Answer:
{-infinity, infinity}
no solution
Step-by-step explanation:
|x| +15≥4
Subtract 15 from each side
|x| +15-15≥4-15
|x| ≥-11
This is always true so x can be and real number
{-infinity, infinity}
-2|5x+3| = 8
Divide by -2
-2/-2|5x+3| = 8/-2
|5x+3| = -4
This can never happen because absolute values are zero or greater
no solution
I'll start 18 and 22 for you, and you should then be able to do the rest on your own!
For 18, what we literally do is apply the distance formula for all the points and add them up. For B to C, we get the distance between them to be
sqrt((x1-x2)^2+(y1-y2)^2)=sqrt((0-4)^2+(3-(-1))^2)=sqrt((-4)^2+4^2)=sqrt(16+16)=sqrt(32). Repeat the process for C to E, E and F, and F to B then add the results up to get your answer!
For 22, since the area of a rectangle is length*width (we know given the right angles and that the opposite sides are equal in how long they are), we can multiply 2 perpendicular lines, for example, BC and CE to get sqrt(32)*sqrt(8)=16 as the area
Y + 8 = 4(x - 5)
distribute the 4 to both x and -5
4(x) = 4x
4(-5) = -20
y + 8 = 4x - 20
isolate the y, subtract 8 from both sides
y + 8 (-8) = 4x - 20 (-8)
y = 4x - 28
plug in the x given, if the y matches the answer given, it is the correct answer.
-8 = 4(5) - 28
-8 = 20 - 28
-8 = -8 (True)
D) (5,-8) should be your answer
hope this helps
18/25 is already simplified. There is no number that can go in both 18 and 25.
