(a−b)+a+(a+b)=45
⟹3a=45
a=15
a(a+b)=300
⟹15(15+b)=300
⟹225+15b=300
⟹15b=300−225
⟹15b15=7515
b=5
a−b=10⟹a=15⟹a+b=20
The three numbers are 10, 15, and 20.
Proof:
10+15+20=45✓
Answer:
(-1,-1)
Step-by-step explanation:
finding y
-6x + 5y = 1
+ (6x + 4y = -10)
---------------------------
9y = -9
y = -1
finding x
-6x + 5(-1) = 1
-6x - 5 = 1
+ 5 = +5
-6x = 6
x= -1
Answer:
21cm
Step by step:
Scale : 9cm :12m
Therefore 1m = 9/12 cm
28m= 9/12 *28 = <u>21 cm</u>
Answer:
<em>The range of f(x) is:</em>
![y\in\{-1,0,1\}](https://tex.z-dn.net/?f=y%5Cin%5C%7B-1%2C0%2C1%5C%7D)
Step-by-step explanation:
<u>Domain and Range</u>
Given a function y=f(x), the domain of f(x) is the set of values that x can take and the range of f(x) is the set of values that f gets when x is in the domain.
We have the function:
![\displaystyle f(x) = \frac{1}{2} x-2](https://tex.z-dn.net/?f=%5Cdisplaystyle%20f%28x%29%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20x-2)
And the domain is
![x\in\{2,4,6\}](https://tex.z-dn.net/?f=x%5Cin%5C%7B2%2C4%2C6%5C%7D)
Compute the range by assigning each value of x:
For x=2:
![\displaystyle f(2) = \frac{1}{2} \cdot 2-2=1-2=-1](https://tex.z-dn.net/?f=%5Cdisplaystyle%20f%282%29%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20%5Ccdot%202-2%3D1-2%3D-1)
![\displaystyle f(2) = -1](https://tex.z-dn.net/?f=%5Cdisplaystyle%20f%282%29%20%3D%20-1)
For x=4:
![\displaystyle f(4) = \frac{1}{2} \cdot 4-2=2-2=0](https://tex.z-dn.net/?f=%5Cdisplaystyle%20f%284%29%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20%5Ccdot%204-2%3D2-2%3D0)
![\displaystyle f(4) = 0](https://tex.z-dn.net/?f=%5Cdisplaystyle%20f%284%29%20%3D%200)
For x=6:
![\displaystyle f(6) = \frac{1}{2} \cdot 6-2=3-2=1](https://tex.z-dn.net/?f=%5Cdisplaystyle%20f%286%29%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20%5Ccdot%206-2%3D3-2%3D1)
![\displaystyle f(6) = 1](https://tex.z-dn.net/?f=%5Cdisplaystyle%20f%286%29%20%3D%201)
The range of f(x) is:
![y\in\{-1,0,1\}](https://tex.z-dn.net/?f=y%5Cin%5C%7B-1%2C0%2C1%5C%7D)
Answer:
y = 9
Step-by-step explanation:
To solve this question we will use the property of perpendicular lines,
![m_1\times m_2=-1](https://tex.z-dn.net/?f=m_1%5Ctimes%20m_2%3D-1)
Where
and
are the slopes of two lines perpendicular to each other.
Slope of a line passing through two points
and
is given by,
![m=\frac{y_2-y_1}{x_2-x_1}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D)
Slope of a line which passes through the points A(4, 2) and B(-1, y) will be
![m_1=\frac{y-2}{-1-4}](https://tex.z-dn.net/?f=m_1%3D%5Cfrac%7By-2%7D%7B-1-4%7D)
![=-\frac{y-2}{5}](https://tex.z-dn.net/?f=%3D-%5Cfrac%7By-2%7D%7B5%7D)
Slope of the line given in the graph [passing through (2, 4) and (-5, -1)]
![m_2=\frac{4+1}{2+5}](https://tex.z-dn.net/?f=m_2%3D%5Cfrac%7B4%2B1%7D%7B2%2B5%7D)
![m_2=\frac{5}{7}](https://tex.z-dn.net/?f=m_2%3D%5Cfrac%7B5%7D%7B7%7D)
From the property of perpendicular lines,
![\frac{-(y-2)}{5}\times \frac{5}{7}=-1](https://tex.z-dn.net/?f=%5Cfrac%7B-%28y-2%29%7D%7B5%7D%5Ctimes%20%5Cfrac%7B5%7D%7B7%7D%3D-1)
![\frac{5(y-2)}{35}=1](https://tex.z-dn.net/?f=%5Cfrac%7B5%28y-2%29%7D%7B35%7D%3D1)
5y - 10 = 35
5y = 45
y = 9