Horizontal lines have a slope of zero, since the "rise" is; zero.
What is the slope?The slope is the ratio of the vertical changes to the horizontal changes between two points of the line.
m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Since we know that Vertical lines have an undefined slope, since the "offset" is zero, and division by zero is not allowed.
If the slope has a value of zero, the line is horizontal, neither increases nor decreases.
Therefore,
Horizontal lines always have an equation of the form; y = a
Vertical lines always have an equation of the form; x = b
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What is the equation of the line that passes through the point (6, -5) and has a slope of -1/3?
y=mx+b
m=slope
b= y-intercept
x=6
y=-5
-5= -1/3(6)+b
-5= 2+b
-2 -2
-7 = b
y= -1/3x-7
Answer:
y=-1/3x-3
Step-by-step explanation:
Write the phrase as an expression
the sum of 18 and 35:
6 times 50:
25 less than a number b:
a number x divided by 4:
the total of a number t and 11:
100 decreased by a number k:
Answer:
1. 18 + 35
2. 6 * 50
3. b - 25
4. x / 4
5. t + 11
6. 100 - k
Step-by-step explanation:
Tony saved enough money to afford a car. He needs to determine if he can afford the car insurance. Tony earns $160 per week. Tony's yearly pay is $8,320 and his monthly pay is $693.
Tony's monthly car insurance will be 1/30 of his rounded yearly pay. Can he afford it?
Explain why or why not.
Tony can afford the car insurance, and he has enough money($426.33) left over each month to cover other expenses.
What is car insurance?Automobile, truck, motorbike, and other types of road vehicles are covered by vehicle insurance. Its main purpose is to offer financial security against property loss or personal injury brought on by auto accidents, as well as against liability that can emerge from related events.
According to the information given,
Tony's yearly pay is $8,320
and his monthly pay is $693.
If we round his yearly pay to $8,000, his monthly car insurance will be 1/30 of that amount, or $266.67.
Since Tony's monthly pay is $693, and his monthly car insurance will cost $266.67, he can afford the insurance. He will have $426.33 remaining each month after paying for the insurance.
Therefore, Tony can afford the car insurance, and he has enough money left over each month to cover other expenses. However, this calculation assumes that Tony has no other major expenses or debts, and it is always a good idea to budget carefully and consider all potential costs before making a significant purchase.
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Please helpppp
if y+3/y-3 = 6
What is the value of y?
f(x) =3(x-2) (x+4)
f(x) = (3x+12) (x-2)
f(x) =3(x+4) (x+2)
f(x) = 3 (x-4) (x+2)
Answer:
Answer is in the attached photo
Step-by-step explanation:
SolutionThe solution is in the attached photo, do take note to find the value of y, we will have to make y the subject.
Write the sentence as an equation.
242 fewer than the quantity 193 times n equals 131
The equation that we want to write is:
193n - 242 = 131
How to write the equation?Here we want to write the sentence:
"242 fewer than the quantity 193 times n equals 131"
As an equation.
The first part means that we need to take a number n, multiply it by 193, and then subtract 242.
193n - 242
And that must be equal to 131, then the equation is:
193n - 242 = 131
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The probability that it rain in any given day in September is 0.3. Stating any assumption made, calculate the probabilitythat in a given week in September it will rain on at most two days
The probability that in a given week in September, it will rain on at most two days is 0.12.
What is probability?It is the chance of an event to occur from a total number of outcomes.
The formula for probability is given as:
Probability = Number of required events / Total number of outcomes.
We have,
The probability that it rains on any given day in September = 0.3.
P ( rains ) = 0.3
And,
The probability that it will not rain on any given day in September.
P (no rain) = 1 - 0.3
P(no rain) = 0.7
Now,
The probability is that in a given week in September, it will rain on at most two days.
= P (x ≤ 2)
= P(no rain) + P(rain) + P(rain)
= 0.7 + 0.3 + 0.3
= 0.12
Thus,
The probability that in a given week in September, it will rain on at most two days is 0.12.
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Determine whether the ordered pair is a solution to the system of equations or inequalities y<4x-1; y>x. Yes or no?
