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Questions tagged [algebra-precalculus]

For questions about algebra and precalculus topics, which include linear, exponential, logarithmic, polynomial, rational, and trigonometric functions; conic sections, binomial, surds, graphs and transformations of graphs, solving equations and systems of equations; and other symbolic manipulation topics.

This tag is for questions typically taught in precalculus, as well as elementary algebra.

These topics include linear, exponential, logarithmic, polynomial, rational, and trigonometric functions; conic sections, binomials, surds, graphs and transformations of graphs, solving equations and systems of equations; and other symbolic manipulation topics.

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algebraic equation with powers

The original statement of the problem : Solve in $\mathbb R$ the following equation : $$ a^{log_b x^2 } + a^{log_x b^2 } = a^{1+log_b x } + b^{1+log_x b } $$ where $a,b>0$ and $b \neq 1$ A more general statement of the problem : Find all real…
Last X
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A simple question regarding inequalities

Consider the following inequality: $\sqrt { 8x-7 } + \sqrt {2x+2} \lt 3$ Attempt a solution: after doing all the calculations I got: $x \gt 7$, or, $\frac 78 \le x \lt 1$. On checking this result, however applying greater than $7$ values to the…
Bak1139
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What is the value of $x$ when $\frac{1}{4\sqrt{x}}=\frac{-1}{5}$?

Q)What is the value of $x$ when $\frac{1}{4\sqrt{x}}=\frac{-1}{5}$ ? Ans) First of all let me tell that I know how to find the value of $x$ in the above equation. $\frac{1}{4\sqrt{x}}=\frac{-1}{5}$ $\implies \sqrt{x}=-\frac{5}{4}$ $\implies…
DEB SANKAR ROY
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Incredibly obvious answer isn't obvious?

Somebody asked me why this was wrong, and I can't think of an answer. It's basically asking you to create an expression for a number divided by 3. So would this not be n/3? If you look in the picture, the answer is marked wrong. Is this a glitch…
Austin
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Getting the $x$-intercept of $f(x) = -16x^2 + 80x + 5$

$$f(x) = -16x^2 + 80x + 5$$ I need to find the bigger value of $x$ that makes $f(x) = 0$. Naturally, I thought to do: $$0=-16x^2+80x+5$$ and I applied the quadratic formula $$0=\frac{-80\pm\sqrt{6080}}{-32}$$ but the answer doesn't seem like it…
Alex
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Given $\log2=0.3010300$, $\log3=0.4771213$, $\log7=0.8450980$, find $\log0.3048$

Given $\log2=0.3010300$, $\log3=0.4771213$, $\log7=0.8450980$, find $\log0.3048$ $\log0.3048=\log\left(\dfrac{3048}{10000}\right)=\log\left(\dfrac{2^3\cdot3\cdot127}{10^4}\right)$ $\Rightarrow 3\log2+\log3+\log127-4\log10$ Problem is I don't know…
ronald christenkkson
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Prove that $\forall x \in \Bbb R, 0 \lt \frac{1}{ x^2+6x+10} \le 1$

I am having trouble understanding the meaning of this pictorially. Do I just have to multiply across the inequality by $x^2+6x+10$ since $x^2+6x+10 \gt 0$ for all real $x$, giving: $0 \lt1 \le x^2+6x+10$, giving that $0 \lt 1 $ and $x^2+6x+10 \ge…
salman
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How to tell the question between subtraction and negative numbrers in algebra

I'm just learning algebra in school, but am having much trouble with it. My teacher makes me re-write the problems into equal expressions as well solve them. One of my many troubles is telling the difference between subtraction and a negative…
Pal
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Are functions $e^x$ and $e^x - 1$ parallel?

"No, they're not equidistant" But you can translate $e^x - 1$ upwards by 1 and they're parallel. All the points, so they are equidistant. Furthermore, I've created (discovered?) a postulate that tests if functions are parallel: If f'(x)=g'(x), and…
Tianyue Ma
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Question on the "range" of $f(x)=2^x$

From a high school (Algebra II) quiz: If the domain of $f(x)=2^x$ is the positive rational numbers, what is the range? Since "range" can be ambiguous at this level, let's assume it means the image, not the codomain. The solution provided by the…
AlgTop1854
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Algebraic puzzle: Infer $x = \frac{y + z}{2}$ from $a^{\frac{1}{x}} = b^{\frac{1}{y}} + c^{\frac{1}{z}}$ and $a = b + c$

I have a suspicion that the following expression is true, however my algebra skills aren't brilliant, so any help would be appreciated: Is it possible to infer $x = \frac{y + z}{2}$ from $a^{\frac{1}{x}} = b^{\frac{1}{y}} + c^{\frac{1}{z}}$ and $a =…
Robert
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Geometric, arithmetic, and harmonic mean ratio proof.

If $G$ be the geometric mean between two quantities $A$ and $B$, show that the ratio of the arithmetic and harmonic means of $A$ and $G$ is equal to the ratio of the arithmetic and harmonic means of $G$ and $B$. $A, G, B$ are in geometric…
ronald christenkkson
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When/What are we allowed to do to identities?

Starting with $(x+1)^2 = x^2 + 2x+1$ we can find new identities by substituting. However if I sub $x=2x^2 - 5$ into the equation, giving $(x+1)^2 = (2x^2 -5)^2 +2x +1%$ I get a true statement which holds for all $x$ such that $x + 5 - 2x^2 = 0$ just…
Nav Bhatthal
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If $x+xy+y=55$, what is $x+y$?

If $x,y\in \mathbb N$ is s.t. $$x+xy+y=55,$$ find $x+y$ ? I tried to write $x+xy+y=65$ as an equation of $x+y$, but can't go anywhare : Using the fact that $$xy=\frac{1}{4}((x+y)^2-(x-y)^2,$$ I have that $$x+xy+y=55\iff…
joshua
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How can we divide an equation by a function, where that function isn't guaranteed to be always non-zero?

Suppose I have the following equation, where r(x) and y(x) are functions of x. r(x)y(x) = y(x)r'(x) My understanding is that we can divide both sides by y(x), only if we know that y(x) != 0 for all values of x. If that's not necessarily the case,…
Aviv Cohn
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