Will someone please look over these? I am so lost on these.
1. find the domain of p(x)=xsquared+10- I said {x|x is a real number
2. find the intercepts of 3x+2y=6- I got (0,3) and (2,0)
4.find the equation of (-6,-6)and (6,6)- got y=x
7. slope and y-intercept of x+2y=4- got slope of 1 and (0,2) and (4,0)
9. are the lines 4x+6=y and 2y=8x-5 parallel? got yes
10. slope of (-13,-16) (-18,-17)- got 1/5
12. find the equation of m=-8,(6,7)- got y=-8x-41
13. equation of (7,9);x+5y=3 - got y=-1/5x+52/5
15. is 6x-5y=9 and 6y-5x=7 perpendicular? I put no
17. slope and y-intercept of 5x=9y+36- got 5/9 for slope and (0,-4)
21. slop and y-intercept of -7/6x-5/3- I got slope of -7/6 and (0,-5/3)
If I missed any of these, will you please explain them to me? I need to understand these and am having a real hard time.
most are correct, you seem to be making small careless errors.
#7 slope = -1/2
#12, the given point does not satisfy your equation.
start with
let the equation be y = -8x + b
sub in (6,7)
7 = -8(6) + b
55 = b
so y = -8x + 55
#13 correct if the new line is supposed to be parallel to the given line, it did not say so.
#21 seems to be a typo
did you mean y = -7/6x-5/3 ?
If so, then correct
Of course! I'm here to help you understand these problems. Let's go through each one step by step.
1. Find the domain of p(x) = x^2 + 10:
To find the domain of a function, we need to determine all the possible values that x can take. In this case, since the function is a polynomial, there are no restrictions on the values of x. Therefore, you are correct in saying that the domain is {x | x is a real number}. Well done!
2. Find the intercepts of 3x + 2y = 6:
To find the intercepts, we set one variable to zero at a time and solve for the other variable.
For the x-intercept, we set y = 0 and solve for x:
3x + 2(0) = 6
3x = 6
x = 2
So, the x-intercept is (2, 0).
For the y-intercept, we set x = 0 and solve for y:
3(0) + 2y = 6
2y = 6
y = 3
Therefore, the y-intercept is (0, 3).
You got both intercepts correct!
4. Find the equation passing through (-6, -6) and (6, 6):
To find the equation of the line passing through two points, we need to calculate the slope and then use the point-slope form of a line.
First, let's calculate the slope using the formula:
m = (y2 - y1) / (x2 - x1)
m = (6 - (-6)) / (6 - (-6))
m = 12 / 12
m = 1
Now that we have the slope, we can use the point-slope form:
y - y1 = m(x - x1)
Let's choose the point (-6, -6) to plug into the equation:
y - (-6) = 1(x - (-6))
y + 6 = x + 6
y = x
So, the equation passing through (-6, -6) and (6, 6) is y = x. Well done!
Continue to next comment for explanations of the remaining problems.