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:
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Answer:
Slope = 3
Step-by-step explanation:
The formula for calculating the slope is expressed as:
m = y2-y1/x2-x1
From the coordinate, x1 = 0 y1 =0 x2 = 5, y2 =15
m = 15-0/5-0
m = 15/5
m = 3
Hence the slope is 3
Answer:
a is less than or equal to 7
Step-by-step explanation:
This is the case because we can treat the less than or equal to sign as an equal sign. The only time it changes is when we divide by a negative, but we do not do that in this problem. First, you subtract 7 from both sides. That leaves us with a 4a on one side and a 28 on the other. Then, you divide both sides by four to get a is less than or equal to 7. I hope this helps!
Answer:
1. the number five plus x
2. the number five minus x
3. five times x
4. five divided by x
5. three fourths of x plus 2
6. two minus three fourths of x
7. three times x plus ten
8. ten times x plus three
Step-by-step explanation:
