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Nataly_w [17]
3 years ago
12

(show the supposition, proof and conclusion)

Mathematics
1 answer:
larisa86 [58]3 years ago
5 0

Answer:

Step-by-step explanation:

We are given that a and b are rational numbers where b\neq0 and x is irrational number .

We have to prove a+bx is irrational number by contradiction.

Supposition:let  a+bx is a rational number then it can be written in \frac{p}{q} form

a+bx=\frac{p}{q} where q\neq0 where p and q are integers.

Proof:a+bx=\frac{p}{q}

After dividing p and q by common factor except 1 then we get

a+bx=\frac{r}{s}

r and s are coprime therefore, there is no common factor of r and s except 1.

a+bx=\frac{r}{s} where r and s are integers.

bx=\frac{r}{s}-a

x=\frac{\frac{r}{s}-a}{b}

When we subtract one rational from other rational number then we get again a rational number and we divide one rational by other rational number then we get quotient number which is also rational.

Therefore, the number on the right hand of equal to is rational number but x is a irrational number .A rational number is not equal to an irrational number .Therefore, it is contradict by taking a+bx is a rational number .Hence, a+bx is an irrational number.

Conclusion: a+bx is an irrational number.

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Answer: segment BC = 36 units

Step-by-step explanation:

As per the given information, we have

B, C and D are three points such that

segment BC = segment BD + segment DC          ... (i)

And segment BD = segment DC                        ... (ii)

If segment BD = 18 units

Then, segment DC = 18 units   [From (ii)]

segment BC = 18 units +  18 units                [From (i)]

⇒segment BC = 36 units

Hence, length of \overline{BC} = 36 units

6 0
3 years ago
For the vectors u and v with magnitudes u = 88 and v = 99​, find the angle θ between u and v which makes u and v = 77.
WARRIOR [948]

Answer:

<h2>89.5°</h2>

Step-by-step explanation:

Using the vector formula u.v = |u||v|cos\theta

|u| = magnitude of vector u

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u.v is the dot product of vector u and v

Given |u| = 88, |v| = 99 and u.v = 77, to get \theta we will substitute the given values into the equation above;

77 = 88*99cos\theta\\cos\theta = \frac{77}{88*99} \\cos\theta = \frac{77}{8712} \\cos\theta = 0.008838\\\theta = cos^{-1} 0.008838\\\theta = 89.5^{0}

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━━━━━━━━━━━━━━━ ♡ ━━━━━━━━━━━━━━━  

So there are five candy bars.

Herself and two sisters equals 3 people in total.

This is a graph of 5 candy bars, each line being 1/2.

━ ━

━ ━

━ ━

━ ━

━ ━

If she ate half of one... the graph would become this.

━ ━

━ ━

━ ━

━ ━

━

Now there are 9 halves. You need to split the 9 halves for 3 people. 9 divided by 3 is 3.

Each person gets 3 halves, or 1 and 1 half.

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Altogether that is 9 halves, AKA the number of halves Mai had after she ate 1/2.

The amount Mai ate in the first place: ━

9 halves plus 1 half, equals 10 halves. Each whole has 2 halves. 10 divided by 2 is 5, AKA the number of candy bars she had in the first place.

━━━━━━━━━━━━━━━ ♡ ━━━━━━━━━━━━━━━  

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