For this case, what we must do is solve the following system of equations:
tan (50) = h / x
tan (40) = h / (x + 50)
Solving the system we have:
(x + 50) * tan (40) = h
(x) * tan (50) = h
Matching:
(x + 50) * tan (40) = (x) * tan (50)
Rewriting:
x (tan (50) - tan (40)) = 50 * tan (40)
x = 50 * tan (40) / (tan (50) - tan (40))
x = 118.9692621
Substituting:
h = (x) * tan (50)
h = (118.9692621) * tan (50)
h = 141.7820455
Answer:
The height of the building is:
h = 141.7820455 ft
For this one, i’ll explain. set it up so it looks like this : 8-4+7+3-11, and then simplify.
One number (a) exceeds another number (b) by 11 so
a = b+11
a + b = 77
Substitute the equation for a into the second equation
(b+11) + b = 77
multiply each side by 1 to remove parentheses
b + 11 + b = 77
Combine like terms
2b + 11 = 77
Isolate the variable
2b = 77-11
Simplify
2b = 66
Divide by 2
b = 33
Now substitute b back into the initial equation for a
a = (33) + 11
a = 44
Check your work by substituting both values into the second equation
44 + 33 = 77
This is true, so 44 and 33 are solutions
Answer:
x = -7/9
Step-by-step explanation:
The usual recommendation is to clear fractions first. Here, you can do that by multiplying both sides of the equation by 6.
6(-1/2(3x -4) +3x) = 6(5/6)
-9x +12 +18x = 5 . . . . . . . . . simplify
9x = -7 . . . . . . . . . . . . . . . . . subtract 12
x = -7/9 . . . . . .divide by 9
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Another way to do this is to eliminate parentheses first.
-3/2x +2 +3x = 5/6
3/2x = -7/6 . . . . . . . . . collect terms, subtract 2
x = (-7/6)(2/3) = -7/9 . . . . multiply by 2/3
The functions are illustrations of function transformations
The transformation from f(x) to g(x) is reflecting across the y-axis, and then shifting 2 units up
<h3>How to determine the transformations</h3>
The equation of the function is given as:
The parent function of the above equation is:
First, the function f(x) is reflected across the y-axis to give
Next, the function is shifted 2 units up.
So, we have:
Rewrite as:
Express f(-x) + 2 as g(x).
So, we have:
Hence, the transformation from f(x) to g(x) is reflecting across the y-axis, and then shifting 2 units up
Read more about function transformation at:
brainly.com/question/1548871
