Select EACH correct answer.
Answer: x = {-3, -1, 1, 7}
Step-by-step explanation:
f(x) = x⁴ - 4x³ - 22x² + 4x + 21
possible roots are: +/- 1, 3, 7, 21
Let's try x = 1
1 | 1 -4 -22 4 21
| ↓ 1 -3 -25 -21
1 -3 -25 -21 0 remainder is 0 so (x - 1) is a factor
(x - 1)(x³ - 3x² - 25x - 21)
Next, let's try x = -1
-1 | 1 -3 -25 -21
| ↓ -1 4 21
1 -4 -21 0 remainder is 0 so (x + 1) is a factor
(x - 1)(x + 1)(x² - 4x - 21)
Then, factor the third polynomial
(x - 1)(x + 1)(x + 3)(x - 7)
Now, set each factor equal to zero and solve each one.
(x - 1) = 0 ⇒ x = 1
(x + 1) = 0 ⇒ x = -1
(x + 3) = 0 ⇒ x = -3
(x - 7) = 0 ⇒ x = 7
Answer:
-3, -1, 1, 7
Step-by-step explanation:
Evaluate the function at each x value in the choices. If the polynomial evaluates to zero, then that x value is a solution.
f(-3) = (-3)^4 - 4(-3)^3 - 22(-3)^2 + 4(-3) + 21 = 0
x = -3 is a solution
f(-1) = (-1)^4 - 4(-1)^3 - 22(-1)^2 + 4(-1) + 21 = 0
x = -1 is a solution
f(0) = (0)^4 - 4(0)^3 - 22(0)^2 + 4(0) + 21 = 21
x = 0 is not a solution
f(1) = (1)^4 - 4(1)^3 - 22(1)^2 + 4(1) + 21 = 0
x = 1 is a solution
f(3) = (3)^4 - 4(3)^3 - 22(3)^2 + 4(3) + 21 = -192
x = 3 is not a solution
f(7) = (7)^4 - 4(7)^3 - 22(7)^2 + 4(7) + 21 = 0
x = 7 is a solution
Answer:
3 measurements of different rectangular prisms that each have a surface area
of 20 square units is given as
(4.5 × 1 × 1)
(2 × 1 × 2.67)
(2 × 3 × 0.80)
Step-by-step explanation:
A rectangular prism is a cuboid and the surface area of a cuboid with length, x, width, y and height, z, is given as
S = 2xy + 2yz + 2xz
S = 2[xy + yz + xz]
So, the question asks us to list 3 different measurements of a rectangular prism with surface area of 20 square units.
S = 2[xy + yz + xz] = 20
[xy + yz + xz] = 10
So, with a little of trial and error, we can vary the values of x, y and z to obtain 3 separate measurements that give a surface area of 20 square units.
[xy + yz + xz] = 10
Let x = 4.5, y = 1, z = 1
(4.5×1) + (1×1) + (4.5×1) = 10, works!!!
(x, y, z) = (4.5, 1, 1)
[xy + yz + xz] = 10
Again, we can fix arbitrary values for two sides and calculate for the last side.
If x = 2 units, y = 1 unit,
(2×1) + (1×z) + (2×z) = 10
2 + 3z = 10
3z = 8
z = (8/3) = 2.667 units
(x, y, z) = (2, 1, 2.67)
[xy + yz + xz] = 10
And lastly, if x = 2, y = 3
(2×3) + (3×z) + (2×z) = 10
6 + 5z = 10
5z = 4
z = (4/5) = 0.80 unit
(x, y, z) = (2, 3, 0.80)
Hope this Helps!!!
a+b=10
Her current purchasing power round to the nearest dollar is $27158
Inflation is an increase in the purchasing power of an individual. Given the following parameters
Carnie's income last year = $29,520
If the inflation rate is eight percent, then her current purchasing power is expressed as:
Current purchasing power = 0.92 * $29,520
Current purchasing power = $27158.4
Her current purchasing power round to the nearest dollar is $27158
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