Hey There!!
The answer to this is: A quadrilateral has vertices A(3, 5), B(2, 0), C(7, 0), and D(8, 5). Which statement about the quadrilateral is true?" Line BC is parallel to line AD because their slopes is equal i.e. (0 - 0) / (7 - 2) = (5 - 5) / (8 - 3) which gives 0 / 5 = 0 / 5 giving that 0 = 0. We check whether line AB is parallel to line CD. Slope of line AB is given by (0 - 5) / (2 - 3) = -5 / -1 = 5. Slope of line CD is given by (5 - 0) / (8 - 7) = 5 / 1 = 5 We have been able to prove that the opposite sides of the quadrilateral are parallel which means that the quadrilateral is not a trapezoid. Next we check whether the length of the sides are equal. Length of line AB is given by sqrt[(0 - 5)^2 + (2 - 3)^2] = sqrt[(-5)^2 + (-1)^2] = sqrt(25 + 1) = sqrt(26) Length of line BC is given by sqrt[(0 - 0)^2 + (7 - 2)^2] = sqrt[0^2 + 5^2] = sqrt(25) = 5 Length of line CD is given by sqrt[(5 - 0)^2 + (8 - 7)^2] = sqrt[5^2 + 1^2] = sqrt(25 + 1) = sqrt(26) Length of line DA is given by sqrt[(5 - 5)^2 + (8 - 3)^2] = sqrt[0^2 + 5^2] = sqrt(25) = 5 Thus, the length of the sides of the quadrilateral are not equal but opposite sides are equal which means that the quadrilateral is not a rhombus. Finally, we check whether adjacent lines are perpendicular. Recall the for perpendicular lines, the product of their slopes is equal to -1. Slope of line AB = 5 while slope of line BC = 0. The product of their slopes = 5 x 0 = 0 which is not -1, thus the adjacent sides of the quadrilateral are not perpendicular which means that the quadrilateral is not a rectangle. Therefore, ABCD is a parallelogram with non-perpendicular adjacent sides. Thus, For (option A).
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ItsNobody~ ☆
Answer:
5(2x-7)=5
10x-35 = 5
10x=40
40/10 = 4
x=4
Step-by-step explanation:
4x+18=7x-12
We move all terms to the left:
4x+18-(7x-12)=0
We get rid of parentheses
4x-7x+12+18=0
We add all the numbers together, and all the variables
-3x+30=0
We move all terms containing x to the left, all other terms to the right
-3x=-30
x=-30/-3
x=+10
Hope this helps :)
You're right! Product of slopes of perpendicular lines must be -1
Answer: The answer is (B) 2x + 3(3x – 5) = 51
.
Step-by-step explanation: We are given three options and we are to select which choice shows the result of substituting 3x – 5 into the second equation for y.
So, y = 3x - 5.
Since the standard form of a linear equation i two variables is ax + by = c, so the second equation as given in the options must be of the form 2x + 3y = 51.
If we substitute y = 3x - 5, then this equation becomes
2x + 3(3x - 5) = 51.
Thus, (B) 2x + 3(3x – 5) = 51 is the correct option.