Answer:
123 km/h
Step-by-step explanation:
the formula for the unit rate would be 82/40
82 divided by 40 is 2.05km/m
Then you have to convert 2.05 km/m to km/h
multiply 2.05 times 60 and your answer is 123 km/h
Let the point_1 = p₁ = (1,4)
and point_2 = p₂ = (-2,1)
and Point_3 = p₃ = (x,y)
The line from point_1 to point_2 is L₁ and has slope = m₁
The line from point_1 to point_3 is L₂ and has slope = m₂
m₁ = Δy/Δx = (1-4)/(-2-1) = 1
m₂ = Δy/Δx = (y-4)/(x-1)
L₁⊥L₂ ⇒⇒⇒⇒ m₁ * m₂ = -1
∴ (y-4)/(x-1) = -1 ⇒⇒⇒ (y-4)= -(x-1)
(y-4) = (1-x) ⇒⇒⇒⇒⇒⇒⇒⇒⇒⇒⇒⇒⇒⇒ equation (1)
The distance from point_1 to point_2 is d₁
The distance from point_1 to point_3 is d₂
d =
d₁ =
d₂ =
d₁ = d₂
∴
![\sqrt{(-2-1)^2+(1-4)^2} = \sqrt{(x-1)^2+(y-4)^2}](https://tex.z-dn.net/?f=%20%5Csqrt%7B%28-2-1%29%5E2%2B%281-4%29%5E2%7D%20%3D%20%5Csqrt%7B%28x-1%29%5E2%2B%28y-4%29%5E2%7D%20)
⇒⇒ eliminating the root
∴(-2-1)²+(1-4)² = (x-1)²+(y-4)²
(x-1)²+(y-4)² = 18
from equatoin (1) y-4 = 1-x
∴(x-1)²+(1-x)² = 18 ⇒⇒⇒⇒⇒ note: (1-x)² = (x-1)²
2 (x-1)² = 18
(x-1)² = 9
x-1 =
![\pm \sqrt{9} = \pm 3](https://tex.z-dn.net/?f=%5Cpm%20%5Csqrt%7B9%7D%20%3D%20%5Cpm%203)
∴ x = 4 or x = -2
∴ y = 1 or y = 7
Point_3 = (4,1) or (-2,7)
Answer:
In the given shapes above, we can see that all shapes have four sides.
Above geometrical shapes could be named as Rectangles, parallelogram or quadrilateral.
First two shapes are Rectangles.
Third is a parallelogram.
Fourth and fifth shapes are Rectangles again.
Also we can say all those shapes with four side as quadrilaterals. (Note: A quadrilateral has four sides.)
Below shown shape has only three sides in it.
It is called a triangle when a shape has three sided close figure.
So, we could drag : Not similar - Different Type of shape.
Answer:
1. Vertical shrink by a factor of ¹/₅
2. Right 5
3. Up 5
Step-by-step explanation:
Transformations of Graphs (functions) is the process by which a function is moved or resized to produce a variation of the original (parent) function.
<u>Transformations</u>
For a > 0
![f(x+a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units left}](https://tex.z-dn.net/?f=f%28x%2Ba%29%20%5Cimplies%20f%28x%29%20%5C%3A%20%5Ctextsf%7Btranslated%7D%5C%3Aa%5C%3A%5Ctextsf%7Bunits%20left%7D)
![f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}](https://tex.z-dn.net/?f=f%28x-a%29%20%5Cimplies%20f%28x%29%20%5C%3A%20%5Ctextsf%7Btranslated%7D%5C%3Aa%5C%3A%5Ctextsf%7Bunits%20right%7D)
![f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}](https://tex.z-dn.net/?f=f%28x%29%2Ba%20%5Cimplies%20f%28x%29%20%5C%3A%20%5Ctextsf%7Btranslated%7D%5C%3Aa%5C%3A%5Ctextsf%7Bunits%20up%7D)
![f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}](https://tex.z-dn.net/?f=f%28x%29-a%20%5Cimplies%20f%28x%29%20%5C%3A%20%5Ctextsf%7Btranslated%7D%5C%3Aa%5C%3A%5Ctextsf%7Bunits%20down%7D)
![y=a\:f(x) \implies f(x) \: \textsf{stretched parallel to the y-axis (vertically) by a factor of}\:a](https://tex.z-dn.net/?f=y%3Da%5C%3Af%28x%29%20%5Cimplies%20f%28x%29%20%5C%3A%20%5Ctextsf%7Bstretched%20parallel%20to%20the%20y-axis%20%28vertically%29%20by%20a%20factor%20of%7D%5C%3Aa)
![y=f(ax) \implies f(x) \: \textsf{stretched parallel to the x-axis (horizontally) by a factor of} \: \dfrac{1}{a}](https://tex.z-dn.net/?f=y%3Df%28ax%29%20%5Cimplies%20f%28x%29%20%5C%3A%20%5Ctextsf%7Bstretched%20parallel%20to%20the%20x-axis%20%28horizontally%29%20by%20a%20factor%20of%7D%20%5C%3A%20%5Cdfrac%7B1%7D%7Ba%7D)
![y=-f(x) \implies f(x) \: \textsf{reflected in the} \: x \textsf{-axis}](https://tex.z-dn.net/?f=y%3D-f%28x%29%20%5Cimplies%20f%28x%29%20%5C%3A%20%5Ctextsf%7Breflected%20in%20the%7D%20%5C%3A%20x%20%5Ctextsf%7B-axis%7D)
![y=f(-x) \implies f(x) \: \textsf{reflected in the} \: y \textsf{-axis}](https://tex.z-dn.net/?f=y%3Df%28-x%29%20%5Cimplies%20f%28x%29%20%5C%3A%20%5Ctextsf%7Breflected%20in%20the%7D%20%5C%3A%20y%20%5Ctextsf%7B-axis%7D)
Identify the transformations that take the parent function to the given function.
