Answer:
Yes, lines M and N intersect because their slopes are different.
Step-by-step explanation:
First, we can start out by finding the slope of Line M and Line N. The slope formula is (y_2 - y_1)/(x_ 2- x_1)
Slope of Line M:
(3--11) / (3--4)
(3+11) / (3+4)
14/7
2
Now we know that the slope of Line M is 2.
Slope of Line N:
(9--2) / (-6-5)
11/-11
The slope of Line N is -1!
Since the slopes of Line N and M are different, they intersect. The answer is Yes, lines M and N intersect because their slopes are different.
If the slopes were the same, Line N and M would NEVER intersect because they are parallel.
Hope this helps
√20 the prime factors are 2, 2, 5 so
-2 * √4 *√5
-2*2*√5
-4√5 is the first part ,
now for √125, use prime factorization ,
all prime factors that make up 125 is
5, 5, 5 so √125 can be separated to √25√5 and √25 = 5 so the second part is 5√5.
now -4√5 - 5√5 = -9√5.
therefore answer is -9√5
Answer:
7. r = -5
8. x = -1
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Equality Properties
Step-by-step explanation:
<u>Step 1: Define</u>
r + 2 - 8r = -3 - 8r
<u>Step 2: Solve for </u><em><u>r</u></em>
- Combine like terms: -7r + 2 = -3 - 8r
- Add 8r to both sides: r + 2 = -3
- Subtract 2 on both sides: r = -5
<u>Step 3: Check</u>
<em>Plug in r into the original equation to verify it's a solution.</em>
- Substitute in <em>r</em>: -5 + 2 - 8(-5) = -3 - 8(-5)
- Multiply: -5 + 2 + 40 = -3 + 40
- Add: -3 + 40 = -3 + 40
- Add: 37 = 37
Here we see that 37 does indeed equal 37.
∴ r = -5 is a solution of the equation.
<u>Step 4: Define equation</u>
-4x = x + 5
<u>Step 5: Solve for </u><em><u>x</u></em>
- Subtract <em>x</em> on both sides: -5x = 5
- Divide -5 on both sides: x = -1
<u>Step 6: Check</u>
<em>Plug in x into the original equation to verify it's a solution.</em>
- Substitute in <em>x</em>: -4(-1) = -1 + 5
- Multiply: 4 = -1 + 5
- Add: 4 = 4
Here we see that 4 does indeed equal 4.
∴ x = -1 is a solution of the equation.
Answer:
false. the y-intercept is -2.
2,920
8 hours multiply by 365 equals 2,920 hours
