MathsGee Answers - Recent questions
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Powered by Question2AnswerFind the partial fraction decomposition of the following expression: $$ \frac{x^{3}+3}{x^{2}-2 x-3} $$
https://mathsgee.com/30112/find-partial-fraction-decomposition-following-expression
Find the partial fraction decomposition of the following expression:<br />
$$<br />
\frac{x^{3}+3}{x^{2}-2 x-3}<br />
$$Mathematicshttps://mathsgee.com/30112/find-partial-fraction-decomposition-following-expressionSat, 19 Jun 2021 02:21:22 +0000What are improper fractions?
https://mathsgee.com/30110/what-are-improper-fractions
What are improper fractions?Mathematicshttps://mathsgee.com/30110/what-are-improper-fractionsSat, 19 Jun 2021 02:18:18 +0000Find the partial fraction decomposition of $\frac{3 x^{4}-2 x^{3}+6 x^{2}-3 x+3}{x^{5}+3 x^{4}+4 x^{3}+12 x^{2}+4 x+12}$.
https://mathsgee.com/30108/find-the-partial-fraction-decomposition-of-frac-x-4-4-x-12-2-12
Find the partial fraction decomposition of $\frac{3 x^{4}-2 x^{3}+6 x^{2}-3 x+3}{x^{5}+3 x^{4}+4 x^{3}+12 x^{2}+4 x+12}$.Mathematicshttps://mathsgee.com/30108/find-the-partial-fraction-decomposition-of-frac-x-4-4-x-12-2-12Sat, 19 Jun 2021 02:15:41 +0000What are repeated quadratic factors?
https://mathsgee.com/30106/what-are-repeated-quadratic-factors
What are repeated quadratic factors?Mathematicshttps://mathsgee.com/30106/what-are-repeated-quadratic-factorsSat, 19 Jun 2021 02:14:02 +0000Find the partial fraction decomposition of the following expression: $$ \frac{6 x^{2}+21 x+11}{x^{3}+5 x^{2}+3 x+15} $$
https://mathsgee.com/30104/find-partial-fraction-decomposition-following-expression
Find the partial fraction decomposition of the following expression:<br />
$$<br />
\frac{6 x^{2}+21 x+11}{x^{3}+5 x^{2}+3 x+15}<br />
$$Mathematicshttps://mathsgee.com/30104/find-partial-fraction-decomposition-following-expressionSat, 19 Jun 2021 02:11:12 +0000What are linear factors?
https://mathsgee.com/30102/what-are-linear-factors
What are linear factors?Mathematicshttps://mathsgee.com/30102/what-are-linear-factorsSat, 19 Jun 2021 02:09:17 +0000What are repeated linear factors?
https://mathsgee.com/30100/what-are-repeated-linear-factors
What are repeated linear factors?Mathematicshttps://mathsgee.com/30100/what-are-repeated-linear-factorsSat, 19 Jun 2021 02:08:08 +0000What are quadratic factors?
https://mathsgee.com/30098/what-are-quadratic-factors
What are quadratic factors?Mathematicshttps://mathsgee.com/30098/what-are-quadratic-factorsSat, 19 Jun 2021 02:06:46 +0000Find the partial fraction of the following expression: $$ \frac{x^{2}+5 x-6}{x^{3}-7 x^{2}+16 x-12} $$
https://mathsgee.com/30096/find-the-partial-fraction-the-following-expression-frac-12
Find the partial fraction of the following expression:<br />
$$<br />
\frac{x^{2}+5 x-6}{x^{3}-7 x^{2}+16 x-12}<br />
$$Mathematicshttps://mathsgee.com/30096/find-the-partial-fraction-the-following-expression-frac-12Sat, 19 Jun 2021 02:04:49 +0000Find the partial fraction decomposition of the following expression: $$ \frac{2 x-1}{x^{3}-6 x^{2}+11 x-6} $$
https://mathsgee.com/30094/find-partial-fraction-decomposition-following-expression
Find the partial fraction decomposition of the following expression:<br />
$$<br />
\frac{2 x-1}{x^{3}-6 x^{2}+11 x-6}<br />
$$Mathematicshttps://mathsgee.com/30094/find-partial-fraction-decomposition-following-expressionSat, 19 Jun 2021 02:01:43 +0000What are partial fractions of functions?
