🧮 algebra

1. The problem asks how the graph of $$g(x) = -|x - 5|$$ relates to the graph of $$f(x) = |x|$$. 2. The base function is $$f(x) = |x|$$, which is a V-shaped graph with vertex at th

1. The problem asks how the graph of $g(x) = -|x - 5|$ is related to the graph of $f(x) = |x|$. 2. Recall the graph of $f(x) = |x|$ is a V-shaped graph with vertex at $(0,0)$ openi

1. Let's start by understanding what simplifying algebraic expressions means. It involves combining like terms and reducing the expression to its simplest form. 2. The key formula

1. **State the problem:** We need to simplify the expression $$\frac{\frac{5}{6} \cdot \frac{7}{5}}{\frac{5}{6} \cdot \frac{7}{5} + \frac{1}{6} \cdot \frac{1}{7}}$$ and write it as

1. **State the problem:** Simplify the expression $$\frac{\frac{5}{6} \cdot \frac{7}{5}}{\frac{5}{6} \cdot \frac{7}{5} + \frac{1}{6} \cdot \frac{1}{7}}$$ as a quotient of integers

1. Problemet är att lösa en ekvation eller ett matematiskt problem där du vill ha en alternativ metod. 2. Ett vanligt sätt att lösa ekvationer är att använda faktorisering, substit

1. Problemet är att lösa ekvationen $5^x = 7$ för $x$. 2. Vi använder logaritmer för att lösa exponentiella ekvationer. Formeln är: $$x = \log_a(b) = \frac{\log(b)}{\log(a)}$$ där

1. **State the problem:** Simplify the expression \n $$\frac{\frac{2}{3}x^2 - 5x + \frac{7}{3}}{\frac{1}{3}x^2}$$\n

1. **State the problem:** Nadya and Emma travel the same distance $y$. Nadya travels by train at 135 mph, Emma by bus at 60 mph. Emma takes 2 hours longer than Nadya. The time Nady

1. **State the problem:** We are given a table of values for a function $f(x)$ and need to determine what type of function it could represent. 2. **Given values:**

1. The problem asks to find the solutions to the equation $p(x) = 0$. 2. To solve $p(x) = 0$, we need to find all values of $x$ such that the polynomial $p(x)$ equals zero.

1. The problem asks us to find the solutions to the equation $p(x) = 0$. 2. To solve $p(x) = 0$, we need to find all values of $x$ such that the polynomial $p(x)$ equals zero.

1. **State the problem:** We are given the quadratic function $$p(x) = (x - 1)^2 - 1$$ and asked to graph it. 2. **Recall the vertex form of a quadratic function:** $$p(x) = a(x -

1. The problem gives a table of values for a linear function $g(x)$ and asks to identify the x-intercept and y-intercept. 2. The x-intercept is the value of $x$ where $g(x) = 0$.

1. **State the problem:** We are given the quadratic function $$f(x) = 2x^2 - 9x - 5$$ and asked to find: (i) The coordinates of point C where the function crosses the y-axis.

1. The problem is to solve the equation $$2x + 3 = 11$$ for $x$. 2. The formula used here is to isolate $x$ by performing inverse operations. We subtract 3 from both sides and then

1. **State the problem:** Multiply the fraction $\frac{3}{4}$ by 300. 2. **Formula used:** To multiply a fraction by a whole number, multiply the numerator by the whole number and

1. The problem is to find the sum of all integers from 236 to 300 inclusive. 2. We use the formula for the sum of an arithmetic series: $$S_n = \frac{n}{2}(a_1 + a_n)$$ where $n$ i

1. **State the problem:** Sara is making 3 batches of chocolate chip cookies and 3 batches of oatmeal cookies. Each batch of chocolate chip cookies uses $2 \frac{1}{4}$ cups of flo

1. **State the problem:** Determine if the ordered pair $(1, -2)$ is a solution to the system: $$\begin{cases}-2x - 2y = 2 \\ 3x - 3y = 8\end{cases}$$

1. **Express as a single power and then evaluate:** **a)** $\frac{(-5)^6}{(-5)^3} = (-5)^{6-3} = (-5)^3$