Complete the explanation to determine whether each statement is always, sometimes, or never true. If quadrilateral PQRS is a rho
mbus and one diagonal has a slope of 4, then the other diagonal has a slope of 1/4 .
The diagonals of a rhombus are , so the product of the slopes of the diagonals is . Therefore, the diagonals of a rhombus have slopes of 4 and
1/4 , since 4 · 1/4 −1. The statement is true.
First find common factor for parameters. I mean to find common factor number 9,15,12 first, write the divisors: Divisors of 9: 1,3,9 divisors of 12: 1,2,3,4,6,12 divisors of 15: 1,2,3,5,15 so see, that GCF of 9,12,15 is 3.
Now, count GCF of x^2, x^4, x^6 GCF 2,4,6 is 2, so the result is x^2 and know finally GCF these terms is
a difference of square is: a² - b² = (a - b)(a + b)
looking at the expression (5z+3)(-5z-3), we see that it does not fit the criteria of the breakdown of a perfect square, as (-5z-3) has a negative <em>a</em> term (-5z)
if we FOILed (5z+3)(-5z-3) out, we would get:
-25z² - 30z - 9, which is not a difference of squares
You are given a rectangle and are told that the length is 1 cm more than twice the width of the rectangle. The area of the rect. is also given, and is 21 cm^2.
Find the length and width. To do this, represent the length by y and the width by x. Then "1 cm more than twice the width" comes out to y=2x+1 (cm).
Since the area of a rect. is equal to the product of its length and width,
x(2x+1)=21 cm^2. Multiply out x(2x+1). show your work. Next, subtract 21 from both sides. Write your algebraic expression on the left side as a quadratic equation in standard form.
Solve this quadratic equation for x. Recall that x (in cm) will represent the width of the rect., and y=2x+1 (in cm) will repr. the length.