https://mathsgee.com/30092/what-are-partial-fractions-of-functions
What are partial fractions of functions?Mathematicshttps://mathsgee.com/30092/what-are-partial-fractions-of-functionsSat, 19 Jun 2021 01:58:37 +0000What is the definition of $e$, the base of the natural logarithm?
https://mathsgee.com/30090/what-is-the-definition-of-e-the-base-the-natural-logarithm
What is the definition of $e$, the base of the natural logarithm?Mathematicshttps://mathsgee.com/30090/what-is-the-definition-of-e-the-base-the-natural-logarithmSat, 19 Jun 2021 01:56:27 +0000Using a right-angled triangle how can we derive the trigonometric identity $1+\cot ^{2} \theta=\csc ^{2} \theta$
https://mathsgee.com/30088/angled-triangle-derive-trigonometric-identity-theta-theta
Using a right-angled triangle how can we derive the trigonometric identity $1+\cot ^{2} \theta=\csc ^{2} \theta$Mathematicshttps://mathsgee.com/30088/angled-triangle-derive-trigonometric-identity-theta-thetaSat, 19 Jun 2021 01:53:29 +0000How is the unit circle and trig functions?
https://mathsgee.com/30086/how-is-the-unit-circle-and-trig-functions
How is the unit circle and trig functions?Mathematicshttps://mathsgee.com/30086/how-is-the-unit-circle-and-trig-functionsSat, 19 Jun 2021 01:48:03 +0000Factor the polynomial $x^{5}+x^{4}-2 x^{3}+4 x^{2}-24 x$.
https://mathsgee.com/30084/factor-the-polynomial-x-5-x-4-2-x-3-4-x-2-24-x
Factor the polynomial $x^{5}+x^{4}-2 x^{3}+4 x^{2}-24 x$.Mathematicshttps://mathsgee.com/30084/factor-the-polynomial-x-5-x-4-2-x-3-4-x-2-24-xSat, 19 Jun 2021 01:44:48 +0000What are the steps and methods for factoring polynomials?
https://mathsgee.com/30082/what-are-the-steps-and-methods-for-factoring-polynomials
What are the steps and methods for factoring polynomials?Mathematicshttps://mathsgee.com/30082/what-are-the-steps-and-methods-for-factoring-polynomialsSat, 19 Jun 2021 01:42:57 +0000What are complex conjugates?
https://mathsgee.com/30080/what-are-complex-conjugates
What are complex conjugates?Mathematicshttps://mathsgee.com/30080/what-are-complex-conjugatesSat, 19 Jun 2021 01:40:47 +0000How are complex numbers related to real numbers?
https://mathsgee.com/30078/how-are-complex-numbers-related-to-real-numbers
How are complex numbers related to real numbers?Mathematicshttps://mathsgee.com/30078/how-are-complex-numbers-related-to-real-numbersSat, 19 Jun 2021 01:39:10 +0000Is $f(x)=2 x-x^{2}$ even, odd, or neither?
https://mathsgee.com/30076/is-f-x-2-x-x-2-even-odd-or-neither
Is $f(x)=2 x-x^{2}$ even, odd, or neither?Mathematicshttps://mathsgee.com/30076/is-f-x-2-x-x-2-even-odd-or-neitherSat, 19 Jun 2021 01:37:30 +0000When is a mathematical function classified as even?
https://mathsgee.com/30074/when-is-a-mathematical-function-classified-as-even
When is a mathematical function classified as even?Mathematicshttps://mathsgee.com/30074/when-is-a-mathematical-function-classified-as-evenSat, 19 Jun 2021 01:36:23 +0000Find the inverse function of $$ f(x)=\frac{5 x+2}{4 x-3} $$
https://mathsgee.com/30072/find-the-inverse-function-of-f-x-frac-5-x-2-4-x-3
Find the inverse function of<br />
$$<br />
f(x)=\frac{5 x+2}{4 x-3}<br />
$$Mathematicshttps://mathsgee.com/30072/find-the-inverse-function-of-f-x-frac-5-x-2-4-x-3Sat, 19 Jun 2021 01:34:41 +0000Can the input of one function be the output of another mathematical function?
