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2 answers:
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Answer:
x + 3y = 30
Step-by-step explanation:
We are given that a line contains the points (12,6) and (-3,11).
We want to write the equation of this line in standard form.
Standard form is written as ax+by=c, where a, b, and c are free integer coefficients, however a and b cannot be 0, and a cannot be negative.
Regardless, before we write an equation in slope-intercept form, we must first write the equation in a different form, such as slope-intercept form.
Slope-intercept form is given as y=mx+b, where m is the slope and b is the value of y at the y-intercept.
So first, let's find the slope of the line.
The slope (m) can be found using the formula , where
and
are points.
Even though we already have 2 points, let's label their values to avoid any confusion and mistakes when calculating.
Now substitute these values into the formula.
m=
m=
Subtract
m=
Simplify
m=
The slope is -1/3
Here is the equation of the line so far in slope-intercept form:
We need to solve for b.
As the equation passes through (12,6) and (-3,11), we can use either one to help solve for b.
Taking (12, 6) for example:
Multiply
Divide
6 = -4 + b
Add 4 to both sides.
10 = b
Substitute 10 as b in the equation.
Here is the equation in slope-intercept form, but remember, we want it in standard form.
In standard form, the values of both x and y are on the same side, so let's add -1/3x to both sides.
Remember that a (the coefficient in front of x) has to be an integer, 1/3 is not an integer.
So, let's multiply both sides by 3 to clear the fraction.
Multiply.
<u>x + 3y = 30</u>
<u></u>
Topic: finding the equation of the line (standard form)
See more: brainly.com/question/27575555
Please find attached to this answer a well labelled diagram of the triangle
Answer:
Approximately 176.6 feet
Step-by-step explanation:
From the question, we are to find the height at which the baseball fan was sitting.
From the attached diagram the height at which the fan was sitting is equivalent to the opposite side of the triangle.
Hence , the appropriate trigonometric function to use to solve this question is the sine function.
Sine = Opposite / Hypotenuse
Opposite is unknown so we refer to it as Y
Hypotenuse = 200feet
While the Angle of depression = 62°
Therefore,
Sine 62° = Y/ 200 feet
Cross multiply
Sine 62° × 200 feet = Y
Y = 176.58951857 feet
Approximately 176.6 feet
Therefore , the height at which the fan is sitting is 176.6 feet
