Answer:
The speed of the first train is 45 mph and the speed of the second train is 75 mph
Step-by-step explanation:
Let x represent the speed of the first train in mph. Since the second train, is 30 mph faster then the first, therefore the speed of the second train is (x + 30).
The first train leaves at 1:00 pm, therefore at 6:00 pm, the time taken is 5 hours. Therefore the distance covered by the first train at 6:00 pm = x mph * 5 hours = 5x miles
The second train leaves at 3:00 pm, therefore at 6:00 pm, the time taken is 3 hours. Therefore the distance covered by the second train at 6:00 pm = (x + 30) mph * 3 hours = (3x + 90) miles
Since the second train overtakes the first at 6:00 pm, hence:
3x + 90 = 5x
2x = 90
x = 45
Therefore the speed of the first train is 45 mph and the speed of the second train is 75 mph (45 mph + 30 mph).
Answer: $585.60
Step-by-step explanation:
The number of years that would have passed is;
= 2016 - 1626
= 390 years
Using simple interest, the investment will be worth;
= Principal * ( 1 + rate * number of years)
= 24 * (1 + 0.06* 390)
= $585.60
• First way to solve:
We'll manipulate the expression of the equation:

If we have y=0:

Then, the function has one real zero (x=3) and two imaginary zeros (4i and -4i).
Answer: B
• Second way to solve:
The degree of the function is 3. So, the function has 3 complex zeros.
Since the coefficients of the function are reals, the imaginary roots are in a even number (a imaginary number and its conjugated)
The function "has only one non-repeated x-intercept", then there is only one real zero.
The number of zeros is 3 and there is 1 real zero. So, there are 2 imaginary zeros.
Answer: B.
The blank spaces in the task content can be filled with; Substitution property, 90° and subtraction property.
<h3>What are the missing statements in the proof?</h3>
Since it follows from the vertical angles theorem that angle 1 = angle 4 as they are congruent.
Additionally, angles 1 and 2 are said to be complementary and hence, the sum of their measures is equal to 90°.
Finally, by virtue of the subtraction property of equality, the measure of angle 2 is; 90° - 40° = 50°.
Read more on complementary angles;
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