Find the product of
(−9−11i) and its conjugate.
Answer:
202
Step-by-step explanation:
First, we can find the conjugate of (-9 -11i)
Given a complex number a + bi, the conjugate would be a - bi.
So, the conjugate of -9 -11i is -9 + 11i.
Now, we multiply!
(-9-11i)(-9+11i)
This resembles the special product (a+b)(a-b) which multiplies out to a^2 - b^2
To apply this we subtract the square of the second number from the first.
(-9)^2 - (11i)^2
81 - 121i^2
i^2 is -1, so we can substitute it in:
81 + 121 = 202
If f(x) = x - 9 and g(x) = -6x - 3,
which statement is true?
Click on the correct answer.
-1 is in the domain of fºg.
-1 is not in the domain of fºg.
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Answer:
-1 is in the domain of fºg
Step-by-step explanation:
Both functions are odd-degree polynomials (as written here), so both functions have a domain and range of "all real numbers."
-1 is in the domain of f(g(x))
Using the Fundamental Theorem of Algebra. Complete the following exercises. Show your work.
Determine how many, what type, and find the roots for f(x) = x^4 + 21x^2 − 100.
Determine how many, what type, and find the roots for f(x) = x^3 − 5x^2 − 25x + 125.
Answer:
A) - Quartic polynomial
- has four roots
- roots are; f(x) = (x + 5i)(x - 5i)(x + 2)(x - 2)
B) - Cubic polynomial
- has 3 roots
- roots are; f(x) = (x - 5)²(x + 5)
Step-by-step explanation:
A) f(x) = x⁴ + 21x² − 100
The highest power in this polynomial is 4 and thus, it is called a quartic polynomial. This means that it will have 4 roots.
Factorizing this polynomial gives;
f(x) = (x² + 25)(x² - 4)
Equating to zero, we can find the roots. Thus, the roots are;
x = 5i
x = -5i
x = 2
x = -2
Thus, the completely factorized polynomial is;
f(x) = (x + 5i)(x - 5i)(x + 2)(x - 2)
B) f(x) = x³ − 5x² − 25x + 125
The highest power in this polynomial is 3. It is therefore a cubic polynomial with 3 roots.
Factorizing this polynomial gives;
f(x) = (x² - 25)(x - 5)
Equating to zero and Factorizing gives;
x = 5
x = -5
x = 5
Thus, completely factorized with the roots is;
f(x) = (x - 5)²(x + 5)
A film on TV starts at 8:30 pm. If the film takes 136 minutes, at
what time does it end?
Answer:
10:46
Step-by-step explanation:
8:30 + 136 min.
= 8:30 + 2:16
= 10:46
determine the value of the expression 4^3 x 4^ -6
A) -12
B)-1/12
C)64
D)1/64
Answer:
D) [tex]\frac{1}{64}[/tex]
Step-by-step explanation:
The -6 will never make it negative, just divide instead if multiply
(4x4x4) x (4÷4÷4÷4÷4÷4)
The population of Nowhere, USA was estimated to be 665,200 in 2004, with an expected increase of 1.9 % per year. At the percent of increase
given what was the expected population in 2005? Round your answer to the nearest whole number.
Answer:
677838 people
Step-by-step explanation:
1.9 percent of 665200 is 12638
665200+12638=677838
The ratio of dogs to cats is 4 to 7. how many dogs are present if there is 49 cats
Answer:
28 dogs are present
Step-by-step explanation:
Dogs : Cats
= 4 : 7
= ? : 49
= 4 x 7 : 7 x 7
= 28 : 49
Which graph represents the equation y=-
--*x+3?
B)
t
Answer:
The correct answer would be the 3rd graph!
Hope this helps!
NO LINKS!!!! Find each measurement indicated. Round your answer to the nearest tenth. Part 2c
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Answer:
BC = 24.0AC = 26.0m∠B = 73.4°m∠B = 30.0°Step-by-step explanation:
The law of sines tells you the ratio of sides is the same as the ratio of sines of their opposite angles.
This post has 2 kinds of problems.
1) 2 angles and the side between them are given.
2) 2 sides and the angle opposite the longest is given.
For the first type, you need to determine the missing angle (opposite the given side). That comes from the sum of angles of a triangle being 180°. Then you find the remaining sides using the ratio of sines.
For the second type, the angle opposite the shorter side is found using the ratio of sides to find the sine of that angle. Then the third side and third angle can be found using the ratio of sides to find the sine of the angle, and using the ratio of sines to find the missing side.
