Find all complex solutions (real and non-real). (Enter your answers as a comma-separated list.) x3 8x2 21x 20
Answer:
The answer is "non-real solution: "i-3 and -i-3" and real solution is -2".
Step-by-step explanation:
In the given equation there is some mistype error so, its correct equation can be defined as follows:
Given value:
[tex]\bold{ f(x) = x^3+ 8x^2 +22x +20}[/tex]
use hit and trial method we put x value are -2:
[tex]f(-2) = (-2)^3+ 8(-2)^2 +22(-2) +20\\\\[/tex]
[tex]= -8 + 8 \times 4 +22 \times -2 +20\\\\= -8 + 32 -44 +20\\\\= -52 + 52\\\\=0[/tex]
So, the real solution to the equation is "-2".
In the above solution, we calculate the f(x) =-2 is its real solution. so, the calculation for non-real solution:
divide the value [tex]x^3+8x^2+ 22x +20[/tex] by ([tex]x+2[/tex]):
Quotient: [tex]x^2+6x+10[/tex]
Remainder: 0
[tex]\to x^2+6x+10 \\\\compare \ with \ ax^2+bx+c: \\\\a= 1\\b= 6\\c=10\\\\\bold{Formula:}\\\\\to D= b^2-4ac\\\\[/tex]
[tex]= 6^2- 4 \times 1 \times 10\\\\ = 36- 40\\\\ = -4[/tex]
Formula for calculate non-real solution:
[tex]\bold{\frac{-b\pm \sqrt{D}}{2}}[/tex]
non-real solution: "i-3 and -i-3"
Picture attached below. Please help
Answer:
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A box is formed by cutting squares from the four corners of a sheet of paper and folding up the sides.
Suppose the paper is 7"-wide by 9"-long.
a. Estimate the maximum volume for this box?
b. What cutout length produces the maximum volume?
Answer:
B
Step-by-step explanation:
To answer this question it is necessary to find the volume of the box as a function of "x", and apply the concepts of a maximum of a function.
The solution is:
a) V (max) = 36.6 in³
b) x = 1.3 in
The volume of a cube is:
V(c) = w×L×h ( in³)
In this case, cutting the length "x" from each side, means:
wide of the box ( w - 2×x ) equal to ( 7 - 2×x )
Length of the box ( L - 2×x ) equal to ( 9 - 2×x )
The height is x
Then the volume of the box, as a function of x is:
V(x) = ( 7 - 2×x ) × ( 9 -2×x ) × x
V(x) = ( 63 - 14×x - 18×x + 4×x²)×x
V(x) = 4×x³ - 32×x² + 63×x
Tacking derivatives, on both sides of the equation
V´(x) = 12×x² - 64 ×x + 63
If V´(x) = 0 then 12×x² - 64 ×x + 63 = 0
This expression is a second-degree equation, solving for x
x₁,₂ = [ 64 ± √ (64)² - 4×12*63
x₁ = ( 64 + 32.74 )/ 24
x₁ = 4.03 this value will bring us an unfeasible solution, since it is not possible to cut 2×4 in from a piece of paper of 7 in ( therefore we dismiss that value)
x₂ = ( 64 - 32.74)/24
x₂ = 1.30 in
The maximum volume of the box is:
V(max) = ( 7 - 2.60) × ( 9 - 2.60)×1.3
V(max) = 4.4 × 6.4 × 1.3
V(max) = 36.60 in³
To chek for maximum value of V when x = 1.3
we find the second derivative of V V´´, and substitute the value of x = 1.3, if the relation is smaller than 0, we have a maximum value of V
V´´(x) = 24×x - 64 for x = 1.3
V´´(x) = 24× 1.3 - 64 ⇒ V´´(x) < 0
Then the value x = 1.3 will bring maximum value for V
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Herman is standing on a ladder that is partly in a hole. He starts out on a rung that is 6 feet under ground, climbs up 14 feet, then climbs down 11 feet. What is Herman’s final position, relative to ground level?
Answer:
Are there answers
Step-by-step explanation:
Answer:
answer
Herman is standing on a ladder that is partly in a hole. He starts out on a rung that is 6 feet under ground, climbs up 14 feet, then climbs down 11 feet. ...
PLEASE ANSWER I WILL GIVE YOU BRAINLIEST!
Name the points which satisfy the conditions. In the second quadrant
9514 1404 393
Answer:
C, M
Step-by-step explanation:
The second quadrant is the upper left quadrant. There, x-values will be negative and y-values will be positive.
__
Point G is on the boundary with the 3rd quadrant, so is probably not considered to be in either of those quadrants.
