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2 years ago

Find the measure of the acute angle that line y=1/3x+4 makes with a horizontal line. Round your answer to the nearest tenth.

Mathematics

1 answer:

Alex Ar [27]2 years ago

6 0

Answer:

The measure of the acute angle is 18.4°

Step-by-step explanation:

The angle between a line of equation y = m x + b and the positive part of the x-axis is Ф = $tan^{-1}$ (m), which means tan Ф = m, where m is the slope of the line

Let us use this rule to solve the question

∵ A line of equation y = $\frac{1}{3}$ x + 4 makes with a horizontal line an acute ∠

→ Compare the equation of the line by the form of the equation above

∴ m = $\frac{1}{3}$

→ Assume that the acute angle is Ф

∴ The acute angle between the line and the horizontal line is Ф

→ By using the rule above

∵ tan Ф = m

∴ tan Ф = $\frac{1}{3}$

→ Use $tan^{-1}$ to find Ф

∵ Ф = $tan^{-1}$ ( $\frac{1}{3}$ )

∴ Ф = 18.43494882

→ Round it to the nearest tenth

∴ Ф = 18.4°

∴ The measure of the acute angle is 18.4°

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Step-by-step explanation:

B is the only answer that will ensure she gets graduate students in the sample without getting too few or too many.

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3 years ago

A professor has recorded exam grades for 10 students in his class, but one of the grades is no longer readable. If the mean sco

Nostrana [21]

Answer:

unreadable score = 35

Step-by-step explanation:

We are trying to find the score of one exam that is no longer readable, let's give that score the name "x". we can also give the addition of the rest of 9 readable s scores the letter "R".

There are two things we know, and for which we are going to create equations containing the unknowns "x", and "R":

1) The mean score of ALL exams (including the unreadable one) is 80

so the equation to represent this statement is:

mean of ALL exams = 80

By writing the mean of ALL scores (as the total of all scores added including "x") we can re-write the equation as:

$\frac{R+x}{10} =80$

since the mean is the addition of all values divided the total number of exams.

in a similar way we can write what the mean of just the readable exams is:

$\frac{R}{9} = 85\\$ (notice that this time we don't include the grade x in the addition, and we divide by 9 instead of 10 because only 9 exams are being considered for this mean.

Based on the equation above, we can find what "R" is by multiplying both sides by 9:

$\frac{R}{9} = 85\\R=85*9= 765$

Therefore we can now use this value of R in the very first equation we created, and solve for "x":

$\frac{R+x}{10} =80\\\frac{765+x}{10} =80\\765+x=80*10=800\\765+x=800\\x=800-765=35$

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2 years ago

Write the standard form of the equation of the line passing through (0, 1) and parallel to x = 4.

Savatey [412]

Answer:

x=0

Step-by-step explanation:

The line x=4 is a vertical line through the x-axis at 4. A line parallel to it will also be a line through the x-axis. It has the form x=a where a is the x-coordinates of any points on the line. Since the line crosses through (0,1), the equation is x=0.

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2 years ago

Alan bought two bikes. He sold one to Beth for $300 taking a 25% loss. He also sold one to Greta for $300 making a 25% profit. D

Mashutka [201]

No Alan did not break even

Alan incured a loss of 6.25 %

Solution:

Given that,

Alan bought two bikes

He sold one to Beth for $300 taking a 25% loss

He also sold one to Greta for $300 making a 25% profit

When a person sells two similar items, one at a gain of say x%, and the other at a loss of x%, then the seller always incurs a loss

Which is given as:

$loss\ \% = (\frac{x}{10})^2$

Here, x = 25

$loss\ \% = (\frac{25}{10})^2\\\\loss\ \% = 2.5^2\\\\loss\ \% = 6.25$

Thus the loss percentage is 6.25 %

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2 years ago

When do you find an area or volume by separating the figure into smaller figures?

brilliants [131]

The question is not defined very well so if u would repeat it

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3 years ago