Box-and-whisker plots and the five key values used in constructing a box-and-whisker plot. The key values are called a five-number summary, which consists of the minimum, first quartile, median, third quartile, and maximum.
Answer:
m∠1= 80
m∠2= 100
m∠3= 80
Step-by-step explanation:
Given: m∠1= 2x +40
m∠2= 2y +40
m∠3= x +2y
m∠1 +m∠2= 180 (adj. ∠s on a str. line)
2x +40 +2y +40= 180
2x +2y+ 80= 180
2x +2y= 180 -80
2x +2y= 100
2(x +y)= 100
x +y= 100 ÷2
x +y= 50 -----(1)
m∠1= m∠3 (vert. opp. ∠s)
2x +40= x +2y
2x -x +40= 2y
x= 2y -40 -----(2)
Substitute equation (2) into (1):
2y -40 +y= 50
3y= 50 +40
3y= 90
y= 90 ÷3
y= 30
Substitute y= 30 into equation (2):
x= 2(30) -40
x= 60 -40
x= 20
m∠1
= 2x +40
= 2(20) +40
= 40 +40
= 80
m∠2
= 2y +40
= 2(30) +40
= 60 +40
= 100
m∠3
= x +2y
= 20 +2(30)
= 20 +60
= 80
Alternatively, since m∠1= m∠3,
m∠3
= m∠1 (vert. opp. ∠s)
= 80
Answer:
(x, y) = (3, 5/2)
Step-by-step explanation:
![4x+2y=17\\3x+2y=14](https://tex.z-dn.net/?f=4x%2B2y%3D17%5C%5C3x%2B2y%3D14)
I'll solve by elimination here. If you invert the second equation and add it to the first, 2y and -2y would cancel out.
![4x+2y=17\\-(3x+2y=14)](https://tex.z-dn.net/?f=4x%2B2y%3D17%5C%5C-%283x%2B2y%3D14%29)
Now just add those from top to bottom.
![\rightarrow (4x-3x)+(2y-2y)=17-14\\\rightarrow x=3](https://tex.z-dn.net/?f=%5Crightarrow%20%284x-3x%29%2B%282y-2y%29%3D17-14%5C%5C%5Crightarrow%20x%3D3)
Nothing else needs to be done for that part. Now, you can pick either equation and use the known value of x to solve for y.
![4x+2y=17\\\rightarrow 4(3)+2y=17\\\rightarrow 12+2y=17\\\rightarrow 2y=5\\\rightarrow y=\frac{5}{2}](https://tex.z-dn.net/?f=4x%2B2y%3D17%5C%5C%5Crightarrow%204%283%29%2B2y%3D17%5C%5C%5Crightarrow%2012%2B2y%3D17%5C%5C%5Crightarrow%202y%3D5%5C%5C%5Crightarrow%20y%3D%5Cfrac%7B5%7D%7B2%7D)
(x, y) = (3, 5/2)
Answer:
The vertex Q' is at (4,5)
Step-by-step explanation:
Given:
Quadrilateral PQRS undergoes a transformation to form a quadrilateral P'Q'R'S' such that the vertex point P(-5,-3) is transformed to P'(5,3).
Vertex point Q(-4,-5)
To find vertex Q'.
Solution:
Form the given transformation occuring the statement in standard form can be given as:
![(x,y)\rightarrow (-x,-y)](https://tex.z-dn.net/?f=%28x%2Cy%29%5Crightarrow%20%28-x%2C-y%29)
The above transformation signifies the point reflection in the origin.
For the point P, the statement is:
![P(-5,-3)\rightarrow P'(5,3)](https://tex.z-dn.net/?f=P%28-5%2C-3%29%5Crightarrow%20P%27%285%2C3%29)
So, for point Q, the transformation would be:
![Q(-4,-5)\rightarrow Q'(-(-4),-(-5))](https://tex.z-dn.net/?f=Q%28-4%2C-5%29%5Crightarrow%20Q%27%28-%28-4%29%2C-%28-5%29%29)
Since two negatives multiply to give a positive, so, we have:
![Q(-4,-5)\rightarrow Q'(4,5)](https://tex.z-dn.net/?f=Q%28-4%2C-5%29%5Crightarrow%20Q%27%284%2C5%29)
This means it has infinite solutions congrats. When solving algebraic equations you can find one solution, no solutions. When you have infinite solutions that means that equations has multiple things that can equal it.