Answer: C M
Step-by-step explanation:
Use the information to find the minimum sample size required to estimate an unknown population mean µ. Margin of error: $110, confidence level: 95%, σ = $500. Group of answer choices
Answer:
The minimum sample size required is 79.
Step-by-step explanation:
The following are given in the question:
e = Margin of error = 110
σ = Standard deviation = 500
Confidence level = 95%
n = Minimum sample size = ?
Therefore, we have:
Zσ = 1.96 at 95% confidence level
s.e. = Standard error = σ / [tex]\sqrt{n}[/tex] = 500 /
Alternatively, margin of error can be calculated as follows:
e = s.e. * Zσ = 110 ................... (1)
Substituting the other values into equation (1) and solve for n, we have:
500 / [tex]\sqrt{n}[/tex] * 1.96 = 110
500 / [tex]\sqrt{n}[/tex] = 110 / 1.96
500 / [tex]\sqrt{n}[/tex] = 56.1224489795918
500 = 56.1224489795918 * [tex]\sqrt{n}[/tex]
[tex]\sqrt{n}[/tex] = 500 / 56.1224489795918
[tex]\sqrt{n}[/tex] = 8.90909090909092
[tex]n^{\frac{1}{2}[/tex] = 8.90909090909092
Squaring both sides, we have:
([tex]n^{\frac{1}{2}[/tex])^2 = (8.90909090909092)^2
n = 79.3719008264465
Approximating to a whole number, we have:
n = 79
Therefore, the minimum sample size required is 79.
Turn 2 1/8 into an improper fraction. Explain your steps
Answer:
17/8
Step-by-step explanation:
2 1/8 multiply 2 times 8 and 1 which equals to 17/8. The whole number times the denominator plus the numerator basically.
Answer:
17/8
Step-by-step explanation:
8 x 2 = 16
16 + 1 = 17
What do I use to make a meat loaf?
answer quick 50 points
Answer: The 1/10, 0.22, then 1/4.
Second Picture: 9.8, Pie^2, then 99
Answer:
The 1/10, 0.22, then 1/4.
Second Picture: 9.8, Pie^2, then 99
Suppose that the probability that a person books a hotel using an online travel website is 0.68. For the question that follows, consider a sample of fifteen randomly selected people who recently booked a hotel.
What is the probability that at least fourteen out of fifteen people used an online travel website when they booked their hotel? Round to three decimal places.
A.0.028
B.0.025
C.0.323
D.0.978
Answer:
the answer is d because 0.978 cool number like yaaaa.
Step-by-step explanation:
Daniel has 15 yards of fabric to make baby blankets. It takes 1 and 1/2 yards of fabric to make each blanket, and the expression that models the situation is 15 minus three-halves y. Which of the following are possible numbers of blankets that Daniel could make? Select all that apply.
Answer:
any number between 0 and 10
Step-by-step explanation:
15 - 3/2y
how many times can 3/2 go into 15?
10 times. The most blankets he can make is 10, so any number less than 10 and greater than zero would be a correct solution
can i get brainliest please?
Answer:
9 and 10
Step-by-step explanation:
Please help!!!- Find the measure of the angle in bold.
Need help to figure out to solve this.
Answer:
11x-6+(19x+6)=180°
11x+19x-6+6=180°
30x=180
x=180/30
x=6
it means that
19x+6=19*6+6=114+6=120°
I toss a coin 60 times. It lands on tails 24 times. What percent of the time does it land on tails?
From their location in the diagram, what are two possible values for n and m?
Answer:
n=7/5 m= 5
Step-by-step explanation:
Complete the point-slope equation of the line through (2,3)(7,4)
y-4=
The inverse of a function is a function. True or False
Answer:
false
Step-by-step explanation:
Answer:
TrueStep-by-step explanation:
The inverse of a function may not always be a function! The original function must be a one-to-one function to guarantee that its inverse will also be a function.
If the graph does not pass the Horizontal Line Test, then the graphed function's inverse will not itself be a function
Two lines in the same plane that do not intersect are.
A.line segment
B.perpendicular
C.parallel
D.midpoint
Look at the coordinate graph.
Which point has coordinates (5, 4)?
Which point has coordinates (-5, -4)?
Which point has coordinates (5, -4)?
Which point has coordinates (-5, 4)?
Answer:
B = (5,4), C = (-5, -4), D = (5, -4), A = (-5, 4)
Step-by-step explanation:
look at x axis first (horizontal), then y axis (vertical)
The coordinates of the points are:
Point A is at (-5, 4)Point B is at (5, 4)Point C is at (-5, -4)Point D is at (5, -4)How to identify the points?Remember that for a point (x, y), we need to count x units on the horizontal axis, and y units on the vertical axis.