Straightforward, and tedious. For more than one, I like to use a spreadsheet to crunch the numbers.
_____
1) BC = 24.0
2) AC = 26.0
3) m∠B = 73.4°
4) m∠B = 30.0°
__
In the spreadsheet, the given values are in the first 3 columns. The 4th column is the first one calculated. As indicated above, the angle calculation for problems 1 and 2 uses the sum of angles relation. For problems 1 and 2, this is the angle opposite the given side. The "first side" is the side opposite the "first angle". c = b·sin(C)/sin(B), for example.
For problems 3 and 4, the first unknown angle is the one opposite the "short side", which is the shorter of the given sides. As it happens, this is the side that is asked for in the question. B = arcsin(c·sin(B)/sin(C))
_____
Additional comment
In a spreadsheet, angles are presumed to be in radians for all of the trig functions. We use the DEGREES( ) and RADIANS( ) functions to convert as appropriate.
A company produces millions of 1-pound packages of bacon every week. Company specifications allow for no more than 3 percent of the 1-pound packages to be underweight. To investigate compliance with the specifications, the company's quality control manager selected a random sample of 1,000 packages produced in one week and found 40 packages, or 4 percent, to be underweight. Assuming all conditions for inference are met, do the data provide convincing statistical evidence at the significance level of α= 0.05 that more than 3 percent of all the packages produced ir one week are underweight?
a. Yes, because the sample estimate of 0.04 is greater than the company specification of 0.03.
b. Yes, because the p-value of 0.032 is less than the significance level of 0.05.
c. Yes, because the p-value of 0.064 is greater than the significance level of 0.05.
d. No, because the p-value of 0.032 is less than the significance level of 0.05.
e. No, because the p-value of 0.064 is greater than the significance level of 0.05.
Answer:
We accept H₀ we don´t have enough evidence to support that more than 3 % of the packages are undeweight
Step-by-step explanation:
Sample size n = 1000
x ( defective packages found) = 40
p = 40 /1000 p = 0,04 p = 4 % then q = 0,96
np = 0,04 * 1000 and nq / 0.96 * 1000 both greater than 5
Then we can use the approximation of binomial distribution to normal distribution.
α is significance level α = 0,05
From z- table we find z(c) for α = 0,05 z(c) = 1,64
Test Hypothesis
Null Hypothesis H₀ p = 0,03
Alternative Hypothesis Hₐ p > 0,03
We can see from alternative Hypothesis that the test is a one tail test to the right of the bell shape curve of the normal distribution
To calculate z(c) = ( 0,04 - 0,03 ) / √ ( p*q)/n
z(c) = 0,01 * 31,62 / √ 0,04*0,96
z(c) = 0,3162 / 0,1959
z(c) = 1,6140 z(c) ≈ 1,61
Comparing z(s) and z(c)
z(c) > z(s) 1.64 > 1.61
Then z(s) is in the acceptance region for H₀ we accept H₀
UYK
♡ The size of a rhombus is half the longer diagonal.
The height of the ronbus is 3cm
and
the area is 21cm². Find the length of the longer
diagonal
Answer:
Step-by-step explanation:
Area = height × side
21 = 3 * side
side = 7 cm
The side of a rhombus is half the longer diagonal
longer diagonal = 2*side =2*7=14cm
-2c + 8 - 7c - 6 -5c + 14 -5c + 14 -9c + 2 -9c + 2 9c - 14 9c - 14 5c + 14 5c + 14
Answer:
= -152c + 32
Step-by-step explanation:
sry if wrong
R, S, and T represent the lengths of the three sides of a right triangle. Select the equation that represent the relationship between R, S and T. (the two's are exponents)
a. R 2+ S 2= T 2
b. R 2+ T 2 = S 2
c. R 2 + R 2= S 2
d. T 2 + S 2= R 2
e. T 2- S 2= R 2
Answer:
a. R 2+ S 2= T 2
Step-by-step explanation:
Is this multiple choice? If not, then I will explain my answer.
I would say that it is R² + S² = T² because, the original pythagorean theorem equation is a² + b² = c².
They are put in an alphabetical order, a, b, c.
R goes first in the alphabet, then S and T. So, that's why I say it is:
R² + S² = T²
I hope this helps! Please tell me if I'm incorrect! Have a great day may God bless you!
(Also, if you have a keyboard like mine, then you can make an exponent 2, by doing alt + 0178 )
² <-or just cut and paste this
I don’t understand how to solve this. Please explain the steps. Thanks.