https://mathsgee.com/30070/can-the-input-function-output-another-mathematical-function
Can the input of one function be the output of another mathematical function?Mathematicshttps://mathsgee.com/30070/can-the-input-function-output-another-mathematical-functionSat, 19 Jun 2021 01:33:22 +0000How you define a mathematical function?
https://mathsgee.com/30068/how-you-define-a-mathematical-function
How you define a mathematical function?Mathematicshttps://mathsgee.com/30068/how-you-define-a-mathematical-functionSat, 19 Jun 2021 01:31:25 +0000Find the domain of the following function: $$ f(x)=\frac{1}{(1-x) \sqrt{5-x^{2}}} $$
https://mathsgee.com/30066/find-the-domain-of-the-following-function-f-frac-1-1-sqrt
Find the domain of the following function:<br />
$$<br />
f(x)=\frac{1}{(1-x) \sqrt{5-x^{2}}}<br />
$$Mathematicshttps://mathsgee.com/30066/find-the-domain-of-the-following-function-f-frac-1-1-sqrtSat, 19 Jun 2021 01:29:56 +0000What is the relationship between sets, subsets and intervals?
https://mathsgee.com/30064/what-is-the-relationship-between-sets-subsets-and-intervals
What is the relationship between sets, subsets and intervals?Mathematicshttps://mathsgee.com/30064/what-is-the-relationship-between-sets-subsets-and-intervalsSat, 19 Jun 2021 01:28:20 +0000Can i ask how you get the 1.75 ?
https://mathsgee.com/30062/can-i-ask-how-you-get-the-1-75
I would just like to know how to do the calculation to get answer C ?Physicshttps://mathsgee.com/30062/can-i-ask-how-you-get-the-1-75Fri, 18 Jun 2021 21:17:09 +0000Given that 5 cos β − 3 = 0 and 0 ∘ < β < 90 ∘ . If α + β = 90 ∘ and 0 ∘ < α < 90 ∘ , calculate the value of cot α .
https://mathsgee.com/30058/given-that-cos-and-90-if-90-and-90-calculate-the-value-of-cot
Trigonometric, finding the value of an alphaMathematicshttps://mathsgee.com/30058/given-that-cos-and-90-if-90-and-90-calculate-the-value-of-cotFri, 18 Jun 2021 16:05:21 +0000Solve the following expression: $$\$ 500\left[\frac{\left(1+\left\{\left(1+\frac{0.07}{2}\right)^{4 / 12}-1\right\}\right)^{4}-1}{\left(1+\frac{0.07}{2}\right)^{4 / 12}-1}\right]$$
https://mathsgee.com/30044/solve-following-expression-left-right-right-right-right-right
Solve the following expression: $$\$ 500\left[\frac{\left(1+\left\{\left(1+\frac{0.07}{2}\right)^{4 / 12}-1\right\}\right)^{4}-1}{\left(1+\frac{0.07}{2}\right)^{4 / 12}-1}\right]$$Mathematicshttps://mathsgee.com/30044/solve-following-expression-left-right-right-right-right-rightThu, 17 Jun 2021 16:05:06 +0000An industry analyst wants to compare the average salaries of two firms, both to each other and to the industry.
https://mathsgee.com/30043/industry-analyst-wants-compare-average-salaries-industry
An industry analyst wants to compare the average salaries of two firms, both to each other and to the industry. Firm A's average salary is $93 \%$ of the industry average, Firm B's average salary is $\$ 58,000$, and the industry average salary is $96 \%$ of Firm B's average salary.<br />
a. Determine the industry average salary.<br />
b. Determine Firm A's average salary.<br />
c. Express Firm B's average salary as a percentage of Firm A's average salary. Round the percentage to two decimals.Mathematicshttps://mathsgee.com/30043/industry-analyst-wants-compare-average-salaries-industryThu, 17 Jun 2021 16:03:02 +0000A local baseball team sells tickets with two price zones. Seats behind the plate from first base to third base are priced at \$20 per ticket.
https://mathsgee.com/30042/local-baseball-tickets-seats-behind-first-third-priced-ticket
A local baseball team sells tickets with two price zones. Seats behind the plate from first base to third base are priced at \$20 per ticket. All other seats down the base lines and in the outfield are priced at \$10 per ticket. At last night's game, 5, 332 fans were in attendance and total ticket revenue was \$ 71,750. How many tickets in each zone were sold?Mathematicshttps://mathsgee.com/30042/local-baseball-tickets-seats-behind-first-third-priced-ticketThu, 17 Jun 2021 16:00:47 +0000Housing starts in Winnipeg for the first half of the 2009 year were down $46.733 \%$ from 2008 , when 1,500 new homes were started. How many housing starts were there in 2009 ?
