Answer:
see below
Step-by-step explanation:
g(x) = (x+2)^2 -1
The function is in the form
g(x) = a(x-h)^2 +k
where (h,k) is the vertex of the parabola
Rewriting
g(x) = (x+2)^2 -1
= (x--2)^2 + -1
The vertex is (-2,-1)
We can find another point by letting x =0
g(0) = (0+2)^2 -1
=2^2 -1
=4-1 =3
The second point is (0,3)
Answer:
Kindly check explanation
Step-by-step explanation:
H0 : μ ≥ 402
H1 : μ < 402
Test statistic :
n = 23
Sample Mean, x = 400
Variance = 900
σ = sqrt(900) = 30
Test statistic = (x - μ) ÷ σ/sqrt(n)
Test statistic = (400 - 402) ÷ 30/sqrt(23)
Test statistic = - 2 / 6.2554324
Test statistic = - 0.3197221
Test statistic = - 0.3197
Critical value :
Using the Tcritical value calculator
Tcrit; α = 0.025, df = n - 1 = 23 - 1 = 22
Tcritical = 2.074
Reject Null : if Test statistic ≤ Tcritical (left tail test)
Since ;
Test statistic ≤ Tcritical ; We reject the Null
Answer:
The area of the cube is 486 inches^2
Step-by-step explanation:
In this question, we are tasked with calculating the area of cube with side 9 inch.
Mathematically, the area can be calculated using the formula A = 6s^2
Now, what we need to do is to substitute 9 inches for s
Thus, A = 6 * 9^2
A = 6 * 81
A = 486 inches^2
Answer:
y = 3
x = 2 - z
Step-by-step explanation:
We have the system:
2*x+y+2*z=7
2*x-y+2*z=1
5*x+y+5*z=13
In the first and second equations we have the term (2*x + 2*z) = A
Then we can rewrite the first two equations as:
A + y = 7
A - y = 1
isolating A in the first equation, we get:
A = 1 + y
Now we replace this in the other equation:
(1 + y) + y = 7
1 + 2*y = 7
2*y = 6
y = 3.
then:
A + y = 7
A + 3 = 7
A = 7- 3 = 4
A = 2*x + 2*z = 4.
Now let's go to the third equation:
(5*x + 5*z) + y = 13
we can rewrite the thing inside the parentheses as:
(5/2)*(2*x + 2*y) + y = 13
And we know that:
2*x + 2*z = 4
y = 3
then this can be written as:
(5/2)*(4) + 3 = 5*2 + 3 = 13
Then we can conclude that:
y = 3
2*z + 2*x = 4
2*(z + x) = 4
(z + x) = 4/2 = 2
x = 2 - z
Notice that the solution is not only a point, we have infinite solutions for this problem.
Step-by-step explanation:
or, 3(5-p)-2(5+p)=3(p+1)
or, 15-3p-10-2p=3p+3
or, 5-5p=3p+3
or, 5-3=3p+5p
or, 2=8p
or, 2/8=p
or, 1/4=p
