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yKpoI14uk [10]
3 years ago
14

What 30+30+30+4+60+9+80

Mathematics
1 answer:
mihalych1998 [28]3 years ago
3 0

Answer:

243

Step-by-step explanation:

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About Exercise 2.3.1: Proving conditional statements by contrapositive Prove each statement by contrapositive
Sladkaya [172]

Answer:

See proofs below

Step-by-step explanation:

A proof by counterpositive consists on assuming the negation of the conclusion and proving the negation of the hypothesis.

a) Assume that n is not odd. Then n is even, that is, n=2k for some integer k. Hence n²=4k²=2(2k²)=2t for some integer t=2k². Then n² is even, therefore n² is not odd. We have proved the counterpositive of this statement.

b) Assume that n is not even, then n is odd. Thus, n=2k+1 for some integer k. Now, n³=(2k+1)³=8k³+6k²+6k+1=2(4k³+3k²+3k)+1=2t+1 for the integer t=4k³+3k²+3k. Thus n³ is odd, that is, n³ is not even.

c) Suppose that n is not odd, that is, n is even. Now, n=2k for some integer k. Then 5n+3=10k+3=2(5k+1)+1, thus 5n+3 is odd, then 5n+3 is not even.

d) Suppose that n is not odd, then n is even. Now, n=2k for some integer k. Then n²-2n+7=4k²-4k+7=2(2k²-2k+3)+1. Hence n²-2n+7 is odd, that is, n²-2n+7 is not even.

e) Assume that -r is not irrational, then -r is rational. Since -1 is rational, then (-1)(-r)=r is rational. Thus r is not irrational.

f) Assume that 1/z is not irrational. Then 1/z is rational. Multiplucative inverses of rational numbers are rational, hence z is rational, that is, z is not irrational.

g) Suppose that z>y. We will prove that z³+zy²≤z²y+y³ is false, that is, we will prove that z³+zy²>z²y+y³. Multiply by the nonnegative number z² in the inequality z>y to get z³>z²y (here we assume z and y nonzero, in this case either z³>0=y³ is true or z³=0>y³ is true). On the other hand, multiply by z² (positive number) to get zy²>y³. Add both inequalities to obtain z³+zy²>z²y+y³ as required.

h) Suppose than n is even. Then n=2k, and n²=4k² is divisible by 4.

i) Assume that "z is irrational or y is irrational" is false. Then z is rational and y is rational. Rational numbers are closed under sum, then z+y is rational, that is, z+y is not irrational.

3 0
3 years ago
3) The foot of a ladder is 1.2 m from a fence
VashaNatasha [74]

Answer: 4.5\ meters

Step-by-step explanation:

Using the data given in the exercise, we can draw the diagram attached, where "h" is the height of the building reached by the top of the ladder.

Notice that there are two similar triangles.

So, you can set up the following proportion:

\frac{1.8}{1.2}=\frac{h}{(1.2+1.8)}

Finally, in order to calculate the height on the building reached by the top of the ladder, you must solve for "h".

Therefore, the value of "h" is :

\frac{1.8}{1.2}=\frac{h}{3}\\\\(3)(\frac{1.8}{1.2})=h\\\\\frac{5.4}{1.2}=h\\\\h=4.5

5 0
3 years ago
Which of the following statements is true?
mariarad [96]

Answer:

Sedimentary rocks usually form in visible layers

Step-by-step explanation:

A is wrong because not all igneous rock is formed by pressure

B is wrong because sedimentary rock is usually a surface rock

C is wrong because the rock cycle is sporadic and doesn't always end in igneous rock

D is correct because sedimentary rock is formed from years and years of sediment layering on top of each other

8 0
3 years ago
Read 2 more answers
Is 5,000 cm greater than 5 m
ANTONII [103]
That is false 5,000cm is bigger you got this way to go

3 0
3 years ago
Read 2 more answers
Help please Asap!!!<br><br> Find the missing fraction<br><br> ?blank??+1/3=3/4
Vaselesa [24]

Answer:

5/12

Step-by-step explanation:

You have to make it a common denomator and then subract until equeal.

8 0
2 years ago
Read 2 more answers
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