https://mathsgee.com/30041/housing-starts-winnipeg-first-started-housing-starts-there
Housing starts in Winnipeg for the first half of the 2009 year were down $46.733 \%$ from 2008 , when 1,500 new homes were started. How many housing starts were there in 2009 ?Mathematicshttps://mathsgee.com/30041/housing-starts-winnipeg-first-started-housing-starts-thereThu, 17 Jun 2021 16:00:00 +0000Simplify the following algebraic expression: PMT $\left[\frac{1-(1+0.0225)^{6}(1+0.044)^{-6}}{0.044-0.0225}\right]+\operatorname{PMT}\left(\frac{1}{0.044}+1\right)$
https://mathsgee.com/30040/simplify-following-algebraic-expression-operatorname-right
Simplify the following algebraic expression: PMT $\left[\frac{1-(1+0.0225)^{6}(1+0.044)^{-6}}{0.044-0.0225}\right]+\operatorname{PMT}\left(\frac{1}{0.044}+1\right)$Mathematicshttps://mathsgee.com/30040/simplify-following-algebraic-expression-operatorname-rightThu, 17 Jun 2021 15:59:21 +0000Simplify the following algebraic expression: $\left(\dfrac{15 a^{7} b^{3} c^{2}}{5 a^{5} c}\right)^{3} \div\left(\dfrac{9 a^{4} b^{6} c^{5}}{3 a^{2} b^{2} c^{3}}\right)^{\frac{3}{2}}$
https://mathsgee.com/30039/simplify-following-algebraic-expression-dfrac-right-right
Simplify the following algebraic expression: $\left(\dfrac{15 a^{7} b^{3} c^{2}}{5 a^{5} c}\right)^{3} \div\left(\dfrac{9 a^{4} b^{6} c^{5}}{3 a^{2} b^{2} c^{3}}\right)^{\frac{3}{2}}$Mathematicshttps://mathsgee.com/30039/simplify-following-algebraic-expression-dfrac-right-rightThu, 17 Jun 2021 15:58:42 +0000Substitute the given values in the following equation and solve:
https://mathsgee.com/30038/substitute-the-given-values-the-following-equation-and-solve
Substitute the given values in the following equation and solve:<br />
$$<br />
a\left[\frac{(1+b)^{c}-1}{b}\right] \text { where } a=\$ 535, b=0.025, \text { and } c=6<br />
$$Mathematicshttps://mathsgee.com/30038/substitute-the-given-values-the-following-equation-and-solveThu, 17 Jun 2021 15:57:26 +0000On average across all industries, full-time employed Canadians worked $39.5$ hours per week. If the typical adult requires eight hours of sleep per day, what percentage of the hours in a single week are left over for personal activities?
https://mathsgee.com/30037/industries-employed-canadians-percentage-personal-activities
On average across all industries, full-time employed Canadians worked $39.5$ hours per week. If the typical adult requires eight hours of sleep per day, what percentage of the hours in a single week are left over for personal activities?Mathematicshttps://mathsgee.com/30037/industries-employed-canadians-percentage-personal-activitiesThu, 17 Jun 2021 15:56:29 +0000A $240 \mathrm{~mL}$ bottle of an orange drink claims that it is made with real fruit juice. Upon examination of the ingredient list, only $15 \%$ of the contents is actually fruit juice. How many millilitres of "other ingredients" are in the bottle?
