1 Move all terms to one side.
{x}^{2}+15x+45=0
x
2
+15x+45=0
2 Use the Quadratic Formula.
x=\frac{-15+3\sqrt{5}}{2},\frac{-15-3\sqrt{5}}{2}
x=
2
−15+3
5
,
2
−15−3
5
3 Simplify solutions.
x=-\frac{3(5-\sqrt{5})}{2},-\frac{3(5+\sqrt{5})}{2}
x=−
2
3(5−
5
)
,−
2
3(5+
5
)
Answer:
something like this?
the top one is valid when x-4 >0
the bottom one is valid when x-4<0
Step-by-step explanation:
absolute value |x-4|
means that in case x-4 is negative, we will use -(x-4)
if it's positive we use x-4
let's find the solution (where the original inequality is true)
negative case:
-(x-4)<9 -x+4 < 9 -x < 5 x>-5
positive case:
x-4 < 9 x < 13
to satisfy both conditions -5 < x < 13
Answer:
f(-2.75)=-1
Step-by-step explanation:
Here we are given a Greatest Integer Function . The characteristic of this function is that it when operated , gives you the greatest integer it has near to it.
Hence if we have any greatest integer function f(x)=[x] , for x = -2.75
[-2.75]=-2 , as -the greatest integer near to -2.75 is -2 as -3<-2
Now coming back to our problem, our function is
f(x)=[x]+1
Hence for x=-2.75
f(x)=[-2.75]+1
as we discussed above [-2.75]=-2
Hence
f(-2.75)=-2+1
f(-2.75)=-1
Answer:
20 sides
Step-by-step explanation:
The formula that relates interior angles with number of sides is:

Where
n is the number of sides.
We know each interior is 162 degrees, so we substitute and cross multiply and solve for n:

THus, the polygon has 20 sides
Answer:
We cannot determine the appropriate hypotheses to test this study because we are only given the data for the sample size and the population mean. Meanwhile, we need to know the data of the sample mean, the standard deviation and the level of significance before we can state the appropriate hypotheses for this test.
Step-by-step explanation:
Given that:
sample size n = 300
population mean μ = 35
The null hypothesis and the alternative hypothesis can be computed as follows:
Null hypothesis

Alternative hypothesis

The degree of freedom df = n -1
df = 300 - 1
df = 299