Mathematics College

Let a be a rational number and b be an irrational number. Which of the following are true statements?

A. The sum of a and b is never rational
B. The product of a and b is rational
C. b^2 is sometimes rational
D. a^2 is always rational
E. √a is never rational
F. √b is never rational

Answers

Answer 1
a and b would be correct 

Related Questions

A car traveled 63 miles on 3 gallons of gas. What proportion can you set up to determine how many miles, m, the car can travel on 7 gallons of gas?

Answers

147 miles is how many miles the car can travel
63/3=21
21 mile per gallon 
7 gallons X 21 =147

calculate each of the following by using scientific notation and product rule. write the answer in scientific notation. 2.3 x 10^4 times 4.2 x 10^6

Answers

remember the associative and commutative properties of multiplcation
ab=ba and (ab)c=a(bc)

also, the exponential rules
[tex](x^m)(x^n)=x^{m+n}[/tex]

also, scientific notation is [tex]a*10^m[/tex] where 1≤x<10 and m is an integer


therefor

[tex](2.3*10^4) \space\ times \space\ (4.2*10^6)=[/tex]
[tex](2.3)(10^4)(4.2)(10^6)=[/tex]
[tex](2.3)(4.2)(10^4)(10^6)=[/tex]
[tex](9.66)(10^{4+6})=[/tex]
[tex]9.66*10^{10}[/tex]

You have 10,600 to 10,425 find the percent decrease

Answers

Step 1) Find the amount decrease by subtracting
10600 - 10425 = 175

Step 2) Divide the result of step 1 over the original value (10600) to get 175/10600 = 0.016509
This value is approximate

Step 3) Multiply the result from step 2 by 100
0.016509*100 = 1.6509%
This value is approximate

The percent decrease is roughly 1.6509%

A mountain climber climbed down a cliff 50 feet at a time . He did this 5 times in one day . What is the overall change in his elevation ?

Answers

-150 if im correct, it goes down 5 times and thats what i got

Multiplication Property of Inequality -1/2x<-12 simplify it all the way through

Answers

Multiply both sides by -2. Doing this will flip the inequality sign. The flip always happens when you multiply both sides by a negative number. 

So we'll go from this
(-1/2)x < -12
to this
x > 24

which is the final answer

Note: If you need to graph x > 24, then plot 24 on the number line. Draw an open circle at 24 and shade to the right of this open circle. The open circle tells the reader "the endpoint 24 is not part of the solution set". 

Edit: the full steps are...

(-1/2)x < -12
-2*(-1/2)x > -2*(-12)
(-2*-1/2)x > 24
2/2x > 24
1x > 24
x > 24

Let me know if that helps or not. Thank you.

can a sequence be both arithmetic and geometric?

Answers

an aritmetic sequence is like this
[tex]a_n=a_1+d(n-1)[/tex] where a1=first term and d=common difference

geometric is [tex]a_n=a_1(r)^{n-1}[/tex] where a1=first term and r=common ratio


can it be both aritmetic and geometric
hmm, that means that the starting terms should be the same

therfor we need to solve [tex]d(n-1)=(r)^{n-1}[/tex]
what values of d and r make all natural numbers of n true?
are there values that make all natural numbers for n true?

when n=1, then d(1-1)=0 and r^(1-1)=1, so already they are not equal

the answer is no, a sequence cannot be both aritmetic and geometric

A sequence can be both arithmetic and geometric, and this is illustrated where terms follow both an arithmetic and geometric progression.

Yes, a sequence can be both arithmetic and geometric. An example of such a sequence is when the terms of the sequence follow both an arithmetic progression, where the difference between consecutive terms is constant, and a geometric progression, where each term after the first is found by multiplying the previous term by a fixed, non-zero number.

Sue and jonah shose nummbers for a place value game.Sue chose the number one hundred.Jonah chose five million for his number.who chose the greater number

Answers

Jonah chose the greater number, since that number is farther to the left of the number line than Sue's number.

Is the product of an irrational number with a rational number always an irrational number??

