Hey there! :)
Answer:
Right 5, down 23
Step-by-step explanation:
Beginning with the parent function f(x) = x²:
Find the translations of the graph g(x) by completing the square to rewrite the equation in vertex form:
g(x) = x² - 10x + 2
-2 = x² - 10x
-2 + 25 = (x² - 10x + 25)
23 = (x - 5)²
Rewrite:
g(x) = (x - 5)² - 23
The translations that we can see from this equation in vertex form are a horizontal translation of 5 units right and 23 units down. Therefore:
Right 5, down 23 is the correct choice.
The answers are A. and B.
I'm pretty sure
5-(-1) or you could simplify it further to 6
Answer:
Step-by-step explanation:
The diagonals of the given parallelogram are QS and RT. We would first determine if its diagonals are congruent.
QS = √(1 - 5)² + (3 - 3)² = 16
RT = √(3 - 3)² + (4 - 2)² = 4
Since QS ≠ RT, it means that they are not congruent and this means that the parallelogram is not a rectangle.
Let us check if the diagonals are perpendicular.
Slope of QS = (3 - 3)/(5 - 1) = 0/4
Slope of RT = (2 - 4)/(3 - 3) = - 2/0
The slopes are not opposite reciprocals. It means that the diagonals are not perpendicular. Therefore, the correct option is
D. QRST is none of these because its diagonals are neither congruent nor perpendicular.
Answer:
The length of the rectangle is 120 feet.
Step-by-step explanation:
The perimeter of a rectangle can be found using the formula: P = 2W + 2L, where P = perimeter, W = width and L = length. Since we know the value of two of the three variables, we can plug them into the equation and solve for the missing value ('L'): 400 = 2(80) + 2L or 400 = 160 + 2L. Using inverse (opposite) operations to isolate the variable, we get: 400 - 160 = 160 - 160 + 2L or 240 = 2L. We then divide both sides of the equation by 2 to get rid of the coefficient: 240/2 = 2L/2 or 120 = L. So, the length of the rectangle is 120 feet.
