Answer: ![(-5,-4)](https://tex.z-dn.net/?f=%28-5%2C-4%29)
Step-by-step explanation:
I assume that you need the new coordinates of the point after the rotation centered at the origin.
For this exercise it is important to remember the definition of "Rotation".
A Rotation is defined as a transformation which a figure is rotated about a fixed point known as "Center of rotation".
The figure before the transformation is called Pre-Image and the figure obtained after the transformation is called "Image".
The 180 degree rotation about the origin Rule states that:
→ ![(-x, -y)](https://tex.z-dn.net/?f=%28-x%2C%20-y%29)
Therefore, knowing that the given point (5,4) is rotated 180 degrees clockwise about the origin, you can conclude that its Image is:
![(-5,-4)](https://tex.z-dn.net/?f=%28-5%2C-4%29)
Answer: The equation is y = 4x+3
Slope = 4
y intercept = 3
========================================================
Explanation:
Let's start off by finding the slope.
![A = (x_1,y_1) = (0,3) \text{ and } B = (x_2,y_2) = (4,19)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{19 - 3}{4 - 0}\\\\m = \frac{16}{4}\\\\m = 4\\\\](https://tex.z-dn.net/?f=A%20%3D%20%28x_1%2Cy_1%29%20%3D%20%280%2C3%29%20%5Ctext%7B%20and%20%7D%20B%20%3D%20%28x_2%2Cy_2%29%20%20%3D%20%284%2C19%29%5C%5C%5C%5Cm%20%3D%20%5Cfrac%7By_%7B2%7D%20-%20y_%7B1%7D%7D%7Bx_%7B2%7D%20-%20x_%7B1%7D%7D%5C%5C%5C%5Cm%20%3D%20%5Cfrac%7B19%20-%203%7D%7B4%20-%200%7D%5C%5C%5C%5Cm%20%3D%20%5Cfrac%7B16%7D%7B4%7D%5C%5C%5C%5Cm%20%3D%204%5C%5C%5C%5C)
The slope is 4.
The y intercept is 3 because of the point (0,3)
We go from y = mx+b to y = 4x+3
m = slope
b = y intercept
---------------
Check:
Plug in x = 0 and we should get to y = 3
y = 4x+3
y = 4(0)+3
y = 0+3
y = 3
That works out. Now try x = 4. It should lead to y = 19
y = 4x+3
y = 4(4)+3
y = 16+3
y = 19
The answer is confirmed.
Answer:
3
Step-by-step explanation:
f^-1 (-3)
-1 times 3
And so the solution is 3
Hope this helps! :)
Answer:
25 %
Step-by-step explanation:
Percentage is given by :
![\%=\dfrac{\text{original value-new value}}{\text{origial value}}\times 100](https://tex.z-dn.net/?f=%5C%25%3D%5Cdfrac%7B%5Ctext%7Boriginal%20value-new%20value%7D%7D%7B%5Ctext%7Borigial%20value%7D%7D%5Ctimes%20100)
Original cost of sweater is $32 and sale cost is $24. So,
![\%=\dfrac{32-24}{32}\times 100\\\\=25\%](https://tex.z-dn.net/?f=%5C%25%3D%5Cdfrac%7B32-24%7D%7B32%7D%5Ctimes%20100%5C%5C%5C%5C%3D25%5C%25)
Hence, 25 % is the markdown on the sweater.