**Problem**

**Solution**

For this case we can conclude that:

DE = r

DF= s

EF= t

Proofs involving a transversal

Thus, it is clear that the **lines **RS and TV in the preceding diagram are **parallel** to each other

If you extend a set of** lines** indefinitely, they will remain **parallel** and never cross each other even though they are on the** same plane**. The symbol || represents the collection of **parallel lines**. All parallel lines are always **equally** spaced apart. Investigate the characteristics of parallel lines.

When two lines in a plane are stretched infinitely in both directions and do not cross, they are said to be parallel.

To solve the given question we know,

angle 1= angle 2 and lines RV // TS

angle 4= angle 3(**interior angles on parallel lines **are equal)

angle 1=angle 4 **(vertically opposite angles** are equal )

angle 1= angle 3 (angle 4=angle 1)

angle 4=angle 2( angle 1=angle 4)

Now we can see that the sum of base angles of the diagram will be 180 because

180-angle 3= angle STV

angle 4=angleSTV+180 (angle 3=angle4)

we proved that the diagram is a parallelogram because base angles of the same side are supplementary:

Therefore , we can conclude that the lines** RS // TV **in the preceding diagram .

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A parents' evening was planned to start at

15h45. There were 20 consecutive

appointments of 10 minutes each and a

break of 15 minutes during the evening. At

what time was the parents evening due to

finish?

C O 19h15

O 19h20

O 19h00

O 20h00

O 19h30

The **time** on which **parents** **evening **was due to finish was 19 hour 20 **minutes.**

**Time **is the ongoing pattern of existence and things that happen in what seems to be an irreversible order from the past, through the present, and into the future.

It is a component quantity of various measurements used to order events, compare the length of events or the **time **gaps between them, and quantify rates of change of quantities in objective reality or in conscious experience. Along with the three spatial dimensions, **time **is frequently considered a fourth dimension.

The International System of **Units **is built upon the seven base **units **of measurement stipulated by the Système International d'Unités (SI), from which all other SI **units **are derived. The primary **unit **of **time **is the second. The second can be shortened using either the letter S or the letter sec.

20 consecutive appointments of 10 mins = 20 × 10 mins

= 200 min

= 3 hours 20 mins

A break of 15 mins = 3 hours 20 mins + 15 min

= 3 hours 35 mins

The **time **that the parents evening due to finish = 15h 45 min +3h 35 mins

= 19h 20min

Thus, the **time **on which parents evening was due to finish was 19h 20min.

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Solve for a.5a== ✓ [?]2aPythagorean Theorem: a2 + b2 = c2=

**ANSWER**

**a = √21**

**EXPLANATION**

This is a right triangle, so we have to apply the Pythagorean Theorem to find the value of a.

We know the length of the hypotenuse which is 5, and the length of one of the legs, which is 2. The Pythagorean Theorem for this problem is,

[tex]a^2+2^2=5^2[/tex]Subtract 2² from both sides,

[tex]\begin{gathered} a^2+2^2-2^2=5^2-2^2 \\ a^2=25-4 \end{gathered}[/tex]And take the square root to both sides,

[tex]\begin{gathered} \sqrt[]{a^2}=\sqrt[]{25-4} \\ a=\sqrt[]{21} \end{gathered}[/tex]Hence, the value of **a is √21**.

Which of the following expressions is equal to -x2 -36

OA. (-x+6)(x-6i)

OB. (x+6)(x-6i)

OC. (-x-6)(x-6i)

OD. (-x-6)(x+6i)

The **expression equivalent** to -x² - 36 is the one in option C.

(-x - 6i)*(x - 6i)

Which of the following expressions is equal to -x² - 36?We can rewrite the given **expression **as:

-x² - 36 = -x² - 6²

And remember that the product of a** complex numbe**r z = (a + bi) and its **conjugate **(a - bi) is:

(a + bi)*(a - bi) = a² + b²

Then in this case we can rewrite:

-x² - 6² = -(x² + 6²) = - (x + 6i)*(x - 6i)

= (-x - 6i)*(x - 6i)

The correct option is C.

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What needs to occur for a geometric series to converge?

Given a Geometric Series:

[tex]\sum_{n\mathop{=}1}^{\infty}a\cdot r^{n-1}[/tex]Where "r" is the ratio.

