Answer:
The sum of the first 880 terms in the sequence is 2,273,920.
Step-by-step explanation:
Arithmetic sequence:
The difference between consecutive terms is always the same, called common difference, and the nth term is given by:
In which d is the common difference.
Sum of the first n terms:
The sum of the first n terms of an arithmetic sequence is given by:
ai = ai-1 + 6
This means that 
In this question:
Sum of the first 800 terms, so 
First term is -53, so 
The 880th term is:
Sum
The sum of the first 880 terms in the sequence is 2,273,920.
Yes. It can be simplified into 1 1/44
Answer: the speed of the boat on the lake is 9 mph
Step-by-step explanation:
Let x represent the speed of the boat on the lake or in still water.
The speed of the current in a river is 6 mph. This means that if the boat goes upstream against the speed of the current, its total speed would be (x - 6)mph. If the boat goes downstream against the speed of the current, its total speed would be (x + 6)mph.
Time = distance/ speed
Every day, his route takes him 22.5 miles each way against the current and back to his dock, and he needs to make this trip in a total of 9 hours. This means that the time taken to travel upstream is
22.5/(x - 6). The time taken to travel downstream is
22.5/(x + 6)
Since the total time is 9 hours, it means that
22.5/(x - 6) = 22.5/(x + 6)
Cross multiplying, it becomes
22.5(x + 6) + 22.5(x - 6) = 9
Multiplying through by (x + 6)(x - 6), it becomes
22.5(x - 6) + 22.5(x + 6) = 9[(x + 6)(x - 6)]
22.5x - 135 + 22.5x + 135 = 9(x² - 6x + 6x - 36)
22.5x + 22.5x = 9x² - 324
9x² - 45x - 324 = 0
Dividing through by 9, it becomes
x² - 5x - 36 = 0
x² + 4x - 9x - 36 = 0
x(x + 4) - 9(x + 4) = 0
x - 9 = 0 or x + 4 = 0
x = 9 or x = - 4
Since the speed cannot be negative, then x = 9
Answer:
x = 112°, y = 68°
Step-by-step explanation:
68° and y are corresponding angles and are congruent, then
y = 68°
x and y are adjacent angles and are corresponding ( sum to 180° ), then
x + y = 180°
x + 68° = 180° ( subtract 68° from both sides )
x = 112°
In the previous activities, we constructed a number of tables. Once we knew the first numbers in the table, we were often able to predict what the next numbers would be. Whenever we can predict numbers in one row of a table by multiplying numbers in another row of a table by a given number, we call the relationship between the numbers a ratio. There are ratios in which both items have the same units (they are often called proper ratios). For example, when we compared the diameter of a circle to its circumference, both measured in centimeters, we were using a same-units ratio. Miles per gallon is a good example of a different-units ratio. If we did not specifically state that we were comparing miles to gallons, there would be no way to know what was being compared!
When both quantities in a ratio have the same units, it is not necessary to state the unit. For instance, let's compare the quantity of chocolate chips used when Mary and Quinn bake cookies. If Mary used 6 ounces and Quinn used 9 ounces, the ratio of Mary's usage to Quinn's would be 2 to 3 (note that the order of the numbers must correspond to the verbal order of the items they represent). How do we get this? One way would be to build a table where the second row was always one and a half times as much as the first row. This is the method we used in the first two lessons. Another way is to express the items being compared as a fraction complete with units:
<span>6 ounces
9 ounces</span>Notice that both numerator and denominator have the same units and thus we can "cancel out" the units. Notice also that both numerator and denominator have values that are divisible by three. When expressing ratios, we generally treat them like fractions and "reduce" or simplify them to the smallest numbers possible (fraction and colon forms use two numbers, as a 3:1 ratio, whereas the decimal fraction form uses a single number—for example, 3.0—that is implicitly compared to the whole number 1).<span>
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