Answer:
1/18
Step-by-step explanation:
-(-5/9) would turn into a positive 5/9. It cancels its own negative out.
The problem then turns to -1/2+5/9. Find the least common denominator and then combine.
Answer:
x = -13/5
Step-by-step explanation:
let x be the number
8x + 6 = 3x - 7
move variables to left and numbers to right
8x - 3x = - 7 -6
5x = -13
x = -13/5
Answer:
6) y = x^(5/3)
7) B
8) C
10) A
Step-by-step explanation:
6) The fifth root is the same as raising to the 1/5 power, so we can write this in exponent form as:
f(x) = (x^(1/5))³
f(x) = x^(3/5)
To find the inverse, switch x and y and solve for y.
x = y^(3/5)
y = x^(5/3)
7) f(x) = 2√(x − 4) + 8
Switch the x and y and solve for y:
x = 2√(y − 4) + 8
x − 8 = 2√(y − 4)
(x − 8) / 2 = √(y − 4)
(x − 8)² / 4 = y − 4
(x² − 16x + 64) / 4 = y − 4
¼x² − 4x + 16 = y − 4
y = ¼x² − 4x + 20
8) Find the inverse:
x = 5√(y + 3) − 2
x + 2 = 5√(y + 3)
(x + 2) / 5 = √(y + 3)
(x + 2)² / 25 = y + 3
y = -3 + (x + 2)² / 25
The inverse function is an upwards parabola with a vertex at (-2, -3). The best fit is C.
desmos.com/calculator/fbabg5wc8b
10) √(4x − 31) = x − 7
Square both sides:
4x − 31 = (x − 7)²
4x − 31 = x² − 14x + 49
Combine like terms:
0 = x² − 18x + 80
Factor:
0 = (x − 8) (x − 10)
x = 8 or 10
Check for extraneous solutions.
√(4×8 − 31) = 8 − 7
1 = 1
√(4×10 − 31) = 10 − 7
3 = 3
x = 8 and x = 10 are both solutions.
Answer:
Step-by-step explanation:
Without brackets, we are not exactly sure what is under the root sign. There are 3 choices.
sqrt(x) + 2 - 15 = - 3
sqrt(x + 2) - 15 = - 3
sqrt(x + 2 - 15) = - 3
I think the middle one is what you intend. If not leave a note.
sqrt(x + 2) - 15 = - 3 Add 15 to both sides.
sqrt(x + 2) - 15+15 = - 3+15 Combine
sqrt(x + 2) = 12 Square both sides
x + 2 = 12^2 Do the right
x + 2 = 144 Subtract 2 from both sides.
x + 2-2 = 144-2
x = 142
