Prove the following statement by contradiction.
If a and b are rational numbers, b ≠ 0, and r is an irrational number, then a + br is irrational.
Proof by contradiction: Select an appropriate statement to start the proof.
A. Suppose not. That is, suppose there exist irrational numbers a and b such that b ≠ 0, r is a rational number, and a + br is rational.
B. Suppose not. That is, suppose there exist rational numbers a and b such that b ≠ 0, r is an irrational number, and a + br is irrational.
C. Suppose not. That is, suppose there exist rational numbers a and b such that b ≠ 0, r is an irrational number, and a + br is rational.
D. Suppose not. That is, suppose there exist irrational numbers a and b such that b ≠ 0, r is an irrational number, and a + br is rational.
E. Suppose not. That is, suppose there exist rational numbers a and b such that b ≠ 0, r is a rational number, and a + br is irrational.
Then by definition of rational,
a = c/d, b = i/j , and a + br = m/n
where c, d, i, j, m, and n are___and____. Since b ≠ 0, we also have that i ≠ 0. By substitution,
c/d + i/j r = m/n
Solving this equation for r and representing the result as a single quotient in terms of c, d, i, j, m, and n gives that
r = c - a/b

Answers

Answer 1

Answer:

spongebob at the bottom of the sea

Step-by-step explanation:

In a plain, robust, conversational style, the author known as “Elena Ferrante” has captivated readers worldwide with her chronicle of a complicated friendship between two women.

Answer 2

The step would be, "Suppose not. That is, suppose there exist irrational numbers a and b such that b ≠ 0, r is a rational number, and a + br is rational." Option A is correct.

Given that,
a and b are rational numbers, b ≠ 0, and r is an irrational number, then a + br is irrational. the first step of the proof with contradiction is to be determined.

What is simplification?

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

here,
For the statement,

a and b are rational numbers, b ≠ 0, and r is an irrational number, then a + br is irrational.

Contradiction will be "suppose there exist irrational numbers a and b such that b ≠ 0, r is a rational number, and a + br is rational."

Thus, the step would suppose not. That is, suppose there exist irrational numbers a and b such that b ≠ 0, r is a rational number, and a + br is rational.

Learn more about simplification here:

https://brainly.com/question/12501526

#SPJ2



Related Questions

2(f-9)=-28 f=?
-3(2t+3)=-21 t=?

Answers

Answer:

1. f= 3/5

2. t= 3/5

Step-by-step explanation:

FYI you can use the app photo math, you just take a pic of the problem and it gives you the answer and explains the steps and it is free.

Answer:

Below in bold.

Step-by-step explanation:

2(f - 9) = -28

2f - 18 = -28

2f = -28 + 18

2f = -10

f = -5.

-3(2t + 3) = -21

2t + 3 = -21/-3

2t + 3 =  7

2t = 4

t = 2.

Jocelyn finds the blueprints for her house in the basement. The kitchen floor measures 12 inches long and 15 inches wide on the drawing. If the scale of the drawing is 1 inch: 4 ft, what are the dimensions of her actual kitchen floor?

Answers

Answer:

Step-by-step explanation:

48 ft by 60 ft

Which equation, when solved, results in a different value of x than the other three?
-7/8x-3/4=20
3/4+7/8x=-20
-7(1/8)x-3/4=20
-7/8(-8/7)x-3/4=20(-7/8)

Answers

Answer:

D. -7/8(-8/7)x-3/4=20(-7/8) is the answer.

I think d is the correct answer

The Arizona Department of Transportation wishes to survey state residents to determine what proportion of the population would like to increase statewide highway speed to 75 from 65 mph. At least how many residents do they need to survey if they want to be at least 99% confident that the sample proportion is within 0.02 of the true proportion?

Answers

Answer:

They need to survey 4145 residents.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].

The margin of error is given by:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

99% confidence level

So [tex]\alpha = 0.01[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.01}{2} = 0.995[/tex], so [tex]Z = 2.575[/tex].

At least how many residents do they need to survey if they want to be at least 99% confident that the sample proportion is within 0.02 of the true proportion?

This is n for which [tex]M = 0.02[/tex]. As we have no estimate for the proportion, we use [tex]\pi = 0.5[/tex]. So

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]0.02 = 2.575\sqrt{\frac{0.5*0.5}{n}}[/tex]

[tex]0.02\sqrt{n} = 2.575*0.5[/tex]

[tex]\sqrt{n} = \frac{2.575*0.5}{0.02}[/tex]

[tex](\sqrt{n})^2 = (\frac{2.575*0.5}{0.02})^2[/tex]

[tex]n = 4144.1[/tex]

Rounding up:

They need to survey 4145 residents.