With that in mind, we can see that:
Point A is at (-5, 4)Point B is at (5, 4)Point C is at (-5, -4)Point D is at (5, -4)Now, answering the questions:
Which point has coordinates (5, 4)?
Point B
Which point has coordinates (-5, -4)?
Point C
Which point has coordinates (5, -4)?
Point D
Which point has coordinates (-5, 4)?
Point A.
If you want to learn more about coordinates, you can read:
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Steam
To save money for his daughter's college tuition, All Invests $250 every quarter in an annuity that pays 6.2% Interest, compounded quarterly
Payments will be made at the end of each quarter. Find the total value of the annuity in 22 years
Do not round any intermediate computations, and round your final answer to the nearest cent. If necessary, refer to the list of financial formulas
Answer:
5436
Step-by-step explanation:
take 6.2 and ÷ 250 then × it by 22
which number is the same as 0.000 000 1: 10^7 or 10^-7
Answer:
= 1 × 10^-7
(scientific notation)
= 1e-7
(scientific e notation)
= 100 × 10^-9
(engineering notation)
(billionth; prefix nano- (n))
= 0.0000001
(real number)
Step-by-step explanation:
10^7 = 10000000
solve the following equation for a: -g + 3/4a = y
9514 1404 393
Answer:
a = (4/3)(y+g)
Step-by-step explanation:
Isolate 'a' term, then multiply by the reciprocal of its coefficient.
[tex]-g+\dfrac{3}{4}a=y\qquad\text{given}\\\\\dfrac{3}{4}a=y+g\qquad\text{add $g$}\\\\\boxed{a=\dfrac{4(y+g)}{3}}\qquad\text{multiply by $4/3$}[/tex]
What is the measure of angle F?
E. 20
D. 90
F.?
Answer:
the answer would be 70 because you take 90-20 and you get 70. you have a 90 degree angle is what you're working on right now
Step-by-step explanation:
Three times two less than a number is greater than or equal to five times the number. Find all of the numbers that satisfy the given conditions.
Let n = a number. Choose the inequality that represents the given relationship.
Answer:
D on edge
3(n – 2) ≥ 5n
Step-by-step explanation:
the next question's answer is B
Six and forty-two ten-thousandths as a decimal
How do you do this question?
Answer:
Diverges
Step-by-step explanation:
an = 7 / n^(1 + 1/n)
As n approaches infinity, an approaches 7 / n.
bn = 7 / n
Apply Limit Comparison Test.
lim(n→∞) an / bn
= lim(n→∞) [7 / n^(1 + 1/n)] / (7 / n)
= lim(n→∞) n / n^(1 + 1/n)
= lim(n→∞) 1 / n^(1/n)
= lim(n→∞) 1 / n⁰
= 1
The limit is greater than 0, and bn diverges, so an also diverges.
Which one of these relationships is different than the other three?
Group of answer choices
A
B
C
D
help!!!1
Answer:
B
Step-by-step explanation:
I got this by looking at the graph and the numbers that I got vertically and horizontally I divided them .
PLEASE HELP IM TIMEZ) What is the value of the arithmetic series below? A. B. C. D.
Answer:
id say its C but I'm not sure
x=4/9,y=1/2, and z=3/5 6wy-3z
Answer: The answer would be - 7/5 or (-0.46)
Plug in the numbers that each letter equals. So you get 6(4/9)(1/2) - 3(3/5). Then you just simplify.
What is the rate of return when 10 shares of Stock
A, purchased for 20 $/share, are sold for $310? The
commission on the sale is $6.
rate of return = [?] %
Give your answer as a percent rounded to the
nearest tenth.
Answer:
Rate of return = 52%
Step-by-step explanation:
Cost of Investment = 10 shares × $20 = $200
Gain on Investment = amount sold - commission on the sale
Gain on Investment = $310 - $6 = $304
Using the formula:
ROR = (Gain on investment - cost of Investment)/cost of Investment × 100
Plug in the values into the formula:
[tex] ROR = \frac{304 - 200}{200} * 100 [/tex]
[tex] = \frac{104}{200} * 100 [/tex]
[tex] = \frac{104*100}{200} [/tex]
[tex] = \frac{104}{2} = 52 [/tex]
Rate of return = 52%
Find the selling price of each item original plate price of gold fish at $7.65 discount 10%
Answer:
6.88 is what I think you're looking for
Step-by-step explanation: