Answer:
A(2,2)
Step-by-step explanation:
Let the vertex A has coordinates 
Vectors AB and AB' are perpendicular, then
Vectors AC and AC' are perpendicular, then
Now, solve the system of two equations:
Subtract these two equations:
Substitute it into the first equation:
Then
Rotation by 90° counterclockwise about A(2,2) gives image points B' and C' (see attached diagram)
Answer:
3x^2 (5x^3 + 4x^2 - 8x - 1)
Step-by-step explanation:
The given expression is 15x^5 + 12x^4-24x^3-3x^2
Here we have to find the GCF of all the above terms.
The GCF is 3x^2, let's take out 3x^2 and write the remaining terms in the parenthesis.
15x^5 + 12x^4-24x^3-3x^2
=3x^2 (5x^3 + 4x^2 - 8x - 1)
Therefore, the factors are 3x^2 and (5x^3 + 4x^2 -8x -1).
15x^5 + 12x^4-24x^3-3x^2 = 3x^2 (5x^3 + 4x^2 -8x -1)
Thank you.
Answer:
Expression is 8(n+2)
Step-by-step explanation:
smallest of 4 consecutive odd numbers =2n + 1
consecutive odd integers are found by adding 2 to the any given odd numbers
Thus, 2nd consecutive odd integers = 2n + 1 + 2 = 2n + 3
3rd consecutive odd integers = 2n + 3 + 2 = 2n + 5
2nd consecutive odd integers = 2n + 5 + 2 = 2n + 7
Thus, 4 consecutive odd integers are
2n + 1 ,2n + 3,2n + 5,2n + 7
sum of these numbers are = 2n + 1 +2n + 3 + 2n + 5+2n + 7 = 8n+16
sum of these numbers are = 8(n+2)
Thus, we see that the sum of numbers are 8(n+2)
As, 8 is common for n+2, whatever is value of n, the number will be multiple of 8 .
thus expression is 8(n+2)
x - 5y = -5, -5x - 25y = 25
First, you'll need to get the x variable by itself.
x - 5y = -5<u>
</u><u> +5 +5</u><u>
</u> x = 0
So x is plotted on the 0.
For the second part of the first equation, you'll be looking for what the y variable represents.
x - 5y = -5
<u>-x -x</u><u>
</u> <u>-5y</u> = <u>-5</u><u>
</u><u> 5 5</u><u>
</u> y = 1
So y is plotted on the 1 on the vertical line above the 0.
For the first part of the second equation, you'll do the same thing as in the first equation.
-5x - 25y = 25
<u> +25 +25</u><u>
</u> <u>-5x</u> = <u>50</u><u>
</u> 5 5
x = 10
So the x for this equation is plotted on 10 on the horizontal line.
For the second part of the second equation, you will do the same thing as in the first equation.
-5x - 25y = 25
<u>+5 +5</u><u>
</u> <u>-25y</u> = <u>30</u><u>
</u> 25 25
y = 1.2
So the y for the second half of the second question is plotted on 1.2 on the vertical line.
<h2>
Answer: B) Perpendicular</h2>
Perpendicular means the lines may or may not be of equal length and they will not be perfectly in line with each other.
Parallel means the lines may or may not be of equal length but will be perfectly in line with each other.
Intersecting means the lines may or may not be of equal length but will touch each other.
The gcf of both 6 and 48 is 6. So, in simplest form, the ration would be: 1:6 or 1 hour:6 minutes :)
