Answer:
6 swimmers in the first heat can be arranged in 1716 different ways.
Step-by-step explanation:
A swim meet has 13 contestants signed up. To calculate the arrangement of first 6 swimmers in first heat we will use combinations because order doesn't matter.
So to select 6 swimmers out of 13 contestants number of different ways
=
=
=
=
=
= 1716
Therefore, 6 swimmers in the first heat can be arranged in 1716 different ways.
The length and width of the rectangle are:
The area of the rectangle is the product of the length and width of a given rectangle.
The area of the rectangle = length × Width
The area of a rectangle is represented by the expression .
The area of the rectangle =
=
So, the length and width of the rectangle are:
Learn more about the area;
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Answer: (a) y = -3x + 10
<u>Step-by-step explanation:</u>
The slope of line CD is perpendicular to line OB, which means they have opposite and reciprocal slopes.
Step 1: Find the slope of OB using the formula:
(x₁, y₁) = (0, 0) and (x₂, y₂) = (3, 1)
Step 2: Find the slope of CD (opposite and reciprocal of OB)
Step 3: Input the perpendicular slope and the slope into the Point-Slope formula: y - y₁ = m(x - x₁)
(x₁, y₁) = (3, 1) because it is the point the line will pass through
y - 1 = -3(x - 3)
y - 1 = -3x + 9 <em>distributed -3 into (x - 3)</em>
y = -3x + 10 <em>added 1 to both sides</em>
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The x-intercept of DQ is the same x-intercept as CD. The x-intercept is when y = 0
y = -3x + 10
0 = -3x + 10
-10 = -3x subtracted 10 from both sides
<em>divided both sides by -3</em>