Answer:
x=−7/5and y=−6/5
Step-by-step explanation:
Step: Substitute−2x−4foryiny=3x+3:
y=3x+3
−2x−4=3x+3
−2x−4+−3x=3x+3+−3x(Add -3x to both sides)
−5x−4=3
−5x−4+4=3+4(Add 4 to both sides)
−5x=7
−5x
−5
=
7
−5
(Divide both sides by -5)
x=−7/5
Answer:
Consider f: N → N defined by f(0)=0 and f(n)=n-1 for all n>0.
Step-by-step explanation:
First we will prove that f is surjective. Let y∈N be any natural number. Define x as the number x=y+1. Then x∈N, and f(x)=x-1=(y+1)-1=y. We conclude that f is surjective.
However, f is not injective. Take x1=0 and x2=1. Then x1≠x2 but f(x1)=0 and f(x2)=x2-1=1-1=0. We have shown that there are two natural numbers x1,x2 such that x1≠x2 but f(x1)=f(x2), that is, f is not injective.
Note:
If 0∉N in your definition of natural numbers, the same reasoning works with the function f: N → N defined by f(1)=1 and f(n)=n-1 for all n>1. The only difference is that you consider x1=1, x2=2 for the injectivity.
Answer: Option 'D' is correct.
Step-by-step explanation:
Since we have given that
Upper P (Upper B vertical line Upper A)
means
It means that probability of getting event B given that Event A is occurred.
D. The probability of event B occurring, given that event A has already occurred. is also expressed as
Hence, Option 'D' is correct.
Answer:
Step-by-step explanation:
Answer:
-0.8x + 4.8y + 16
Step-by-step explanation:
4(0.5x+2.5y-0.7x-1.3y+4) = 4( 0.5x - 0.7x + 2.5y - 1.3y + 4)
= 4( -0.2x + 1.2y + 4)
= 4*(-0.2x) + 4 *1.2y + 4*4
= -0.8x + 4.8y + 16
