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

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.

Answer:

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

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]

Answer:

Step-by-step explanation:

48 ft by 60 ft

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]

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

Answer:

please write the question in english than I may help you

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

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.

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

Answer:

Step-by-step explanation:

Step-by-step explanation:

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

nb

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 :)

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!!

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

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.

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 :)

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]

Answer:

here is your answer

Step-by-step explanation:

b

c

a answer

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]

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.

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

Answer:

Q3. 9

Q4. 6

Step-by-step explanation:

[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]

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 )

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.

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.

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