1. What are the x- and y-intercepts of the line described by 6x - 2y = 4?
a. x-intercept: 2/3; y-intercept: 2
b. x-intercept: -2/3; y-intercept: 2
c. x-intercept: 2/3; y-intercept: -2
d. x-intercept: -2; y-intercept: 2/3
My answer: ?
2. Which expression is equivalent to 3m^2n/5m x 20mn/n^6?
a. 12m^2/n^4
b. 12m^3/n^3
c. 12m^2n^3
d. 12m/n
My answer: a?
3. Simplify 3/x + 3/5x.
a. 1/x
b. 18/10x
c. 18/5x
d. 1/2x
My answer: ?
1. for the x-intercept let y = 0 ---> x = 2/3
for the y-intercept , let x = 0 ---> y = -2
2. (3m^2 n)/(5m)(20mn/n^6)
= (3mn/5)(20m/n^5)
= 12m^2/n^4 ------> a)
3.
3/x + 3/(5x)
LCD = 5x
= 15/(5x( + 3/(5x)
= 18/(5x)-----> c)
To find the x-intercept of a line, you set y=0 and solve for x. To find the y-intercept, you set x=0 and solve for y. Let's solve each problem step by step:
1. What are the x- and y-intercepts of the line described by 6x - 2y = 4?
To find the x-intercept, set y=0:
6x - 2(0) = 4
6x = 4
x = 4/6
x = 2/3
To find the y-intercept, set x=0:
6(0) - 2y = 4
-2y = 4
y = -4/2
y = -2
So the x-intercept is 2/3 and the y-intercept is -2. Therefore, the correct answer is (c) x-intercept: 2/3; y-intercept: -2.
2. Which expression is equivalent to 3m^2n/5m x 20mn/n^6?
To simplify this expression, we can simplify each fraction individually and then multiply:
3m^2n/5m x 20mn/n^6 = ((3m^2n)/(5m)) x ((20mn)/(n^6))
Canceling out common factors, we get:
= (3m^2n x 20mn) / (5m x n^6)
= (3 x 20 x m^3 x n^2) / (5 x n^6)
= (60m^3n^2) / (5n^6)
= 12m^3/n^4
So the correct answer is (a) 12m^2/n^4.
3. Simplify 3/x + 3/5x.
To simplify this expression, we need to find a common denominator:
3/x + 3/5x = (3(5) + 3)/(5x)
= (15 + 3)/(5x)
= 18/(5x)
So the correct answer is (c) 18/(5x).
Therefore, the answers are:
1. (c) x-intercept: 2/3; y-intercept: -2
2. (a) 12m^2/n^4
3. (c) 18/(5x)