57 miles because of they are driving 38 miles per hour that means in 1 hour they drive 38 miles. So if they drove for an hour and a half you take 38 and half of 38( which is 15) and you add them together.
If tan theta is -1, we know immediately that theta is in either Quadrant II or Q IV. We need to focus on Q IV due to the restrictions on theta.
Because tan theta is -1, the ray representing theta makes a 45 degree angle with the horiz axis, and a 45 degree angle with the negative vert. axis. Thus the hypotenuse, by the Pythagorean Theorem, tells us that the hyp is sqrt(2).
Thus, the cosine of theta is adj / hyp, or +1 / sqrt(2), or [sqrt(2)]/2
The secant of theta is the reciprocal of that, and thus is
2 sqrt(2)
---------- * ------------ = sqrt(2) (answer)
sqrt(2) sqrt(2)
Use a calculator like calculator soup or symbolab
The scale factor is -2. The answer is choice A
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How did I get this answer? By picking any pair of preimage and corresponding image points. Let's pick on preimage point A and its paired image value A'.
Note how the x coordinate jumps from -11 to +22. So we multiplied by -2 to do this jump. We can see that 22/(-11) = -2 is another way to get this. Similarly, the same happens to the y coordinates as well: -14/7 = -2.
In short, you multiply the preimage coordinate by the scale factor -2 to get the corresponding image coordinates. Points B and C will follow the same pattern.
