the expression (4x^2-3x+1)-(x^3+2x+7)
what is the coefficient of the x term in the simplified expression?
what is an equation of a line parallel to the line with equation 2 y=14-6x
a.y=-6x+18 b.y=-3x-9 c.y=6x+3 d.y=3x+8
Solve linear system, which substitution of unkowns is proper?
a. sub 5x-16 for y in first eqn
b. sub 5x+16 for y in first eqn
c. sub 5x+12 for y in first eqn
d. sub 7y-4 for x in second eqn
Use line with eqn x+5y=5 and 5x+py=5
a. find p if the lines are parallel
b. find p if the lines perpendicular
I don"t know what to do here, help!
a line passes through the points (6,4) and (5.3), so what is the equation of the line in point-slope form?
In your first question, do you know how to simplify an expression - that is remove parentheses?
Question #2 parallel lones have the same slope
I don't understand question #3
Question #4 perpendicular lines have slopes that are negative reciprocal s of each other.
To find the coefficient of the x term in the simplified expression (4x^2-3x+1)-(x^3+2x+7), we need to combine like terms.
Let's simplify the expression step by step:
(4x^2-3x+1)-(x^3+2x+7)
First, distribute the negative sign to the terms within the parentheses:
4x^2-3x+1-x^3-2x-7
Next, combine the like terms:
- x^3 + 4x^2 - 3x - 2x + 1 - 7
Combine the x terms:
- x^3 + 4x^2 - 5x - 6
The coefficient of the x term is -5.
Now, moving on to the next question:
To find an equation of a line parallel to the line with equation 2y=14-6x, we need a line with the same slope (-6).
The equation of a line in slope-intercept form is y = mx + b, where m represents the slope and b represents the y-intercept.
The given equation, 2y = 14-6x, can be rewritten as y = -3x + 7 by dividing both sides by 2.
Since we want a line parallel to this line, the slope should be -3.
The options provided are:
a. y=-6x+18
b. y=-3x-9
c. y=6x+3
d. y=3x+8
The correct answer is option b, y=-3x-9, as it has the same slope (-3) as the given line.
Moving on to the next question:
To solve a linear system, there are different methods, such as substitution, elimination, or using matrices.
The question asks for the proper substitution of unknowns in the first equation. Let's look at the options:
a. sub 5x-16 for y in the first equation
b. sub 5x+16 for y in the first equation
c. sub 5x+12 for y in the first equation
d. sub 7y-4 for x in the second equation
The correct substitution here is option b, sub 5x+16 for y in the first equation. This means replacing y with 5x+16 in the first equation.
Finally, let's address the last question:
To find the equation of a line in point-slope form given two points (6,4) and (5,3), we can use the formula:
y - y1 = m(x - x1)
where (x1, y1) represents the coordinates of one of the points and m is the slope.
Using the formula and the given points:
m = (y2 - y1) / (x2 - x1) = (3 - 4) / (5 - 6) = -1
Choosing the first point (6,4) as (x1, y1), we substitute the values into the formula:
y - 4 = -1(x - 6)
Now, we simplify:
y - 4 = -x + 6
Rearranging the equation to the slope-intercept form, we get:
y = -x + 10
Therefore, the equation of the line in point-slope form passing through the points (6,4) and (5,3) is y = -x + 10.