C) Work out 3/4 × 5 (Give your answer as the simplest mixed fraction).​

Given:

Expression is

[tex]3r^2-2r+4[/tex]

To prove:

If r is any rational number, then [tex]3r^2-2r+4[/tex] is rational.

Step-by-step explanation:

Property 1: Every integer is a rational number. It is Theorem 4.3.1.

Property 2: The sum of any two rational numbers is rational. It is Theorem 4.3.2.

Property 3: The product of any two rational numbers is rational. It is Exercise 15 in Section 4.3.  

Let r be any rational number.

We have,

[tex]3r^2-2r+4[/tex]

It can be written as

[tex]3(r\times r)-2r+4[/tex]

Now,

3, -2 and 4 are rational numbers by property 1.

[tex]r^2=r\times r[/tex] is rational by Property 3.

[tex]3r^2\text{ and }-2r[/tex] are rational by Property 3.

[tex]3r^2+(-2r)+4[/tex] is rational by property 2.

So, [tex]3r^2-2r+4[/tex] is rational.

Hence proved.

We want to prove that if r is rational, then:

[tex]3*r^2 - 2r + 4[/tex]  Is also rational.

The proof is below:

Remember that a rational number is any number that can be written as a quotient of two integer numbers.

Then we have:

[tex]r = \frac{a}{b}[/tex]

Where a and b are integers.

If we replace that in our equation, we get:

[tex]3*(\frac{a}{b}) ^2 - 2*(\frac{a}{b}) + 4\\\\\frac{3a^2}{b^2} - \frac{2a}{b} + \frac{4}{1}[/tex]

Note that if a is an integer, then 3*a^2 is also an integer.

If b is an integer, then b^2 is also an integer.

Now we can perform the sum of these fractions to get:

[tex]\frac{3a^2}{b^2} - \frac{2a}{b} + \frac{4}{1}\\\\\frac{3a^2 - 2ab + 4b^2}{b^2}[/tex]

And because integers are closed under the addition, then the numerator of that fraction is also an integer, then we have that the given expression can be written as a quotient of two integers, thus, it is a rational number.

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Answer:

Divide by P

Step-by-step explanation:

i = P x M

divide by P to get M alone, which means you have to do it to both sides

i/P = M

Answer:

i sorry but idk the annswer

Answer:

240

Step-by-step explanation:

200/25=8

30x8=240

hope this helps i didn't really understand the question much

Answer:

8

Step-by-step explanation:

scince it has the lines that mean that it will always be positive.

Answer:

8

Step-by-step explanation:

Have a nice day!

Answer:

(a+b)(a+b)

Step-by-step explanation:

Answer:

75 cm

Step-by-step explanation:

Given:

Perimeter of the triangular yield sign = 225 cm

Side lengths = x, x and x

Required:

Length of each side

SOLUTION:

Perimeter of the triangular yield sign = sum of all sides of the triangular yield sign

225 cm = x + x + x

Solve for x

225 = 3x

Divide both sides by 3

225/3 = 3x/3

75 = x

x = 75

The length big each side is 75 cm

Answer:

1

Step-by-step explanation:

The probability of this happening would be a 1 when placing a value between zero and one inclusive. One in this case would indicate a 100% probability. This is the case because in the question it is stated that it is "certain" that you will get 2 kings when selecting 50 cards, this means that no matter what it will happen every time 50 cards are drawn, thus making the probability 100%. If the question were phrased differently such as "what is the probability of getting 2 kings from 50 cards drawn?" then the probability would be 0.04 or 4% which is 2/50.

Using probability concepts, it is found that the likelihood is of 1.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

A few observations regarding probabilities are important.

In this problem, you are certain to get 2 Kings when selecting 50 cards from a shuffled deck, hence the likelihood is of 1.

You can learn more about probabilities at https://brainly.com/question/15536019

Answer:

40

Step-by-step explanation:

Answer:

-1.71 the answer is d

Step-by-step explanation:

.........

Let [tex]a_n[/tex] denote the n-th term in the progression. So

[tex]a_n=a_{n-1}+d[/tex]

for some constant difference between terms d.

Solve for [tex]a_n[/tex] explicitly:

[tex]a_4=a_3+d[/tex]

[tex]a_5=a_4+d=a_3+2d[/tex]

[tex]a_6=a_5+d=a_3+3d[/tex]

and so on, up to

[tex]a_n=a_3+(n-3)d[/tex]

We're told that the third term is [tex]a_3=4m-2n[/tex], and the ninth term is [tex]a_9=2m-8n[/tex], and according to the recursive rule above, we have

[tex]a_9=a_3+6d[/tex]

Solve for d :

[tex]2m-8n=(4m-2n)+6d[/tex]

[tex]-2m-6n=6d[/tex]

[tex]d=-\dfrac{2m+6n}6=\boxed{-\dfrac{m+3n}3}[/tex]

Answer:

$43,260

Step-by-step explanation:

You have the 3% annual income, which you can convert to a decimal. This gives:

42000 * 1.03

42000 represents Blair's initial income, and 0.03 represents the 3% increase.

