# Evaluate angles and unit circle value of csc(34pi/3)

## Answers

a. she will receive a refund of $278.

step-by-step explanation:

c. x=2.4cm

step-by-step explanation:

similar triangles are triangles which have the same shape but not the same size. this means their angle measures are equal but their side lengths are not instead they are proportional. to solve, we will set up a proportion and solve.

a proportion is two equal ratios set equal to each other. we form the ratios by finding corresponding sides (sides which match to each other on both triangles by their position). out ratios will be one side of the small triangle over the corresponding side on the big triangle as shown below:

[tex]\frac{little}{big} =\frac{side mn}{side ab}=\frac{side on}{side cb}[/tex].

[tex]\frac{0.96}{1.2}=\frac{x}{3}[/tex]

to solve the proportion, we'll cross multiply by multiplying numerator with denominator across the equal sign.

[tex]0.96(3)=1.2(x)\\2.88=1.2x\\\frac{2.88}{1.2}=\frac{1.2x}{1.2} \\2.4=x[/tex]

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step-by-step explanation:

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the speed is [tex]135[/tex]miles per hour > is false

step-by-step explanation:

we know that

a relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]y/x=k[/tex] or [tex]y=kx[/tex]

in a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

the graph shown in the figure represent a direct variation

the slope of the line represent the speed

[tex]y/x=k[/tex]

for the point [tex](1.5,90)[/tex]

substitute the values of x and y

[tex]k=90/1.5=60\ miles/hour[/tex]

the linear equation is equal to

[tex]y=60x[/tex]

statements

case a) it takes [tex]2[/tex] hours to go [tex]120[/tex]miles

the statement is true

because

substitute

for [tex]x=2[/tex]

find the value of y in the linear equation

[tex]y=60(2)=120\ miles[/tex] > is correct

case b) the speed is [tex]135[/tex]miles per hour

the statement is false

because the speed is [tex]60\ miles/hour[/tex]

case c) the unit rate for the trip is [tex]60\ miles/hour[/tex]

the statement is true

because the speed is equal to the slope of the linear equation

case d) it took [tex]20[/tex] minutes to go the first [tex]20[/tex]miles

the statement is true

because

substitute

for [tex]x=20\ minutes=(1/3)\ hour[/tex]

find the value of y in the linear equation

[tex]y=60(1/3)=20\ miles[/tex] > is correct