Linear, exponential, logarithmic, polynomial, rational, and trigonometric functions, conic sections, binomial, surds, graphs and transformations of graphs, equation- and system-solving, and other symbolic-manipulation topics.

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1answer
19 views

Find total number of painted cubes

Suppose that a wooden cube, whose edge is 5 inch, is painted red, then cut into 125 pieces of 1 inch edge. Find total number of painted cubes ?
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1answer
14 views

Plug in numbers to find relationship between numbers

A total of k passengers went on a bus trip. Each of the n buses that were used to transport the passengers could seat a maximum of x passengers. If one bus had 3 empty seats and the remaining buses ...
3
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2answers
25 views

Piecewise linear function and absolute value

While writing a solution to homeworks for my students, I had to write the function $$f(x)=\left\{\begin{array}{ll} \frac{x+2}{2}, & x\leqslant -4\\ \frac{x}{4}, & -4\leqslant x\leqslant 4 \\ ...
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2answers
30 views

If two sides of an equilateral triangle measures $(6x+1)$ units and $\frac{11x+5}{2}$ units, find the perimeter of the triangle.

If two sides of an equilateral triangle measures $(6x+1)$ units and $\frac{11x+5}{2}$ units, find the perimeter of the triangle. I tried the following, Let the third side measure $x$ units ...
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2answers
32 views

How many boys, girls, men and women are there?

In a village, there are exactly $10$% more boys than girls; $15$% more women than men; $20$% more children than adults. The population is less than $6000$. Solution: $b = g + 0.1g$--------(i), ...
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0answers
13 views

Sharing and Distributing Surplus and Shortage Problem [on hold]

Allison, Beverly, and Christine have some pieces of chessmen. Half of Allison's chessmen and shared by Beverly and Chris equally, the half of Beverly's are shared by Allison and Chris equally. Lastly, ...
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1answer
10 views

Distributing Giving out Quarters Suplus and Shortage Problem

Amy, Betty, and Chloe have some quarters. Amy gives some of her quarters to Betty and Chloe, making their quarters doubled. Then Betty dos the same thing, making Amy and Chloe's quarters doubled. And ...
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2answers
72 views

Finding all solutions to the equation $|||||x|-1|-1|-1|-1|=0$

I was presented this question by a student I was tutoring: Suppose $x \in \mathbb{R}$. Find all solutions of the equation $$|||||x|-1|-1|-1|-1|=0.$$ What I explained to the student: Given ...
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6answers
61 views

Adding $2$ absolute values together: $|x+2| + |x-3| =5.$

I came across a very basic absolute value question $|x+2| + |x-3| =5.$ Initially, I thought the answer was $x=-2$ and $x=3$ because I let each absolute values be either positive and negative and ...
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4answers
40 views

Physics problem, stuck in algebra.

I end up with the equations; $$u=u_1' \cos(a)+u_2' \cos(b)$$ $$u_1' \sin(a)=u_2' \sin(b)$$ $$u^2=u_1'^2+u_2'^2$$ I have to show that $$a+b=\frac{\pi}{2}$$ $x'$ isn't the derivative of $x$, it's a ...
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1answer
38 views

Solve an equation involving fractional powers

doing some BASIC programming, and have this exponential equation that works perfectly: Constants: $K=10,A=64,B=1023,D=1000$ The real variable input is $C\in[0,D]$ I have ...
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0answers
31 views

A Discount equation. [on hold]

I am have trouble remembering how to do a discount equation that it will not give more than $40\%$. So if I say I sell more than $1$ of the product it will decrease by a percentage, but it will only ...
0
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4answers
39 views

Find algebraic function to describe number of people “x”

For a group of x people, Joe ordered 5 pizza pies, each of which was cut into 12 slices. Each person was originally supposed to have an equal number of slices. However, four people did not want any ...
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3answers
26 views

Find the slope-intercept form of the equation of the line passing through the points. Sketch the line.

Find the slope-intercept form of the equation of the line passing through the points. Sketch the line. (-8,1),(-8,7) (-1,4),(6,4) Progress The slope that I get for number 1 is ...
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1answer
38 views

First degree or second degree quadratic equation?

$X-\sqrt{121}= 0$ $Y^2-121=0$ When I try to solve by squaring on both sides the first equation changes to $X^2-121 =0$, where $x = \pm 11$. When I try to solve it this way: $x= \sqrt{121} = +11$, ...
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3answers
48 views

The $n^{th}$ root of $1$

How do I prove that the $n^{th}$ root of $1$ forms the vertices of a unit $n$-gon in the complex plane? For example when I graph the $3$ solutions of $\sqrt[3]{1}$ they form the vertices of a unit ...
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6answers
104 views

Tangent to $e^x$

I have been asked to find the tangent to $y=e^x$ that passes through origin. This is what i came up with. Tangent $f(x)=e^x(x-a)+f(a)$, where a is zero, I therefore conclude with $e^xx$ to be the ...
4
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1answer
61 views

Is there an injective function such that $f(x^2)-f^2(x)\ge \frac{1}{4}$?

