Mrs. Kermit has 29 markers. She gives 12 markers to Mr. Cooke and divides the rest among 5 other teachers. If each of the teache
1 answer:
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Answer:
The solutions and the x-intercepts of the polynomial are:
Step-by-step explanation:
Given a function <em>f</em> a solution or a root of <em>f</em> is a value at which
.
An x-intercept is a point on the graph where y is zero.
To find the solutions of the polynomial and the x-intercepts you need to:
First, we need to factor the polynomial expression
Factor the common term
We can treat as a quadratic function with respect to
Let . We can rewrite
in terms of
as follows:
We need to solve the quadratic equation
for this we can use the Quadratic Equation Formula:
For a quadratic equation of the form the solutions are
the solutions to the quadratic equation are:
Therefore,
Recall that so
Using the Zero factor Theorem: If ab = 0, then either a = 0 or b = 0, or both a and b are 0.
roots are
;
roots are
;
The solutions and the x-intercepts are:
Because all roots are real roots the x-intercepts and the solutions are equal.
Answer:
see explanation
Step-by-step explanation:
Using the Cosine rule
a² = b² + c² - 2abcosA ← Rearranging for cosA gives
cosA =
(a)
let a = 10, b = 7, c = 8 and A = α, then
cosα = =
=
, thus
α = (
) ≈ 83° ( to the nearest degree )
(b)
let the angle opposite side 7 be x
Using the Sine rule
=
( cross- multiply )
10sinx = 7sin83 ( divide both sides by 10 )
sinx = , thus
x = (
) = 44°
The third angle can be found using the sum of angles in a triangle
third angle = 180° - (83 + 44)° = 180° - 127° = 53°
The 3 angles are 83°, 44°, 53°