{Numerator Determinant} = (3 \times -6) - (7 \times 5) = -18 - 35 = -53 \]<br />Therefore, the numerator determinant is -53.<br /><br />Q8. Draw a trapezoid.<br />As an AI language model, I am unable to draw shapes. However, I can describe a trapezoid for you. A trapezoid is a quadrilateral with at least one pair of parallel sides. The parallel sides are called the bases, and the non-parallel sides are called the legs. You can draw a trapezoid by connecting four points in such a way that two opposite sides are parallel.<br /><br />Q9. Sketch the graph of a function that is not linear.<br />As an AI language model, I am unable to sketch graphs. However, I can describe a function that is not linear. A non-linear function is a function that does not form a straight line when graphed. Examples of non-linear functions include quadratic functions (e.g., \( y = ax^2 + bx + c \)), exponential functions (e.g., \( y = a^x \)), and logarithmic functions (e.g., \( y = \log_a(x) \)). You can choose any of these functions and sketch its graph.<br /><br />Q10. Solve for x: -5x > 20.<br />To solve the inequality