The exercise asks me this: Is there an injective function such that $f(x^2)-f^2(x)\ge \frac{1}{4}$? ps: $f: \mathbb{R}\to \mathbb{R}$ I really don't know how to start :c, I appreciate hints.
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0answers
36 views

Reverse engineer applying fees

So I am having an interesting problem that I am unable to solve. Let me just start by saying I know absolutely nothing about math but that doesn't stop me from trying to solve this equation in the ...
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3answers
47 views

Horse Betting Odds - But Guaranteed Win!

Suppose four horses - $A, B, C$, and $D$ - are entered in a race and the odds on them, respectively, are $6$ to $1$, $5$ to $1$, $4$ to $1$, and $3$ to $1.$ If you bet $\$1$ on $A$, then you receive ...
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3answers
185 views

Is$\frac{\sqrt{a}}{\sqrt{b}}$ the same as $\sqrt{\frac{a}{b}}$?

My idea is that the two functions are not the same since for the first function, the domain of the function is only non negative reals for the numerator and positive reals for the denominator. ...
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1answer
33 views

Trigonometric inequality question [on hold]

Let $0 < A < \frac {\pi}{2}$ and $0 < B < \frac {\pi}{2}$. (a) prove that $\sec^2 A + \csc^2 A \cdot \csc^2 B \cdot \sec^2 B \geq 9.$ (b) determine values of $\sec A$ and $\sec B$ when ...
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2answers
80 views

The juice-problem

I have got an exercise. 7 men are in a room, sitting at a table. In front of each people is a cup. In some cups are juice. The cups altogether have got 3 liters juice in them. Now the first man pour ...
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2answers
30 views

Conversion of dosage based on body weight

Infant ibuprofen containes 100mg/5.0mL suspension. The recommended dose is 10mg/kg body to weight. How many mL of this suspension should be given to an infant weighing 18 lb? That's not a serious ...
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1answer
25 views

Completing the square, optimizing [on hold]

Express the quadratic function y=-3x^2+18x-3 in the form of y=a(x-p)^2+q. Hence determine the maximum or minimum point of the function.
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4answers
189 views

Finding $\frac{\mathrm d}{\mathrm dx} x!$

I'm trying to differentiate $x!$ but I just can't seem to do it right. I define the function as follows: $$x! = \prod_{r = 0}^{x}(x-r) \quad,\quad x \in \mathbb N$$ I've tried attempted to try it by ...
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6answers
66 views

Graph of the $\sqrt { x } $

Why does the graph only go to the right and up? Wouldn't there be negative values of y as well? Since, for example, the $\sqrt{4}$ is $2$ and $-2$
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2answers
22 views

Question about the graphs of functions

If the point $(2,3)$ is on the graph of $f$, then what can we say about $f(2)$? I have an idea of what this question is asking me but nothing more. I suspect that it has something to do with linear ...
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1answer
43 views

Solving system of equations with complex numbers

Equation 1$$ \frac{V_{1}}{5} + \frac{V_{1}-V_{2}}{10+j6} - 10\angle45^\circ = 0 $$ Equation 2 $$ -4V_{1} + \frac{V_{2}-V_{1}}{10+j6} + \frac{V_{3}}{-j2} + \frac{V_{3}}{8+j7} = 0 $$ Equation 3 $$ ...
2
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4answers
43 views

Simplifying/solving a logarithm $\log_24^{2n}$

Need help with simplifying this logarithm. $$\log_24^{2n}$$ Would I just pull the 2n to the front: $$2n*\log_24$$ So it would simplify to $$4n$$ Is this correct or am I completely wrong?
2
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4answers
39 views

Complete the squares to find the center and radius of the circle

I've had trouble on this one problem for a couple days. Complete the square on the X and Y terms to find the center and radius of the circle. $x^2+2x+y^2-4y=-4\:\:$
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2answers
24 views

How to find the slope of a secant line of the graph of a function?

