312 x 32 standard algorithm

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:

she has no more money

Step-by-step explanation:

Answer:

7.78 if u subtract

but no more money i guess

Answer:

To solve fractions, you MUST HAVE THE SAME DENOMINATORS WHEN DEALING WITH ADDITION AND SUBTRACTION.

Step-by-step explanation:

For example, 2/3 + 3/6

The denominators in this case have a common denominator which is 6.

All you have to do is multiply the 2/3 by 2 in the numerator and the denominator. Once you do, you'll get 4/6 which you could then add to 3/6 to get 7/6 which would equal 1 1/6 or 7/6 either is fine.

Hope this helps! :)

Answer:

To solve fractions, you MUST HAVE THE SAME DENOMINATORS WHEN DEALING WITH ADDITION AND SUBTRACTION.

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:

C

Step-by-step explanation:

a straight line is 180, 180-40=140

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:

(a+b)(a+b)

Step-by-step explanation:

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:

64π or 201.0619298297

Step-by-step explanation:

Area of a circle: πr²

To find r, the radius of the circle, take the diameter (16) and halve it to get 8. You can now place 8 into the equation to get π8². Square 8 to get 64. You now now have π64, or 201.0619298297.

Answer:

True

Step-by-step explanation:

In a translation, the figures face the same direction and are congruent.

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:

(3x+14°) + (7x-4)° = 180°

=> 10x + 10 = 180

=> 10x = 180 – 10

=> x = 170/10

=> x = 17

The value of x is 17

Answer:

r=4.5% daily

Step-by-step explanation:

Exponential Growth

The natural growth of some magnitudes can be modeled by the equation:

[tex]P=P_o(1+r)^t[/tex]

Where P is the actual amount of the magnitude, Po is its initial amount, r is the growth rate and t is the time.

We know after t=32 days, the population has increased by 309%. Being the original population P the 100%, then the population reached 309+100= 409%.

Substitute the given values into the model function:

[tex]409\%P_o=100\%P_o(1+r)^{32}[/tex]

Simplifying:

[tex]4.09=(1+r)^{32}[/tex]

We need to solve for r. Taking the 32nd root:

[tex]\sqrt[32]{4.09}=\sqrt[32]{(1+r)^{32}}[/tex]

Simplifying:

[tex]1+r=\sqrt[32]{4.09}=1.045[/tex]

Solving:

[tex]r=1.045-1\Rightarrow r=0.045[/tex]

r=4.5% daily

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:

35

Step-by-step explanation:

7 * 5 = 35

Answer:

which class you are plz say dude

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:

$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:

either a full cup or 1 1/2

Answer:  so, 60 hours = 60/24 days = 2 days 12 hrs

Step-by-step explanation:

jfjkejkiydtmhfsngdjfs

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:

I think 21 is it right ...

Answer:

The solution to 9x10^-2 is 0.09 or (3/10)^2. The solution to 3x10^-4 is 0.0003 or 3/10000. Based on that, 9x10^-2 fits into 3x10^-4 three-hundred (300) times.