By definition:

[tex]undefined[/tex]Randy has $12 which he decides to put into his savings account. Every week Randy does chores to earn a $6 allowance which he continues to save and put into his savings account.Like Randy, Becky decides to be more responsible with her money and also save her money. Right now she owes her parents $8. Becky also earns $7 a week for doing chores, If both Randy and Becky save up beginning today whose savings account would reach $50first?A. RandyB. BeckyC. They would reach $50 at the same time.D. There is not enough given information to determine who will save up $50 first

*Randy's initial money = $12*

*Randy's earnings per week = $6*

*Becky's initial money = -$6 (she owes )*

*Becky's earnings per week = $7*

*Number of weeks: x *

The equation for each:

• Randy:

50 = 12 + 6x

• Becky:

50 = -6 + 7x

Solve each for x:

Randy:

50= 12 + 6x

50-12 = 6x

38 = 6x

38/6=x

**x= 6.3**

Becky:

50= -8 + 7x

50+8 =7x

58=7x

58/7=x

**x= 8.28**

Randy will take 6.33 weeks and Becky 8.28 weeks.

**Answer:**

**A. Randy**

Enter the solution to the inequality below. Enter your answer as an inequality.

Use =< for and >= for >

√x ≥ 17

Answer here

SUBMIT

The **solution** of the **inequality** is [tex]x \geq 289[/tex].

**What is inequality?**

**Inequalities** specify the connection between two **non-equal numbers**. Equal does not imply inequality. Typically, we use the "**not equal sign** (** **[tex]\neq[/tex]) " to indicate that two values are not equal. But several inequalities are utilised to compare the numbers, whether it is less than or higher than.

The given inequality is, [tex]\sqrt{x} \geq 17[/tex]

Taking square on both sides, we get

[tex]x\geq 289[/tex].

Therefore, the **solution** of the **inequality** is [tex]x \geq 289[/tex].

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Figure A has a perimeter of 48 m and one of theside lengths is 18 m. Figure B has a perimeter of 80 m.What is the corresponding side length of Figure B?

We have to use proportions to solve this question.

According to the given information, the perimeter of Figure A is to the sidelength of that figure as the perimeter of Figure B is to the sidelength of that figure:

[tex]\begin{gathered} \frac{48}{18}=\frac{80}{x} \\ x=\frac{80\cdot18}{48} \\ x=30 \end{gathered}[/tex]The corresponding sidelength of Figure B is 30.

Need help answering all these questions for the black bird. Exponential equation for the black bird: g(x) = 2^x-8 + 1King Pig is located at (11,9)Moustache Pig is located at (10,4)

**Given:**

Exponential equation for the black bird is,

[tex]g(x)=2^{x-8}+1[/tex]**Required:**

To find the starting point of bird and graph the given function.

**Explanation:**

(1)

The bird starting point is at x = 0,

[tex]\begin{gathered} g(0)=2^{0-8}+1 \\ \\ =2^{-8}+1 \\ \\ =1.0039 \\ \\ \approx1.004 \end{gathered}[/tex](2)

The graph of the function is,

**Final Answer**

(1) 1.004

(2)

4. Sean bought 1.8 pounds of gummy bears and 0.6 pounds of jelly beans and paid $10.26. He went back to the store the following week and bought 1.2 pounds of gummy bears and 1.5 pounds of jelly beans and paid $15.09. What is the price per pound of each type of candy?Directions: For each problem - define your variables, set up a system of equations, and solve.

Let

the price of gummy bears per pound = x

the price of jelly beans per pound = y

[tex]\begin{gathered} 1.8x+0.6y=10.26 \\ 1.2x+1.5y=15.09 \\ 1.2x=15.09-1.5y \\ x=12.575-1.25y \\ \\ 1.8(12.575-1.25y)+0.6y=10.26 \\ 22.635-2.25y+0.6y=10.26 \\ -1.65y=10.26-22.635 \\ -1.65y=-12.375 \\ y=\frac{-12.375}{-1.65} \\ y=7.5 \\ \\ 1.8x+0.6y=10.26 \\ 1.8x+0.6(7.5)=10.26 \\ 1.8x+4.5=10.26 \\ 1.8x=10.26-4.5 \\ 1.8x=5.76 \\ x=\frac{5.76}{1.8} \\ x=3.2 \end{gathered}[/tex]**price per pound of gummy bear = $3.2**

**price per pound of jelly beans = $7.5**

what is the area of a circular pool with a diameter of 36 ft?

