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:
60
Step-by-step explanation:
let a = 22 / kg, and b = 12 / kg
a + b = 20 kg
22a + 12b = 15 * 20
12a + 12b = 240
10a = 60
Answer:
-10/3 or -3.33
Step-by-step explanation:
substitute 0 for y
0 = 6x + 20
-20 = 6x + 20 - 20 subtract 20 on both sides
-20 = 6x divide by 6 on each side
-20/6 = 6x/6
x = -20/6 simplify
x = -10/3
Answer:
-139
Step-by-step explanation:
Evaluate 1/4 (4 x^3 - 2 y - 2 z^3) y^2 - 16 x^2 where x = 2, y = -5 and z = 3:
(4 x^3 - 2 y - 2 z^3)/4 y^2 - 16 x^2 = (4×2^3 - -5×2 - 2×3^3)/4×(-5)^2 - 16×2^2
(4×2^3 - 2 (-5) - 2×3^3)/4×(-5)^2 = ((4×2^3 - 2 (-5) - 2×3^3) (-5)^2)/4:
((4×2^3 - 2 (-5) - 2×3^3) (-5)^2)/4 - 16×2^2
(-5)^2 = 25:
((4×2^3 - 2 (-5) - 2×3^3) 25)/4 - 16×2^2
2^3 = 2×2^2:
((4×2×2^2 - 2 (-5) - 2×3^3) 25)/4 - 16×2^2
2^2 = 4:
((4×2×4 - 2 (-5) - 2×3^3) 25)/4 - 16×2^2
2×4 = 8:
((4×8 - 2 (-5) - 2×3^3) 25)/4 - 16×2^2
3^3 = 3×3^2:
((4×8 - 2 (-5) - 23×3^2) 25)/4 - 16×2^2
3^2 = 9:
((4×8 - 2 (-5) - 2×3×9) 25)/4 - 16×2^2
3×9 = 27:
((4×8 - 2 (-5) - 227) 25)/4 - 16×2^2
4×8 = 32:
((32 - 2 (-5) - 2×27) 25)/4 - 16×2^2
-2 (-5) = 10:
((32 + 10 - 2×27) 25)/4 - 16×2^2
-2×27 = -54:
((32 + 10 + -54) 25)/4 - 16×2^2
| 3 | 2
+ | 1 | 0
| 4 | 2:
(42 - 54 25)/4 - 16×2^2
42 - 54 = -(54 - 42):
(-(54 - 42) 25)/4 - 16×2^2
| 5 | 4
- | 4 | 2
| 1 | 2:
(-12×25)/4 - 16×2^2
(-12)/4 = (4 (-3))/4 = -3:
-3×25 - 16×2^2
2^2 = 4:
-3×25 - 164
-3×25 = -75:
-75 - 16×4
-16×4 = -64:
-64 - 75
-75 - 64 = -(75 + 64):
-(75 + 64)
| 7 | 5
+ | 6 | 4
1 | 3 | 9:
Answer: -139
Answer:
(a)
h=3x
(b)
(c)
(d)
units^3
Step-by-step explanation:
We are given a regular hexagon pyramid
Since, it is regular hexagon
so, value of edge of all sides must be same
The length of the base edge of a pyramid with a regular hexagon base is represented as x
so, edge of base =x
b=x
Let's assume each blank spaces as a , b , c, d
we will find value for each spaces
(a)
The height of the pyramid is 3 times longer than the base edge
so, height =3*edge of base
height=3x
h=3x
(b)
Since, it is in units^2
so, it is given to find area
we know that
area of equilateral triangle is
h=3x
b=x
now, we can plug values
(c)
we know that
there are six such triangles in the base of hexagon
So,
Area of base of hexagon = 6* (area of triangle)
Area of base of hexagon is
(d)
Volume=(1/3)* (Area of hexagon)*(height of pyramid)
now, we can plug values
Volume is
units^3
