Is 8.73 a rational number

Answer/Step-by-step explanation:

A. [tex] -7x^2y^2(8x^2y - 5xy + 11xy^2 - 31) [/tex]

[tex] -7x^2y^2(8x^2y) - (-7x^2y^2)(5xy) + (-7x^2y^2)(11xy^2) - (-7x^2y^2)(31) [/tex] (distributive property)

[tex] -56x^4y^3 + 35x^3y^3 - 77x^3y^4 + 217x^2y^2 [/tex] (note: - × - = + and - × + = -)

B. [tex] (\frac{4}{5}t^3 - 5t)(\frac{1}{4}t^2 - 3t) [/tex]

[tex] (\frac{4}{5}t^3)(\frac{1}{4}t^2 - 3t) - 5t(\frac{1}{4}t^2 - 3t) [/tex] (distributive property)

[tex] \frac{4*1}{5*4}t^3*t^2 - \frac{4*3}{5}t^3*t - \frac{5*1}{4}t*t^2 + 15t^2 [/tex]

[tex] \frac{1}{5}t^5 - \frac{12}{5}t^3 - \frac{5}{4}t^3 + 15t^2 [/tex]

Combine like terms

[tex] \frac{1}{5}t^5 - \frac{73}{20}t^3 + 15t^2 [/tex] (note: -12/5 - 5/4 = -73/20)

C. (4x² - 7x + 5)(2x - 5)

4x²(2x - 5) - 7x(2x - 5) + 5(2x - 5) (distributive property)

8x³ - 20x² - 14x² + 35x + 10x - 25

Combine like terms

8x³ - 34x² + 45x - 25

D. (3m² - 5m + 2)²

= (3m² - 5m + 2)(3m² - 5m + 2)

= 3m²(3m² - 5m + 2) - 5m(3m² - 5m + 2) + 2(3m² - 5m + 2) (distributive property)

= 9m⁴ - 15m³ + 6m² - 15m³ + 25m² - 10m + 6m² - 10m + 4

Combine like terms

= 9m⁴ - 15m³ - 15m³ + 6m² + 25m² + 6m² - 10m - 10m + 4

= 9m⁴ - 30m³ + 37m² - 20m + 4

Answer:

10000

Step-by-step explanation:

First, highlight parts of the question. Since it says round to the nearest ten, draw a number line to start. Start by drawing a number line from 9990 to 10000. Whenever a number has the digit from 5 till any number less than 10, you round up. If the number you are trying to round to any digit is less than 5, then you can round down. Since the part of the number that is important for the question is 5.2, we round above. You get 10000 from this.

Answer:

x=8   x=5

Step-by-step explanation:

X^2 - 13x + 40 = 0

What two numbers multiply to 40 and add to -13

-8*-5 = 20

-8-5 = -13

( x-8) (x-5) =0

Using the zero product property

x-8=0    x-5 =0

x=8   x=5

To solve this polynomial equation, we will first factor the left side.

On the left, we have a special type of trinomial

that can be factored as the product of two binomials.

X² breaks down as x · x and we are looking for

the factors of 40 that add to the middle term, -13.

Since the middle term is negative, we use negative factors of 40.

The factors that work are -8 and -5.

So we have (x - 8)(x - 5) = 0.

If (x - 8)(x - 5) = 0, that means that either x - 8 = 0 or x - 5 = 0.

Solving for x in each equation, we have x = 8 or x = 5.

We can write this as the set of numbers {8, 5}.

Answer:

11

Step-by-step explanation:

f(x) = 2x - 13

9 = 2x - 13                   Add 13 to both sides

9 + 13 = 2x                  Add the left

22 = 2x                       Divide by 2

22/2 = x

x = 11

Answer:

12

Step-by-step explanation:

G(2)= 2^2 +4(2)

Solve via order of operations

G(2)=4 +8

G(2)=12

Answer:

2/5 divided 1/2 as a unit rate .what do you mean

Answer:

32 cm²

Step-by-step explanation:

SA = 2(lw + lh + hw)

      = 2(2x2 + 2x3 + 3x2)

      = 2(4 + 6 + 6)

      = 2(16)

      = 32 cm²

the answer is C). y= 1/4x + 2

Answer:a) x =−1

B) x=1/2y+12

C) m=13

D) x=2

Step-by-step explanation:a) Let's solve your equation step-by-step.

5(3x+7)=20−2(x+1)

Step 1: Simplify both sides of the equation.

5(3x+7)=20−2(x+1)

(5)(3x)+(5)(7)=20+(−2)(x)+(−2)(1)(Distribute)

15x+35=20+−2x+−2

15x+35=(−2x)+(20+−2)(Combine Like Terms)

15x+35=−2x+18

15x+35=−2x+18

Step 2: Add 2x to both sides.

15x+35+2x=−2x+18+2x

17x+35=18

Step 3: Subtract 35 from both sides.

17x+35−35=18−35

17x=−17

Step 4: Divide both sides by 17.

17x/17=−17/17

x=−1

B) Let's solve for x.

2x−y=24

Step 1: Add y to both sides.