**Answer:**

**1,017.36ft^2**

**Explanation:**

Area of the circular pool = \pi r^2

r is the radius of the pool

Given

r = d/2

r = 36/2

r = 18ft

Area of the circular pool = 3.14(18)^2

Area of the circular pool = 3.14 * 324

Area of the circular pool = 1,017.36ft^2

A student rolled 2 dice. What is the probability that the first die landed

on a number less than 3 and the second die landed on a number

greater than 3?

So what’s the probability you ask?

So the first dice can get either 1 or 2 and the second dice can have 4 5 or 6

So we need any one of these outcomes

(1,4) (1,5) (1,6) (2,5) (2,6) (2,4)

Clearly total no of outcomes is 36 (6x6)

Thus probability= 6/36 = 1/6

So the first dice can get either 1 or 2 and the second dice can have 4 5 or 6

So we need any one of these outcomes

(1,4) (1,5) (1,6) (2,5) (2,6) (2,4)

Clearly total no of outcomes is 36 (6x6)

Thus probability= 6/36 = 1/6

Ziba brought 4 bottles of water to the park. Each bottle held 6 ounces of water. Ziba drank an equal number of ounces of water each hour. If she was at the park 3 hours, how many ounces of water did she drink each hour

By taking the** quotient** between the total volume and the number of hours, we conclude that she drinks **8 ounces per hour.**

We know that Ziba has 4 bottles, each one with 6 ounces, so the **total volume** of water is:

V = 4*6 ounces = 24 ounces.

We know that she drinks that in 3 hours, so the amount that she drinks each hour is:

24 oz/3 = 8 oz

She drinks 8 ounces of water each hour.

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What is the probability of drawing a red card from a pack of cards and rolling an even number on a standard six-sided die?

Select one:

1/12

1/2

1/4

1/8

**Answer:**

**1/2 because half the cards are red and half the numbers are even**

Solve the system [tex]\left \{ {{5x1 + 5x2 = 5} \atop {2x1 + 3x2 = 4}} \right.[/tex]

The** solution** for the given **system of equations** is **x[1] = -1 **and **x[2] = 2**.

A system of linear equations (or linear system) is a collection of **one **or **more linear** equations involving the **same variables.**

Given are the following equations as -

**5 x[1] + 5 x[2] = 5**

**2 x[1] + 3 x[2] = 4**

Assume that -

**x[1] = a **

**x[2] = b**

Then, we can write the equations as -

**5a + 5b = 5**

**2a + 3b = 4**

Now -

5a + 5b = 5

5(a + b) = 5

a + b = 1

a = 1 - b

So, we can write -

2a + 3b = 4

as

2(1 - b) + 3b =4

2 - 2b + 3b = 4

b = 4 - 2

**b = 2 = x[2]**

Then

a = 1 - 2

**a = -1 = x[1]**

Therefore, the** solution** for the given **system of equations** is **x[1] = -1 **and **x[2] = 2**.

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Simplify completely.a.4x212 xwhen x +0.b. (2t)(3t)(t)c. (3x² - 4x +8)+(x² +6x-11)d. (3x² + 4x – 8) - (x² + 6x +11)

The expression in 4a) is given below

[tex]\frac{4x^2}{12x}[/tex]Collecting similar terms using the division rule of indices, we will have

[tex]\frac{a^m}{a^n}=a^{m-n}[/tex]The above expression therefore becomes

[tex]\begin{gathered} \frac{4x^2}{12x} \\ =\frac{4x^2}{12x^1} \\ =\frac{1}{3}\times x^{2-1} \\ =\frac{1}{3}\times x \\ =\frac{x}{3} \end{gathered}[/tex]**Hence,**

**The final answer = ****x/3**

Write the equation of a Circle with the given information.End points of a diameter : (11, 2) and (-7,-4)

The form of the equation of the circle is

[tex](x-h)^2+(y-k)^2=r^2[/tex]Where (h, k) are the coordinates of the center

r is the radius

Since the endpoints of the diameter are (11, 2) and (-7, -4), then

The center of the circle is the midpoint of the diameter

[tex]\begin{gathered} M=(\frac{11+(-7)}{2},\frac{2+(-4)}{2}) \\ M=(\frac{4}{2},\frac{-2}{2}) \\ M=(2,-1) \end{gathered}[/tex]The center of the circle is (2, -1), then

h = 2 and k = -1

Now we need to find the length of the radius, then

We will use the rule of the distance between the center (2, -1) and one of the endpoints of the diameter we will take (11, 2)

