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lys-0071 [83]
3 years ago
5

Fill in the missing reason for the last step.

Mathematics
1 answer:
jek_recluse [69]3 years ago
6 0

Answer:

Division

Step-by-step explanation:

You divided both sides of the inequality by -3. Multiplying/dividing by negative numbers change the sign of the inequality, so you have ">" turned into "<".

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Give an example of a function f : N → N that is surjective but not injective. You must explain why your example is surjective an
Helen [10]

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.

7 0
2 years ago
The price of Stock A at 9 A.M. was ​$14.83. Since​ then, the price has been increasing at the rate of ​$0.12 each hour. At noon
BARSIC [14]

Answer:

  • 0.5 hours

Step-by-step explanation:

Let the x be the number of hours after noon.

<u>We have the following equation:</u>

  • 14.83 + 0.12(x + 3) = 15.33 - 0.15x
  • 14.83 + 0.12x + 0.36 = 15.33 - 0.15x
  • 0.12x + 0.15x = 15.33 - 15.19
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3 years ago
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2 years ago
Use right triangle tools to find the unknown measures. Round lengths to the nearest tenth and angle measures to the nearest degr
timama [110]

Step-by-step explanation:

OP=11.2

m<Q= 42⁰

m<R=48⁰

The tools used are....

I have used the property of Pythagoras Theorm to get the length of side QP, I have also used the property of inverse function of sin to get the measure of angle Q and the property of sum of angles of triangle to get measure of angle of R

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