Answer:
k = 3
Step-by-step explanation:
Expand the left side and compare the coefficients of like terms on both sides.
(2x - 1)(kx + 1) ← expand using FOIL
= 2kx² + 2x - kx - 1
Compare the coefficients of the x² term on both sides
2k = 6 ( divide both sides by 2 )
k = 3
Mathematical proofs are used to prove or disprove mathematical statements.
<h3>Mathematical theorems </h3>
The theorems to use are:
- The sum of angles on a straight line is 180 degrees
- Alternate angles are congruent
<h3>The proof</h3>
From the question, we have:
This means that, ABC is a triangle
Also, we have:
BP || AC
This means that lines BP and AC are parallel
So, the following angles are congruent by alternate angle theorem
.
The angles on a straight line add up to 180 degrees.
So, we have:

By substitution, the above equation becomes

Rewrite the equation as:

Hence, the statement that
has been proved
Read more about mathematical proofs at:
brainly.com/question/25296908
Answer:
30 cups
Step-by-step explanation:
mango: 16 cups x 3/4 = 12 cups
pomegranate: 1 pint = 2 cups
cranberry: 1 gallon= 16 cups
Cups of fruit punch: 12+2+16= 30
<h2>Roberto made 30 cups of Fruit punch</h2><h2 />
( Hopefully this helped )