Answer:
~1.8 mile
Step-by-step explanation:
Michael lives at the closest point to the school (the origin) on Maple Street, which can be represented by the line y = 2x – 4.
This means Michael's house will be the intersection point of line y1 (y = 2x - 4) and line y2 that is perpendicular to y1 and passes the origin.
Denote equation of y2 is y = ax + b,
with a is equal to negative reciprocal of 2 => a = -1/2
y2 pass the origin (0, 0) => b = 0
=> Equation of y2:
y = (-1/2)x
To find location of Michael's house, we get y1 = y2 or:
2x - 4 = (-1/2)x
<=> 4x - 8 = -x
<=> 5x = 8
<=> x = 8/5
=> y = (-1/2)x = (-1/2)(8/5) = -4/5
=> Location of Michael' house: (x, y) = (8/5, -4/5)
Distance from Michael's house to school is:
D = sqrt(x^2 + y^2) = sqrt[(8/5)^2 + (-4/5)^2) = ~1.8 (mile)
Odd number on a fair die:
50%, as 1,3,5 are all odd and there are 6 sides on a die
tails: 50% as 2 sides.
But if you are asking together: for each possible side on the die, there is a possibility of heads or tails
1: H T
2: H T
3: H T
4: H T
5: H T
6: H T
so 12 possibilities.
to roll an odd number and have a coin land on tails
1: T
3: T
5: T
3 different possibilities satisfy that
so then the answer becomes: 3/12
so 25%
Hope This helps!
Answer:
a +2b
Step-by-step explanation:
2(a + 2b) - a - 2b
Distribute
2a +4b -a -2b
Combine like terms
2a -a + 4b-2b
a +2b
Answer:
Step-by-step explanation:
For finding the system of equations you can use one of two methods. There's the elimination method and also the substitution method. For this I think the best way we could go at solving this is by using the elimination method. Since we can eliminate the 2y. We can then solve for x and then we'll go from there.
Now that we know what x is we can substitute it for one of the equations and then we will be able to solve for y.
So now we have the x and the y and once we place them together we can get the solution of those two equations, and the solution is .
Answer:
m=243/4 when v=9.
Step-by-step explanation:
We know that when y varies directly with x², the formula of direct proportion is
where 'k' is the constant of variation.
so
As m varies directly with v², and m=3 when v=2
m=kv²
k=m/v²
= 3/(2)²
=3/4
Hence, k=3/4
so when v=9 then the expression becomes
m=kv²
substituting v=9 and k=3/4
m= 3/4(9)²
=3/4 × 81
=243/4
Therefore, m=243/4 when v=9.
