Find the angle of incilination of the pq

Step-by-step explanation:

We notice that if the gradient changes, then the value of \(\theta\) also changes, therefore the angle of inclination of a line is related to its gradient. We know that gradient is the ratio of a change in the \(y\)-direction to a change in the \(x\)-direction:

\[m=\frac{\Delta y}{\Delta x}\]

From trigonometry we know that the tangent function is defined as the ratio:

\[\tan \theta = \frac{\text{opposite side}}{\text{adjacent side}}\]

And from the diagram we see that

\begin{align*} \tan \theta &= \dfrac{\Delta y}{\Delta x} \\ \therefore m &= \tan \theta \qquad \text{ for } \text{0}\text{°} \leq \theta < \text{180}\text{°} \end{align*}

Therefore the gradient of a straight line is equal to the tangent of the angle formed between the line and the positive direction of the \(x\)-axis.

x + y = 90 5x – 10y = 90 90 – 10y = 5x 90 + 10y = 5x

step-by-step explanation:

last month maria hiked the 5-mile mountain trail a number of times and she hiked the 10-mile canal trail several times. let x represent the number of times she hiked the 5-mile trail, and let y represent the number of times she hiked the 10-mile trail. if she hiked a total of 90 miles, which equation can be used to find the number of times maria hiked each trail? x + y = 90 5x – 10y = 90 90 – 10y = 5x 90 + 10y = 5x