(1,3)
(0,0)
Answer:
Step-by-step explanation:
To determine whether an ordered pair is a solution to a system of equations or inequalities, we need to substitute the values for x and y into each equation or inequality and see if the resulting expression is true. If it is true for all of the equations or inequalities, then the ordered pair is a solution to the system.
Here's the step-by-step process for each ordered pair:
(1,3):
Substitute x = 1 and y = 3 into y < 4x - 1: 3 < 4(1) - 1 = 3 < 3, which is true.
Substitute x = 1 and y = 3 into y > x: 3 > 1, which is true.
Since both inequalities are true, the ordered pair (1,3) is a solution to the system y < 4x - 1 and y > x.
(0,0):
Substitute x = 0 and y = 0 into y < 4x - 1: 0 < 4(0) - 1 = -1, which is false.
Substitute x = 0 and y = 0 into y > x: 0 > 0, which is false.
Since at least one inequality is false, the ordered pair (0,0) is not a solution to the system y < 4x - 1 and y > x.
Dividends Per Share Sandpiper Company has 15,000 shares of cumulative preferred 2% stock, $50 par and 50,000 shares of $10 par common stock. The following amounts were distributed as dividends: 20Y1 20Y2 20Y3 Determine the dividends per share for preferred and common stock for each year. Round all answer to two decimal places. If an answer is zero, enter '0'. 20Y1 2012 $30,000 6,000 45,000 20Y3 Preferred Stock (dividends per share) Common Stock (dividends per share) LA
Answer: To calculate the dividends per share for preferred and common stock for each year, we need to divide the total dividends by the number of shares for each type of stock.
20Y1:
Preferred Stock: $30,000 / 15,000 shares = $2.00 per share
Common Stock: $6,000 / 50,000 shares = $0.12 per share
20Y2:
Preferred Stock: $30,000 / 15,000 shares = $2.00 per share (cumulative preferred stock means that if the company misses a dividend, they still have to pay it in the future, so the dividends per share remain the same)
Common Stock: $45,000 / 50,000 shares = $0.90 per share
20Y3:
Preferred Stock: $30,000 / 15,000 shares = $2.00 per share
Common Stock: $0 (there is no information about dividends for the common stock in 20Y3)
So, the dividends per share for each year would be:
20Y1:
Preferred Stock: $2.00 per share
Common Stock: $0.12 per share
20Y2:
Preferred Stock: $2.00 per share
Common Stock: $0.90 per share
20Y3:
Preferred Stock: $2.00 per share
Common Stock: $0.00 per share
Step-by-step explanation:
The product of two rational numbers is______ (1.A rational, 2.An irrational)
number because multiplying two rational numbers is
equivalent to the ratio of_____ (1.Two irrational numbers, 2.a rational and an irrational number, 3.Two integers)
which is_____ (1.a rational, 2.an irrational)
number.
The product of two rational numbers is 1 . A . Rational number because multiplying two rational numbers is equivalent to the ratio of 3 . Two integers which is 1 . a rational number .
What is the product of two rational numbers ?The product of two rational numbers is always a rational number. This is because a rational number is defined as a number that can be expressed as the ratio of two integers.
When you multiply two rational numbers, you are simply multiplying two ratios, which is still a ratio and therefore a rational number.
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Evaluate the expression:(2-1/2 • 7 1/3)^6
Write the answer in the most simplified form. Use fractions instead of decimal numbers.
The simplified form of the expression [tex]( 2^{-\frac{1}{2}} * 7^{\frac{1}{3} )^6[/tex] is [tex]6\frac{1}{8}[/tex].
