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.
To solve these problems, I'll go through each one and explain how to arrive at the correct answer.
1. Are the following lines parallel, perpendicular, or neither? L1 with equation x – 5y = 10, L2 with equation 5x + y = 5.
To determine if two lines are parallel, perpendicular, or neither, we need to compare their slopes. The slope-intercept form of a line is y = mx + b, where m is the slope.
For L1, rearrange the equation to y = (1/5)x - 2. The slope is 1/5.
For L2, rearrange the equation to y = -5x + 5. The slope is -5.
Since the slopes of L1 and L2 are not equal and also not negative reciprocals, they are neither parallel nor perpendicular.
2. Divide: a^10 / a^4
When dividing terms with the same base, subtract their exponents. Therefore, a^10 / a^4 simplifies to a^(10-4) = a^6.
3. A rectangle has sides of 3x – 4 and 7x + 10. Find the expression that represents its perimeter.
The perimeter of a rectangle is given by the formula P = 2(length + width). In this case, the length is 3x - 4 and the width is 7x + 10. Plugging these values into the formula, we get P = 2(3x - 4 + 7x + 10). Simplifying further, P = 2(10x + 6) which equals 20x + 12.
4. Write the equation of the line that passes through point (–6, 7) with a slope of 0.
A line with a slope of 0 is a horizontal line. For a horizontal line passing through point (x1, y1), the equation is y = y1. Therefore, the equation of the line passing through (-6, 7) with a slope of 0 is y = 7.
5. Find the slope of the line passing through the points (1, 1) and (3, 3).
To find the slope of a line passing through two points (x1, y1) and (x2, y2), we use the slope formula: m = (y2 - y1) / (x2 - x1). Plugging in the values from the given points, we get m = (3 - 1) / (3 - 1), which simplifies to m = 1.
6. Evaluate. 5 • 4 ÷ 2 – 42.
To evaluate this expression, start by performing the multiplication and division from left to right. 5 • 4 = 20, and 20 ÷ 2 = 10. Then, subtract 42 from 10 which gives -32 as the answer.
7. Find the slope and the y-intercept.
To find the slope and y-intercept of a line in slope-intercept form (y = mx + b), we need the equation of the line. The question does not provide an equation, so the slope and y-intercept cannot be determined without further information.