Julian practiced the clarinet for a total of 2 hours and 15 minute on wednesday and friday. he practiced twice as long on friday as he did on wednesday. how many minutes did he practice on friday?
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He practiced 90 minutes on Friday.

Step-by-step explanation:

Let be "w" the amount of minutes Julian practiced the clarinet on Wednesday and "f" the amount of minutes Julian practiced the clarinet on Friday.

Convert the total time he praticed on Wednesday and Friday to minutes. Since ,  2 hours and 15 minutes is:

Set up a System of equations:

Applying the Substitution Method, you can subsitute the second equation into the first equation and solve for "w":

Finally, substitute this value into the second equation to find "f":

Therefore, he practiced 90 minutes on Friday.

the length of o'p' is .

step-by-step explanation:

it is given that the quadrilateral m'n'o'p' is the image of quadrilateral mnop after dilation.

the center of dilation is origin and the scale factor is 1.5.

in dilation the image and preimge are similar figures. it means the sides of image and preimage are proportional.

the scale factor is defined as

the scale factor is 1.5.

multiply both sides by op.

note: if the value of op is given, then multiply the value of op with 1.5 to get the length of side o'p'.

therefore length of o'p' is .

$54.99

step-by-step explanation:

$54.99 includes 500 min. if she does not exceed 500 min then her bill is $54.99