F(x) = -x + 4
g(x) = -2x - 3
f(g(x)) = -(-2x - 3) + 4 = 2x + 3 + 4 = 2x + 7
f(g(2)) = 2(2) + 7 = 4 + 7 = 11
Answer:
thats the equation for slope-intercept form
Step-by-step explanation:
m is the slope and b is where the line intercepts on the y axis
Answer:z>-5
Step-by-step explanation:
The right angles triangle has three sides including the hypotenuse which is opposite to the right angle.
If the hypotenuse - H
Then one side is - H - 2
Third side is 7 cm shorter then H-2
Therefore it’s H -2-7 = H -9
According to Pythagoras theorem
Square of hypotenuse = sum of the squares of the other 2 sides
H² = (H-9)² + (H-2)²
H² = H² -18H + 81 + H² -4H + 4
0 =H² -22H +85
This is a quadratic equation
0 = H² - 17H -5H +85
0 = H (H - 17) -5(H-17)
(H-17) (H-5) =0
H -17=0 or H-5=0
H could be 17 cm or 5 cm
If H =5 cm then
Side 1 -H-2 = 3 cm
And side 2 - H-9 = -4 cm
Since lengths cannot be negative values
H isn’t 5 cm
Therefore H =17 cm
1 side is H-2 = 15 cm
2nd side H -9 = 8 cm
Three sides are 17 cm, 15 cm and 8 cm
Answer:
Step-by-step explanation:
Probability is the possibility for an event to occur or not to occur.
The formula for a combination is:
n choose r = n! / (r! x (n-r)!)
Given
n=14
r= 11 to 13
Hence, we shall add up the cases for 11 through 13.
nCr
14C11 + 14C12 + 14C13
14!/11!(14-11)! + 14!/12(14-12)! + 14!/13(14-13)!
= 14!/11!•3! + 14!/12!•2! + 14!/13!•1!
= 14*13*12*11!/11!•(3*2*1) + 14*13*12!/12!•(2*1) + 14*13!/13!•(1*1)
= 2184/6+182/2+14/1
= 364+91+14
= 469 ways