https://mathsgee.com/30036/examination-ingredient-actually-millilitres-ingredients
A $240 \mathrm{~mL}$ bottle of an orange drink claims that it is made with real fruit juice. Upon examination of the ingredient list, only $15 \%$ of the contents is actually fruit juice. How many millilitres of "other ingredients" are in the bottle?Mathematicshttps://mathsgee.com/30036/examination-ingredient-actually-millilitres-ingredientsThu, 17 Jun 2021 15:55:39 +0000Evaluate the following: $$\left[\frac{1+\frac{0.0975}{4} \times \$ 3,225}{\$ 255}\right]$$
https://mathsgee.com/30035/evaluate-the-following-left-frac-frac-0975-times-225-255-right
Evaluate the following: $$\left[\dfrac{1+\dfrac{0.0975}{4} \times \$ 3,225}{\$ 255}\right]$$Mathematicshttps://mathsgee.com/30035/evaluate-the-following-left-frac-frac-0975-times-225-255-rightThu, 17 Jun 2021 15:54:03 +0000Simplify the following expression: $$(0.06)(\$ 1,725)\left[\frac{1-\left(1+\frac{0.14}{4}\right)^{-7}}{\frac{0.14}{4}}\right]$$
https://mathsgee.com/30034/simplifythe-following-expression-left-frac-right-frac-right
Simplify the following expression: $$(0.06)(\$ 1,725)\left[\frac{1-\left(1+\frac{0.14}{4}\right)^{-7}}{\frac{0.14}{4}}\right]$$Mathematicshttps://mathsgee.com/30034/simplifythe-following-expression-left-frac-right-frac-rightThu, 17 Jun 2021 15:51:59 +0000In Canadian five-pin bowling, the maximum score per game is $450 .$ Alexandria just finished bowling a game of $321 .$ What percentage of a perfect score does this represent?
https://mathsgee.com/30033/canadian-alexandria-finished-percentage-perfect-represent
In Canadian five-pin bowling, the maximum score per game is $450 .$ Alexandria just finished bowling a game of $321 .$ What percentage of a perfect score does this represent?Mathematicshttps://mathsgee.com/30033/canadian-alexandria-finished-percentage-perfect-representThu, 17 Jun 2021 15:50:57 +0000Simplify the following algebraic expression: $\frac{16 x^{2}}{4 x}-\frac{21 x^{3} y^{2}}{7 x^{2} y^{2}}$
https://mathsgee.com/30032/simplify-the-following-algebraic-expression-frac-16-frac-21
Simplify the following algebraic expression: $\frac{16 x^{2}}{4 x}-\frac{21 x^{3} y^{2}}{7 x^{2} y^{2}}$Mathematicshttps://mathsgee.com/30032/simplify-the-following-algebraic-expression-frac-16-frac-21Thu, 17 Jun 2021 15:50:18 +0000Solve the following equation for $r:-2 r-2.25=3.75-8 r$
https://mathsgee.com/30031/solve-the-following-equation-for-r-2-r-2-25-3-75-8-r
Solve the following equation for $r:-2 r-2.25=3.75-8 r$Mathematicshttps://mathsgee.com/30031/solve-the-following-equation-for-r-2-r-2-25-3-75-8-rThu, 17 Jun 2021 15:49:35 +0000Demonstrate that $3 \times \ln (2)=\ln \left(2^{3}\right)$
https://mathsgee.com/30030/demonstrate-that-3-times-ln-2-ln-left-2-3-right
Demonstrate that $3 \times \ln (2)=\ln \left(2^{3}\right)$Mathematicshttps://mathsgee.com/30030/demonstrate-that-3-times-ln-2-ln-left-2-3-rightThu, 17 Jun 2021 15:49:03 +0000Find the roots for the following pairs of equations. Verify the solution through substitution into both equations.
https://mathsgee.com/30029/following-equations-solution-through-substitution-equations
Find the roots for the following pairs of equations. Verify the solution through substitution into both equations.<br />
$$<br />
\begin{gathered}<br />
3 \frac{4}{5} q+0.18 r=12.2398 \\<br />
-5.13 q-\frac{13 r}{5}=-38.4674<br />
\end{gathered}<br />
$$Mathematicshttps://mathsgee.com/30029/following-equations-solution-through-substitution-equationsThu, 17 Jun 2021 15:46:57 +0000Simplify the following equation into the format of $\#_{z}=\#$ and find the root. Verify the solution through substitution.
https://mathsgee.com/30028/simplify-following-equation-solution-through-substitution
Simplify the following equation into the format of $\#_{z}=\#$ and find the root. Verify the solution through substitution.<br />
$$<br />
z\left(1+0.073 \times \frac{280}{365}\right)-\frac{z}{1+0.073 \times \frac{74}{365}}+\$ 1,000=\$ 2,764.60<br />
$$Mathematicshttps://mathsgee.com/30028/simplify-following-equation-solution-through-substitutionThu, 17 Jun 2021 15:45:58 +0000A mall is being constructed and needs to meet the legal requirements for parking availability.