How do I solve this

Answers

Answer:

P(A or B) = 1.16

Step-by-step explanation:

Given probability:

Probability of event A = P(A) = 0.46

Probability of event B = P(B) = 0.7

P(A and B) = 0.43

Find:

P(A or B)

Computation:

If A is an incident and B is a separate event, P(A or B) is the possibility of either A, B, or both events occurring.

P(A or B) = P(A) + P(B)

P(A or B) = 0.46 + 0.7

P(A or B) = 1.16

santino is renting a canoe from a local shop that charges a $10 fee, plus an hourly rate of $7.50. For how long can santino rent a canoe if he pays a total of $70

Answers

Answer:

Santino rented the canoe for 8 hours.

Step-by-step explanation:

The total bill is represented by the formula r(h) = $10 + ($7.50/hour)h,

where h is the number of hours over which the canoe is rented.

If the total bill is $70, then $70 = $10 +  ($7.50/hour)h.

Solve this for h.  Start by subtracting $10 from both sides, obtaining:

$60 =  ($7.50/hour)h.

Dividing both sides by ($7.50/hour), we get:

           $60

h = --------------------- = 8 hours

      ($7.50/hour)

Santino rented the canoe for 8 hours.

1.) The grade 6 class harvested 3 44 kg of tomatoes, 53 kg of eggplants and 2 42 kg of green pepper from their "Gulayan sa Paaralan”. How many kilograms of vegetables did they harvest in all? a. What is asked in the problem? b. What are the given facts? c. What operation will be used? d. What is the number sentence? e. What is the answer?​

Answers

Answer:

649 kg of vegetables

Step-by-step explanation:

What is asked?

The total number of vegetables planted

The given facts?

[tex]Tomatoes= 344kg[/tex]

[tex]Eggplants =53kg[/tex]

[tex]Green\ pepper =242kg[/tex]

The operation to be used?

The addition operation

The number sentence?

[tex]344 + 53 + 242[/tex]

The answer?

[tex]344 + 53 + 242 =639[/tex]

5 x 10 - 2 = ??
HALP MOIIIIIIIIIIIIIIIIIIIIII

Answers

Answer:

48

Step-by-step explanation:

the answer is 48 I got this answer by multiplying 5 by 10 and subtracting is from 2 which gives me 50 - 2 which is 48

Answer:

48

Step-by-step explanation:

5×10-2=50-2

=48

hope it helps!!

What is the left-hand limit of this function as x approaches 2? f(x)=x/x-2

Answers

9514 1404 393

Answer:

  B.  -∞

Step-by-step explanation:

There is a vertical asymptote at x=2. Left of that line, the denominator is negative. As x approaches 2 from the left, the function approaches negative infinity.

how to solve 4 > 11 - x/3

Answers

Answer:

21 < x

Step-by-step explanation:

4 > 11 -x/3

Subtract 11 from both sides

4 - 11 > -x/3

-7 > -x/3

Multiply both sides by 3

-7*3 > -x

-21 > -x

Multiply both sides by (-1)  

21 < x

When we are multiplying by negative, then inequality sign changes.

Determine the equation of the line that is perpendicular to the given line, through the given point.

y=3x+4; (9, -7)​

Answers

Answer:

The equation of the line is [tex]y + 7 = -\frac{1}{3}(x - 9)[/tex]

Step-by-step explanation:

Equation of a line:

The equation of line, in point-slope form, is given by:

[tex]y - y_0 = m(x - x_0)[/tex]

In which m is the slope and the point is [tex](x_0, y_0)[/tex]

Perpendicular lines:

If two lines are perpendicular, the multiplication of their slopes is -1.

Through (9,-7)

This means that [tex]x_0 = 9, y_0 = -7[/tex]

So

[tex]y - y_0 = m(x - x_0)[/tex]

[tex]y - (-7) = m(x - 9)[/tex]

[tex]y + 7 = m(x - 9)[/tex]

Perpendicular to y = 3x + 4

This line has slope 3, so:

[tex]3m = -1[/tex]

[tex]m = -\frac{1}{3}[/tex]

Thus

[tex]y + 7 = m(x - 9)[/tex]

[tex]y + 7 = -\frac{1}{3}(x - 9)[/tex]

Mathematics

Evaluate the equations or inequalities. Write the Letter of your answer to the corresponding boxes at the bottom of the page to discover the answer to the title questions.