[tex]\begin{gathered} r=\sqrt[]{(11-2)^2+(2--1)^2} \\ r=\sqrt[]{9^2+3}^2 \\ r=\sqrt[]{81+9} \\ r=\sqrt[]{90} \\ r^2=90 \end{gathered}[/tex]Now substitute them in the rule above

[tex]undefined[/tex]20 >= 4/5 w

Solve the inequality. Grab the solution

Solve the inequality. Grab the solution

-8<-1/4m

In **inequality **20 >= 4/5 w, w is 25 or any real no. lower than< 25 and in **inequality **-8<-1/4m, m = any real no. greater than> 24 is are the **solution**.

An **inequality **compares two values and indicates whether one is lower, higher, or simply not equal to the other.

A B declares that a B is not equal.

When a and b are equal, an is less than b.

If a > b, then an is bigger than b.

(those two are called strict **inequality**)

The phrase "a b" denotes that an is less than or equal to b.

The phrase "a > b" denotes that an is greater than or equal to b.

We have give the **inequality **to solve

20 = 4/5w

w = 20 × 5/4

= 25 or any real no. lower than< 25

Let -8 = -1/4m

m = -8 × -4

m = 24

so m = any real no. greater than> 24

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Two cars start moving from the same point. One travels south at 24 mi/h and the other travels west at 18 mi/h. At what rate (in mi/h) is the distance between the cars increasing four hours later?

mi/h

The** rate** at which the **distance** between the two cars increased four hours later is 30 mi/h.

First of all, we would determine the **distances** travelled by each of the cars. The **distance** travelled by the first car after four (4) hours is given by:

Distance, x = **speed/time**

Distance, x = 24/4

**Distance**, x = 6 miles.

For the second car, we have:

Distance, y = **speed**/time

Distance, y = 18/4

**Distance**, y = 4.5 miles.

After four (4) hours, the total **distance** travelled by the two (2) cars is given by this mathematical expression (Pythagorean theorem):

z² = x² + y²

Substituting the parameters into the mathematical expression, we have;

z² = 6² + 4.5²

z² = 36 + 20.25

z² = 56.25

z = 7.5 miles.

Next, we would differentiate both sides of the mathematical expression (Pythagorean theorem) with respect to **time**, we have:

2z(dz/dt) = 2x(dx/dt) + 2y(dy/dt)

Therefore, the **rate** of change of **speed** (dz/dt) between the two (2) cars is given by:

dz/dt = [x(dx/dt) + y(dy/dt)]/z

dz/dt = [6(24) + 4.5(18)]/7.5

dz/dt = [144 + 81]/7.5

dz/dt = 225/7.5

dz/dt = 30 mi/h.

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**Answer:**

30 mi / hr

**Step-by-step explanation:**

First find out how far the cars are apart after 4 hours

24 * 4 = 96 mi = y

18 * 4 = 72 mi = x

Now use the pythagorean theorem

s^2 = ( x^2 + y^2 ) shows s = 120 miles apart at 4 hours

Now s^2 = x^2 + y^2 Differentiate with respect to time ( d / dt )

2 s ds/dt = 2x dx/ dt + 2y dy / dt

ds/dt = (x dx/dt + y dy/dt)/s

= (72(18) + 96(24)) / 120

ds/dt = 30 mi/hr

URGENT!! ILL GIVE

BRAINLIEST!!!!! AND 100

POINTS!!!!!

If angle a measures 42 degrees, then what other angles would be congruent to angle a and also measure 42 degrees?

If **angle "a"** measures 42° the the other angles that will be** congruent** to angle "a" and also **measure 42°** will be angle d, angle e and angle h .

In the question ,

a figure is given ,

From the figure we can see that 2 parallel lines are cut by a** transversal** .

So ,

angle a = angle d .......because vertically opposite angles .

angle a = angle e ...because **corresponding angles** are equal in measure

also

angle e = angle h .... because vertically opposite angles .

Therefore , If angle "a" measures 42° the the **other angles** that will be congruent to angle "a" and also **measure 42° **will be angle d, angle e and angle h , the correct option is (a) .

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HELP ME PLEASE !!!

REASONING An absolute value function is positive over its entire domain. How many x-intercepts does the graph of the function have?

● None

01

02

O Infinite

The **absolute value** function can intersect a horizontal **x-axis** at zero, one, as well as two points.