https://mathsgee.com/30027/being-constructed-needs-requirements-parking-availability
A mall is being constructed and needs to meet the legal requirements for parking availability. Parking laws require one parking stall for every 100 square feet of retail space. The mall is designed to have $1,200,000$ square feet of retail space. Of the total parking stalls available, $2 \%$ need to be handicap accessible, there need to be three times as many small car spaces as handicap spaces, RV spaces need to be one-quarter of the number of small car spaces, and the rest of the spaces are for regular stalls. How many of each type of parking space does the mall require?Mathematicshttps://mathsgee.com/30027/being-constructed-needs-requirements-parking-availabilityThu, 17 Jun 2021 15:45:03 +0000Marianne, William, Hendrick, and Charlotte have all decided to go into business together.
https://mathsgee.com/30026/marianne-william-hendrick-charlotte-decided-business-together
Marianne, William, Hendrick, and Charlotte have all decided to go into business together. They need $\$ 175,000$ in initial capital funding. William was able to contribute $20 \%$ less than Marianne, Hendrick contributed $62.5 \%$ more than William, and Charlotte contributed $\$ 5,000$ less than half as much as Marianne. How much did each partner contribute to the initial funds?Mathematicshttps://mathsgee.com/30026/marianne-william-hendrick-charlotte-decided-business-togetherThu, 17 Jun 2021 15:43:55 +0000Two cellphone companies are offering different rate plans.
https://mathsgee.com/30025/two-cellphone-companies-are-offering-different-rate-plans
Two cellphone companies are offering different rate plans. Rogers is offering \$19.99 per month, which includes a maximum of 200 weekday minutes plus \$ 0.35 for every minute above the maximum. TELUS is offering \$ 39.99 for a maximum 300 weekday minutes, but it charges \$ 0.10 for every minute above the maximum. Above how many minutes would TELUS be the better choice?Mathematicshttps://mathsgee.com/30025/two-cellphone-companies-are-offering-different-rate-plansThu, 17 Jun 2021 15:42:02 +0000Jacob owns 15,000 shares in a corporation, which represents $2 \%$ of all issued shares for the company. He sold $\frac{2}{5}$ of his shares to another investor for $\$ 7,800$. What is the total value for all of the shares issued by the company?
https://mathsgee.com/30024/corporation-represents-company-another-investor-company
Jacob owns 15,000 shares in a corporation, which represents $2 \%$ of all issued shares for the company. He sold $\frac{2}{5}$ of his shares to another investor for $\$ 7,800$. What is the total value for all of the shares issued by the company?Mathematicshttps://mathsgee.com/30024/corporation-represents-company-another-investor-companyThu, 17 Jun 2021 15:41:18 +0000An accountant is trying to allocate production costs from two different products to their appropriate ledgers. Unfortunately, the production log sheet for last week has gone missing.
https://mathsgee.com/30023/accountant-production-appropriate-unfortunately-production
An accountant is trying to allocate production costs from two different products to their appropriate ledgers. Unfortunately, the production log sheet for last week has gone missing. However, from other documents he was able to figure out that 1,250 units in total were produced last week. The production machinery was run for $2,562.5$ minutes, and he knows that Product A takes $1.5$ minutes to manufacture while Product B takes $2.75$ minutes to manufacture. How many units of each product were produced last week?Mathematicshttps://mathsgee.com/30023/accountant-production-appropriate-unfortunately-productionThu, 17 Jun 2021 15:40:24 +0000St. Boniface Hospital raises funds for research through its Mega Lottery program.
https://mathsgee.com/30022/boniface-hospital-raises-research-through-lottery-program
St. Boniface Hospital raises funds for research through its Mega Lottery program. In this program, 16,000 tickets are available for purchase at a price of one for $\$ 100$ or three for $\$ 250 .$ This year, the lottery sold out with sales of $\$ 1,506,050 .$ To better plan next year's lottery, the marketing manager wants to know how many tickets were purchased under each option this year.Mathematicshttps://mathsgee.com/30022/boniface-hospital-raises-research-through-lottery-programThu, 17 Jun 2021 15:39:27 +0000