What is the simplified form of the expression?Given the expression in the question:
[tex]( 2^{-\frac{1}{2}} * 7^{\frac{1}{3} )^6[/tex]
To simplify the given expression [tex]( 2^{-\frac{1}{2}} * 7^{\frac{1}{3} )^6[/tex], first, rewrite the expression using the negative exponent rule:
[tex]( \frac{1}{2^{\frac{1}{2} }} * 7^{\frac{1}{3} )^6[/tex]
Next, combine the fractions:
[tex]( \frac{7^{\frac{1}{3} }}{2^{\frac{1}{2} }} )^6[/tex]
Simplify the numnerator:
[tex]\frac{49}{(2^{\frac{1}{2} })^6}[/tex]
Simplify the denpminator:
[tex]\frac{49}{8}\\ \\6\frac{1}{8}[/tex]
Therefore, the simplified form is [tex]6\frac{1}{8}[/tex]
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Need help quick with this problem!!! [tex]\frac{6x^{-1} y^{-1}}{\sqrt[4]{xy^{4}} }[/tex]
[tex]~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hfill \begin{array}{llll} \textit{rational exponents} \\\\ a^{\frac{ n}{ m}} \implies \sqrt[ m]{a^ n} \end{array} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\cfrac{6x^{-1}y^{-1}}{\sqrt[4]{xy^4}}\implies \cfrac{6}{x^1 y^1 \left( xy^4 \right)^{\frac{1}{4}}}\implies \cfrac{6}{x^1 y^1 \left( x^{\frac{1}{4}}y^1 \right)}\implies \cfrac{6}{x^1x^{\frac{1}{4}} y^1 y^1} \\\\\\ \cfrac{6}{x^{1+\frac{1}{4}} y^{1+1}}\implies \cfrac{6}{x^{\frac{5}{4}} y^2}\implies {\Large \begin{array}{llll} \stackrel{a\quad b \quad ~~ c}{6x^{-\frac{5}{4}}y^{-2}} \end{array}}[/tex]
Polygon DEFG has coordinates D(2, 5), E(3, 1), F(4, 6), and G(6, 6). If the polygon is translated 3 units to the left, what are the coordinates of F'?
( , )
The polygon DEFG is translated 3 units left to get F'(1, 6)
What is transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, translation, rotation and dilation.
Translation is the movement of a point either up, down, left or right in the coordinate plane. Translation is a rigid transformation that preserves the shape and size.
Polygon DEFG has coordinates D(2, 5), E(3, 1), F(4, 6), and G(6, 6). The polygon is translated 3 units left to get F'(1, 6)
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examine whether you can construct a triangle PQR such that QR=3 cm, PQ=6 cm, PR=3 cm. Justify your answer
You cannot construct a triangle PQR such that QR=3 cm, PQ=6 cm, PR=3 cm, as the sum of the lengths of the two smaller sides is not greater than the length of the larger side.
What is the condition for 3 lengths to represent a triangle?In a triangle, the sum of the lengths of the two smaller sides has to be greater than the length of the greater side.
The lengths for this problem are given as follows:
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el avión más grande el airbus a380 tiene una longitud de 239 ft 6 pulgadas una embarga dura de 261 ft y 10 pulgadas y una altura de 79 ft 1pulgada expresa estás dimensiones en metros
Please help!
Directions: if QS represents an angle bisector, solve for x.
(Ignore my answer)
The value of x are:
1)
81/2
2)
33/4
3)
13
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
First question:
Since QS is the angle bisector.
We can write as,
PQ/PS = RQ/RS
45/20 = x/18
9/4 = x/18
x = 18 x 9 / 4
x = 9 x 9/2
x = 81/2
Second question:
Since QS is the angle bisector.
We can write as,
PQ/PS = RQ/RS
22/8 = x/6
11/4 = x/6
x = 6 x 11 / 4
x = 66/4
x = 33/4
Third question:
Since QS is the angle bisector.
We can write as,
PQ/PS = RQ/RS
21/15 = (5x - 16)/(3x - 4)
7/5 = (5x - 16)/(3x - 4)
7(3x - 4) = 5(5x - 16)
21x - 28 = 25x - 80
80 - 28 = 25x - 21x
52 = 4x
x = 13
Thus,
The value of x is 81/2, 33/4, and 13.
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e 1.5 Checkpoint: Rational and irrational numbers SNE
Select all the numbers that are irrational.
√55
36
39
√40
L
√√49
√55 and √40 are the irrational numbers.
What is Number system?A number system is defined as a system of writing to express numbers.
A rational number is the one which can be represented in the form of P/Q where P and Q are integers and Q ≠ 0.
But an irrational number cannot be written in the form of simple fractions.
