🧮 algebra

1. The problem asks to find the perimeter $P$ of a trapezoid in terms of $x$. 2. The trapezoid has four sides: the vertical side $3x$, the top side $2 + x$, the bottom side $2 + 5x

1. The problem describes a function machine where the input is labeled $d$ and the operation inside the machine is adding 72 to the input. 2. This means the function can be written

1. The problem shows a transformation from inputs 20, 17, and 9 to outputs 13, A, and B respectively. 2. We need to find the values of A and B based on the pattern or rule applied

1. The problem is to analyze the linear function $y = 5X - 8$. 2. This is a linear equation where the slope is 5 and the y-intercept is -8.

1. The problem presents multiple linear equations in two variables $x$ and $y$. 2. Each equation is either in slope-intercept form $y = mx + b$ or can be rearranged into that form.

1. **State the problem:** We have a rectangle with dimensions $2x - 12$ and $3x + 9$, and its area is $60$ cm$^2$. We need to find the actual dimensions of the rectangle. 2. **Writ

1. **Problem statement:** Determine the type of angle (acute or obtuse) formed by the part of the graph above the x-axis with the positive x-axis direction, and whether the functio

1. Problema 21: Calculați determinantul \(D(x,y) = \begin{vmatrix} 1 & 1 & 1 \\ x & y & 2 \\ x^2+1 & y^2+1 & 5 \end{vmatrix}\). 2. a) Calculăm \(D(1,-1)\):

1. The problem asks to determine the domain on which the given function is decreasing. 2. From the description, the function is a parabola opening upwards with vertex at approximat

1. The problem asks us to find all values of $x$ for which $f(x) > 0$ given the graph of $y = f(x)$. 2. From the graph description, the parabola crosses the x-axis at $x = 1$ and $

1. **State the problem:** Nadia converted some pounds at either Shop A or Shop B and received €64.96. We need to find the smallest amount in pounds she could have converted. 2. **I

1. **State the problem:** A student answered 120 True/False questions. Each correct answer gives 1 mark, each wrong answer deducts 1/4 mark. The student scored 95 marks. All guesse

1. The problem is to solve an equation or expression, but since the exact problem is not specified, let's consider a common example: solve the quadratic equation $x^2 - 5x + 6 = 0$

1. **Plot the graphs of the functions:** a) The function is $y=3x^2-7$.

1. Stating the problem: We need to find the determinant of the 3x3 matrix $$\begin{bmatrix} x & 3 & 7 \\ 2 & x & 2 \\ 7 & 6 & x \end{bmatrix}$$. 2. Recall the formula for the deter

1. The problem is to find the determinant of the 2x2 matrix \(\begin{bmatrix} x & 3 \\ 7 & ? \end{bmatrix}\). However, the matrix is incomplete as the bottom right element is missi

1. **State the problem:** We are given the line equation $y = 4x - 1$ and the conic equation $x^2 + 2x + y^2 = k$. We want to analyze the relationship between these two equations.

1. **Problem (a): Solve the system by substitution:** Given:

1. **Problem statement:** We have two pairs of sequences. For each pair, the second sequence is formed from the first by adding, subtracting, or multiplying by a number. We need to

1. The problem gives two sequences: - First sequence: 7, 10, 13, 16, ... with nth term $3n + 4$

1. The problem states that the exchange rate graph is a straight line passing through points (0,0), (5,600), (10,1200), (15,1800), and (20,2400). 2. Since the graph is linear and p