Answer:
y=-2/3x+10.3333333333333334
Step-by-step explanation:
to make it perpendicular 2/3 becomes -2/3
There are total of 5 digits, of which we arrange 3 of them.
Therefore using permutations we can find total possible 3-number combinations.
5P3 = 5*4*3 = 60
To be greater than 600 means first digit must be 6. (1 possibility)
A number is even only if last digit is even, 2 or 4. (2 possibilities)
The 2nd digit then can only be 3,5, (2 or 4). (3 possibilities)
The total possible even 3-digit numbers greater than 600 is product of each digit's possibilities.
---> 1*3*2 = 6
Therefore probability is 6/60 = 1/10.
Answer:
12m²
Step-by-step explanation:
For a rectangle, with length L and width W,
the perimeter is given as
Perimeter,
P = (2 x Length) + (2 x Width)
P = 2L + 2W
It is given that the perimeter is 48, hence
48 = 2L + 2W (divide both sides by 2)
24 = L + W
or
L = 24 - W -----> eq 1
Also realize that the Area of a Rectangle is given by
A = L x W -----> eq 2
Substituting eq 1 into eq 2,
A = (24 - W) x W
A = -W² + 24W
Recall that for a quadratic equation y = ax² + bx + c, the maxima or minima is given by y(max) = -b/2a
In this case, b = 24 and a = -1
-b/2a = -24/[ 2(-1) ] = 12
Hence for A to be maximum A(max) = 12m² (Answer)
You never told us how much money he has
Answer:
m<C = 42°
Step-by-step explanation:
Given:
m<A = (2x - 2)°
m<C = (4x - 6)°
m<DBC = (5x + 4)°
Thus:
m<DBC = m<A + m<C (exterior angle theorem of a triangle)
(5x + 4)° = (2x - 2)° + (4x - 6)°
Solve for x
5x + 4 = 2x - 2 + 4x - 6
Collect like terms
5x + 4 = 6x - 8
5x - 6x = -4 - 8
-x = -12
Divide both sides by -1
x = 12
✔️m<C = (4x - 6)°
Plug in the value of x
m<C = 4(12) - 6 = 48 - 6
m<C = 42°