√55 is an irrational number
√40 is an irrational number
√49 value is 7 which is a natural number
Hence, √55 and √40 are the irrational numbers.
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How can credit cards be safer than cash? a. It is harder to lose a single credit card than a large number of bills. b. A credit card requires a signature, so it is impossible for anyone other than you to use. c. If a merchant does not hold up their end of an agreement, you can call the credit company and dispute the charges. d. Cash can be miscounted, but credit cards cannot.
If a merchant does not hold up their end of an agreement, you can call the credit company and dispute the charges. This way, credit cards can be safer than cash.
What is credit card?
A credit card is a small plastic payment card that is provided by a person's bank and enables the cardholder to pay a merchant for products and services depending on the cardholder's accumulated debt.
To be on the safe side in the event that a merchant breaches an agreement, a cardholder may contact the credit bureau to resolve the disputed charges.
So, this way credit cards can be safer than cash.
Hence, option C is the correct solution.
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the frame of a bike weighs16 pounds. each tire weighs 9 ounces. the seat weighs 12 ounces. the handlebars weigh 24 ounces. how punds does the bike weigh
19.375 pounds is the weight of bike.
What is Unit of Measurement?A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity.
Given that the frame of a bike weighs16 pounds.
each tire weighs 9 ounces.
In a bike there are 2 tires, so total weight of tires is 2×9=18 ounces.
The seat weighs 12 ounces
The handlebars weigh 24 ounces.
Convert the ounces to pounds.
We know that 1 pound=16 ounces
So The total number of weight in ounces is 18+12+24=54 ounces
Divide by 16 to convert 54 ounces to pounds
54/16=3.375
Now total weight=16+3.375 pounds
=19.375
Hence, 19.375 pounds is the weight of bike.
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Help MEEE I HAVE UNTIL TOMORROW
The actual width and length of the bedroom are respectively; 9 ft and 12 ft
How to interpret Scale Drawing?The parameters are given as;
Width of house = 30 feet = 360 inches
Length of house = 45 feet = 540 inches
Scale drawing width of house = 4 inches
Scale drawing length of house = 6 inches
Thus;
Scale factor width = 360/4 = 90
Scale factor length = 540/6 = 90
Scale drawing width of bedroom = 1.2 inches
Scale drawing length of bedroom = 1.6 inches
Thus;
Actual width of bedroom = 1.2 inches * 90 = 108 inches or 9 ft
Actual length of bedroom = 1.6 inches * 90 = 144 inches or 12 ft
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Please help with this equation
Answer:
Step-by-step explanation:
Adjacent angles is defined as
Opposite,congruent angles formed when two lines intersect.
26 gallons of gas cost $80.08. What is the unit rate for 1 gallon of gas?
A. O$2.98 per gallon
B. O$3.08 per gallon
C. O$4.16 per gallon
D. O$308.00 per gallon
Which set of measurements would prove that ΔABC and ΔDEF are similar?
A. DE = 15, EF = 20 and m∠D = 35
B. DE = 16, DF = 21 and m∠D = 35
C. DE = 12, DF = 16 and m∠D = 35
D. DE = 18, EF = 24 and m∠D = 70
Option (c) is correct answer.
(C) DE = 12, DF = 16 and m∠D = 35
which states, length of DE is 12 units , length of DF is 16 units and m/D=35 degrees.
Similar Triangles :If two figures possess the same shape but not necessarily the same size, they are considered to be similar. We may remark that all circles are similar as an example. Equilateral triangles and squares are similar to one another. Although similar figures need not be congruent, all congruent figures are similar.
Property 1:
Two triangles are similar if their respective sides have the same ratio and their corresponding angles are equal.
Property 2:
The corresponding angles of two similar triangles will have equal values . Equiangular triangles are what they are called.
Now by property 1,
The pairs of corresponding sides of similar triangles are proportional .
Therefore, in the given triangles,
[tex]\frac{AB}{DE} =\frac{AC}{DF} \\\\\frac{AB}{AC} =\frac{DE}{DF} \\\\\frac{9}{12} =\frac{DE}{DF} \\\\\frac{3}{4} =\frac{DE}{DF}[/tex]
Therefore, in the given options, option (c) satisfies the condition.
