Write the equation of a line that passes through (-1, -2) and has a slope of 2 in point-slope form. 2.) Given the function f(x)=5x^2-2f ( x ) = 5 x 2 − 2, find f(-3)f ( − 3 ). Please show your work.

3.) For inequalities, when do you use a solid line versus a dotted line? How is the shading determined?

Step-by-step explanation:

Equation of straight line: y=mx+b

Given slope=2, hence m=2

y=2x+b

Replace y and x values as stated in the question (-1, -2)

(-2)=2(-1)+b

-2+2=b

b=0

rewrite the equation:

y=2x+0

y=2x

For 3) a solid line is used when the equation is <= or => while dotted line is for when the equation is < or >

Could you elaborate on question 2? I dont quite get what the question is asking for

the range of a function is the range of y-values for which it is defined, or exists. given that we are only looking at the y-values, we can already discount the first two answers as they deal with the domain of the function (range of x-values).

now, what we need to do is find the smallest and highest y-values for which the function is defined. if you'd like, you could take a ruler and start at the very bottom of the graph, find the lowest point, then move the ruler higher and higher until you reach the highest point. doing so either in your head or with an actual ruler, we can see that the lowest y-value is -5 and the highest y-value is -1.

the question now remains as to whether they are included in the range (fourth answer) or excluded (third answer). the key here is to recognise whether they are marked with an open or a closed circle. since both (-2, -5) and (2, -1) are marked with a closed circle, they are points that exist on the graph and are thus included in the range (note that if they were marked with an open circle like (4, -2) then that would signify that there is a break in the graph at that point).

thus, the fourth answer, (y | -5 ≤ y ≤ -1), is correct.

also note that usually it is good practice to scan your eye inbetween the highest and lowest point for any breaks in the graph - we do have one here at (4, -2), however -2 is still included in the range because there is another point that is included in the graph with the same y-value, ie. point (1, -2).

i hope that but if you require any further explanation don't hesitate to comment below.

answer: 1722

step-by-step explanation:

given: the mass of saturn=

the mass of mercury=

the number of times the mass of saturn is greater than the mass of mercury

hence, the mass of saturn is 1722 times greater than the mass of mercury.