<u>Question 1</u>
![\textsf{Parent function}: \quad f(x)=x^3](https://tex.z-dn.net/?f=%5Ctextsf%7BParent%20function%7D%3A%20%5Cquad%20f%28x%29%3Dx%5E3)
![\textsf{Given function}: \quad f(x)=\dfrac{1}{5}x^3](https://tex.z-dn.net/?f=%5Ctextsf%7BGiven%20function%7D%3A%20%5Cquad%20f%28x%29%3D%5Cdfrac%7B1%7D%7B5%7Dx%5E3)
Comparing the parent function with the given function, we can see that the <u>parent function</u> has been <u>multiplied</u> by ¹/₅.
Therefore, the transformation is:
![y=\dfrac{1}{5}\:f(x) \implies f(x) \: \textsf{stretched parallel to the y-axis (vertically) by a factor of}\:\dfrac{1}{5}](https://tex.z-dn.net/?f=y%3D%5Cdfrac%7B1%7D%7B5%7D%5C%3Af%28x%29%20%5Cimplies%20f%28x%29%20%5C%3A%20%5Ctextsf%7Bstretched%20parallel%20to%20the%20y-axis%20%28vertically%29%20by%20a%20factor%20of%7D%5C%3A%5Cdfrac%7B1%7D%7B5%7D)
As 0 < a < 1, the transformation visually is a compression in the y-direction, so we can also say: Vertical shrink by a factor of ¹/₅
<u>Question 2</u>
![\textsf{Parent function}: \quad f(x)=x^3](https://tex.z-dn.net/?f=%5Ctextsf%7BParent%20function%7D%3A%20%5Cquad%20f%28x%29%3Dx%5E3)
![\textsf{Given function}: \quad f(x)=(x-5)^3](https://tex.z-dn.net/?f=%5Ctextsf%7BGiven%20function%7D%3A%20%5Cquad%20f%28x%29%3D%28x-5%29%5E3)
Comparing the parent function with the given function, we can see that 5 has been <u>subtracted from the x-value</u> of the parent function.
Therefore, the transformation is:
![f(x-5) \implies f(x) \: \textsf{translated}\:5\:\textsf{units right}](https://tex.z-dn.net/?f=f%28x-5%29%20%5Cimplies%20f%28x%29%20%5C%3A%20%5Ctextsf%7Btranslated%7D%5C%3A5%5C%3A%5Ctextsf%7Bunits%20right%7D)
<u>Question 3</u>
![\textsf{Parent function}: \quad f(x)=x^3](https://tex.z-dn.net/?f=%5Ctextsf%7BParent%20function%7D%3A%20%5Cquad%20f%28x%29%3Dx%5E3)
![\textsf{Given function}: \quad f(x)=x^3+5](https://tex.z-dn.net/?f=%5Ctextsf%7BGiven%20function%7D%3A%20%5Cquad%20f%28x%29%3Dx%5E3%2B5)
Comparing the parent function with the given function, we can see that 5 has been <u>added to the parent function</u>.
Therefore, the transformation is:
![f(x)+5 \implies f(x) \: \textsf{translated}\:5\:\textsf{units up}](https://tex.z-dn.net/?f=f%28x%29%2B5%20%5Cimplies%20f%28x%29%20%5C%3A%20%5Ctextsf%7Btranslated%7D%5C%3A5%5C%3A%5Ctextsf%7Bunits%20up%7D)
Learn more about graph transformations here:
brainly.com/question/27845947
There's nothing u can do to that equation it's in its simplista form