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3 years ago

Find the constant of proportionality (r) in the equation y=rx

Mathematics

2 answers:

ahrayia [7]3 years ago

8 0

Answer:

r = $\frac{1}{4}$

Step-by-step explanation:

Given the proportional equation

y = rx ← r is the constant of proportion

Divide both sides by x

$\frac{y}{x}$ = r

Use any ordered pair from the table.

Using (8, 2 ) , then

r = $\frac{2}{8}$ = $\frac{1}{4}$

Vlad1618 [11]3 years ago

4 0

Answer:

1/4

Step-by-step explanation:

Multiplying the input (x) by (1/4) results in the output. This is direct proportion, and the constant of proportionality is (1/4).

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Liono4ka [1.6K]

C; 120 because 24x=360 so x=15. Then ABC is 8x, so 8*15=120.

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4 years ago

The glass container is shown filled to a height of 2.25 inches. How much sand is currently in the container.

JulijaS [17]

2.25 inches of sand.

3 0

3 years ago

Evaluate each finite series for the specified number of terms. 1+2+4+...;n=5

zaharov [31]

Answer:

Step-by-step explanation:

The series are given as geometric series because these terms have common ratio and not common difference.

Our common ratio is 2 because:

1*2 = 2

2*2 = 4

The summation formula for geometric series (r ≠ 1) is:

$\displaystyle \large{S_n=\frac{a_1(r^n-1)}{r-1}}$ or $\displaystyle \large{S_n=\frac{a_1(1-r^n)}{1-r}}$

You may use either one of these formulas but I’ll use the first formula.

We are also given that n = 5, meaning we are adding up 5 terms in the series, substitute n = 5 in along with r = 2 and first term = 1.

$\displaystyle \large{S_5=\frac{1(2^5-1)}{2-1}}\\\displaystyle \large{S_5=\frac{2^5-1}{1}}\\\displaystyle \large{S_5=2^5-1}\\\displaystyle \large{S_5=32-1}\\\displaystyle \large{S_5=31}$

Therefore, the solution is 31.

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Summary

If the sequence has common ratio then the sequence or series is classified as geometric sequence/series.

Common Ratio can be found by either multiplying terms with common ratio to get the exact next sequence which can be expressed as $\displaystyle \large{a_{n-1} \cdot r = a_n}$ meaning “previous term times ratio = next term” or you can also get the next term to divide with previous term which can be expressed as:

$\displaystyle \large{r=\frac{a_{n+1}}{a_n}}$

Once knowing which sequence or series is it, apply an appropriate formula for the series. For geometric series, apply the following three formulas:

$\displaystyle \large{S_n=\frac{a_1(r^n-1)}{r-1}}\\\displaystyle \large{S_n=\frac{a_1(1-r^n)}{1-r}}$

Above should be applied for series that have common ratio not equal to 1.

$\displaystyle \large{S_n=a_1 \cdot n}$

Above should be applied for series that have common ratio exactly equal to 1.

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Topics

Sequence & Series — Geometric Series

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Others

Let me know if you have any doubts about my answer, explanation or this question through comment!

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7 0

3 years ago

Which phrase best describes the scatterplot below? strong negative correlation strong positive correlation weak negative correla

s344n2d4d5 [400]

*the scatter plot of the question is attached below

Answer:

Strong negative correlation

Step-by-step explanation:

In the scatter plot attached below, as the variable in the x-axis increases, the variable on the y-axis decreases. Thus, if a line of best fit is drawn, it would show a line that slopes downwards to our right. This shows a negative correlation between both variables in the scatter plot.

Also, we also see that the data points represented on the scatter plot are clustered more closely along the slope, showing strong negative correlation.

Therefore, the phrase that best describes the scatter plot is: strong negative correlation.

3 0

3 years ago

What’s the axis of symmetry and the vertex of x^2-4x-32

konstantin123 [22]

<span>x^2 -4x -32
</span>a =1b= -4c= -32
The x,y points of the vertex are usually referred to as Vertex = (h, k)where h = -b / (2 * a)
h = --4 / (2 * 1)h = 4 / 2h = 2
k = ah^2 +bh + ck =1*4 -4*2 -32k = 4 -8 -32k = -36
vertex = (2, -36)axis of symmetry = x position = 2
Source:http://www.1728.org/quadr3.htm

6 0

3 years ago