Could someone correct my answers and help with the other problems?
1. Are the following lines parallel, perpendicular, or neither? L1 with equation x – 5y = 10, L2 with equation 5x + y = 5.
Answer: Neither (I'm not to sure but i think this is the right answer)
2. Divide: a^10/a^4
How would I complete this problem?
3. A rectangle has sides of 3x – 4 and 7x + 10.Find the expression that represents its perimeter.
Answers: Answer: P = 20x + 12
4. Write the equation of the line that passes through point (–6, 7) with a slope of 0.
Answer: y = 7
5. Find the slope of the line passing through the points (1, 1) and (3, 3).
Answer: 1
6. Evaluate. 5 • 4 ÷ 2 – 42
Answer: -6
7. Find the slope and the y-intercept.
y = x
Answer: Slope is 1, y-intercept (I'm not sure what that answer is)
1. The lines L1 with equation x – 5y = 10 and L2 with equation 5x + y = 5 are actually perpendicular to each other. Therefore, your answer is incorrect.
2. To divide the powers of the same base, subtract the exponents: a^10/a^4 = a^(10-4) = a^6. So your answer is a^6.
3. The perimeter of a rectangle is given by the sum of all its sides. In this case, the sides are 3x - 4 and 7x + 10. The expression that represents the perimeter would be: P = (2 * (3x - 4)) + (2 * (7x + 10)) = 6x - 8 + 14x + 20 = 20x + 12. Therefore, your answer is correct.
4. The equation of a line in slope-intercept form is y = mx + b, where "m" is the slope and "b" is the y-intercept. The slope is given as 0, and the point (–6, 7) lies on the line. Using the point-slope form, we can write the equation as: y - 7 = 0(x - (-6)) => y - 7 = 0 => y = 7. Therefore, your answer is correct.
5. The slope of a line is given by the change in y divided by the change in x between two points. For the given points (1, 1) and (3, 3), the change in y is 3 - 1 = 2, and the change in x is 3 - 1 = 2. Therefore, the slope is 2/2 = 1. Your answer is correct.
6. To evaluate the expression 5 • 4 ÷ 2 – 42, we follow the order of operations (also known as PEMDAS/BODMAS). First, perform the multiplication: 5 • 4 = 20. Then, perform the division: 20 ÷ 2 = 10. Finally, subtract 42: 10 - 42 = -32. Therefore, your answer is -32.
7. The equation y = x is in slope-intercept form (y = mx + b), where "m" represents the slope. In this case, the slope "m" is 1. The equation does not contain a y-intercept term (b = 0), so the y-intercept is at the origin (0,0). Therefore, the slope is 1 and the y-intercept is (0,0).
1. To determine if two lines are parallel or perpendicular, we need to compare their slopes. The given equations of the lines are L1: x - 5y = 10 and L2: 5x + y = 5.
To find the slope of L1, rearrange the equation in the slope-intercept form (y = mx + b), where m is the slope:
x - 5y = 10
-5y = -x + 10
y = (1/5)x - 2
The slope of L1 is 1/5.
To find the slope of L2, rearrange the equation in the slope-intercept form:
5x + y = 5
y = -5x + 5
The slope of L2 is -5.
Since the slopes of L1 and L2 are not equal, the lines are not parallel. Additionally, the product of their slopes (-5 * 1/5 = -1) is not -1, indicating that the lines are not perpendicular. Therefore, the correct answer is "Neither."
2. When dividing variables with the same base, we subtract the exponent of the divisor from the exponent of the dividend. In this case, we have a^10 divided by a^4:
a^10 / a^4 = a^(10-4) = a^6
So, the answer is a^6.
3. The perimeter of a rectangle is found by adding the lengths of all its sides. In this case, the rectangle has sides of 3x - 4 and 7x + 10.
The expression for the perimeter is:
Perimeter = 2 * (length + width)
= 2 * (3x - 4 + 7x + 10)
= 2 * (10x + 6)
= 20x + 12
So, the expression that represents the perimeter is P = 20x + 12.
4. To write the equation of a line, we need to know its slope and a point it passes through. In this case, the line has a slope of 0 and passes through the point (-6, 7).
Since the slope is 0, the line is horizontal, meaning that the y-coordinate remains constant along the line. From the given point (-6, 7), we can determine that the equation of the line is y = 7.
5. The slope of a line passing through two points (x1, y1) and (x2, y2) can be found using the formula:
slope = (y2 - y1) / (x2 - x1)
In this case, the points are (1, 1) and (3, 3). Substituting the values into the formula:
slope = (3 - 1) / (3 - 1) = 2 / 2 = 1
Therefore, the slope of the line passing through the points (1, 1) and (3, 3) is 1.
6. To evaluate the expression 5 • 4 ÷ 2 - 42, we follow the order of operations (PEMDAS/BODMAS):
First, perform multiplication and division from left to right:
5 • 4 = 20
20 ÷ 2 = 10
Next, perform subtraction:
10 - 42 = -32
Therefore, the answer is -32.
7. The given equation is y = x. In slope-intercept form, this equation can be written as y = 1x + 0.
From the equation, we can see that the slope (m) is 1 and the y-intercept (b) is 0.
So, the slope is 1 and the y-intercept is (0, 0).