in plain and short, to graph an inequality, we first graph its EQUALITY graph, and then we do the shading.
so to graph y > x + 3, we first graph y = x + 3, which is just a line, and then do a true/false check on a point to see which side we shade.
let's hmmm check the point say (0,2), x = 0, y = 2.
y > x + 3
2 > 0 + 3
2 > 3 <--- is that true? is 2 really larger than 3? nope, so is false.
that simply means that the point (0, 2) is on the false area, so that's the area we do NOT shade, so <u>we shade the other side</u>.
y > x + 3, means "y" is greater than or larger than that line, but not equals, larger not equal, meaning the values on the borderline are not included, so the line is a dashed line.
check the picture below.
F(x)=-1x-1
1) Pick 2 points on the line (i chose (-4,3) and (3,-4)
2) Find slope of the line using the 2 points. (work below)
3) Find y-intercept, which is the point where y-axis and the line cross (y-intercept is -1).
4) Place both slope and y-intercept into slope-intercept form, y=mx+b (m=slope and b=y-intercept.)
5) Change y to f(x) (meaning function of x).
Work:
3-(-4)/-4-3=3+4/-4-3=7/-7=-1
y-intercept equals -1 also.
y=mx+b
y=-1x+(-1)
y=-1x-1
f(x)=-1x-1<---Answer
Answer:
a = (v – u)/t
Step-by-step explanation:
We know,
v = u+ at
v-u=at
(v-u) /t=a
The answer for the exercise shown above is the last option (Option D), which is:
D. log base 5 of 56
The explanation is show below:
1. You have the following logarithm expresssion:
<span>log5(4*7 )+log5(2)
</span>
2. By the logarithms properties, you can rewrite the logarithm expression as following:
log5(28)(2)
log5(56)
3. Therefore, as you can see, the answer is the option mention before.
Answer:
k = 3
Step-by-step explanation:
If p-1 is a factor of p⁴+p²+p-k, then we can express the polynomial in form
p⁴+p²+p-k = (p-1) * (ap³ + bp² + cp + d)
where a,b,c,d are constants. The important thing is that we can subst in p = 1 to make the polynomial zero. We can do this for original polynomial. WE must have to equal to 0 when we use p = 1 substitution...
1⁴+1²+1-k = 0
3 - k = 0
k = 3