Thus, depending on the way the graph has indeed been shifted and reflected, it could or might not intersect the horizontal axis.

The absolute value function can intersect the** x-axis** at zero, one, or two points.

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savings 50,000 in 30 years with a saving compounded monthly at an interest rate of 6%. How much would I need to deposit a month?

The **amount **that needs to be **deposited **to have a saving of $50,000 in 30 years at the given interest rate is $8,302.10.

The **compound interest **formula is expressed as;

P = A / (1 + r/n)^nt

Where P is principal, A is amount accrued, r is interest rate is compound period and t is time elapsed.

Given the data in the question;

Accrued amount A = $50,000Interest rate r = 6%Compounded monthly n = 12Elapsed time t = 30 yearsPrincipal P = ?First, convert rate from percent to decimal.

Rate r = 6%

Rate r = 6/100

Rate r = 0.06 per year

To determine the **principal**, plug the given values into the formula above and solve or P

P = A / (1 + r/n)^nt

P = $50,000 / (1 + 0.06/12)^( 12 × 30 )

P = $50,000 / (1 + 0.05)³⁶⁰

P = $50,000 / (1.05)³⁶⁰

P = $8,302.10

Therefore, the **principal investment **is $8,302.10.

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What point in the feasible region maximizes the objective function?

x>0

Y≥0

Constraints

-x+3≥y

{ y ≤ ½ x + 1

objective function: C = 5x - 4y

**Answer:**

(3, 0)

Maximum Value of Objective Function = 15

**Step-by-step explanation:**

This is a problem related to Linear Programming(LP)

In linear programming, the objective is to maximize or minimize an **objective function** subject to a set of **constraints.**

For example, you may wish to maximize your profits from a mix of production of two or more products subject to resource constraints.

Or, you may wish to minimize cost of production of those products subject to resource constraints..

The given LP problem can be stated in standard form as

Max 5x - 4y

s.t.

-x + 3 ≥ y

y ≤ 0.5x + 1

x ≥ 0, y ≥ 0

The last two constraints always apply to LP problems which means the **decision variables** x and y cannot be negative

It is standard to express these constraints with the decision variables on the LHS and the constant on the RHS

Rewriting the above LP problem using standard notation,

Let's rewrite the constraints using the standard form:

- x + 3 ≥ y

→ -x - y ≥ -3

→ x + y ≤ 3 [1]

y ≤ 0.5x + 1

→ -0.5x + y ≤ 1 [2]

The LP problem becomes

Max 5x - 4y

s. t.

x + y ≤ 3 [1]

-0.5x + y ≤ 1 [2]

x ≥ 0 [3]

y ≥0 [4]

With an LP problem of more than 2 variables, we can use a process known as the Simplex Method to solve the problem

In the case of 2 variables, it is possible to solve analytically or graphically. The graphical process is more understandable so I will use the graphical method to arrive at the solution

The feasible region is the region that satisfies all four constraints shown.

The graph with the four constraint line equations is attached. The feasible region is the dark shaded area ABCD

The feasible region has 4 corner points(A, B,C, D) whose coordinates can be computed by converting each of the inequalities to equalities and solving for each pair of equations.

It can be proved mathematically that the maximum of the objective function occurs at one of the corner points.

Looking at [1] and [2] we get the equalities

x + y = 3 [3]

-0.5x + y = 1 [4]

Solving this pair of equations gives x = 4/3 and y = 5/3 or (4/3, 5/3)

Solving y = 0 and x + y = 3 gives point x = 3, y =0 (3,0)

The other points are solved similarly, I will leave it up to you to solve them

The four corner points are

A(0,0)

B(0,1)

C(4/3, 5/3)

D(3,0)

The objective function is 5x - 4y

To find the values of x and y that maximize the objective function,

plug in each of the x, y values of the corner points

Ignoring A(0,0)

we get the values of the objective function at the corner points as

For B(0,1) => 5(0) - 4(1) = -4

For C(4/3, 5/3) => 5(4/3) - 4(5/3) = 20/3 - 20/3 = 0

For D(3, 0) => 5(3) - 4(0) = 15

So the values of x and y which maximize the objective function are x = 3 and y = 0 or point D(3,0)