Hence, DE = 12 , and DF = 16.
By property 2 we know that , corresponding angles of similar triangles are equal.
hence, /A=/D
therefore, /D=35.
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Selecting from millimeter, meter, and kilometer, determine the best unit of measure to express the given length.
Millimeter is the best unit to define the radius of the pencil.
What is a radius?The distance from a circle's centre to any point on its periphery is known as the radius. The radius of a circle is also known as the distance separating any two points on the circle from its centre. The radius of a circle is the separation between its centre and circumference. Always, the diameter is twice the radius. As a result, the formula is created by multiplying the diameter by two.
Define millimeter.The smallest unit of measurement is the millimetre. There are a thousand millimetres in a metre, and a dime is somewhat thicker than a millimetre. When measuring anything's length in metric units, you'll be working with meters and variants on meters, including millimeters.
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1. If you get a new job, outline the three forms you will have to deal with to file your taxes. Which one do you have to fill out when you start? Which one does your employer send you? Which one do you use to file your taxes?
2. What is the difference between gross income, taxable income, and adjusted gross income?
If you get a new job, outline the forms you will have to deal with to file your taxes. The form has to fill in Form W-9 sent by the employer and given use to file your taxes.
What is the purpose of Form W - 9?The company determines what information to include in the Form 1098 or Form 1099 based on the information provided on the Form W-9.
Information about taxpayers is gathered using Form W-9 to assist with informational reporting to the IRS.
Although it is utilised in other contexts as well, the Form W-9 is most frequently employed when working with businesses that employ independent contractors.
The form requests that a taxpayer enter their name, residence, tax bracket, and withholding specifications.
Therefore, from the following conditions are:
1. Outline the forms you will need to file your taxes if you get a new job. Form W-9 must be completed and returned to the employer in order to file your taxes.
A W-2 will be given to you detailing your profits. New employees are frequently required to complete a Form W-4 rather than a Form W-9 in order to supply their company with information about their taxpayers.
2. Gross income is all income from whatever source derived that is not excluded or deferred from income. AGI is gross income minus "for AGI" deductions. Taxable income is AGI minus "from AGI" deductions.
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Given the following parallelogram, solve for x.
X =
(18x - 79) °
(7x + 9) °
Find the value of C that makes 16x^2 -24x + C a perfect square
The required value of C is 3 which makes 16x² - 24x + C a perfect square.
What is Perfect Square?A perfect Square is defined as an integer multiplied by itself to generate a perfect square, which is a positive integer. Perfect squares are just numbers that are the products of integers multiplied by themselves.
The expression is given in the question, as follows:
16x² - 24x + C
(4x)² - 24x + C
As we know that the factoring identity:
(a - b)² = a² - 2ab + b²
After comparing, we have a = 4x and 2ab = 24x
Solving for b:
2(4x)b = 24x
b = 24x/8x
b = 3
So 16x² - 24x + 3 = (4x - 3)²
This means the required value of C is 3 which makes a perfect square.
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What is the average rate of change? Problem in the picture
The average rate of change of the function f(x) over the interval (-1, 2) is; 3.
What is the difference quotient of the function over the given interval?As evident in the task content; the given function is as represented by the graph of f(x).
Hence, the average rate of change of the function over the given interval; (-1, 2) is;
= ( f (2) - f (-1) ) / (2 - (-1))
where; f (2) = 5 and f (-1) = -4.
Therefore, the average rate of change is;
= (5 - (-4)) / (2 - (-1))
= 9 / 3.
= 3.
Ultimately, the difference quotient of f (x) over the given interval is; 3.
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Can anyone explain this question about complex numbers ?