How does an ESP Expert send his mail?
☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐
7 11 1 8 2 9 11 3 1 8 9 4 6 9 4 9 1 2 10 5

help po.

Answers

Step-by-step explanation:

ejdjbd x bxbx k wbu y DJ UK j HK JM dz

nb

Which expression is equivalent to (6x2 + 4)(x + 5) ?
A 6x2 + 20
B 6x2 + 16x + 20
C 603 + 30x2 + 4x + 20
D) 6x3 + 11x2 + 3x + 20​

Answers

Answer: [tex]6x^3 +30x^2 +4x+20[/tex]

Step-by-step explanation:

[tex](6x^2 +4)(x+5)\\\\ =6x^3 +30x^2 +4x+20[/tex]

A giant cube-shaped die measures 20 cm on a side. Find the volume of the die.​

Answers

Answer:

8,000 cm cubed

Step-by-step explanation:

Volume of a cube = length x width x height

All sides on a cube are the same length

If one is 20 cm, all are.

20x20x20=8,000.

Quadrilateral FGHI is similar to quadrilateral JKLM. Find the measure of side JK. Round your answer to nearest tenth if necessary,

Answers

Answer:

JK ≈ 12.3

Step-by-step explanation:

Since the figures are similar then the ratios of corresponding sides are equal, that is

[tex]\frac{FI}{JM}[/tex] = [tex]\frac{FG}{JK}[/tex] , substitute values

[tex]\frac{59}{26}[/tex] = [tex]\frac{28}{JK}[/tex] ( cross- multiply )

59 JK = 728 ( divide both sides by 59 )

JK ≈ 12.3 ( to the nearest tenth )

please help me please help me please help me please help me please help me please help me please​

Answers

Answer:

Q3. 9

Q4. 6

Step-by-step explanation:

Question 1 of 25 f(x) = 2x2 + 6x - 4 g(x) = 5x3 - 6x? - 3 Find (f + g)(x).​

Answers

Answer:

option B

Step-by-step explanation:

[tex]f(x) = 2x^2 + 6x -4\\\\g(x) = 5x^3 - 6x^2 - 3\\\\(f + g)(x) = f(x) + g(x) \\\\[/tex]

               [tex]= (2x^2 + 6x - 4) + ( 5x^3 -6x^2 - 3) \\\\= 2x^2 + 6x - 4 + 5x^3 - 6x^2 - 3\\\\= 5x^3 + 2x^2 - 6x^2 + 6x - 4 - 3 \\\\= 5x^3 - 4x^2 + 6x - 7[/tex]

Answer:

the answer is b

Step-by-step explanation:

hope this helps :)

the points -6/5 and -5/6 will line in which quadrant​

Answers

A negative x is to the left of the y axis and a negative y value is below the x axis. Any value to the left and below the axis’ will be in the 3rd quadrant.

Answer: 3rd quadrant

How many different 5 digit natural numbers are there starting with odd numbers or ending with even numbers.

Answers

I would help you but I read another language

2. A bag contains one red, one blue and one white marble. One marble is chosen at random
from the bag, and then replaced into the bag. A second marble is chosen.
a) Draw a probability tree and find the sample space.
(3 marks)​

Answers

Answer:

Step-by-step explanation:

Zari folds the net shown into model of a solid figure. How many edges, faces, and vertices does the model have?

Answers

Answer:

Faces = 6

Vertices = 8

Edges = 12

Step-by-step explanation:

In a solid geometric shape :

         A face is a flat surface : faces = 6

         A vertex (plural: vertices) is a Corner : vertices = 8

         An edge is a particular type of line segment joining

                                                          two vertices : Edges = 12

                       

1. A photograph measures eleven inches wide and fourteen inches long. The picture is enlarged to fit on a wall. If the new larger picture is 231 inches wide, how long is it?
234 inches
294 inches
181.5 inches
412.5 inches
.

Answers

Answer:

294 in

Step-by-step explanation:

set a ratio w/l

11/14

set it equal to 231/x

x = length

[tex]\frac{11}{14}[/tex] = [tex]\frac{231}{x}[/tex]

cross multiply

11x = 3234

divide by 11

x = 294

Anyone plz show how to work it out step by step.​

Answers

Answer:

168cm^3

Step-by-step explanation:

Q to P is going to be 3cm. it is identical to the length T to U.

R to T , W to Q, S to U is going to be identical to P to V. P to V has been identified as 12 cm.

in the middle of the shape, there are 4 identical triangles. the height time length will give us the area of that one shape:

e.g for shape P to V to W to Q and back to P is one rectangle. the length is 12 cm and the width is 3 cm.

