Answer:
Step-by-step explanation:
1. To find x make these 2 equations equivalent to each othe.

2. Subtract x terms from both sides

3. Subtract constant from left side.



4. Divide be x term from the left side.
<h3>
Answer:</h3>
B. 3x +y = 4
<h3>
Step-by-step explanation:</h3>
It is perhaps easiest to simply try the equations to see which one works.
For x=0, there are two different kinds of answers:
... A and C: -y = 4
... B and D: y = 4
Since we know y=4 when x=0 (from the point (0, 4)), we can eliminate choices A and C.
___
Using the point (1, 1), you can try choices B and D to see which works:
... B: 3·1 +1 = 4 . . . . true (put 1 where x and y are in the equation)
... D: -3·1 +1 = -2 = 4 . . . . false
The appropriate choice is the equation of B: 3x +y = 4.
_____
<em>Derive the equation from the given points</em>
There are several ways you can derive the equation. Since you have the y-intercept (the point with x=0), you can use the slope-intercept form to start.
The slope (m) is ...
... m = (change in y)/(change in x) = (4 -1)/(0 -1)
... m = -3
We know the y-intercept (b) is 4, so the slope-intercept form of the equation is ...
... y = mx +b
... y = -3x +4
Adding 3x puts this in standard form:
... 3x +y = 4
18x-8x2=0
Two solutions were found :
x = 9/4 = 2.250
x = 0
Step by step solution :
Step 1 :
Equation at the end of step 1 :
18x - 23x2 = 0
The smaller is the rounding factor, the more accurate the estimation is
532668 rounded to the nearest ten is 532670
532668 rounded to the nearest hundred is 532700
532668 rounded to the nearest thousand is 533000
532668 rounded to the nearest ten thousand is 530000
532668 rounded to the nearest hundred thousand is 500000
We can use either 532700 or 533000 as a reasonable estimate because these values don't give much difference to the original value
Answer:
(a) 2.29 km/h
(b) 9 km/h
Step-by-step explanation:
For part (a) you have to apply<em> the average speed formula</em>, which is defined by:

where d is the total distance traveled and t is the total time needed.
km/h
For part (b) you have to calculate the running time (T) , which is the total time of the race minus the nap time:
The nap time in hours is:
90/60 = 1.5 h (because there are 60 minutes in one hour)
The running time is:
T= 1.75 - 1.5 = 0.25 h
Let t1 represent the time before the nap and t2 the time after the nap:
t1+t2 = T
t1+t2 = 0.25
You have to apply the formula d=vt before and after the nap:
-Before the nap, the distance traveled was 0.50 km
0.50 = v1t1
-Afer the nap, the distance traveled was 3.50 km
3.50=v2t2
But v2=2v1 (because after the nap the rabbit runs twice as fast)
You have to solve the system of equations:
t1=0.25-t2 (I)
v1t1=0.50 (II)
2v1t2=3.50 (III)
Replacing (I) in (II)
v1(0.25-t2)=0.50
Applying distributive property and solving:
0.25v1-v1t2=.050
For (III) you have that v1t2=3.50/2=1.75. Hence:
0.25v1-1.75=0.50
Solving for v1:
v1 = 9 km/h