Representing Proportional Relationships with Equations

Mathematics

1 answer:

Nata [24]3 years ago

3 0

Answer:

a. 0.9

b. y=0.9x, where y is the cost and x is the amount of songs.

c. She should use the package price from the online music vendor (the first option)

Step-by-step explanation:

The constant of proportionality is k in y=kx. Take a point form the graph ( lets say (5,4.5) ) and sub it in:

y=kx

4.5=5k

k=0.9

The equation of a line is y=kx when it passes though the origin (which this one does). We know the value of k, so our equation is y=0.9x, where y is the cost and x is the amount of songs.

Susan downloads 60 songs monthly. We're being asked if it would be cheaper to use the service where you play $58 total, or $0.90 per song. So for the package price, let's figure out the total cost (y) for 60 songs (x=60):

y=0.9x

y=0.9(60)=$54

So it would be cheaper to use the package price from the online music vendor.

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Some people take the early retirement option at age 62. According to the Social Security Administration, if you retire at age 62

Vera_Pavlovna [14]

Answer:

$3900.

Step-by-step explanation:

If retirement is taken at the age of 67 years, income = $1300 per month.

% Loss, if retirement taken at the age of 62 years = 25% per month

Loss in dollars per month if retirement taken at the age of 62 years = 25% of Monthly income if retirement is taken at the age of 67 years

$\Rightarrow \dfrac{25}{100} \times 1300\\\Rightarrow \dfrac{1300}{4}\\\Rightarrow 325 \$$

We know that there are 12 months in an year.

So, annual loss in total annual income over one year:

Loss in dollars per month $\times$ 12 :

325 $\times$ 12 = <em>3900$</em>

7 0

3 years ago

Read 2 more answers

Write the equation is logarithmic form 33 = 27

Vikki [24]

$\bf log_{{ a}}{{ b}}=y \iff {{ a}}^y={{ b}}\qquad\qquad 
% exponential notation 2nd form
{{ a}}^y={{ b}}\iff log_{{ a}}{{ b}}=y \\\\
-----------------------------\\\\
33=27\iff 33=3^{\underline{3}}\iff log_3(33)=\underline{3}$