I will give you everything I can do:
11)
Lets say Car A travels at x mph. That means Car B travels at x+2 mph.
Both of them are traveling towards each others, so we can say the total speed is 2x+2.
Now i takes 3 hrs and we know the distance.
Since R*T=D
Then 3(2x+2)=270
So 2x+2=90
2x=88
x=44
12)
To find perpendicular we want to find the opposite reciprocal of the original slope. Therefore the slope is 3/2.
Now we must find the equation of the line with the given variable.
First find b.
5=3/2*4+b
b = -1
So the equation of this line is:
y=3/2x-1
13) All work will be shown below.
6-3(-2-4x)=2(3(x-4)+7)
6+6+12x=2(3x-12+7)
12+12x=2(3x-5)
12+12x=6x-10
6x=-2
x = -1/3
14)
First we must find the amount each train traveled.
The speed of F train(Freight train)=x
The speed of P train(passenger train)=x+6
Their combined speed is 2x+6
It takes 2 hrs to cover 100 miles
So 2(2x+6)=100
2x+6=50
2x=44
x=22
So the freight train covered 44 miles and the passenger train covered 56 miles.
To find average speed you must do Total Distance/Total Time.
44/2 and 56/2
Which are 22 and 28.
The average speed of F train is 22 mph and average speed of P train is 28 mph.
15) Again opposite reciprocal.
3/5 -> -5/3
Work:
-4=-3*-5/3+b
-4=5+b
b=-9
y = -5/3x-9
16)
F=kx-kx0
First kx0 = 0
So F=kx
So x=F/k
Answer:
If it is less than 3, Player 1 earns 3 points.
If not, Player 2 earns 2 points.
Step-by-step explanation:
<u>Player 1</u> :
p(N < 3) = p(N = 1 or N = 2) = 2/5
<u>Player 2</u> :
p(N ≥ 3) = p(N = 3 or N = 4 or N = 5) = 3/5
<u>We notice that</u> :
p(N < 3) × 3 = (2/5) × 3 = 6/5
On the other hand,
p(N ≥ 3) × 2 = (3/5) × 2 = 6/5
since ,the probability player 1 win multiplied by the associated number of points (3)
is equal to
the probability player 2 win multiplied by the associated number of points (2).
Then the game is fair.
Answer:
21022.
Step-by-step explanation:
Find the prime factors of 10508:
2 ) 10508
2 ) 5254
37 ) 2627
71.
50208 = 2*2*37*71.
Now there is no integer value for a that would fit (a+ 1)(a - 5) = 10508 .
But we could try multiplying the LCM by 2:-
= 21016 = 2*2*2*37*71.
= 2*2*37 multiplied by 2 * 71
= 148 * 142.
That looks promising!!
a - 5 = 142 and
a + 1 = 148
This gives 2a - 4 = 290
2a = 294
a = 147.
So substituting a = 147 into a^2 - 4a + 1 we get:
= 21022.