Answers

Yes the product of any rational number with an irrational number is always irrational. For example, 2/3 times pi is going to be an irrational result. In this case simply (2/3)pi or (2pi)/3

So the template is
(rational)*(irrational) = irrational

-------------------------------------------------------------------------------------

Here's proof of the claim. Let's make p, q, r, s to be integers. Let's also make m be some irrational number

For now let's assume that multiplying a rational number with an irrational number leads to a rational result. The aim is to use contradiction to prove the opposite.

p/q is rational by definition (make q nonzero)
so is r/s
m is irrational

So the claim so far is
(p/q)*m = r/s

Now multiply both sides by the reciprocal of p/q. That would be q/p
(p/q)*m = r/s
(q/p)*(p/q)*m = (q/p)*(r/s)
m = (q*r)/(p*s)
The right side of the last equation is a rational number since q*r and p*s are integers (p and s are nonzero)

But m was originally irrational. So this is where the contradiction kicks in. This invalidates the initial claim "the product of a rational and irrational number is rational" proving the claim made by your textbook. 

So this completes the proof. 

Given the point and it''s image, determine the scale factor. A (3, 6) A'' (4.5, 9) G'' (3, 6) G (1.5, 3) B (2, 5) B'' (1, 2.5).

Answers

Put the value of the letters with " over the original
So for A we have 3 in the front and 4.5 for A"
4.5/3 = 1.5
We can check if this is actually the scale factor but using the other numbers
The second numbers for A and A" are 6 and 9
6 * 1.5 = 9
So for point A it is 1.5
Use the same thing for G. That gives you 2
For B, you get 0.5
So the scale factors are 1.5, 2, and 0.5

Final answer:

The scale factors for the points given are 1.5 for A to A', indicating an enlargement, and 0.5 for B to B', indicating a reduction. G to G' also indicates a reduction with a factor of 0.5.

Explanation:

To determine the scale factor given the point and its image, you can find the ratio between the coordinates of the image and the original coordinates. Let's analyze the pairs of points you've provided:

A (3, 6) and A' (4.5, 9)

G (1.5, 3) and G' (3, 6)

B (2, 5) and B' (1, 2.5)

We can find the scale factor by dividing the x-coordinates of the image by the original x-coordinate and doing the same for the y-coordinates. For point A:

Scale factor for x: 4.5 / 3 = 1.5

Scale factor for y: 9 / 6 = 1.5

For point G, we see that it's actually the reverse (original to image), but you can still calculate:

Scale factor for x: 3 / 1.5 = 2

Scale factor for y: 6 / 3 = 2

Lastly, for point B:

Scale factor for x: 1 / 2 = 0.5

Scale factor for y: 2.5 / 5 = 0.5

So, the scale factors for A to A' and for B to B' are 1.5 and 0.5, respectively, showing that A to A' is an enlargement while B to B' is a reduction. For G to G', the reverse is a reduction with a factor of 0.5.

40.8 gallons of paint among 8 containers

Answers

divide the two

40.8 / 8 = 5.1 gallons per container

there are some numbers that can be made into only one array. Find all of these numbers up to 50.

Answers

Numbers that can be made into only one array are called prime numbers.

The prime numbers up to 50 are:

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43 and 47

what is bigger 4/5 or 5/9

Answers

4/5

It is 0.8

5/9
is 0.555....
Work: 4/5 or 5/9
Find common denominator
Common denominator is 45
4/5×9/9= 36/45
5/9×5/5=25/45
36/45 is bigger than 25/45
Answer: 4/5
Check your work:

Prime factorization practice all factors 1.- 25 2.- 49 3.- 7 4.- 13 5.- 24 6.- 48 7.- 168

Answers

Do u still need the answer

a number x plus 9 is 3036 write equation solve for x

Answers

3036-9=x Hope this helped
Hi Lolgirl44

The equation would be 3027 + 9 = 3036

I figured out this answer by subtracting 3036 - 9 which is 3027 so to check back and make sure I was right I added 9 + 3027 and it equaled 3036 so I knew I was 100% true on that so x + 9 = 3036 is really 3027 + 9 = 36 which is true and that would be your answer.

Need help with this one!!!

Answers

[tex]\bf (2x^2)^4(5x^6)\impliedby \textit{distributing the exponent} \\\\\\ 2^4x^{2\cdot 4}5x^6\implies 2^4\cdot 5x^{2\cdot 4}x^6\implies 16\cdot 5x^8x^6\implies 80x^{8+6} \\\\\\ 80x^{14}[/tex]

Six less than the product of 9 and a number is equal to 4

Answers

9x - 6 = 4

9x = 4 + 6

9x/9 = 10/9

x = 10/9

hope this helps
if you're searching for the equation, then: 9x - 6 = 4

what is 63.75 minus 13.25 please really need help.

