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3 years ago

9

Jim's uncle is 4 times as old as his nephew jim. in 10 years, jim's uncle's age will be 20 years more than twice jim's age. how

old is jim's uncle right now?

1 answer:

xxTIMURxx [149]3 years ago

5 0

Jim is currently 15 years old.

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Work out the formula of the nth term in the following quadratic sequence:<br> 19, 15, 9, 1...

Butoxors [25]

In a quadratic sequence we'll get a linear first difference and a constant second difference. Let's verify that.

n 1 2 3 4

f(n) 19 15 9 1

1st diff -4 -6 -8

2nd diff 2 2

We see that we got a constant second difference. We could just extend that and work back up to get more values.

n 1 2 3 4 5 6 7

f(n) 19 15 9 1 -9 -21 -35

1st diff -4 -6 -8 -10 -12 -14

2nd diff 2 2 2 2 2

That's just an aside; we're after the general formula. We have

f(1)=19, f(2)=15, f(3)=9

In general we can assume

f(n) = an² + bn + c

We get three equations in three unknowns,

19 = a(1²)+b(1)+c = a+b+c

15 = a(2²) + b(2) + c = 4a + 2b + c

9 = a(3²) + b(3) + c = 9a + 3b + c

That's a 3x3 linear system; it's easy to solve directly. Subtracting pairs,

4 = -3a - b

6 = -5a - b

Subtracting those,

-2 = 2a

a = -1

b = -3a -4 = -1

c = 19-a-b = 21

Answer: f(n) = -n² - n + 21

Check:

f(1) = -1 - 1 + 21 = 19, good

f(2) = -4 - 2 + 21 = 15, good

f(3) = -9 - 3 + 21 = 9, good

f(4) = -16 - 4 + 21 = 1, good

Let's check our extended table, how about

f(7)= -49 - 7 + 21 = -35, good

6 0

3 years ago

Erin gets her exercise by running. The graph shows the distances she covers in a given amount of time. How many hours does it ta

soldi70 [24.7K]

The correct answer is c. 2 $\frac{1}{2}$ hours

Explanation:

The graphic shows the relationship between the distance Erin covers by running and the time this requires. Additionally, to know the specific time that takes for Erin to run a specific distance or vice versa it is necessary to observe at which point the two variables intersect in the line of the graph.

According to this, Erin runs 25 miles (y-axis) in 2.5 hours (x-axis), which you can know because in the line shown by the graph the distance 25 miles that is in the middle of 20 and 30 miles intersects with 2.5 hours or the middle between 2 and 3. Additionally, this number can be expressed as 2 and a half hours, 2.5 or even 2 $\frac{1}{2}$ hours because the fraction represents half. This makes option C the answer.

6 0

3 years ago

There were 10 bunches of roses and tulips. Each bunch had 5 of the same flowers. There were 2 more bunches of tulips than roses.

____ [38]

Answer:

7

Step-by-step explanation:

6 0

3 years ago

Compare the slopes of parallel lines and perpendicular lines?

Gnesinka [82]

Answer: C

Step-by-step explanation: l-7&!:

4 0

3 years ago

suppose a charity received a donation of $22.8 million. if this represents 58% of the charity's donated fund, what is the total

Mrac [35]

The total amount is "x", so, if 22.8 is 58%, "x" is the 100%,

$\bf \begin{array}{ccllll}
amount&\%\\
\text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\
22.8&58\\
x&100
\end{array}\implies \cfrac{22.8}{x}=\cfrac{58}{100}\implies \cfrac{22.8\cdot 100}{58}=x$

6 0

3 years ago