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lidiya [134]
3 years ago
12

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:

a.

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

b.

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.

c.

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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X2−10x+29=5
Irina18 [472]

Answer:

(x-6)(x-4) = 0

Step-by-step explanation:

Subtract 5 from both sides to make the equation equal to 0. You will get the equation x2-10x+24=0. Now think of two numbers that multiply to get 24 but add to get -10. These numbers are -6 and -4. The factors of x2 are x and x which multiply to get x2.  Now put two linear factors into parathesis to get (x-6)(x-4) = 0.

7 0
3 years ago
Identify the independent variable in the statement: the time it takes to travel 50 miles and the speed of the truck
morpeh [17]
The time changes depending on how fast the truck is going-so it's dependent 
50 miles and the truck do not change no matter what-so they are constant
The speed of the truck changes the time-so the speed is the independent

3 0
3 years ago
Jake needs 8 cups of milk to make a chocolate shake for his family. His measuring device measures liquids by the pint. If 1 pint
zvonat [6]
If you would like to know how many pints should Jake measure, you can calculate this using the following step:

1 pint ... 2 cups
x pints = ? ... 8 cups

1 * 8 = 2 * x
8 = 2 * x       /2
x = 8/2 = 4 pints

The correct result would be 4 pints.
8 0
3 years ago
Read 2 more answers
The table below shows how much Joe earns, y, after working x hours. Joe’s Earnings Hours worked Money earned 4 $30 10 $75 12 $90
lesya692 [45]

Answer:

Both slopes are equal

Step-by-step explanation:

The general form of a linear function is:

y = mx + c

where m is the slope and c is the y-intercept

We can, thus, note that the slope is constant across the linear function.

Since we are given that the relation between the salary and hours worked is linear, therefore, the slope will be equal between any two points belonging to the function

Verification:

slope can be calculated as follows:

slope =  \frac{ y_{2} -  y_{1}  }{ x_{2} -  x_{1} }

1- In case of (4,30) and (12,90):

slope = slope =  \frac{ 90 - 30 }{ 12 - 4 }  = 7.5

2- In case of (4,30) and (10,75):

slope =  \frac{ 75 - 30 }{ 10 - 4 }  = 7.5

Hope this helps :)

5 0
3 years ago
Read 2 more answers
PLEASE can someone explain why The exact value of sec ( π/6) is 2 /√ 3 ??
Umnica [9.8K]
\bf sec\left( \frac{\pi }{6} \right)\qquad recall\to sec(\theta)=\cfrac{1}{cos(\theta)}\qquad thus
\\\\
sec\left( \frac{\pi }{6}\right)\iff \cfrac{1}{cos\left( \frac{\pi }{6}\right)}
\\\\\\
\textit{check your Unit Circle for what the }cos\left( \frac{\pi }{6}\right)\ is
\\\\\\
\cfrac{1}{\frac{\sqrt{3}}{2}}\implies \cfrac{\frac{1}{1}}{\frac{\sqrt{3}}{2}}\implies 
\cfrac{1}{1}\cdot \cfrac{2}{\sqrt{3}}\implies \cfrac{2}{\sqrt{3}}
3 0
3 years ago
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