Answer: 22
explanation: the easiest way is to separate one of the diagonals into a triangle and use the pythagorean theorem.
a^2 + b^2 = c^2
4^2 + 3^3 = c^2
16 + 9 = c^2
25 = c^2
5 = c
you now know that both of the diagonals have a length of 5.
by counting the units on the two straight, you know that their length is 6.
6 + 6 + 5 + 5 = 22
Answer:
x=-1
Step-by-step explanation:
The axis of symmetry is along the vertex
The vertex is at (-1,-2)
The x coordinate is -1
x=-1
Answer:
Step-by-step explanation:
From the information given,
Mean, μ = (10.31 + 17.22 + 26.62 + 22.84)/4 = 19.2475
Standard deviation, σ = √summation(x - mean)/n
Summation(x - mean) = (10.31 - 19.2475)^2+ (17.22 - 19.2475)^2 + (26.62 - 19.2475)^2 + (22.84 - 19.2475)^2 = 151.249475
σ = √(151.249475/4)
σ = 6.15
number of sample, n = 4
The z score for 98% confidence interval is 2.33
We will apply the formula
Confidence interval
= mean ± z ×standard deviation/√n
It becomes
19.2475 ± 2.33 × 6.15/√4
= 19.2475 ± 2.33 × 3.075
= 19.2475 ± 7.16
The lower end of the confidence interval is 19.2475 - 7.16 = 12.09
The upper end of the confidence interval is 19.2475 + 7.16 = 26.41
∠ABF and ∠CBE are vertical angles
3x + 25 + 7x - 19 = 10x - 6
Set them equal to each other
∠ABF = ∠CBE
6x + 26 = 10x - 6
Isolate the x. Subtract 6x from both sides and add 6 to both sides
6x (-6x) + 26 (+6) = 10x (-6x) - 6 (+6)
26 + 6 = 10x - 6x
Simplify
32 = 4x
Divide 4 from both sides
32/4 = 4x/4
x = 32/4
x = 8
m∠ABF = 6x + 26
Plug in 8 for x
6(8) + 26 = m∠ABF
48 + 26 = m∠ABF
m∠ABF = 74°
74° is your answer for m∠F
hope this helps