2x−y+y=24+y

2x=y+24

Step 2: Divide both sides by 2.

2x/2=y+24/2

x=1/2y+12

C) Let's solve your equation step-by-step.

m(3−4m)=7+4(8−m2)

Step 1: Simplify both sides of the equation.

−4m2+3m=−4m2+39

Step 2: Add 4m^2 to both sides.

−4m2+3m+4m2=−4m2+39+4m2

3m=39

Step 3: Divide both sides by 3.

3m/3=39/3

m=13

D) Let's solve your equation step-by-step.

5x(x+3)=x(5x−3)+36

Step 1: Simplify both sides of the equation.

5x2+15x=5x2−3x+36

Step 2: Subtract 5x^2 from both sides.

5x2+15x−5x2=5x2−3x+36−5x2

15x=−3x+36

Step 3: Add 3x to both sides.

15x+3x=−3x+36+3x

18x=36

Step 4: Divide both sides by 18.

18x/18=36/18

x=2

The answer would be 16 all you have to do is multiply the length by the width which is 2 and 8.

Answer:

the answer to this question is b

Answer:

[tex]-57-39i[/tex]

Step-by-step explanation:

So we have the expression:

[tex](7+2i)(-9-3i)[/tex]

FOIL:

[tex]=7(-9)+7(-3i)+2i(-9)+2i(-3i)[/tex]

Simplify:

[tex]=-63-21i-18i-6i^2[/tex]

Recall that i² is just -1. Thus:

[tex]=-63-21i-18i-6(-1)[/tex]

Simplify:

[tex]=-63-21i-18i+6[/tex]

Combine like terms:

[tex]=(-63+6)+(-21i-18i)[/tex]

Add:

[tex]=-57-39i[/tex]

And we're done!

Answer:

0.3

Step-by-step explanation:

1 foot = 12 inches so 3.60/12=0.3

Answer:

The answer is (1,-1)

Step-by-step explanation:

The best approach for this problem is to plug in the coordinates into the given inequality.

[tex]7x-3y\geq 10\\[/tex]

(3,4) ------> [tex]7(3)-3(4)=9[/tex]

9 is less than 10 so, we can rule this one out.

(1,0) -------> [tex]7(1)-3(0)=7[/tex]

7 is less than 10 so, we can rule this one out.

(1,2) -------> [tex]7(1)-3(2)=1[/tex]

1 is less than 10 so, we can rule this one out.

(1,-1) -------> [tex]7(1)-3(-1)=10[/tex]

10 is equal to 10, so this is the answer.

Hope this helps!

As mentioned by Mark there are an unlimited number of pairs that satisfy your equation. So let us see how you can characterize these solutions

if 7x - 3y > 10 then

7x > 10 +3y

Now we can substitute any value for y and get the appropriate value for x. For example I can choose y to be 6

then by substitution

7  must be > 10+ 3*6

or 7x must be > 28

or x must be > 4

So all pairs such that x is > 4 and y = 6 are solutions.

I can create an infinite number of pairs choosing any number for y. Likewise I could have chosen x and solved the problem for y. In the above example I chose 6 for y to make the division easy. I could have chosen any number(real or integer) for y and solved the equation for x  to derive appropriate  pairs

Answer:

[tex]\huge\boxed{\sf \frac{x}{3} = 12}[/tex]

Step-by-step explanation:

Let the number be x

4x = 156

Dividing both sides by 4

x = 36

Dividing both sides by 3

[tex]\frac{x}{3}= \frac{36}{3}[/tex]

[tex]\frac{x}{3} = 12[/tex]

Answer:

$400.27

Step-by-step explanation:

owes $424.04

returns an item for $49.95

-424.04 + 49.95 = -374.09

he now owes $374.09

returns an item for $50.42

-374.09 + 50.42 = -323.67

he now owes $323.67

makes a purchase of $39.19

-323.67 - 39.19 = -362.86

he now owes $362.86

makes a purchase of $37.41

-362.86 - 37.41 = -400.27

he now owes $400.27

Answer:

-7/12

Step-by-step explanation:

Find common denominators. Note that what you do to the denominator, you do to the numerator.

Set the common denominator to 12:

(-5/6)(2/2) = -10/12

(1/4)(3/3) = 3/12

Combine the terms:

-10/12 + 3/12 = 3/12 - 10/12 = -7/12

-7/12 is your answer.

~

Answer:

-0.5

Step-by-step explanation:

30x - 6x = -6(2)

24x           -12

24              24

x         =      -.5

Answer:

20,27

Step-by-step explanation:

let 13,a,b,34 be consecutive numbers.

a=13

l=34

n=4

l=a+(n-1)d

34=13+(4-1)d

34-13=3d

21=3d

d=21/3=7

a=13+7=20

b=20+7=27

Answer:

  20, 27

Step-by-step explanation:

The difference 34-13 = 21 must be divided into three equal parts. Each is 21/3 = 7.

The numbers are 13+7 = 20, 20+7 = 27. As a check, 27 +7 = 34

The missing numbers are 20 and 27.

