Recent questions tagged rational
Solve for \(x\) \[ 4 x^2-4 x-1=0 \] (leave your answers in simplest surd form)
surd
How do you simplify an expression with exponents?
Convert the recurring decimal \(2, \dot{5} \dot{3}\) into a common fraction.
Solve the equation $\frac{3x - 5}{x^2 - 4x + 3} = 0$
Solve the rational equation $\frac{x^2 - 4x + 3}{x - 1} = 0$
What is a rational equation?
What percent of \(897.77\) is \(84.95 \)?
State whether the following statement is true or false. The point \(\mathrm{A}(-1 ;-2)\) lies in the \(3^{\text {rd }}\) quadrant.
multiplicative
Calculate \(8\left(\frac{1}{8}-\sqrt{\frac{1}{16}}\right)\)
Calculate \(\sqrt{\frac{9}{16}} \div \sqrt{\frac{1}{4}}\).
asked Nov 27, 2022 in Mathematics by ♦MathsGee Platinum (163,818 points) | 8 views
Construct a function with a vertical asymptote at \(x=5\) and a horizontal asymptote at \(y=5 .\)
asked Sep 12, 2022 in Mathematics by ♦Gauss Diamond (71,991 points) | 44 views
What are the Limits of Rational Functions at Infinity?
How do you determine the Limits of Functions Equal At All But One Point?
How do you determine Limits of Polynomial and Rational Functions?
What is a surd?
asked Sep 7, 2022 in Mathematics by ♦MathsGee Platinum (163,818 points) | 94 views
What are irrational numbers?
What is a rational number?
How do I round real numbers to an appropriate degree of accuracy?
How do I understand the fact that real numbers can be rational or irrational?
How do I apply the laws of exponents to expressions involving rational exponents?
involving
Find a rational number between \(\frac{5}{7}\) and \(\frac{3}{4}\).
asked Aug 16, 2022 in Mathematics by ♦Gauss Diamond (71,991 points) | 73 views
Sum of rational terms in \((\sqrt{2}+\sqrt[5]{3})^{10}\) is
denominator
rationalize
Show that the following numbers are rational: (a) 0,1 (b) \(1, \dot{7} \dot{5}\)
Describe and give examples of rational numbers
If \(p\) is a prime, does it imply that \(\sqrt{p}\) is irrational?
terminating
Determine if \(\sqrt[5]{5}\) is irrational.
Prove that \(\sqrt{5}-\sqrt{3}\) is not a rational number.
asked Jul 28, 2022 in Mathematics by ♦MathsGee Platinum (163,818 points) | 80 views
Give an example of two irrational numbers whose quotient is a rational number.
Determine rational numbers \(p\) and \(q\) if \(\frac{7+\sqrt{5}}{7-\sqrt{5}}-\frac{7-\sqrt{5}}{7+\sqrt{5}}-p-7 \sqrt{5} q\).
Express with a rational denominator: \(\frac{1}{\sqrt{10}+\sqrt{20}+\sqrt{40}-\sqrt{5}-\sqrt{80}}\).
Simplify and express the result in simplest form: \(\frac{\sqrt{x^{2}-y^{2}}+x}{\sqrt{x^{2}+y^{2}}+y} \div \frac{\sqrt{x^{2}+y^{2}}-y}{x-\sqrt{x^{2}-y^{2}}}\).
Express with rational denominator: \(\dfrac{y^{2}}{\sqrt{x^{2}+y^{2}}+x}\).
Express with rational denominator: \(\dfrac{4}{\sqrt{5}-1}\).
Examine, whether the following numbers are rational or an irrational:
number-line
The graph of the rational function \(\frac{q(x)}{x^{6}-4 x^{5}+3 x^{3}+x^{2}-1}\) has a horizontal asymptote. What is the largest possible degree of \(q(x)\) ?
How many distinct four-tuples \((a, b, c, d)\) of rational numbers are there with
Prove that \(\sum 1 / p\) diverges; the sum extends over all primes.
non-real
Show that \(p^2=2\) is not satisfied by a rational number
State the possible rational zeros for the function \(f(x)=3 x^{3}+11 x^{2}+5 x-3\)
Write the decimal expansion of \(\dfrac{73}{2^{4} \times 5^{3}}\)
Give an example of two irrational whose sum is rational.
Without actual division, show that each of the following rational number is a terminating decimal. Express in decimal form: \(\dfrac{23}{\left(2^{3} \times 5^{2}\right)}\).
Would you accept a gamble that offers a 10-percent chance to win \(\$ 95\) and a 90-percent chance to lose \$5?
The rational function $\frac{x^{5}+1}{\left(x^{2}-1\right)^{2}}$ has a partial fraction expansion of the form
A rational decision maker does which of the following?
asked Nov 16, 2021 in General Knowledge by ♦MathsGee Platinum (163,818 points) | 359 views
Show that \(\frac{1-\sqrt{2}}{3+2 \sqrt{2}}\) can be written as \(7-5 \sqrt{2}\)
surds
Show that \(\frac{5+2 \sqrt{3}}{2+\sqrt{3}}\) can be written as \(4-\sqrt{3}\)
Show that \(\frac{5+\sqrt{3}}{2-\sqrt{3}}\) can be written as \(13+7 \sqrt{3}\)
Find the value of \(x\) such that \[ \frac{1+x}{x}=\sqrt{5} \] Giving your answer in the form \(a+b \sqrt{5}\) where \(a\) and \(b\) are rational numbers.
Solve the equation \(\frac{1}{3}(1-x)^3=9\)
asked Oct 24, 2021 in Mathematics by ♦MathsGee Platinum (163,818 points) | 170 views