## All Tasks

#### Conjunction of conditions (I_E)

Give all integer values of $x$ that fulfil the
following two conditions:
1. The function values of $f(x) = -1-x$ are not negative.
2. The function values of $g(x) = -3x-9$ are negative.

# Linear functions

Training

9

#### Race time

Three friends decided to take a run. Ana used a bicycle, Filipa and Joana used cars. Joana's car is faster than Filipa's.
Looking at the figure, fill in the spaces with f, g, h, or a number.

# Linear functions

Training

9

#### Matrix equation 0.4

Let $A$, $B$, $C$ and $X$ be matrices with real values, and suppose that all the matrices involved have an inverse and the operations involved are all possible. Solve in order of $X$ the following matrix equation:
$(B^{-T} X^T)^T - A = C$
Then, considering
$$A=\begin{bmatrix} 0 & -1\\ 4 & 1 \end{bmatrix}$$, $$B=\begin{bmatrix} -2 & \frac{3}{2}\\ 1 & -\frac{1}{2} \end{bmatrix}$$ and
$$C=\begin{bmatrix} 3 & -1\\ 0 & 2 \end{bmatrix}$$
compute the matrix $X$.

# Equations

Training

13

#### The subway

Determine the gradient at which the subway descends into the ground. Enter the absolute value of the slope in percentage.
Note: Find a suitable gradient triangle to determine the slope of the subway. You can use the person as a reference object. Make a sketch before your calculation.

# Linear functions

Modeling

8

#### Linear Function: Determine the Parameter

The linear function $a\cdot x\;+2\cdot\;y\;=\;24\;-\;a\;$, crosses the x-axis in the point with abscissa $2$. Can you find the parameter $a$?

# Linear functions

# Linear equations

Training

8

#### Slope: Line of two given points

Can you find the slope of a linear function that passes through the points $A(2,-1)$ and $B(5,2)$?

# Linear functions

Training

8