🧮 algebra

1. **State the problem:** Factor the cubic polynomial $$-0.8t^{3}+17t^{2}-35t+70$$. 2. **Simplify the polynomial:** To make factoring easier, multiply the entire polynomial by $-5/

1. **State the problem:** Solve the system of equations using determinants (Cramer's Rule): $$4x - 5y - 7 = 0$$

1. **State the problem:** Solve the system of equations using determinants: $$3r = -3s - 3$$

1. **State the problem:** Solve the system of equations using the substitution method: $$x + 3y = 4$$

1. **State the problem:** Solve the system of linear equations by graphing: $$3x - 4y = -12$$

1. The problem gives two expressions for $y$: $y = x + 4x$ and $y = -x - 6$. 2. First, simplify the expression $y = x + 4x$ by combining like terms:

1. State the problem: Solve the system of equations using the addition method: $$3x - 2y = 1$$

1. The problem gives two equations: $$4x = -2 + 3y$$

1. Stating the problem: Solve the equation $$\log^2|x^2+5x+4|=\log^2 3 + \log^2|x+1|.$$\n\n2. Recognize that $$\log^2 a$$ means $$(\log a)^2$$ and rewrite the equation as $$ (\log|

1. **Problem statement:** Find the inverse functions for each given function and graph them if requested. 2. **Part c:** Given $f(x) = \frac{3}{4}x + 5$, find the inverse.

1. **State the problem:** We need to write the equation of a circle in standard form given its center and a point on the circle. 2. **Identify the center and a point on the circle:

1. **State the problem:** Write the equation in standard form for the circle with center $\left(-\frac{5}{2}, \frac{1}{2}\right)$ passing through the point $\left(-\frac{5}{2}, \fr

1. The problem asks to write the equation of a circle in standard form given its center and radius. 2. The standard form of a circle's equation with center $(h, k)$ and radius $r$

1. **State the problem:** Solve the system of equations using determinants: $$2r = -4s - 6$$

1. **Problem statement:** Given the function $f(x) = \frac{x}{2} + 1$, find the inverse function values for specific inputs and evaluate transformations involving the inverse funct

1. **State the problem:** Solve the system of equations using the addition method: $$-3x - 10y = 1$$

1. **State the problem:** Solve the system of equations using determinants (Cramer's Rule): $$4x - 4y - 8 = 0$$

1. প্রথমে বুঝি সময় এবং কাজের সম্পর্ক কী। ধরুন, একটি কাজ সম্পন্ন করতে একজন ব্যক্তি $t$ সময় নেয়। 2. কাজের পরিমাণ ধরা যাক $W$। কাজের গতি বা কর্মদক্ষতা হলো প্রতি একক সময়ে কত কাজ করা হয়

1. The problem is to find the gradient (slope) between two points using the formula $$m=\frac{y_2 - y_1}{x_2 - x_1}$$. 2. For points (5, 4) and (7, 0):

1. **State the problem:** Solve the system of equations by elimination: $$3x = -6 + 4y$$

1. **State the problem:** Solve the system of equations by elimination: $$3x = -6 - 6 + 44y$$