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3 years ago

11

Classrooms on one side of the science building are all numbered with consecutive odd integers. If the first room, the room with

the smallest classroom number, on this side of the building is numbered k, write an expression in k for the sum of the first five classroom numbers in a row. Then simplify this expression. The sum of the first five classroom numbers in a row is

1 answer:

liubo4ka [24]3 years ago

8 0

Answer:

The sum of the first five classroom numbers in a row is 5k + 20

Step-by-step explanation:

Since the smallest classroom number on the side of the building is numbered k and each consecutive odd integer is separated by a difference of

2.

Therefore:

k is the first class room.

k + 2 is the second class room.

k + 4 is the third class room.

k + 6 is the third class room.

k + 8 is the fifth class room.

The sum of the five consecutive class rooms are given as:

k + (k + 2) + (k + 4) + (k + 6) + (k + 8)

collecting alike terms we get

= k + k + k + k + k + 2 + 4 + 6 + 8

= 5k + 20

Therefore, The sum of the first five classroom numbers in a row is 5k + 20.

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6 0

3 years ago

If you know please help me

MrRa [10]

Average rate of change of the function $=\frac{75}{2}$

Solution:

Given function: $f(x)=5(2)^{x}$ from x = 1 to x = 5

Substitute x = 1 and x = 5 in f(x).

$f(1)=5(2)^{1}=10$

$f(5)=5(2)^{5}=160$

Let us find the average rate of change of the function.

Average rate of change

$$=\frac{f(b)-f(a)}{b-a}$

Here a = 1 and b = 5.

$$=\frac{f(5)-f(1)}{5-1}$

Substitute f(5) and f(1).

$$=\frac{160-10}{4}$

$$=\frac{150}{4}$

$$=\frac{75}{2}$

Average rate of change of the function $=\frac{75}{2}$

4 0

3 years ago

Would you rather receive $10,000 a day for 31 days or a penny that doubles in value every day for 31 days?

bagirrra123 [75]

This shows how much you would make per day for both choices.

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Explanation

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Explanation

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Day 2: $0.02

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Day 4: $0.08

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7 0

2 years ago

What does it mean if the x-coordinate in an ordered pair is zero? What if the y-coordinate is zero? Both? Explain.

Harman [31]

If the x-axis ordered pair is (0,0) and the y-axis ordered pair is (0,0), it is just where the lines intersect or also known as the origin. Both x and y can have a (0) in it.

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or if it was just (0,0) it would be a dot in the middle

Don't know if it helped much, but there ya go

5 0

3 years ago

Write an explicit rule in function form for the sequence represented by the given terms.

hram777 [196]

Answer:

The general relation about a geoemtric sequence is

$a_{n}=a_{1}r^{n-1}$

For the first sequence, we have

$3=a_{1}r^{5-1}$

$147=a_{1}r^{7-1}$

Which is a system of equations. We can isolate a variable in the first equation to replace that expression into the second equation.

$a_{1}=\frac{3}{r^{4} }$

$147=\frac{3}{r^{4} }r^{6}$

$r^{2}=\frac{147}{3}\\ r=\sqrt[2]{49}\\r=7$

Now, we replace this value to find the other one

$3=a_{1}(7)^{4}\\ a_{1}=\frac{3}{2401}$

Therefore, the explicit rule function is

$a_{n}=\frac{3}{2401} \times (7)^{n-1}$

Now, we use the same process for the second sequence.

$10=a_{1}r^{3-1} \\a_{1}=\frac{10}{r^{2} }$

The second equation is

$1440=a_{1}r^{5-1}\\a_{1}=\frac{1440}{r^{4} }$

Now, we solve the following expression

$\frac{10}{r^{2} }=\frac{1440}{r^{4} }$

We solve for $r$

$\frac{r^{4} }{r^{2} }=\frac{1440}{10}\\r^{2}=144\\ r=\sqrt{144} \\r=12$

Then

$a_{1}=\frac{10}{(12)^{2} } =\frac{10}{144}=\frac{5}{72}$

Therefore, the function that models the second sequence is

$a_{n}=\frac{5}{72} \times (12)^{n-1}$

Notice that $a_{n}$ is the dependent variable and $n$ is the independent variable.

5 0

3 years ago