The point $P(5,-2)$ lies on the curve $y=\large\frac{2}{4-x}$. (a). If $Q$ is the point $(X,\large\frac{2}{4-x})$, find the slope $M_{pq}$ of the secant line $PQ$ (correct to six decimal places). ...
0
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0answers
27 views

sketch the region in the xy-plane

Sketch the region in the xy-plane defined by the equation or inequalities $|x|<7$ and $|y|<4$ Im not quite sure how I am supposed to do this.
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4answers
143 views

Proof by induction (exponents)

Use proof by induction and show that the formula holds for all positive integers:$$1+3+3^2+\dots+3^{n-1}=\frac{3^n -1}2$$ The confusing step in my opinion is the first expression: $3^{n-1}$, when ...
0
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4answers
66 views

perpendicular bisector of AB

Let $A(-6,9)$ and $B(10,-3)$ be points in the plane Find an equation of the perpendicular bisector of $AB$ the answer I get is $y=(4/3)x+(1/3)$ but it is not correct.
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1answer
25 views

Logistic population: determine parameter $r$

The general forumla for a logistic population is: $$ P_{n+1} = P_n + r*P_n*(1-\frac{P_n}{K}) $$ I was given $P_{12} = 95.75$ and $P_{14} = 98$, as well as $K = 100$. To solve for $r$, I decided to ...
6
votes
3answers
100 views

Confused about the $\pm$ sign?

I have multiple questions about the $\pm$ sign, since it seems to confuse me in general... Question 1: Say I have $15=\pm(a+x)$, Can I use the distributive property so it becomes $15=\pm a \pm x$? ...
2
votes
5answers
71 views

Algebraic process to find numbers so that $xy=45$ and $x+y=18$

Can someone help me with the following question? The sum of two numbers is $18$ and their product is $45$. Find the numbers. I know that the answer is $15$ and $3$. But how do I find that answer ...
2
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3answers
28 views

Help with finding a vertex

I am having trouble with this math problem. The coordinate of the vertex of $f(x) = ax^2 + bx +c, a \ne 0$, is______. Now I know that to find the $x$ coordinate I would use this formula. $x = ...
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vote
2answers
56 views

If $\frac{5x}{2x^2+5x+1}=\frac13$ then the value of $x+\frac{1}{2x}$ is

If $\frac{5x}{2x^2+5x+1}=\frac13$ then the value of $x+\frac{1}{2x}$ is note $5x=1$ $2x^2+5x+1=3$ or $15x=2x^2+5x+1$ so $2x^2-10x+1$ so $\frac{5+\sqrt{23}}2$ or $\frac{5-\sqrt{23}}2$
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2answers
55 views

If the equation $2x^2-7x+12=0$ has two roots alpha and beta ,then the value of alpha/beta+beta/alpha is

If the equation $2x^2-7x+12 =0$ has two roots $\alpha$ and $\beta$ , then the value of $\frac{\alpha}{\beta}+\frac{\beta}{\alpha}$ is note $x=\frac{-7+\sqrt{47}}{4},\frac{-7-\sqrt{47}}{4}$ then ...
3
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1answer
39 views

If $ab+bc+ca=0$ then the value of $1/(a^2-bc)+1/(b^2-ac)+1/(c^2-ab)$ is

If $ab+bc+ca=0$ then the value of $1/(a^2-bc)+1/(b^2-ac)+1/(c^2-ab)$ is...
1
vote
1answer
25 views

How much above the cost price must he marks his goods above the cost price to make a profit of 17%

A businessman allows a discount of $10$% on written price. How much above the cost price must he mark his goods to make a profit of $17$% ? note: $x\times\frac{90}{100}=x\times\frac{117}{100}$ ...
0
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1answer
27 views

In how many days $Y$ alone finish the work

$X$ and $Y$ do a piece of work in $30$ days .They work together for $6$ days and then $X$ quits and $Y$ finishes the work in $32$ more days.In how many days $Y$ alone finish the work. note:$X+Y=1/30$ ...
0
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1answer
19 views

A math question related to creating a risk formula..

If I'm not using correct terminology, or this isn't clear, I will gladly edit/clarify. I'm trying to figure out how to create method or formula(s) to produce a score based on 4 variables, all real ...
1
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1answer
30 views

Simplifying a product written in Capital Pi Notation

I'm having some trouble figuring out how to simplify Capital Pi Notation. What I tried was to expand the multiplication with various n and tried to find a pattern. Could someone point me in the ...
0
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1answer
25 views

How do I multiply $2(\frac{4}{y})$?

How do I multiply $2(\frac{4}{y})$? I'm having abit of trouble understanding how the answer is 8y...
1
vote
2answers
49 views

Find the equation for the circle

Find an equation for the circle that has center $(−3, 4)$ and passes through the point $(4, −2)$ I keep getting $(x+3)^2+(y-4)=113$
4
votes
2answers
20 views

Condensing Fractional Logarithms

Does the following condense to the following: $\log_2z+(\log_2x)/2+(\log_2y)/2 = \log_2(z\sqrt{x}\sqrt{y})$ or to $\log_2(z\sqrt{xy})$ ?
3
votes
3answers
79 views

Rationalize the denominator and simplify

So the problem I have says rationalize the denominator and simplify. $$ \frac{ \sqrt{15}}{\sqrt{10}-3}$$ My answer I got was $\frac{5 \sqrt6}{7}$. Am I doing this wrong or is this the wrong ...