Question

the number line shows two unknown numbers, s and t. is t + s positive or negative? positive negative submit

Explanation:

Step1: Analyze positions on number line

From the number line, \( s \) is to the left of \( t \), and both are to the left of \( 0 \) (since \( -1 \) and \( 0 \) are marked, and \( s, t \) are above \( -1 \) and \( 0 \) but direction: wait, actually, the number line has arrow up (positive direction) and down (negative? Wait no, standard number line: arrow to right is positive. Wait the image: the number line has arrow up (maybe vertical? Wait, the labels: \( s \) (red) above a point, \( t \) (blue) below \( s \), then \( -1 \), then \( 0 \) at bottom. Wait, maybe vertical number line: upward is positive? Wait, \( 0 \) is at the bottom, \( -1 \) above \( 0 \)? No, standard is \( 0 \) above negative numbers? Wait no, maybe the number line is vertical, with upward as positive. So \( 0 \) is at the bottom, \( -1 \) above \( 0 \), \( t \) above \( -1 \), \( s \) above \( t \). So \( s \) and \( t \) are both negative? Wait no, if upward is positive, then \( 0 \) is bottom, \( -1 \) is above \( 0 \) (so \( -1 \) is more negative? No, that's reversed. Wait, maybe the number line is horizontal, but drawn vertically. Let's reorient: horizontal number line, right is positive. So the top is left, bottom is right? No, the text: "the number line shows two unknown numbers, s and t". The marks: \( s \) (red) at a point, \( t \) (blue) below \( s \), then \( -1 \), then \( 0 \) at the bottom. So if we consider horizontal (right is positive), then bottom is right (positive), top is left (negative). So \( 0 \) is at bottom (rightmost), \( -1 \) above \( 0 \) (left of \( 0 \)), \( t \) above \( -1 \) (left of \( -1 \)), \( s \) above \( t \) (more left). So \( s \) and \( t \) are both negative, with \( s < t < -1 < 0 \).

Step2: Analyze sum \( t + s \)

Since both \( t \) and \( s \) are negative (less than \( -1 \), so negative), the sum of two negative numbers is negative (because adding two negatives: \( (-a) + (-b) = -(a + b) \), where \( a, b > 0 \), so result is negative). Wait, but wait: if \( s \) and \( t \) are both negative, their sum is negative. But wait, maybe I misread the number line. Wait, the arrow: the top arrow is up, bottom is down. Maybe the number line is vertical, with upward as positive. So \( 0 \) is at the bottom, \( -1 \) above \( 0 \) (so \( -1 \) is more negative? No, that's incorrect. Standard number line: positive direction is right (horizontal) or up (vertical), with \( 0 \) as origin, positive numbers above/below? No, vertical number line: upward is positive, so \( 0 \) is middle, positive above, negative below. But in the image, \( 0 \) is at the bottom, \( -1 \) above \( 0 \), \( t \) above \( -1 \), \( s \) above \( t \). So that would mean \( s \) and \( t \) are above \( -1 \) and \( 0 \), so if upward is positive, \( s \) and \( t \) are positive? Wait, no, \( 0 \) is at bottom, so above \( 0 \) is positive. Wait, \( 0 \) is at the bottom, then \( -1 \) is above \( 0 \)? That can't be. So maybe the number line is drawn with the arrow direction: the top arrow is left (negative direction), bottom arrow is right (positive direction). So \( 0 \) is at the bottom (right), \( -1 \) above \( 0 \) (left of \( 0 \)), \( t \) above \( -1 \) (more left), \( s \) above \( t \) (most left). So \( s \) and \( t \) are both negative (left of \( 0 \)), and \( s < t < -1 < 0 \). Then \( t + s \): two negative numbers, sum is negative. Wait, but let's check magnitudes. If \( s \) and \( t \) are both less than \( -1 \) (since \( -1 \) is between \( t \) and \( 0 \)? No, \( t \) is above \( -1 \), so \( t \) is between \( -1 \) and \( 0 \)? Wait, maybe \( t \) is between \( -1 \) and \( 0 \), and \( s \) is between \( t \) and \( -1 \)? No, the red dot (s) is above the blue dot (t), then \( -1 \), then \( 0 \) at bottom. So vertical: bottom is \( 0 \), then \( -1 \) above \( 0 \), \( t \) above \( -1 \), \( s \) above \( t \). So if upward is negative direction (since \( 0 \) is bottom, negative numbers are above \( 0 \)), then \( s \) and \( t \) are negative, with \( s < t < -1 < 0 \) (since \( s \) is higher up, more negative). Then \( t + s \): both negative, sum is negative. Wait, but maybe I got the direction wrong. Alternatively, maybe the number line is horizontal, with right as positive. The image is rotated. So \( 0 \) is on the right, \( -1 \) to the left of \( 0 \), \( t \) to the left of \( -1 \), \( s \) to the left of \( t \). No, the blue dot (t) is between \( -1 \) and \( 0 \), red dot (s) is to the left of \( t \), so \( s < t < 0 \), both negative. Then \( t + s \): sum of two negative numbers is negative.

Step3: Conclusion on sum sign

Since both \( t \) and \( s \) are negative (as they lie to the left of \( 0 \) on the number line, considering standard horizontal number line with right as positive), the sum of two negative numbers is negative.

Answer:

negative