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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0
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4answers
35 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 ...
-1
votes
2answers
17 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 ...
0
votes
1answer
36 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: $x= \sqrt{121} = +11$, ...
0
votes
3answers
43 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 ...
2
votes
6answers
96 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
votes
1answer
56 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.
0
votes
0answers
34 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 ...
0
votes
3answers
45 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 ...
14
votes
3answers
180 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. ...
1
vote
1answer
31 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 ...
3
votes
2answers
79 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 ...
0
votes
2answers
27 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 ...
-2
votes
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.
4
votes
4answers
162 views

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

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 ...
1
vote
6answers
65 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 $-2$
0
votes
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 ...
-1
votes
0answers
36 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
votes
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
votes
4answers
36 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. $x^2+2x+y^2-4y=-4\:\:$
0
votes
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
votes
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.
1
vote
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
votes
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.
0
votes
1answer
24 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
votes
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 = ...
1
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 $\frac{5-\sqrt{23}}2$
1
vote
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
votes
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
votes
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
votes
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
vote
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
votes
1answer
24 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
47 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
77 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 ...
-1
votes
3answers
75 views

The sum of the $n$ smallest odd numbers is equal to $n^2$ [duplicate]

if given a positive integer $n$ is the sum of the $n$ smallest odd numbers equal to $n^2$
0
votes
1answer
30 views

Quadratics help please [on hold]

Does it matter when you are solving quadratics and you get an or would it matter if you said does x always go first $x<9$ or is it the same as $9<x$?
11
votes
3answers
263 views

What happens to a function when it is undefined?

If I have the function $$f(x) = {x^2 - 2 \over x + \sqrt 2}$$ this is undefined for $x = -\sqrt 2$, am I correct? Since the denominator would be zero. But the numerator is a difference of ...
0
votes
2answers
52 views

Finding equations with known roots

I have the equation .The roots are a, b ,c. How can I find another equation whose roots are without using Vieta??
0
votes
2answers
35 views

How would I solve this for the indicated variable?

$a^{ 2 }x+(a-1)=(a+1)x$; for $x$ I have been able to manipulate and solve for the indicated variable in these type of equations pretty easily until I came across this one. I know that I have to ...
1
vote
2answers
41 views

Proof of logarithmic identity $\log_g x=\log_a x\cdot\log_g a$

I have to prove the alleged link between the logarithms in base g and a $$\log_g x=\log_a x\cdot\log_g a$$ I know that this can be written as: $$\frac{\ln x}{\ln g}=\frac{\ln x}{\ln g}$$ But does ...
0
votes
1answer
17 views

Calculate Growth rate of one day

I was given that a population doubles in 4.8 days. Now I need to calculate the growth rate of one day. This question is in the topic of the Malthus model. To get the intrinsic growth rate: birth rate ...
0
votes
2answers
54 views

process of summing series [on hold]

I'm trying to solve the following exercises, but I have a difficulty: a) Find the sum of the telescoping series : b) Find the sum of this series :
0
votes
1answer
43 views

Simplify the expression $(2x^2 - 2)/(x+1)$ to 2x + 2

So I want to Simplify the expression $(2x^2 - 2)/(x+1)$. I've used wolfram alpha and even looked up the answer witch is 2x + 2. But I totaly forgot how! (I know it's pretty simple I have just ...
2
votes
1answer
12 views

Exponential Form Conversion

Does $(\sqrt[3]{3k})^4 = (3k)^{4/3}$ or $((3k)^{1/3})^4$? I thought the first one is correct, but when I looked at it again I saw that $(3k)^{4/3} = \sqrt[3]{(3k)^4} $
0
votes
1answer
21 views

Expressing a solution in interval notation

I am faced with this problem. I am told to express the answer in interval notation. |3x| > 12 I solve like usual, by doing this: ...
0
votes
0answers
35 views

Mortgage bond monthly repayment

I was given the following question: A mortgage bond of 280000 is taken out on a house at a rate of 19.25% p.a., compounded monthly over 25 years. Question: Calculate the monthly payment ...