Master Algebra 1 Word Problems with our Comprehensive Practice

Find the equation of the line perpendicular to y=9x/10 that passes through (−1,5)

The perimeter of a rectangular carpet is 54ft. The lenght is 3ft greater than the width. How do you find the length and width?

Why differentiate between irrational and transcedental numbers?

Find the slope of a line perpendicular to y=2−5x

Explanation why irrationals are uncountable? I am a beginner and any help would be greatly appreciated.

Find the slope of any line perpendicular to the line passing through (3,8) and (20,−5)

In the standard (x, y) coordinate plane, a line parallel to y = (1/2)x + 3 must have an equal slope to?

${\displaystyle x^2-9x+18>0}$

Fast way to come up with solutions to $x(x-<!--\; -\; -->1)(x-<!--\; -\; -->2)(x-<!--\; -\; -->3)=1$?

Find the first five terms of the geometric sequence ${\displaystyle a_1=1}$ and r=4

Rational and irrational numbers under base pi

Write an equation in standard form for the line parallel to x−2y+7=0 and contains the point (-4,0)

Find the slope of a line that is perpendicular to a slope of 0

Let $f:\mathbb{R}\to <!--\; \to \; -->\mathbb{R}$ be a continuous map such as each irrational number is mapped to a rational number (i.e.$f(\mathbb{R}\mathrm{\setminus <!--\; \setminus \; -->}\mathbb{Q})\subset <!--\; \subset \; -->\mathbb{Q}$). Show that $f$ is a constant map.

Find the perimeter of an isosceles triangle whose base is 16 cm and whose height is 15 cm

Very need to find the slope of the line perpendicular to ${\displaystyle y=\frac{12}{11}x-9}$

I want to know why the equation $y^2=1-<!--\; -\; -->\frac{4x^{{10}^{12}}}{{\mathrm{\pi <!--\; \pi \; -->}}^2}$ gives an approximate square.
Background
I was just playing around with functions and I wanted to see if $y=|\sin <!--\; \; -->({\displaystyle \frac{\mathrm{\pi <!--\; \pi \; -->}x}{2}})|$ (radians) would give a semicircle for the interval [0,2] as the distance of (1,0) is the same from (0,0), (2,0) and (1,1), all of which will lie on the curve. The equation of a unit semicircle with its centre at (1,0) is $y=\sqrt{2x-<!--\; -\; -->x^2}$
I know that the curves of both the equations don't resemble each other much but I still thought of approximating the sine function using this because I thought that it could still be combined with another approximation to make a better approximation. Anyway, I did it and for $\mathrm{\varphi <!--\; \varphi \; -->}=x\mathrm{r}\mathrm{a}\mathrm{d}\mathrm{i}\mathrm{a}\mathrm{n}\mathrm{s}$, the value of sinϕ can to be approximately ${\displaystyle \frac{2}{\mathrm{\pi <!--\; \pi \; -->}}}\sqrt{\mathrm{\pi <!--\; \pi \; -->}x-<!--\; -\; -->x^2}$. It looked like a semi-ellipse and so I verified it to find that it was a semi-ellipse. I thought of using this to derive the equation for an ellipse with it's centre at the origin and the value of $a$ and b being ${\displaystyle \frac{\mathrm{\pi <!--\; \pi \; -->}}{2}}$ and 1 respectively.
The equation came out to be : $y^2=1-<!--\; -\; -->\frac{4x^{{10}^{12}}}{{\mathrm{\pi <!--\; \pi \; -->}}^2}$
Finally, I thought of playing with this equation and changed the exponent of x. I observed that as I increased the power, keeping it even, the figure got closer and closer to a square.
$y^2=1-<!--\; -\; -->\frac{4x^{{10}^{12}}}{{\mathrm{\pi <!--\; \pi \; -->}}^2}$ gave a good approximation of a square. For the exponent of x being some power of 10 greater than 1012, a part of the curve began to disappear.

Find the equation of the line that passes through (−2,1) and is perpendicular to the line that passes through the following points: (1,4),(−2,3)

You have three numbers. The sum of these numbers are 7.2. The second number is twice as large as the first one. The third number is three times as large as the first one.
This is easily solveable by setting up an equation system such as:
$$a+b+c=7.2$$
$$b=2a$$
$$c=3a$$

Find the slope of any line perpendicular to the line passing through (−4,8) and (2,−7)