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Iteru [2.4K]
3 years ago
11

What is the solution to x?​

Mathematics
1 answer:
Sonja [21]3 years ago
3 0

Answer:

Step-by-step explanation:

By geometric mean theorem,

In a triangle ABC,

\frac{BC}{AC}=\frac{CD}{BC}

\frac{y}{(4+6)}=\frac{6}{y}

y² = 60

y = √60

y = 7.75

Similarly, \frac{AB}{AC}=\frac{AD}{AB}

\frac{x}{(4+6)}=\frac{4}{x}

x² = 40

x = √40

x = 6.32

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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
If a number ends in zero, then it is divisible by five
kramer

Answer:

Yes

Step-by-step explanation:

10,20,30,40,50 are all divisible by 5.

8 0
3 years ago
Read 2 more answers
How long will it take to travel 200km traveling 10 m/s
jolli1 [7]

Answer:

time = distance / speed

time = 200/10

= 20

Step-by-step explanation:

6 0
3 years ago
Brooke has 24 pencils and 36 erasers. If she makes identical goodie bags for her friends with no pencils or erasers left over, w
Licemer1 [7]
I think the answer is 12 because the greatest common factor of 24 and 36 is 12.

Hope this helped☺☺

(That means each goody bag will have 2 pencils and 3 erasers)
8 0
3 years ago
Paula has containers of colored sand that she uses for sand art. She has 1/3 cup of each blue, gray,and orange. She has 2/3 cup
tangare [24]
3 pictures.

1/3 + 1/3 + 1/3 = 3/3 = 1
2/3 + 2/3 = 4/3 = 1 1/3

1 + 1 + 1 1/3 + 1/2
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1 1/3 * 3 = 1 2/6
   1/2 * 3 =    3/6
              = 1 5/6

2 + 1 5/6
3 5/6

Paula can make 3 pictures.

8 0
3 years ago
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