Answers

63.75 - 13.25 = x

.75 - .27 = .50

63 - 13 = 60

x = 60.50

hope this helps
The correct answer is 50.5! Good luck :)

3.4 divided by 0.16728

Answers

The answer is 20.32520325 but rounded that would be 20.33 depending on what your teacher wants you to round to
20.32520 but you put a line above the 32520


Let f(x) = 2x - 7 and g(x) = -6x - 3. Find f(x) + g(x) and state its domain.

Answers

2x-7+-6x-3                                                                                                             2x+-6x=-4x                                                                                                          
 -4x-10=0                                                                                                          
-5/2 is the answer  

Answer:

[tex]\( f(x) + g(x) = -4x - 10 \).[/tex]

To find the domain of [tex]\( f(x) + g(x) \)[/tex], we need to consider the values of [tex]\( x \)[/tex] for which the function is defined. Since [tex]\( f(x) \)[/tex]  and [tex]\( g(x) \)[/tex] are both linear functions, their domain is all real numbers.

So, the domain of [tex]\( f(x) + g(x) \)[/tex] is [tex]\( \mathbb{R} \)[/tex] , which means that [tex]\( x \)[/tex] can be any real number.

Explanation:

To find [tex]\( f(x) + g(x) \)[/tex] , we simply add the functions [tex]\( f(x) \) and \( g(x) \)[/tex] together:

[tex]\[ f(x) + g(x) = (2x - 7) + (-6x - 3) \][/tex]

Now, let's simplify:

[tex]\[ f(x) + g(x) = 2x - 7 - 6x - 3 \][/tex]

[tex]\[ f(x) + g(x) = (2x - 6x) + (-7 - 3) \][/tex]

[tex]\[ f(x) + g(x) = -4x - 10 \][/tex]

x/21 = 3/63 solve the proportion

Answers

x/21 = 3/63
63x = 21 * 3
63x = 63
x = 63/63
x = 1
x/21 = 3/63
x = 3*21/63 = 63/63 = 1

What is the next number in the sequence: 4, 11, 25, 53...?

Answers

Answer:

109

Step-by-step explanation:

Given that there is a sequence of numbers as

4,11,25,53,...

We have to find the next number.

To find the next number, let us see the pattern from the given four numbers

We have

I number = 4

II number = 4+7

III number = II number + 2(7)

Iv number = III number +4(7)

So if we guess this pattern continues the next number namely v number would be

V number = IV number +8(7)

=53+56

109

i.e. I number is added by 7, II number by 2(7), III number by 2^2(7)

hence next number 2^3(7)

Answer is 109

The next number in the sequence is:

109

Obtaining the sequence

As can be seen, the first number is a selected number, which in this case is four, to which seven are added to obtain:

4 + 7 = 11

Then double 7 is added to that number, that is 14, with which you get:

11 + 14 = 25

The double of 14 is added to that number, which is 28, so the next number is:

25 + 28 = 53

And to get the next number, double 28 must be added, which is 56, therefore:

53 + 56 = 109

By this reason, the next number in the sequence is 109.

If you want to learn more about Sequences, you can visit the following link: https://brainly.com/question/16130064

What is the relationship between the 6s in 660, 472?

Answers

The 6 is in the hundred thousands place and ten thousands place

hope this helps

Answer:

1st 6 is 1/10 of 2nd 6 and 2nd 6 is 10 times the 2nd 6.

Step-by-step explanation:

We are asked to find the relationship between the 6s in 660,472.

Upon looking at our given number, we can see that 1st see is in 10 thousands place and 2nd 6 is in hundred thousands place.

Place value of 1st 6: 60,000

Place value of 2nd 6: 600,000

Let us compare our both numbers as:

We can see that 600,000 is 10 times greater than 60,000, therefore, 1st 6 is 1/10 of 2nd 6 and 2nd 6 is 10 times the 2nd 6.

25/5 as a mixed number

Answers

25/5 as a mixed number would be 5.
[tex]\bf \textit{well, 5 goes into 25 \underline{5 times}, with a \underline{remainder} of 0} \\\\\\ 5\frac{0}{5}\implies 5+\frac{0}{5}\implies 5+0\implies \implies 5[/tex]

The manager at Jessica's Furniture Store is trying to figure out how much to charge for a couch that just arrived. If the couch was bought at a wholesale price of $113.00 and Jessica's Furniture Store marks up all furniture by 45%, at what price should the manager sell the couch?

Answers

the couch would be 163.85

Answer: The manager sold the couch at $163.85.

