We have 5 Republican Candidates and 6 Democratic Candidates
We have a total 11 candidates to choose from
First pick of Democratic Candidates = 6/11
Second pick of Democratic Candidates = 5/10
Third pick of Democratic Candidates = 4/9
Fourth pick of Democratic Candidates = 3/8
The probability of four Democratic candidates in the committee is
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By concepts of polynomials and systems of linear equations, the constants c and d of the expression p(x) = x⁴ - 5 · x³ - 7 · x² + c · x + d are 29 and 30.
<h3>How to determine the missing coefficients of a quartic equation</h3>
A value x is a root of a polynomial if and only if p(x) = 0. We must replace the given equation with the given roots and solve the resulting system of <em>linear</em> equations:
(- 1)⁴ - 5 · (- 1)³ - 7 · (- 1)² + (- 1) · c + d = 0
- c + d = 1 (1)
3⁴ - 5 · 3³ - 7 · 3² + 3 · c + d = 0
3 · c + d = 117 (2)
The solution of this system is c = 29 and d = 30.
By concepts of polynomials and systems of linear equations, the constants c and d of the expression p(x) = x⁴ - 5 · x³ - 7 · x² + c · x + d are 29 and 30.
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The answer is:
a = c ÷ 2
b = P - a - c
The perimeter is the sum of all sides of a polygon. The perimeter of the triangle is:
P = a + b + c
where
P - perimeter of the triangle,
a, b, c - sides of the triangle.
It is given:
P = 14.5 cm
c = 6.2 cm
If, t<span>he longest side (c) is twice that of the shortest side (a), then
c = 2a
</span><span>Therefore, the equation that can be used to find the length of the shortest side is <u>a = c ÷ 2</u>.</span><span>
</span>⇒ a = c ÷ 2 = 6.2 cm ÷ 2
⇒ a = 3.1 cm
By knowing two sides (c and a) and perimeter (P), we can calculate the length of the third side (b).
If P = a + b + c, then <span>the equation that can be used to find the length of the side b is <u>b = P - a - c</u>.
</span>⇒ b = P - a - c = 14.5 cm - 6.2 cm - 3.1 cm
⇒ b = 5.2 cm<span>
</span>
Answer:
Isosceles
Step-by-step explanation:
In order to figure what type of triangle this is out, we need to start by plotting the given points. That will help us visualize the triangle better and see if our conclusions make sense. (See attached picture).
Once we got the triangle, the strategy to follow is to use the distance between two points formula to see what the measurement of each side of the triangle is. This will help us determine if 2, 3 or none of the sides of the tirangle are the same.
The distance formula is the following:
so now we can find the desired distances, let's start with the distance between P and Q:
which yields:
next, let's find the distance between P and R:
which yields:
and finally the distance between Q and R:
which yields:
As you may see from the result, only two of the three sides are the same, |PQ| and |PR|, so this will be an Isosceles triangle.
You would divide 973 by 2 and your answer would be 486.5
