Answer:
6 years
Step-by-step explanation:
So each person's age can be represented as a linear equation, since each year our age increases by 1. It can be represented in the slope-intercept form: y=mx+b. The slope in this case is going to be 1, since the time is going to be years, and each year everyone's age goes up by 1 (of course if you're still alive...) and y-intercept in this case represents their current age.
So the father can be represented as: y=x+38
The sons can be represented as: y = x+13 and y=x+5
The daughter can be represented as: y=x+8
So adding up all his children you get:
(x+13)+(x+5)+(x+8)
This gives you the equation:
3x+26
Now set this equal to the father's age to solve for x (in this context it's years)
3x+26=x+38
Subtract from both sides
2x+26=38
Subtract 26 from both sides
2x=12
Divide both sides by 2
x=6
So in 6 years the father will be the same age as his children put together
Answer:
S= z (y-x)/(x+y)
Step-by-step explanation:
Lets the speed of high speed train = u
Lets the regular speed train = v
We know that
Distance = Speed x time
For high speed train
z = u .x
u= z/x ----------1
For regular speed train
z = v .y
v = z/y -------------2
Both are traveling in opposite direction so relative speed
Vr = z / x+ z /y
Lets in time t they will meet
z = (z / x+ z /y) t
t= xy/ (x+y)
Lets take distance cover by high speed train is m when it moves A to B and speed cover by regular train is n when it is moving B to A.They meet at time t.
m = u .t
m = z / x .xy/ (x+y)
m = zy/ (x+y) -----------3
n = v .t
n = z / y .xy/ (x+y)
n = zx/ (x+y) -----------4
From equation 3 and 4
So
m - n= zy/ (x+y) - zx/ (x+y)
S= z (y-x)/(x+y)
Option a is correct.
A+b=32
a-b=8
let's subtract bottom equation from the top:
a+b-(a-b)=32-8
2b=24
b=12
Then a=20
Answer:
-2+2x=y
Step-by-step explanation:
got it correct on imagine math
Answer:
A. A reflection over the x-axis and a vertical stretch.
Step-by-step explanation:
Let 
, to obtain 
, we need to use the following two operations:
(i) Vertical stretch
, 
(ii) Reflection over the x-axis
Let prove both transformations in 
:
Step 1 - Vertical stretch (
)
Step 2 - Reflection over the x-axis
Hence, correct answer is A.
