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Arturiano [62]
3 years ago
7

Hello! :)

Mathematics
2 answers:
zlopas [31]3 years ago
7 0

Answer:

A

Step-by-step explanation:

The two triangles are congruent because if each triangle's angles add up 180 degrees, you can deduce that the triangles have atleast two congruent angles.

Triangle RST:

48 + 73 = 121

180 - 121 = 59

Angle R = 59

Angle T = 48

Angle S = 73

59 + 48 + 73 = 180

Triangle ABC:

73 + 59 = 132

180 - 132 = 48

Angle A = 59

Angle B = 73

Angle C = 48

59 + 48 + 73 = 180

Alja [10]3 years ago
4 0
The correct answer would be A
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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
There are 24 students in a science class.Mr.Sato will give each pair of students 3 Magnets.So far,Mr.Sato has given 9 pairs of s
Flauer [41]

Answer:

Mr. Sato needs 9 more magnets.

Step-by-step explanation:

The 24 students will form 12 pairs. The total number of magnets needed is 12*3 = 36. Mr. Sato  gave out 9*3=27 magnets already and so he will need 36 - 27 = 9 more magnets.

8 0
3 years ago
Two trains leave Cleveland at the same time. One train travels east and the other travels west. The speed of the westbound train
OlgaM077 [116]

Answer:

The eastbound train travels at 92 mph and the westbound train travels at 96 mph.

Step-by-step explanation:

We know that Velocity = distance / time

If the eastbound train travels at x miles per hour, the westbound train travels at x + 4 mph.

After 3.5 hours, they are 658 miles apart. If we solve for distance the formula given above we have: Distance = velocity x time. We have that the total distance between both trains is 658 miles.

Substituting the values of the problem and solving for x we have

658 = 3.5x+3.5(x+4)\\658=3.5x+3.5x+14\\644=7x\\92=x

Thus, the eastbound train travels at 92 mph and the westbound train travels at 96 mph.

6 0
3 years ago
When an integer is subtracted from 5 times the next consecutive integer, the difference is 17. Find the value of the greater int
Mars2501 [29]

Answer:

4

Step-by-step explanation:

5(x + 1) -x = 17  Distribute the 5

5x + 5 - x = 17 Combine like terms

4x + 5 = 17  Subtract 5 from both sides

4x = 12  Divide both sides by 4

x = 3  

Three is the smaller integer and 4 is the greater integer.

5 0
1 year ago
A 25-foot tall flagpole casts a 42-foot shadow. What is the angle (to the neasrest tenth of degree) that the sun hits the flagpo
Maurinko [17]
Tan^-1 (tan x) = 42/25
x=tan^-1 42/25

x= 59.237 degrees.
8 0
3 years ago
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