1.Tell whether the sequence is arithmetic. If it is, what is the common difference?

-19,-11,-3,5...
A.yes;5
B.yes;6
C.yes;8
D.no

2.What is the slope of that passes through the pair of points?
(-6,8),(2,3)
A.-3/8
B.-1/8
C.-7/8
D.-5/8

3.Write an equation in point-slope form for the line through the given point with the given slope.
(-3,5);m=2/3
A.y+3=2/3(x-5)
B.y+5=(2/3)(x+3)
C.y-5=2/3(x-3)
D.y-5=2/3(x+3)

4.Write y=-2/5x-3 in standard form using integers.
A.2x+5y=-15
B.2x+y=-3
C.2x+5y=-3
D.x+y=-15

5.Write the equation of a line that is perpendicular to the given line and that passes through the given point.
y-2=-1/4(x+3);(-3,5)

A.y=-3x-5
B.y=1/4x-6
C.y=4x+17
D.y=4x+5

6.How many solutions doe the system of equations have?

3x+15y=9
y=-1/5x+9/15
A.one
B.two
C.infinitely many
D.none

I think
#1.D
#2.C
#3.A
#4.B
#5.A
#6.A
(Pleas correct me if im wrong)

#1 C did you actually check the differences?

#2 D (3-8)/(2-(-6)) = -5/8
#3 D better review that topic
#4 B same advice
#5 C same advice
#6 C they are the same equation

Next time you want a check on your work, it would be better to show what you did.

1. That sequence is arithmetic. The common difference is 8. So the correct answer is C. (yes; 8)

2. The slope of the line passing through (-6,8) and (2,3) is -5/8. So the correct answer is D. (-5/8)

3. The equation in point-slope form for the line through (-3,5) with slope 2/3 is y-5=2/3(x+3). So the correct answer is D. (y-5=2/3(x+3))

4. The equation y=-2/5x-3 can be written in standard form as 2x+5y=-15. So the correct answer is A. (2x+5y=-15)

5. The equation of a line that is perpendicular to y-2=-1/4(x+3) and passes through (-3,5) is y=-3x-5. So the correct answer is A. (y=-3x-5)

6. The system of equations 3x+15y=9 and y=-1/5x+9/15 has infinitely many solutions. So the correct answer is C. (infinitely many)

Your answers are correct except for #6. Let me guide you step by step to find the correct answer.

6. How many solutions does the system of equations have?

3x + 15y = 9
y = -1/5x + 9/15

To determine the number of solutions, we can compare the slopes of the two equations. If the slopes are equal, then the lines are parallel and there are no solutions. If the slopes are different, then the lines intersect at a single point, and there is one solution.

The slope of the first equation is -1/5, and the slope of the second equation is also -1/5. Since the slopes are equal, the lines are parallel.

Therefore, the correct answer is D. None.

If you have any more questions, feel free to ask!

Let's go through each question to find the correct answers:

1. To determine if a sequence is arithmetic, we need to check if there is a constant difference between consecutive terms. In this case, if we subtract each term from the next, we get: (-11) - (-19) = 8, (-3) - (-11) = 8, and so on. This means there is a common difference of 8, so the answer is C.

2. The slope of a line passing through two points can be found using the formula: slope = (change in y) / (change in x). For the given points (-6,8) and (2,3), the change in y is 3 - 8 = -5, and the change in x is 2 - (-6) = 8. Thus, the slope is -5/8, so the answer is D.

3. The point-slope form of an equation for a line passing through a point (x1, y1) with slope m is: y - y1 = m(x - x1). Given the point (-3,5) and slope m = 2/3, substituting these values into the formula, we get y - 5 = (2/3)(x - (-3)), which simplifies to y - 5 = (2/3)(x + 3). Therefore, the answer is B.

4. To write the equation y = -2/5x - 3 in standard form, we need to rearrange the equation so that the coefficients of x and y are integers and the constant term is on the other side of the equation. By multiplying through by 5 to eliminate the fraction, we get: 5y = -2x - 15. Rearranging further to have the variables and constants on the same side, we get 2x + 5y = -15. So the answer is A.

5. Two lines are perpendicular if the product of their slopes is -1. The given line has a slope of -1/4. So, the perpendicular line's slope will be the negative reciprocal of -1/4, which is 4. Using the point-slope form with the point (-3,5), we have y - 5 = 4(x - (-3)), which simplifies to y - 5 = 4(x + 3). Therefore, the answer is D.

6. To determine the number of solutions in a system of equations, we can examine the slopes of the two equations. If the slopes are different, there is only one solution (the lines intersect at a single point). If the slopes are the same, the lines are parallel and there are no solutions. In this case, the first equation is in the form y = mx + b, where m (slope) is 0 and the second equation is also in the form y = mx + b, with m (slope) equal to -1/5. Since the slopes are different, the lines intersect at a single point, so the answer is A.

Based on these explanations, the correct answers to the questions are:
1. C
2. D
3. B
4. A
5. D
6. A

Your answers are mostly correct, except for #3 and #4. If you adjust your answers according to the explanations above, the correct answers should be:
#3: B
#4: A

Overall, great effort!