Answer:
x = - 2, x = 6
Step-by-step explanation:
Given f(x) = 18 we require to solve
3 | x - 2 | + 6 = 18 ( subtract 6 from both sides )
3 | x - 2 | = 12 ( divide both sides by 3 )
| x - 2 | = 4
The absolute value function always returns a positive value, however, the expression inside can be positive or negative, thus
x - 2 = 4 ( add 2 to both sides )
x = 6
OR
- (x - 2) = 4
- x + 2 = 4 ( subtract 2 from both sides )
- x = 2 ( multiply both sides by - 1 )
x = - 2
As a check substitute these values into the left side of the equation and if equal to the right side then they are the solutions
x = 6 → 3|6 - 2| + 6 = 3|4| + 6 = 3(4) + 6 = 12 + 6 = 18 ← True
x = - 2 → 3|- 2 - 2| + 6 = 3|-4| + 6 = 3(4) + 6 = 12 + 6 = 18 ← True
Hence solutions are x = - 2, x = 6
Answer:
1) A - 42°
2) 74°
3) B - 45°
4) B - 66°
Step-by-step explanation:
1) E = D+H
87 = 45 + H
H = 42°
2) 180 - 50 - D
D = 180 - 44 - 62 = 74°
3) F = 105
H = 180-105 = 75
I + H = C + E
I + 75 = 83 + 37
I = 45°
4) D = 180 - (E + F)
D = 180 - (30 + 57) = 93°
93 = A + 27
A = 66°
Answer:
x = i and x = i
Step-by-step explanation:
Given
+ 6x² + 5 = 0
Using the substitution u = x², then
u² + 6u + 5 = 0 ← in standard form
(u + 1)(u + 5) = 0 ← in factored form
Equate each factor to zero and solve for u
u + 1 = 0 ⇒ u = - 1
u + 5 = 0 ⇒ u = - 5
Convert solutions back into terms of x
x² = - 1 ⇒ x = 
= i
x² = - 5 ⇒ x = 
= i
Answer:
A
Step-by-step explanation:
Steps to take to determine the answer
- Because the length is in yards, it has to be converted to foot
- Find the area of the patio using the length and width measured in foot
- Determine the area of the square brick
- Multiply the cost of the brick by the area
1 yards = 3 foot
5 x 3 = 15 foot
Area of a rectangle = length x breadth
15 x 10 = 150 ft^2
Cost = 150 x 4 = $600
Answer:
The pattern form is 8,15,34,71 which follows the rule 
Step-by-step explanation:
Given : Rule
To find : Create a number pattern that follows the rule. Use at least three terms in the pattern ?
Solution :
Rule
Put n=1,
Put n=2,
Put n=3,
Put n=4,
The pattern form is 8,15,34,71 which follows the rule