A

piece of ribbon

was cut into

three parts in the ratio of 1:3'5

If the shortest was 11cm how long was the ribbon

1:3:5

11:33:55=99

99cm

11:33:55=99

99cm

**Answer: Total Length of ribbon is 99 cm**

**Step-by-step explanation:**

** Here ribbon was cut into three parts in the ratio 1:3:5**

**let x be the common multiple of the above ratio**

**therefore, the lengths of the three parts of the ribbon is 1x,3x,5x**

**now, given is that the shortest part i.e 1x is equals to 11cm**

**i.e 1x=11 **

** x=**[tex]\frac{11}{1}[/tex]=11cm

now lengths of the ribbon will be

1x=11cm, 3x=3*11=33cm, 5x=5*11=55cm

now total length of piece of ribbon = 1x+3x+5x=9x=9*11=99cm

Solve-2x-16=2x-20.

Ox=1

O no solutions

○ * = −1

all real numbers

x = 1

First, move the terms.

-2x - 2x = -2 + 20

Collect like terms

-4x = -20 + 16 —> -4x = -4

Divide both sides

x = 1

First, move the terms.

-2x - 2x = -2 + 20

Collect like terms

-4x = -20 + 16 —> -4x = -4

Divide both sides

x = 1

15 Which of the digits from 2 to 9 is 5544

divisible by?

**Answer:**

All of em, except 5

**Step-by-step explanation:**

5544 / 2 = 2772

5544 / 3 = 1848

5544 / 4 = 1386

5544 / 6 = 924

5544 / 7 = 792

5544 / 8 = 693

5544 / 9 = 616

Last year, Mrs.Sclair’s annual salary was $88,441. This year she received a raise and now earns $96,402 annually. She is paid weekly. a. What was her weekly salary last year? Round to the nearest cent. b.What is Mrs.Sclair’s weekly salary this year? Round to the nearest cent. c.On a weekly basis, how much more does Mrs.Sclair earn as a result of her raise?

We have the following:

old salary: $88441

new salary: $96402

The year is approximately 52 weeks, therefore:

a. old salary for week:

[tex]\begin{gathered} \frac{88441}{52}=1700.8 \\ \end{gathered}[/tex]b. new salary for week:

[tex]\frac{96402}{52}=1853.9[/tex]c. weekly raise

[tex]1853.9-1700.8=153.1[/tex]I really need help please!

**Answer:**

n < -15/4

**Step-by-step explanation:**

You want to use the **discriminant** to find the **values of n** for which the **quadratic 3z² -9z = (n -3)** has only **complex solutions**.

The discriminant of quadratic equation ax²+bx+c = 0 is ...

d = b² -4ac

The given quadratic can be put in this form by subtracting (n-3):

3z² -9z -(n -3) = 0

This gives us ...

a = 3b = -9c = -(n -3)and the discriminant is ...

d = (-9)² -4(3)(-(n-3)) = 81 +12(n -3)

d = 12n +45

Complex solutionsThe equation will have only complex solutions when the discriminant is negative:

d < 0

12n +45 < 0 . . . . . use the value of the discriminant

n +45/12 < 0 . . . . . divide by 12

** n < -15/4** . . . . . . . subtract 15/4

**There will be two complex solutions when n < -15/4**.

Hi, can you help me answer this question please, thank you!

**Given:**

The test claims that night students' mean GPA is significantly different from the mean GPA of day students.

Null hypothesis: the population parameter is equal to a hypothesized value.

Alternative hypothesis: it is the claim about the population that is contradictory to the null hypothesis.

For the given situation,

[tex]\begin{gathered} \mu_N_{}=\text{ Night students} \\ \mu_D=Day\text{ students} \end{gathered}[/tex]**Null and alternative hypothesis is,**

**Answer: option f) **

the number 0.3333... repeats forever; therefore, its irrational

The **statement** is** false**, the number can be rewritten as:

0.33... = 3/9

So it is a **rational number**, not irrational

Here we have the **statement**:

"the number 0.3333... repeats forever; therefore, its irrational"

This is **false**, and let's prove that.

our number is:

0.33...

Such that the "3" keeps repeating infinitely.

If we multiply our number by 10, we get:

10*0.33... = 3.33...

If we subtract the original number we get:

10*0.33... - 0.33... = 3

9*0.33... = 3

Solving that for our number we get:

0.33... = 3/9

So that number can be written as a **quotient **between two integers, which means that it is **a rational number.**

Learn more about **rational numbers:**

**https://brainly.com/question/12088221**

**#SPJ1**

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