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Mathematics

(2x+8)(5x-7) A.36x-56 B.10x^2-56 C.10x^2+26x-56 D.10x^2+54x+56

In order to make 6 dozen cookies, you must use 3 eggs in the batter. How many eggs would be required to make 48 dozen cookies? Use a proportion to solve. A 3 B 96 C 8 D 24

Mrs. Del Pup bought 20 yards of border for her classroom bulletin board. a. What is the greatest rectangular area she can frame with the border?b. What are the dimensions of the rectangle with greatest area?c. If each dimension of the above rectangle were increased by 2 yards, what would be the dimensions and area of the new rectangle?d. How much more is the new area?​

An electrician charges a set fee of $100 for every house call and then charges an additional hourly rate. One day, the electrician earned a total of $250 for a 2-hour job. Write an equation for the function C(t), representing the total cost of the electrician's services if the electrician spends two hours in the house working.

Simplify this equation 6√40 -2√90 +3√160

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.

how much larger is 8,000,000 than 200 ?​

Find the LCM of 13 and 52

5y+10=6x+6 solve for y

How would you get the ancwer to stephanie ran 1 lap in 6 minutes .At this rate, how far would she run in 30 minutes

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