The number is x
4x+40=100-x
add x to both sides
5x+40=100
minus 40 both sides
5x=60
divide both sides by 5
x=12
the number is 12
Vertex form is y=a(x-h)^2+k, so we can rearrange to that form...
y=3x^2-6x+2 subtract 2 from both sides
y-2=3x^2-6x divide both sides by 3
(y-2)/3=x^2-2x, halve the linear coefficient, square it, add it to both sides...in this case: (-2/2)^2=1 so
(y-2)/3+1=x^2-2x+1 now the right side is a perfect square
(y-2+3)/3=(x-1)^2
(y+1)/3=(x-1)^2 multiply both sides by 3
y+1=3(x-1)^2 subtract 1 from both sides
y=3(x-1)^2-1 so the vertex is:
(1, -1)
...
Now if you'd like you can commit to memory the vertex point for any parabola so you don't have to do the calculations like what we did above. The vertex of any quadratic (parabola), ax^2+bx+c is:
x= -b/(2a), y= (4ac-b^2)/(4a)
Then you will always be able to do a quick calculation of the vertex :)
Answer:
Step-by-step explanation:
This is a test of the mean difference between 2 independent groups or populations.
Let μ1 be the mean annual bonus of Company A's employees and μ2 be the mean annual bonus of Company B's employees.
The random variable is μ1 - μ2 = difference in the mean annual bonus of Company A's employees and the mean annual bonus of Company B's employees
We would set up the hypothesis.
The null hypothesis is
H0 : μ1 ≤ μ2 H0 : μ1 - μ2 ≤ 100
The alternative hypothesis is
H1 : μ1 > μ2 H1 : μ1 - μ2 > 100
This is a right tailed test because of the inequality sign at the alternative hypothesis. We need to take samples of annual bonuses from both company's employees and find the averages. Then we would determine the test statistic as well as the p value. We would use the p value with the level of significance to make decisions
Answer:
n < -10
Step-by-step explanation:
In order to get the variable n by itself subtract 7 from both sides across the inequality
n + 7 < -3
-7 -7
n < -10
