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Nicholas wants to buy a $200 CD with a 3% annual percentage rate (APR), compounded quarterly. The CD will mature in 5 years, and he will receive the interest earned every quarter. How much interest will Nicholas have earned on this CD after the first quarter? A. $3.00 B. $6.00 C. $1.50 D. $0.75
Which word is derived from the Latin root that means "to run"? A) accumulate B) cosmonaut C) excursion D) reduce
How can the growth of a business lead to cultural diffusion? Take McDonald's as an example.
Which picture shows the figure before it was reflected over the line y = x?
In what cases would you denormalize tables in your database?
In one or two sentences, describe which is greater: gross pay or net pay.
Which is the correct total area for this cylinder?A) 1010.08 sq ftB) 1011.08 sq ftC) 1011.16 sq ftD) 1012.08 sq ft
which phrase is the best example of parallelism? A. She looked up to the sky.The sun was a blazing orange ball. B. The snow fell softly the sky. Soon, everything in sight was in a pillow of white. C. He collected rocks, pine cones, shells, twigs, and anything else he could find outside. D. The mud covered his hands. it covered his face. it covered his jeans.
Which was the first state to call for a special convention to consider secession?
To prove that the quadrilateral ABCD, with vertices A(2,1), B(1,3), C(-5,0), and D(-4,-2), is a rectangle, we need to demonstrate that it has four right angles and opposite sides that are equal in length. First, calculate the slopes of the sides to verify that consecutive sides are perpendicular, implying that all angles are right angles. The slope of line segment AB is given by: m_AB = (y2 - y1) / (x2 - x1) = (3 - 1) / (1 - 2) = 2 / -1 = -2. Similarly, calculate the slopes of the other sides: m_BC = (y_C - y_B) / (x_C - x_B) = (0 - 3) / (-5 - 1) = -3 / -6 = 1/2, m_CD = (y_D - y_C) / (x_D - x_C) = (-2 - 0) / (-4 - -5) = -2 / 1 = -2, m_DA = (y_A - y_D) / (x_A - x_D) = (1 - (-2)) / (2 - (-4)) = 3 / 6 = 1/2. Notice that slopes m_AB and m_CD are both -2, indicating AB and CD are parallel. Similarly, slopes m_BC and m_DA are both 1/2, indicating BC and DA are parallel. Additionally, the slopes of AB and BC, and CD and DA are negative reciprocals, implying that AB is perpendicular to BC and CD is perpendicular to DA, thus confirming that all angles are right angles. Next, verify that opposite sides are of equal length using the distance formula: d = √((x2 - x1)² + (y2 - y1)²). The length of side AB is: d_AB = √((1 - 2)² + (3 - 1)²) = √((-1)² + (2)²) = √(1 + 4) = √5. Calculate the lengths of the other sides: d_BC = √((-5 - 1)² + (0 - 3)²) = √((-6)² + (-3)²) = √(36 + 9) = √45, d_CD = √((-4 - -5)² + (-2 - 0)²) = √((1)² + (-2)²) = √(1 + 4) = √5, d_DA = √((2 - -4)² + (1 - -2)²) = √((6)² + (3)²) = √(36 + 9) = √45. The lengths of AB and CD are both √5, and the lengths of BC and DA are both √45, confirming that opposite sides are equal. Since both pairs of opposite sides are parallel and equal in length, and all four angles are right angles, quadrilateral ABCD is indeed a rectangle. To graph the rectangle, plot the points on a coordinate plane and draw lines connecting them in order, from A to B, B to C, C to D, and D back to A. Use graphing tools or software for precise visualization and to provide graphical evidence to support the analytical proof.
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