Answer:
True:
D.
E.
F
Step-by-step explanation:
First, you should know that the square of any odd number is also odd.
The easiest way to go about this is to plug in an odd number for n. Lets use 3:
Plug 3 into A:
Plug 3 into B:
Plug 3 into C:
Plug 3 into D:
Plug 3 into E:
Plug 3 into F:
Answer: The answer is 8.
Step-by-step explanation: The first step is to convert the expression into figures. We shall call the unknown number Y. So if we are told “the square of a number,” that means Y squared, or better still, Y^2. Further we are told “the difference between the square of a number and 40” and that can be written as;
Y^2 - 40.
Next we are told that this expression is equal to 3 times that number (that is 3Y). That can now be written out as follows,
Y^2 - 40 = 3Y
If we move all expressions to one side of the equation, what we would have is,
Y^2 - 3Y -40 = 0
(Remember that when a positive value crosses to the other side of an equation it becomes negative and vice versa)
We now have a quadratic equation
Y^2 -3Y - 40 = 0
By factorizing we now have
(Y -8) (Y + 5) = 0
Therefore Y - 8 = 0 or
Y + 5 = 0
Hence, Y = 8 or Y = -5
Since we are asked to calculate the positive solution, Y = 8
Part A
The first thing we must do in this case is to hide the slopes of each line.
line m:
m = (- 4-3) / (0 - (- 4))
m = -7 / 4
Line n:
n = (- 2-2) / (3-1)
n = -4 / 2
n = -2
Answer:
Lines m and n are not parallel because their slopes are different.
Part B:
We look for the slope of the K line:
k = (1 - (- 3)) / (4 - (- 3))
k = 4/7
We observe that it is true that:
k = -1 / m
Answer:
The lines are perpendicular.
Answer:
Step-by-step explanation:
In the first triangle, using Pythagorean's theorem, x^2+3^2=5^2, x = 4
In the second triangle, using Pythagorean's theorem, x^2+7^2=24^2, x = 25
In the third triangle, using Pythagorean's theorem, 8^2+15^2=x^2, x = 17
In the fourth triangle, using Pythagorean's theorem, x^2+8^2=10^2, x = 6
In the fifth triangle, using Pythagorean's theorem, 5^2+12^2=x^2, x = 13