12 x 3= 36

36cm^3 is one rectangles surface area, we have 4 identical triangles that means we need to times 36 by 4.

so 36x4=144.

now on the left and right side, we have two squares. on the right, we have T to U to V to W back to T this has the height of 3 width of 4 then we do 3 X 4 which is 12, we times it by 2 because we have two identical squares.

12 X 2=24

finally we add 24 and 144 = 168cm^3.

hope this helps :)

Find the length of the third side. If necessary, round to the nearest tenth

Answers

Answer:

30

Step-by-step explanation:

third side is the hypotenuse since it is opposite to 90 degree.

using pythagoras theorem

a^2 + b^2 = c^2

24^2 + 18^2 = c^2

576 + 324 = c^2

900 = c^2

[tex]\sqrt{900}[/tex] = c

30 = c

therefore third side is 30.

Answer:

30

Step-by-step explanation:

[tex] {24}^{2} + 18 {}^{2} = c {}^{2} \\ 576 + 324 = c {}^{2} \\ \sqrt{900 = \sqrt{c }^{2} } \\ = 30[/tex]

There are 400 animals that live at a zoo. You find that 22 of 65 randomly chosen animals are
monkeys. About how many animals in the entire zoo are likely to be monkeys?

Answers

Answer:

About 135.

Step-by-step explanation:

As the sample is random the number of monkeys likely to be in the zoo

=  (22/65) * 400

= 135.38

Need help with practice problem please

Answers

the answer would be x=3, y=6, z=-3 or 3,6,-3

Consider the following number line:

Answers

Answer:

here is your answer

Step-by-step explanation:

b

c

a answer

Cho hàm ẩn z=z(x,y) xác định từ phương trình x+y+xz+yz2−1=0. Tính vi phân toàn phần dz(1,0).

Answers

Answer:

please write the question in english than I may help you

4(x+9)=8x-7
Solve for x

Answers

Answer:

x = 10.75

Step-by-step explanation:

4(x+9)=8x-7

Step 1: Distribute the 4 to the x and 9

4 * x = 4x

4 * 9 = 36

We now have 4x + 36 = 8x - 7

Step 2: add 7 to both sides

36 + 7 = 43

-7 + 7 cancels out

We now have 4x + 43 = 8x

Step 3 subtract 4x from both sides

4x - 4x cancels out

8x - 4x = 4x

We now have 4x = 43

step 4 divide both sides by 4

4x / 4 ( the 4s cancel out and we're left with x )

43/4 = 10.75

We're left with x = 10.75

find the area of the given figure

Answers

[tex]\sf \bf {\boxed {\mathbb {GIVEN:}}}[/tex]

Radius of the circle "[tex]r[/tex]" = 5.5 yd

[tex]\sf \bf {\boxed {\mathbb {TO\:FIND:}}}[/tex]

The area of the given figure.

[tex]\sf \bf {\boxed {\mathbb {SOLUTION :}}}[/tex]

[tex]\implies {\blue {\boxed {\boxed {\purple {\sf {b. \:47.5\:sq\:yd.}}}}}}[/tex]

[tex]\sf \bf {\boxed {\mathbb {STEP-BY-STEP\:EXPLANATION:}}}[/tex]

We know that,

[tex]\sf\pink{Area\:of\:a\:semi-circle}[/tex] = [tex]\frac{\pi \: {r}^{2} }{2} [/tex]

Using 3.14 for π, we have

[tex] = \frac{3.14 \times ( {5.5 \: yd})^{2} }{2} \\[/tex]

[tex] = \frac{3.14 \times 5.5 \times 5.5 \: {yd}^{2} }{2}\\ [/tex]

[tex] = \frac{94.985 \: {yd}^{2} }{2} \\[/tex]

[tex] = 47.5 \: {yd}^{2} \\[/tex]

Using [tex]\frac{22}{7} [/tex] for π,

[tex] = \frac{22 \times 5.5 \times 5.5 \: {yd}^{2} }{7 \times 2} \\[/tex]

[tex] = \frac{665.5 \: {yd}^{2} }{14}\\ [/tex]

[tex] = 47.5 \: {yd}^{2} \\[/tex]

Therefore, the area of the semi-circle is [tex]47.5\: yd²[/tex].

[tex]\huge{\textbf{\textsf{{\orange{My}}{\blue{st}}{\pink{iq}}{\purple{ue}}{\red{35}}{\green{♨}}}}}[/tex]

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