Answer:
1/6
Step-by-step explanation:
-4/9 * (-3/8) =
= 12/72
= 1/6
Using the points (5, 1273) and (10, 2546), equation for the line is 5y = 1273x.
<h3>Define equation.</h3>
There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign. Mathematical algebraic equations typically have one or more variables.
Given,
Coordinates (5, 1273) and (10,2546)
For slope, m
m = y₂ - y₁/ x₂ - x₁
m = 2546 - 1273/10 -5
m = 1273/5
Equation in y = mx form,
y = 1273/5 x
Cross multiplying,
5y = 1273x
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Answer:
The answer is 5040.
Step-by-step explanation:
If we know that Jose have to sit first place, and the rest of family need to follow him, we can consider this event as making 7 people from his family sit in an order. There is no difference. So, 7 people can be sit in 7! different ways.
X + (2 10)/(30 x)
The gcd of 10 and 30 is 10, so 10/30 = (10×1)/(10×3) = 10/10×1/3 = 1/3:
x + 2/(3 x)
Put each term in x + 2/(x 3) over the common denominator 3 x: x + 2/(x 3) = (3 x^2)/(3 x) + 2/(3 x):
(3 x^2)/(3 x) + 2/(3 x)
(3 x^2)/(3 x) + 2/(3 x) = (3 x^2 + 2)/(3 x):
Answer: (3 x^2 + 2)/(3 x)
The triangle is a right triangle with sides aligned with the x- and y-axes. The desired volume can be found several ways. Perhaps the easiest is to make use of the fact that the volume is the product of the area of the triangle and the length of the path of revolution of the centroid of the triangle.
The centroid of a triangle is located at the intersection point of the medians, one-third of the distance from any side toward the opposite vertex. Here, we want the radius to the centroid from the y-axis, so the side of interest is the one parallel to the y-axis.
In the x-direction, the altitude of the triangle is 6-2=4, so the centroid is located at 4/3 units from the left side, which is x=2. The x-coordinate of the centroid is then 2+4/3 = 10/3, and this is the radius of revolution for the area of the triangle.
The sides of the right triangle are of length 5 and 4, so the area is
... area = (1/2)bh = (1/2)·5·4 = 10 . . . . . square units
Then the volume of interest is
... V = 2π·(radius of revolution)·(area)
... V = 2π·(10/3)·10
... V = 200π/3 ≈ 209.44 . . . units³
