Answer: the solutions to the system of equations are x = 2 and x = 1
Step-by-step explanation:
The system of equations given equation is
y = 3x - 2 - - - - - - - - - - 1
y = x^2 - - - - - - - - - - - - 2
Substituting 1 into equation 2, it becomes
x^2 = 3x - 2
x^2 - 3x + 2 = 0
We would apply the method of factorization in solving the equation. We will get two numbers such that when added, the result would be - 3x and when multiplied, the result would be 2x^2. The numbers are - 2x and - x. It becomes
x^2 - 2x - x + 2 = 0
x(x - 2) - 1(x - 2) = 0
(x - 2)(x - 1) = 0
x - 2 = 0 or x - 1 = 0
x = 2 or x = 1
.
The next Numbers in the pattern is 40,41
Answer:
The reactant that acts as an acid, by contributing an H⁺ ion to create H3O+ in the chemical equation is C₆H₅OH.
Step-by-step explanation:
According to Brønstend-Lowry, an acid is a substance that transfer a proton (hydrogen cation, H⁺) to a base, forming a base conjugate for the first and an acid conjugate for the second.
From the following reaction:
C₆H₅OH(aq) + H₂O(l) → C₆H₅O⁻(aq) + H₃O⁺(aq)
We have that the C₆H₅OH transfer a proton to the water to form its conjugate base C₆H₅O⁻ and the conjugate acid of water H₃O⁺. Hence, the C₆H₅OH is the acid and the water is the base.
Therefore, the reactant that acts as an acid, by contributing an H⁺ ion to create H3O+ in the chemical equation is C₆H₅OH.
I hope it helps you!
The a and b determine how big or small the shape of the conic section is.
<span>For the different conic sections given through the equations </span>
<span>Circle: x^2/a^2 + y^2/a^2=1 </span>
<span>Ellipse: x^2/b^2+y^2/a^2 = 1 </span>
<span>Hyperbola: x^2/a^2 - y^2/b^2 = 1 </span>
<span>When trying to isolate cos and sin from those equations to get cos^2t + sin^2 t = 1 you can determine the conic section when substituting cos t = x/a and sint = y/b into cos^2t+sin^2t square it and then refer to the conic section equations to determine the conic section. x defines the major axis and y is the minor axis. a and b provide the coordinate pairs</span>
Answer:
45°
Step-by-step explanation:
Using the cosine ratio in the right triangle
cosB = 
= 
= 
, hence
B = 
( ) = 45°
