To determine the distance between two points, we use the equation,
distance = √(x₂ - x₁)² + (y₂ - y₁)²
Substituting the known values for the abscissa and ordinates of the points,
distance = √(0 - 2)² + (0 - 5)² = √29 ≈ 5.39
Therefore, the distance between these two points is approximately equal to 5.39.
You can take the log of the left and right hand side, and then apply the <span>logarithm rules:
log(a</span>ˣ) = x·log(a)
log(ab) = log(a) + log(b)
log(9^(x-1) * 2^(2x+2)) = log(6^(3x))
log(9^(x-1)) + log(2^(2x+2)) = 3x log(6)
(x-1) log(9) + (2x+2) log(2) - 3x log(6) = 0
x(log9 + 2log2 - 3log6) = log9 - 2log2
x = (log9 - 2log2) / (log9 + 2log2 - 3log6)
simplifying by writing log9 = 2log3 and log6 = log2+log3
x= 2(log3 - log2) / (2log3 + 2log2 - 3log2 - 3log3) =
x= -2(log3 - log2) / (log3 + log2) = -2 log(3/2) / log(6)
So 6^x = 4/9
We have been given that a rectangle has a height to width ratio of 3:4.5.
Let h be height and w be width of rectangle.
We can set our given information in an equation as:
Now we will substitute h=1 in this equation.
We can see that width of rectangle is 1.5 times height of rectangle.
Our one set of dimensions of rectangle will be: height=1 and width=1.5.
We can get many set of dimensions for our rectangle by multiplying both height and width of rectangle by same number.
Multiplying by 5 we will get our dimensions as: height 5 and width 7.5.
Therefore, (1 and 1.5) and (5 and 7.5) dimensions for rectangle will be scaled version of our rectangle.
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First, apply the rule (easiest way if you have learned it):
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×
×
Second, apply the last rule:
×
Third, multiply 5 × 10 to get 50.
Fourth, multiply 6 × 9 to get 54.
Fifth, find the GCF of 50 and 54.
The GCF should be 2.
Sixth, divide the numerator by the GCF.
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Seventh, divide the denominator by the GCF.
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Eighth, now put 25 and 27 together to get the simplified fraction.
Answer as fraction:
Answer as decimal: 0.9259
Answer:
576π in² and 1,809 in².
Step-by-step explanation:
To find the answer, the formula for the area of a circle, or A = πr², will need to be used.
In this question, we are only given the diameter. Simply divide by 2 to calculate the radius:
48/2 = 24 inches.
Now, plugging this into the equation for the Area of a Circle, gets us:
A = π24²
A = 576π or 1808.64 in².
Looking at the answer choices, we can choose 576π in² and 1,809 in² (as 1808.64 ≈1809)