Step-by-step explanation:

Since we have given that

Wholesale price of the couch = $113.00

If Jessica's Furniture Store marks up all furniture by 45%.

So, Increment in whole sale price is given by

[tex]\frac{45}{100}\times 113\\\\=\frac{5085}{100}\\\\=\$50.85[/tex]

So, the manager sold the couch at the price is given by

[tex]\$113.00+\$50.85\\\\=\$163.85[/tex]

Hence, the manager sold the couch at $163.85.

which of the following inequality has solution set

Answers

I4Ix-3 has a solution set.

Write out the sample space for the given experiment. use the letter b to indicate boys and g for girls. a couple plans to have 33 children.

Answers

An example of one possible outcome in the sample space:

[tex]\[ \text{bgbbggbggbgbgbggbbgbgbgbbggbgbgb} \][/tex]

To create the sample space for the given experiment, where a couple plans to have 33 children, we'll represent the possible outcomes using the letters "b" for boys and "g" for girls. The sample space for having 33 children can be represented as a sequence of "b" and "g", where each letter represents the gender of a child. Since there are 33 children, the sample space will consist of all possible sequences of 33 "b"s and "g"s.

[tex]\[ \text{bgbbggbggbgbgbggbbgbgbgbbggbgbgb} \][/tex]

Each letter in the sequence represents the gender of a child, with "b" indicating a boy and "g" indicating a girl. The sample space consists of all possible sequences of 33 "b"s and "g"s, representing all possible combinations of boys and girls the couple could have among their 33 children.

The time to fly between new york city and chicago is uniformly distributed with a minimum of 120 minutes and a maximum of 150 minutes. what is the probability that a flight is less than 135 minutes

Answers

Do you have multiple choices?

A factory produces 5−packs of pencils. To be within the weight specifications, a pack of 5 pencils should weigh between 60 grams and 95 grams. Each package has a mass of 15 grams. Enter a compound inequality to represent the mass of a single pencil in a pack. Can each pencil have a mass of 10.5 grams?

Answers


Divide the weight variance of a pack by 5, yielding
12 to 19 grams.
Then a single pencil can be between 12 < pencil < 19 grams.
Therefore each pencil cannot have a mass of 10.5 grams.

The compound inequality will be:  [tex]9\leq x\leq 16[/tex], where [tex]x[/tex] is the mass of a single pencil and each pencil can have a mass of 10.5 grams.

Explanation

Suppose, the mass of a single pencil in the pack is  [tex]x[/tex] gram.

So, the total mass of 5 pencils will be:  [tex]5x[/tex] grams.

Each package has a mass of 15 grams. So, the total weight of the pack of 5 pencils [tex]=(5x+15)[/tex] grams.

To be within the weight specifications, a pack of 5 pencils should weigh between 60 grams and 95 grams. So, the compound inequality will be..........

[tex]60\leq 5x+15\leq 95\\ \\ 60-15\leq 5x+15-15\leq 95-15\\ \\ 45\leq 5x\leq 80\\ \\ \frac{45}{5}\leq \frac{5x}{5}\leq \frac{80}{5}\\ \\ 9\leq x\leq 16[/tex]

So, the compound inequality to represent the mass of a single pencil in a pack will be:  [tex]9\leq x\leq 16[/tex], where [tex]x[/tex] is the mass of a single pencil.


As 10.5 grams lies inside the interval [tex]9\leq x\leq 16[/tex] , so each pencil can have a mass of 10.5 grams.

Answer:
-7(k+9)=9(k-5)-14k

Answers

-7(k+9)=9(k-5)-14k
-7k-63=(9k-45)-14k
-7k-63=-5k-45
-7k=-5k+18
-2k=18
k=-9

If g(x)=5x-3 and h(x) = x find (goh) (4)

Answers

Goh means

G(h(4))
G(4)
5*4-3
17

In this composition, we first apply the function h, which is simply the identity function, to the input 4, resulting in 4. Then, we apply the function g to this result. As g(x) = 5x - 3, g(4) equals 17. Hence, (g◦h)(4) = 17.

To find (g◦h)(4), which represents the composition of functions g and h evaluated at x = 4, we first need to find h(4), then substitute the result into g(x).

Given h(x) = x, h(4) = 4.

Now, we substitute h(4) into g(x).

So, g(h(4)) becomes g(4).

Given g(x) = 5x - 3, substituting x = 4 into g(x), we get g(4) = 5(4) - 3 = 20 - 3 = 17.

Therefore, (g◦h)(4) = 17.

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