Answer:
Step-by-step explanation:
(a) Using de Moivre's Theorem, we have that:
z^n = cos(nθ) + i sin(nθ)
1/z^n = cos(-nθ) + i sin(-nθ)
So, we can find z^n + 1/z^n as:
z^n + 1/z^n = (cos(nθ) + i sin(nθ)) + (cos(-nθ) + i sin(-nθ)) = 2 cos(nθ)
And z^n - 1/z^n as:
z^n - 1/z^n = (cos(nθ) + i sin(nθ)) - (cos(-nθ) + i sin(-nθ)) = 2i sin(nθ)
(b) To express the equation 2z^4 - 5z^3 + 7z^2 - 5z + 2 = 0 in terms of cos(θ), we can substitute z with cos(θ) + i sin(θ):
2(cos(4θ) + i sin(4θ)) - 5(cos(3θ) + i sin(3θ)) + 7(cos(2θ) + i sin(2θ)) - 5(cos(θ) + i sin(θ)) + 2 = 0
Expanding the right hand side using the trigonometric identities, we get:
2 cos(4θ) - 5 cos(3θ) + 7 cos(2θ) - 5 cos(θ) + 2 = 0
Note that the real and imaginary parts are separate, so we can simplify this equation to a real equation by equating the real and imaginary parts to 0.
(c) To solve the equation 2 cos(4θ) - 5 cos(3θ) + 7 cos(2θ) - 5 cos(θ) + 2 = 0, we can use numerical methods or analytical methods such as the roots of unity.
Once the roots are found, they can be represented on an Argand diagram by plotting the real and imaginary parts of each root as a point in the complex plane. The magnitude of each point represents the magnitude of the complex number, and the argument (angle) represents the argument of the complex number.
How do I simplify this into a radical?
Answer:
Step-by-step explanation:
To simplify the expression X^(12/7) * Y^(35/7) into its simplest form, we need to find the greatest common divisor (GCD) of the exponents 12/7 and 35/7 and divide both exponents by the GCD. Here's the step-by-step process:
Find the GCD of 12/7 and 35/7. To do this, we'll use the Euclidean algorithm method:
a. Divide the larger number, 35, by the smaller number, 12, and get the remainder: 35 ÷ 12 = 2 with a remainder of 11.
b. Divide the smaller number, 12, by the remainder, 11, and get the quotient and remainder: 12 ÷ 11 = 1 with a remainder of 1.
c. The last non-zero remainder, 1, is the GCD of 12/7 and 35/7.
Divide both exponents by the GCD, 1:
a. X^(12/7) becomes X^(12/7 ÷ 1) = X^12.
b. Y^(35/7) becomes Y^(35/7 ÷ 1) = Y^35.
Replace the original exponents in the expression with the simplified exponents: X^12 * Y^35.
So, the expression X^(12/7) * Y^(35/7) is simplified as X^12 * Y^35, which is written as a single radical in its simplest form.
[tex]~\hspace{7em}\textit{rational exponents} \\\\ a^{\frac{ n}{ m}} \implies \sqrt[ m]{a^ n} ~\hspace{10em} a^{-\frac{ n}{ m}} \implies \cfrac{1}{a^{\frac{ n}{ m}}} \implies \cfrac{1}{\sqrt[ m]{a^ n}} \\\\[-0.35em] ~\dotfill\\\\ x^{\frac{12}{7}}y^{\frac{35}{7}}\implies \left( x^{12} y^{35} \right)^{\frac{1}{7}}\implies \sqrt[7]{x^{12} y^{35}}\implies \sqrt[7]{x^{7+5} (y^5)^7} \\\\\\ \sqrt[7]{x^7 x^5 (y^5)^7}\implies {\Large \begin{array}{llll} x y^5\sqrt[7]{x^5} \end{array}}[/tex]
Help me with this question…..
The decimal number is -5.690134489..... irrational number. Therefore, option C is the correct answer.
What are irrational numbers?Irrational numbers are the set of real numbers that cannot be expressed in the form of a fraction, p/q where p and q are integers. The denominator q is not equal to zero (q ≠ 0). Also, the decimal expansion of an irrational number is neither terminating nor repeating.
Here,
-9.121212121212......
This decimal number is non terminating, but repeating
So, the decimal number is rational number
-1.5000000000.....
This decimal number is non terminating, but only zeros are repeating
So, the decimal number is rational number
-5.690134489.....
This decimal number is non terminating and non repeating
So, the decimal number is irrational number
-9.121212121212....
This decimal number is non terminating, but repeating
So, the decimal number is rational number
Therefore, option C is the correct answer.
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