🧮 algebra

1. Problem 57: Given the function $y = x^2 - 1$, we stretch it vertically by a factor of 3. 2. Vertical stretching means multiplying the entire function by 3:

1. Problem: Solve the simultaneous equations $3x^2-xy=0$ and $2y-5x=1$. 2. Factor the first equation to find relations between $x$ and $y$.

1. Problem: Sketch the graph of the piecewise function $$f(x) = \begin{cases}-2x - 1, & x \leq 2 \\ -x + 4, & x > 2\end{cases}$$

1. The problem states that the thickness of the ice sheet $s$ in meters is modeled by the linear equation $$s=-0.25t+4$$ where $t$ is the time in weeks after the beginning of sprin

1. The problem states that the thickness of the ice sheet $s$ (in meters) depends on the number of weeks $t$ after the beginning of spring, modeled by the equation $$s = -0.25t + 4

1. **State the problem:** Solve the simultaneous equations: $$3x^2 - xy = 0$$

1. Problème 7: Développer et réduire les expressions A et B. A = (\sqrt{2} + 1)^4.

1. المشكلة هي نشر المعادلة التالية: $$(a+b)^2$$. 2. نستخدم صيغة التربيع لمجموع حدين: $$(a+b)^2 = a^2 + 2ab + b^2$$.

1. **Problem Statement:** 15. A sum of money is divided among Albert, Brian and Chrissy in ratio 3:5:7. Chrissy's share is 3500.

1. **State the problem:** Given the function $f(x)$ defined by the piecewise points from the graph:

1. The problem is to graph the piecewise function: $$f(x) = \begin{cases} 2x - 1 & \text{if } x < 0 \\ -1 & \text{if } x \geq 0 \end{cases}$$

1. **Énoncé du problème :** Effectuer les calculs suivants, rendre le dénominateur rationnel et résoudre une équation :

1. Solve each equation by factoring. ### a) $x^4 - 16x^2 + 75 = 2x^2 - 6$

1. State the problem. Determine the x-intercept(s) of the function $y=3(x+6)^4-48$.

1. **Problem statement:** We analyze the relations given by the equations $$x^{2} + y^{2} = 25$$ and $$y = \\sqrt{25 - x^{2}}$$ to graph them, determine whether they are functions,

1. The problem provides two quartic functions and their graph transformations. 2. First function: $y = \frac{5}{4}x^4 + 3$.

Problem: Factor $x^2 + 5x - 6$. 1. Identify the coefficients for the quadratic in the form $ax^2 + bx + c$: we have $a=1$, $b=5$, and $c=-6$.

1. **Stating the problem**: Given $\log_4 x = y$, where $x > 0$, find: a) $\log_2 x$

1. The problem asks for equations of lines passing through the point $(2, -5)$ under different conditions. 2. (a) A line with slope $-3$ passing through $(2,-5)$:

1. The problem is to factor the quadratic expression $$x^2 + 5x + 6$$. 2. We look for two numbers that multiply to the constant term 6 and add up to the coefficient of the linear t

1. The problem is to factor the expression $x^2$. 2. Notice that $x^2$ is a perfect square since it is $x$ multiplied by itself.