I chose 1.03 because I don't have to subtract 97% and add it to 42000.

Answer:

Is B

Step-by-step explanation:

The dividend is 2  and the divisor is 2/5

A division is a process of splitting a specific amount into equal parts.

The given fraction is 2 ÷ 2/5

The number which is getting divided here is called the dividend.

The number which divides a given number is the divisor.

In the given division the dividend is 2

The divisor is 2/5

Hence,  the dividend is 2  and the divisor is 2/5

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Answer:

y=2(4^x)

Step-by-step explanation:

if you notice, all the y-values are multiplied by 4 for each x-value. this means 4 is raised to the power of x. however, when you plug this in, you realize that the value produced is only half the actual y-values, so you multiply this whole thing by 2.

y=2(4^x)

Answer:

f(x) = 2^(2x+1)

Step-by-step explanation:

You can tell that each of the outputs of f(x) are powers of 2, so all you have to do is figure out the pattern of the exponents.

2^3 = 8

2^5 = 32

2^7 = 128

2^9 = 512

the relationship between the sequence

3,5,7,9

when you start on 1 is

2x+1

2(1)+1 = 3

2(2)+1 = 5

etc.

Answer:

9.3333333

Step-by-step explanation:

Answer:

[tex] \frac{9}{4} \div \frac{1}{4}

\frac{9}{4} \times \frac{4}{1}

= \frac{34}{4} \\ \\ \\ \\ = 9[/tex]

Answer:

A

Step-by-step explanation:

Answer:

The midpoint is ( -2.5, 6.5)

Step-by-step explanation:

To find the x coordinate of the midpoint, add the x coordinates of the endpoints and divide by 2

(-2+-3)/2 = -5/2 = -2.5

To find the y coordinate of the midpoint, add the y coordinates of the endpoints and divide by 2

(6+7)/2 = 13/2 = 6.5

The midpoint is ( -2.5, 6.5)

Answer:

2x-3y=2

x=6y-5

2(6y-5)-3y=2

use the distributive property.

2*6y=12y

2*-5=-10

12y-10-3y=2

combine like terms

12y-3y=9y

9y-10=2

add 10 to both sides.

9y-10+10=9y

2+10=12

9y=12

divide both sides by 9

9y/9=y

y=about 1.33

plug in the value of y in the expression equal to the value of x.

x=6(1.33)-5

solve

6*1.33=7.98

x=7.98-5

7.98-5=2.98

Step-by-step explanation:

x=2.98

y=1.33

Answer:

See below

Step-by-step explanation:

Given formula

Year 2005, finding number of trout

Year 2010, finding number of trout

Year 2015, finding number of trout

Number of trout is trending up with significant increase over yeas

Answer:

Step-by-step explanation:

Number of trout in 2005.

Find the number of years apart from 2000 to 2005.

2005 - 2000 = 5

Substitute for x and solve for y.

y = x² + 3x + 2

y = (5)² + 3(5) + 2

y = 25 + 15 + 2

y = 40 + 2

y = 42 million

Number of trout in 2010.

Find the number of years apart from 2000 to 2010.

2010 - 2000 = 10

Substitute for x and solve for y.

y = x² + 3x + 2

y = (10)² + 3(10) + 2

y = 100 + 30 + 2

y = 130 + 2

y = 132 million

Number if trout in 2015.

Find the number of years apart from 2000 to 2015.

2015 - 2000 = 15

Substitute for x and solve for y.

y = x² + 3x + 2

y = (15)² + 3(15) + 2

y = 225 + 45 + 2

y = 270 + 2

y = 272 million

Best of Luck!

Answer:

(3x+14°) + (7x-4)° = 180°

=> 10x + 10 = 180

=> 10x = 180 – 10

=> x = 170/10

=> x = 17

The value of x is 17

Answer:12

Step-by-step explanation:

The prime factorization of 84 is 2×2×3×7 . The prime factorization of 48 is 2×2×2×2×3 . . Therefore, the GCF is 2×2×3=12

Answer:

6.16.

Step-by-step explanation:

hope this helps.

Answer:

37/6

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

a straight line is 180, 180-40=140

Answer:

c is incorrect they just made me fail my quiz... :(

Step-by-step explanation:

Answer:

7/10 divided by 1/10

Step-by-step explanation:

Answer:

11

Step-by-step explanation:

11 + 10 = 21

Answer:

y=1/3x+5/3

Step-by-step explanation:

y=1/3x+b

1=1/3(-2)+b (plug in ya points)

1=-2/3+b

5/3=b

y=1/3x+5/3

Answer:

the answer is y=1/3x+5/3

Step-by-step explanation:

hope this helps

did it on edge