The formula of g(x) is g(x) = -0.8x - 1.6
<h3>How to determine the
formula of g(x)?</h3>
The equation is given as:
-4x - 6 = 5y + 2
Subtract 2 from both sides
5y = -4x - 8
Divide through by 5
y = -0.8x - 1.6
Express as a function
g(x) = -0.8x - 1.6
Hence, the formula of g(x) is g(x) = -0.8x - 1.6
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Answer:
• c = √89 ≈ 9.434
• A = arcsin(8/√89) ≈ 57.995°
• B = arcsin(5/√89) ≈ 32.005°
Step-by-step explanation:
By the law of cosines, ...
c² = a² + b² -2ab·cos(C)
Since c=90°, cos(C) = 0 and this reduces to the Pythagorean theorem for this right triangle.
c = √(8² +5²) = √89 ≈ 9.434
Then by the law of sines (or the definition of the sine of an angle), ...
sin(A) = a/c·sin(C) = a/c = 8/√89
A = arcsin(8/√89) ≈ 57.995°
sin(B) = b/c·sin(C) = b/c = 5/√89
B = arcsin(5/√89) ≈ 32.005°
4x-3=5y
it would be : 4x - 5y = 3
ANSWER
x = 1.2226
EXPLANATION
To solve this equation we have to apply the property of the logarithm of the base,
Thus, we can apply the natural logarithm - whose base is e, to both sides of the equation,
Now we apply the property of the logarithm of a power,
In our equation,
Then divide both sides by 4 and solve,
The solution to this equation is x = 1.2226, rounded to four decimal places.
Let the area of the original rectangle be A₁.
A₁ = (12 ft)(8 feet) = 96 ft²
To determine the area of the reduced triangle, let's compute the new dimensions first.
Length = 12 ft * 3/4 - 9 ft
Width = 8 ft *3/4 = 6 ft
Thus, the area of the new rectangle denoted as A₂ is
A₂ = (9 ft)(6 ft) = 54 ft
The ratio of the areas are:
A₂/A₁ = 54/96 = 9/16
The ratio of the sides are given to be 3/4.
Finally the ratios of the area to side would be:
Ratio = 9/16 ÷ 3/4 = 3/4
Therefore, the ratio of the areas is 3/4 of the ratio of the corresponding sides.