Answer:

x = 45°

Step-by-step explanation:

x + 3x = 180°

--> 4x = 180°

--> x = 180 / 4 = 45°

Step-by-step explanation:

x+3x=180 (sum of linear pair=180)

or, 4x =180

or, x = 180/4

therefore x =45

Answer:

50%

Ste50p-by-step explan%ation:

Answer:

Seven isn't part of the set of irrational numbers.

Step-by-step explanation:

Start with the smallest set among the choices. The set of all natural numbers, [tex]\mathbb{N}[/tex], starts with [tex]0[/tex] (or [tex]1[/tex], for some people.) A number [tex]n[/tex] is in [tex]\mathbb{N}\!\!\![/tex] (write [tex]n \in \mathbb{N}[/tex]) if and only if [tex](n - 1)[/tex] is in [tex]\mathbb{N}\![/tex]. Conversely, if [tex]n\![/tex] is indeed in [tex]\mathbb{N}\!\!\!\!\![/tex], then [tex](n + 1)[/tex] would also be in [tex]\mathbb{N}\!\!\!\!\!\!\![/tex]. For [tex]7[/tex]:

[tex]1 \in \mathbb{N} \implies 2 \in \mathbb{N}[/tex].

[tex]\vdots[/tex].

[tex]6 \in \mathbb{N} \implies 7 \in \mathbb{N}[/tex].

Therefore, [tex]7[/tex] is indeed in the set of all natural numbers.

Similarly, a number [tex]n[/tex] is in the set of integers, [tex]\mathbb{Z}[/tex], if and only if either [tex](n - 1)[/tex] or [tex](n + 1)[/tex] is (or both are) in [tex]\mathbb{Z}\!\![/tex].

Conversely, if a number [tex]n[/tex] is in [tex]\mathbb{Z}[/tex], then both [tex](n - 1)[/tex] and [tex](n + 1)[/tex] will be in [tex]\mathbb{Z}\![/tex].

It can be shown in a similar iterative way that [tex]7 \in \mathbb{Z}[/tex].

Alternatively, consider the fact that the set of all natural numbers, [tex]\mathbb{N}[/tex], is a subset of the set of all integers, [tex]\mathbb{Z}[/tex]. Therefore, [tex]7 \in \mathbb{N}[/tex] implies that [tex]7 \in \mathbb{Z}[/tex].

A number [tex]m[/tex] is a member of the set of all rational numbers [tex]\mathbb{Q}[/tex] if and only if there exists two integers [tex]p[/tex] and [tex]q[/tex] such that:

[tex]\displaystyle m = \frac{p}{q}[/tex].

[tex]1[/tex] and [tex]7[/tex] are both integers. If [tex]p = 7[/tex] and [tex]q = 1[/tex], then [tex]\displaystyle 7 = \frac{7}{1} = \frac{p}{q}[/tex]. Hence,

Alternatively, note that the set of all integers, [tex]\mathbb{Z}[/tex], is a subset of the set of all rational numbers, [tex]\mathbb{Q}[/tex]. Therefore, the fact that [tex]7 \in \mathbb{Z}[/tex] would imply that [tex]7 \in \mathbb{Q}[/tex].

A number is in the set of all irrational numbers if and only if:

Therefore, the fact that [tex]7[/tex] is a rational number implies that it is not an irrational number.

Answer:

irrational numbers

Step-by-step explanation:

Answer:

3. 2x+18=4x+26

Step-by-step explanation:

2(x+9)=4(x+7)+2

2x+18=4x+28+2

2x+18=4x+30

The step that made an error in solving this linear equation is step 3.

Hope this helps ;) ❤❤❤

Answer:

x=[tex]-\frac{10}{9}[/tex]

Step-by-step explanation:

We start by moving the constant to the right. In this case -1 (it becomes positive 1).

9x=-11 +1

9x= - 10

divide 9 by both sides.

x=- [tex]\frac{10}{9}[/tex]

Answer:

A.

Step-by-step explanation:

Retirement funds are not liquid assets. You fund them with investment assets.  However, Roth IRA's and 401 (k) are not assets in the traditional sense. It may be confusing, but the way they grow is by investments. The answer is A.

The amount of money invested in a retirement fund is an example of an investment asset. which is the correct answer would be an option (A)

An Investment is defined as an asset or object purchased with the intention of generating income or appreciation is referred to as an investment. The term "appreciation" describes a rise in an asset's worth over time. When a person buys a product as an investment, they don't intend to utilize it right away; instead, they plan to use it to make money later on.

An investment always entails the expenditure of some capital today—time, effort, money, or an asset in the anticipation of receiving a larger return than what was first invested.

Investment portfolios are not movable property. They are financed by investments. One type of investing asset is the amount of money invested into a retirement fund.

Hence, the amount of money invested in a retirement fund is an example of an investment asset. which is the correct answer would be an option (A)

Learn more about an Investment asset here:

https://brainly.com/question/23611837

#SPJ2

Answer:

25.12 inches

Step-by-step explanation:

To find the circumference or the perimeter of a circle it is the diameter times pi. (pi = 3.14) Or you can do radius times 2 times pi.

Answer is 4 times 2 times 3.14 which is 25.12