Answer:
Given the 2 values, height and the base, of these 2 triangles, we can assume that they are similar (meaning they share the same angles) as we have no other information to determine the height of the tree.
Therefore, if these triangles are similar, their corresponding sides are proportional. In other words, PZ/RT = QZ/ST or RT/PZ=ST/QZ
Hence, if we find the ratio of this, we can use it to find the side <em>h</em>
<em>QZ/ST=PZ/RT</em>
<em>48/12=PZ/4</em>
<em>PZ/4=48/12</em>
<em>(PZ/4)3=48/12</em>
<em>PZ(3)/12=48/12</em>
<em>48/3=16</em>
16=PZ.
3Step-by-step explanation:
Let the walker’s speed be W, then the biker’s is W+1.5W=2.5W. Difference in speed is 1.5W. Distance=speed times time, so 12.5=1.5W×1.5=2.25W, and W=12.5/2.25=1250/225=50/9=5.56 mph. The biker’s speed is 2.5W=125/9=13.89 mph to 2 Dec places.
(Note: “1.5 times faster than a walker’s speed” could not reasonably mean the biker’s speed=1.5W because this would give W=16.67 mph, which is very fast for a runner, let alone a walker (!), and a biker’s speed of 25mph.)
The answer would by 16 if you wanted the quick answer
Answer:
- (x, y) = (8, -1)
- (x, y) = (7, 10.5)
Step-by-step explanation:
1. You can use the expression for y to substitute into the first equation:
2x +4(1/4x -3) = 12
2x +x -12 = 12 . . . . . . eliminate parentheses
3x = 24 . . . . . . . . . . . add 12; next divide by 3
x = 8 . . . . . matches choice C
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2. You can use the expression for y to substitute into the second equation:
x -2(2x -3.5) = -14
-3x +7 = -14 . . . . . . eliminate parentheses
21 = 3x . . . . . . . . . . add 3x+14; next divide by 3
7 = x . . . . . matches the third choice
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When the answer choices are sufficiently different, you only need to find one value to determine which is the correct choice. (If you want to check your work further, you can substitute the other answer value into the two equations to see if it works.)
Answer:
Step-by-step explanation:
Let's start with the simple ones:
a = amplitude = (highest - lowest) divided by 2 = (11-1)/2 = 5
d = offset = (highest + lowest) divided by 2 = (11+1)/2 = 6
Now, if x goes 'untreated', the cos would make a full swing after 2pi.
Here, it repeats after 3. To achieve that, we divide by 3 and multiply by 2pi.
b = 2pi/3
You can try it out (assuming c=0 for a minute): x=3 puts bx at 2pi.
Now for the final one, the shift left by one. We cannot say c=1 because that would be a 1 on the 2pi scale.
Rather, the shift would be c'=1 if the formula were acos(b(x+c')).
If we work out the parenthesis with c'=1, we get bx + b, so the actual c is 2pi/3