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)
I will help you with 1 another time. Someone might beat me to it. Just have time to answer a few right now.
2) think of a^10/a^4 as:
aaaaaaaaaa/aaaa
Start crossing off an a on the top and one on the bottom. Once you get the answer, you'll probably see an easier way to do it.
3) Yes
4) y=mx+b "b" is the y intercept. -6*0=0 So yes...y=7
6) I don't know what that is between the 5 and 4.
7) y=mx+b Slope is 1 (correct) What's "b" in the equation of "y=x"?
If there's no "b" listed, it is ... (you'll probably have a "d'oh" moment once you get it) Or should I give a bigger hint and say a d' *OH* moment. Oh...those letters that look so much like numbers at times. HIJKLMN...O....if only we could figure out what it is. ;-)
Matt
1) why don't you rewrite the equations in slope intercept form and see if the slope is same, negative reciprocal, or other?
2) a^b/a^c= a^(b-c)
6) recompute
7) right on slope.
Y=mx + b. What is b in this problem?
1. 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 of the line.
For L1, the given equation is x - 5y = 10. To put it into slope-intercept form, we need to isolate y:
-5y = -x + 10
Divide everything by -5:
y = (1/5)x - 2
So the slope of L1 is 1/5.
For L2, the given equation is 5x + y = 5. To put it into slope-intercept form, we isolate y:
y = -5x + 5
So the slope of L2 is -5.
Since the slopes of L1 and L2 are not the same and not negative reciprocals of each other, the lines are neither parallel nor perpendicular.
2. To divide two exponential expressions with the same base, we subtract their exponents: a^b / a^c = a^(b-c).
In this case, we have a^10 / a^4. Using the division rule, we subtract the exponents: 10 - 4 = 6.
Therefore, a^10 / a^4 = a^6.
3. To find the perimeter of a rectangle, you add up all the sides.
The given rectangle has sides of 3x - 4 and 7x + 10.
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 find the equation of a line given a point and slope, we use the point-slope form: y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope.
The given point is (-6, 7) and the slope is 0. Plugging these values into the point-slope form, we get:
y - 7 = 0(x - (-6))
y - 7 = 0(x + 6)
y - 7 = 0
y = 7
So the equation of the line is y = 7.
5. To find the slope of a line passing through two points (x1, y1) and (x2, y2), we use the formula: slope = (y2 - y1) / (x2 - x1).
The given points are (1, 1) and (3, 3). Plugging the values into the formula, we get:
slope = (3 - 1) / (3 - 1) = 2 / 2 = 1
So the slope of the line passing through the points is 1.
6. To evaluate the given expression, we use the order of operations (PEMDAS/BODMAS): Parentheses/Brackets, Exponents/Orders, Multiplication/Division, Addition/Subtraction.
The given expression is 5 * 4 ÷ 2 - 42.
First, we perform the multiplication and division from left to right:
5 * 4 = 20
20 ÷ 2 = 10
Now, we perform the subtraction:
10 - 42 = -32
So the evaluation of the expression is -32.
7. For the equation given, y = x, we can see that the coefficient of x is 1, which represents the slope of the line. So the slope is 1.
In the slope-intercept form, y = mx + b, the value of "b" represents the y-intercept, which is the y-coordinate where the line intersects the y-axis. In this case, the equation y = x doesn't have a constant term, so we can see that b = 0.
Therefore, the slope of the line is 1 and the y-intercept is 0.