Find an equation of the line that satisfies the given conditions. x-intercept 1; y-intercept −4

The reference angle is simply the acute angle between the terminal side and the x-axis

The terminal angles in the four quadrants are

The given parameters are:

[tex]\theta \to[/tex] reference angle

[tex]\bar \theta \to[/tex] terminal angle

(a) If the reference angle is in the first quadrant

In the first quadrant, the x-axis is at [tex]0\ rad[/tex]

So, the terminal angle is:

[tex]\bar \theta = \theta - 0[/tex]

[tex]\bar \theta = \theta[/tex]

(b) If the reference angle is in the second quadrant

In the second quadrant, the x-axis is at [tex]\pi \ rad[/tex],

While the reference angle is between [tex]\frac{\pi}{2}[/tex] and [tex]\pi \ rad[/tex]

It means that, we have to subtract the reference angle from the x-axis

So, the terminal angle is:

[tex]\bar \theta = \pi - \theta[/tex]

(c) If the reference angle is in the third quadrant

Here, the x-axis is still at [tex]\pi \ rad[/tex],

But the reference angle is between [tex]\pi \ rad[/tex] and [tex]\frac{3}{2}\pi[/tex]

It means that, we have to subtract the x-axis from the reference angle.

So, the terminal angle is:

[tex]\bar \theta = \theta - \pi[/tex]

(d) If the reference angle is in the fourth quadrant

Here, the x-axis is at [tex]2\pi \ rad[/tex]

And the reference angle is between  [tex]\frac{3}{2}\pi[/tex] and [tex]2\pi \ rad[/tex]

It means that, we have to subtract the reference angle from the x-axis.

So, the terminal angle is:

[tex]\bar \theta = 2\pi - \theta[/tex]

See attachment for illustration of terminal angles

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Final answer:

When dealing with angles in radians and their reference angles, each quadrant has a specific relationship for determining the reference angle based on the given angle θ.

Explanation:

Radian Measure with Reference Angles:

If θ is in QI, then θ hat = θ

If θ is in QII, then θ hat = π - θ

If θ is in QIII, then θ hat = θ - π

If θ is in QIV, then θ hat = 2π - θ

Answer: Option 'B' is correct.

Step-by-step explanation:

Since we have given that

A section of a roller coaster track forms a parallelogram ABCD.

If m∠ABC = 72°

We need to find the  m∠DAB,

Since ABCD is a parallelogram .

So, "Sum of interior angles on the same side is supplementary":

[tex]m\angle ABC+m\angle DAB=180\textdegree\\\\72\textdegree+m\angle DAB=180\textdegree\\\\m\angle DAB=180\textdegree-72\textdegree\\\\m\angle DAB=108\textdegree[/tex]

Hence, Option 'B' is correct.

The solution of expression is, x = 6

We have to give that,

An expression to simplify as,

⇒ 45 + 5/6x = 50

Now, Simplify the expression by combining like terms,

⇒ 45 + 5/6x = 50

Subtract 45 on both sides,

⇒ 45 + 5/6x - 45 = 50 - 45

⇒ 5/6x = 5

Multiply by 6 on both sides,

⇒ 5x = 5 × 6

⇒ 5x = 30

Divide by 5 on both sides,

⇒ x = 30/5

⇒ x = 6

So, The solution is, x = 6

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1. at a discount

2. add all the items together at their sales cost then add salves tax

3. $26.75

4. $66.23

The answer in siplest form is -

The athlete spends 20 minutes on the treadmill and 10 minutes on the elliptical machine. This is determined by setting up and solving a system of linear equations based on the calorie burn rate of each machine and the total calories burned during the workout.

To solve the problem of how many minutes an athlete spends on each machine during their workout, we must set up a system of linear equations. The athlete burns 12 calories per minute on a treadmill and 8.5 calories per minute on an elliptical machine. In a 30-minute workout, the athlete burns a total of 325 calories. Let's denote the time spent on the treadmill as t minutes and the time spent on the elliptical machine as e minutes.

We now have two equations and two unknowns, which can be solved simultaneously.

Using these steps, we find that:

Therefore, the athlete spends 20 minutes on the treadmill and 10 minutes on the elliptical machine during their 30-minute workout.

To solve the formula F=J+Jrt for 't', first, subtract 'J' from both sides to get F-J=Jrt. Then, divide both sides by 'Jr', for the final equation for 't' = (F-J)/Jr.

This physics-related mathematics question is asking you to solve the given formula F=J+Jrt for 't'. To isolate 't', we first want to eliminate 'J' from the right side. We do this by subtracting 'J' from both sides of the equation. This gives us F-J=Jrt.

Then, we divide both sides by 'Jr'. When we do this, we are left with t=(F-J)/Jr as the rearranged formula with 't' as the subject. This results in 't' being isolated in the equation, which answers the student's question.

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Answer:

3x + 5

Step-by-step explanation:

The ratios of sin (x) and cos (y) are both identical  [tex](\frac{6}{10}\; and\; \frac{6}{10})[/tex].

A triangle is classified as a right triangle when it presents one of your angles equal to 90º.  A math tool applied for finding angles or sides in a right triangle is trigonometric ratios.

The main trigonometric ratios are:

[tex]sin(\alpha )=\frac{opposite\;side}{hypotenuse} \\ \\ cos(\alpha )=\frac{adjacent\;side}{hypotenuse}\\ \\ tan(\alpha )=\frac{sin (\alpha )}{cos(\alpha } =\frac{opposite\;side}{adjacent\;side}[/tex]

The question asks the sin x and cos y, for solving this you should apply the trigonometric ratios. Therefore,

[tex]sin (x)=\frac{opposite\; side}{hypotenuse} =\frac{6}{10}[/tex]

and

[tex]cos (y)=\frac{adjacent\; side}{hypotenuse} =\frac{6}{10}[/tex]

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