Master Algebra 1 Word Problems with our Comprehensive Practice

How Do you Write the Recursive Formula For The Following sequence 4, 11, 18, 25, 32?

How do you write y=x+3 in standard form?

Find the slope that is perpendicular to the line y=−1

Find the term n=12, given the arithmetic sequence ${\displaystyle a_1=5}$ and d=1/3

If a number is multiplied by each term of an arithmetic sequence, is the resulting sequence still arithmetic of is it geometric?

Find the Nth term in the geometric sequence where the first term is 3 and the fourth term is ${\displaystyle 6\sqrt{2}}$

Write the point slope form of the equation given (5,5) and slope 3/5

Solving Cubic Equations with Lagrange Resolvent?
I'm having difficulties understanding my textbook's decription of solving cubic equations using Lagrange Resolvents and symmetric polynomials.
Here's what I understand:
$$x^3+px-<!--\; -\; -->q=(x-<!--\; -\; -->r)(x-<!--\; -\; -->s)(x-<!--\; -\; -->t)$$
We can also write:
$$\mathrm{\lambda <!--\; \lambda \; -->}=r+ws+w^{2}t$$
$$\mathrm{\mu <!--\; \mu \; -->}=wr+s+w^{2}t$$
where $1,w,w^2$ are the cubic roots of 1. I then understand that ${\mathrm{\lambda <!--\; \lambda \; -->}}^2+{\mathrm{\mu <!--\; \mu \; -->}}^3$ and ${\mathrm{\lambda <!--\; \lambda \; -->}}^3{\mathrm{\mu <!--\; \mu \; -->}}^3$ are symmetric polynomials in r, s, and t. It is also solvable that the elemntary symmetric functions in r, s, t are 0,p,q where
$$r+s+t=0$$
$$rs+rt+st=p$$
$$rst=q$$
The part where I get confused is that the book claims that ${\mathrm{\lambda <!--\; \lambda \; -->}}^3$ and ${\mathrm{\mu <!--\; \mu \; -->}}^3$ are the roots of the quadratic polynomial $q(x)=x^2-<!--\; -\; -->({\mathrm{\lambda <!--\; \lambda \; -->}}^3+{\mathrm{\mu <!--\; \mu \; -->}}^3)x+{\mathrm{\lambda <!--\; \lambda \; -->}}^3{\mathrm{\mu <!--\; \mu \; -->}}^3$, which seems obvious to me. Then they claim you can use the quadratic formula to solve for ${\mathrm{\lambda <!--\; \lambda \; -->}}^3$ and ${\mathrm{\mu <!--\; \mu \; -->}}^3$ in terms of p and q, thus allowing you to solve a system of equations to acquire r,s,t.
How can you use the quadratic formula to "explicitly solve for ${\mathrm{\lambda <!--\; \lambda \; -->}}^3$ and ${\mathrm{\mu <!--\; \mu \; -->}}^3$ in terms of p and q"?

Find the two square roots of 36i.

What does a graph of linear equations in two variables look like?

1) Convert $90{}^{\circ <!--\; \circ \; -->}C$ to Fahrenheit. Use the formula $F=\frac{9}{5}C+32$
$A)81.5{}^{\circ <!--\; \circ \; -->}FB)219.6{}^{\circ <!--\; \circ \; -->}FC)168.4{}^{\circ <!--\; \circ \; -->}FD)194{}^{\circ <!--\; \circ \; -->}F$
2) Convert $122{}^{\circ <!--\; \circ \; -->}F$ to Celsius. Use the formula $C=\frac{5}{9}(F-<!--\; -\; -->32)$. Round to the nearest tenth if necessary.
$A)35.8{}^{\circ <!--\; \circ \; -->}CB)251.6{}^{\circ <!--\; \circ \; -->}CC)50{}^{\circ <!--\; \circ \; -->}CD)70{}^{\circ <!--\; \circ \; -->}C$

Quadratic Division - How to divide two quadratics?
My studies into graphs and models following examples from Khan Academy has helped me on my goal to learn how to chart and model via the quadratic formula.
However, while I have been successful in understanding addition, subtraction and multiplication of 'g' and 'f':
Say
$f(x)=2x^2+15x-<!--\; -\; -->8$
$g(x)=x^2+10x+16$
I have been unsuccessful in understanding division,
Where f(x)/g(x)
Would one start by grouping the functions into their own families?, for example:
$2x^2/x^2$
$15x/10x$
$-<!--\; -\; -->8/16$
I only came to this conclusion as with multiplication you times as so: $(A+B)\cdot <!--\; \cdot \; -->(C+D)=AC+AD+BC+BD$
However from the example on Khan Ac. this seems wrong, it appears that division departs from any systematic way to find the answer, and that Khans division explanation is not as clear as his others on +, -, and * (appears to me!)
I decided to try and explore division once more in its most simple form to see if I was missing something.
$\frac{2}{3}=\mathrm{0.666666666...}$
$\frac{2}{4}=0.5$
Here clearly, certain division of numbers produces what seems like a simple solution into irrational numbers, If I were to divide a cake the same way I would think of each piece as a ratio, however in decimals these numbers are not clearly defined.
And when one starts dividing multiple factors as with above, how does one find the correct way to divide a quadratic equation, without relying on cheap tricks.

Write the equation in point slope form given (-1, -2), perpendicular to y = -3x + 3

The recursive formula for an arithmetic sequence is ${\displaystyle a_n=a_{n-1}+d}$ if the common difference is −15 and ${\displaystyle a_6=7}$ what is the value of ${\displaystyle a_7}$?

Find the slope of the line perpendicular to ${\displaystyle y=-\frac{4}{15}x+15}$

Find the slope of a line parallel to y=-4x+7

For real numbers 𝑎,𝑏, if 𝑎+𝑎𝑏+𝑏=3, then find the range of 𝑚=𝑎−𝑎𝑏+𝑏. Is there any inequalities here to use?

How does the golden ratio relate to the Fibonacci sequence?

Find the number if four less than the product of a number and 8 is twice the sum of the number and 10

${\displaystyle 2p^2-7p+3>0}$