Answer:
D
Step-by-step explanation:
When you are raising something to a fractional power, you are raising it to the power of the numerator and finding the root denoted by the denominator. The explanation above is kinda confusing, so here is an example:
x^(3/5)
This would be written as:
[tex]\sqrt[5]{x^3}[/tex]
Now for the actual problem. Since the numerator is 4, we start by raising x to the 4th power, x^4.
Because the denominator is 5, we find the 5th root:
[tex]\sqrt[5]{x^4}[/tex]
This matches none of the answers shown, so the answer is none of the above or D.
Answer:
D
Step-by-step explanation:
The answer would be 5 square root x^4
See Image Below:)
write equation that represents the balance hanger above 6x+15=4x+20 unit 1
Answer:
x = 5/2
Step-by-step explanation:
6x+15=4x+20
Collect like terms
6x - 4x = 20 - 15
2x = 5
x = 5 / 2
monkeeeeeeeeeeeeeeeeeeeeeee also help
[tex] \frac{9}{27} = \frac{1}{3} [/tex]
This is the simplest form of the fraction.
9/27 9 Council it self 1 and goes into 27 three times so the answer will be 1/3.
pls help. due tmrw. will give brainliest
Answer:
0
Step-by-step explanation:
A dry cleaning establishment claims that a new spot remover will remove more than 70% of the spots to which it is applied. To check this claim, the spot remover will be used on 15 spots chosen at random. If fewer than 11 of the spots are removed, we shall not reject thenull hypothesis that p= 0.7; otherwise, we conclude that p > 0.7.
Required:
a. Evaluate α, assuming that p = 0 .7.
b. Evaluate β for the alternative p = 0.9.
Answer:
α = 1 - 0,915 = 0.085
β = 0.314
Step-by-step explanation:
Dry cleasning clain that spot remover will remove the 70% of spot. The claim support the spot and chose at random.
Null hypothesis:
H0 : p = 0.7
If 11 of spot are removed then hypothesis rejected.
If 11 spots are not removed then hypothesis accepted
H1 : p >0/7
X is the number of spot and binomial random variable.
For a)
The probability of committing the type 1 error use alpha such as
α = P ( type I error)
where X > 10
and p = 0.7
for the given values where n = 12 and r = 10 and p - 0.7
we get
α = 1 - 0,915 = 0.085
b)
The nonrejection of the hypothesis where type II error is false .
The hypothesis for this is 0.9
This is Type II error
β = P ( type II error) = P ( X <= 10 where p = 0.9 )
Where n = 12 , r = 10 and p = 0.9
then
β = 0.314
4
3
3
2+
-4
-3
-2 -1
1
1
2
3
4
-1+
-2+
-3
-4
What is the slope of the line?
Answer:
2/3
Step-by-step explanation:
rises 2 units and east 3 units
rise / run = 2 / 3
Plz help me well mark brainliest if correct,.........??
Answer: A
Step-by-step explanation:
Because to find the area I multiplied and got 72 then I looked up how to find them perimeter
Answer:
both A and B
Step-by-step explanation:
a's perimeter is 36 (6+6+12+12)
b's perimeter is 36 (4+4+14+14)
c's perimeter is 34 (9+9+8+8)
all the options equal to 72 sq. centi. if u multi
6*12=72
4*14=72
9*8=72
what is matter and it function
Answer:
In classical physics and general chemistry, matter is any substance that has mass and takes up space by having volume.
Step-by-step explanation:
In classical physics and general chemistry, matter is any substance that has mass and takes up space by having volume.
Q8. How many solutions does the system of equations have?
Answer:
it would be the first answer
Step-by-step explanation:
a solution is where the lines meet, and the coorinate is (1,4)
please help and hurry!
Answer:
a-16 and a half c-12
Step-by-step explanation:
I'm a bit confused about this, can anyone help? Giving 69 points to whoever answers by 12:30 PM (PST)!!
Find the area of the polygon:
Answer: i can give you tips of how to find the area of a polygon.
OK SO To find the area of a regular polygon, all you have to do is follow this simple formula: area = 1/2 x perimeter x apothem. Here is what it means: Perimeter = the sum of the lengths of all the sides.
Step-by-step explanation:
And you have to add all the sides of the lengths of the sum of the polygon
please help with this math question
P and q are points on the line 2y-5x=10
Answer:
[tex]2y-5x =10\\when \ x = 0, \ 2y = 10 => y = 5\\\\\\when \ y = 0, -5x =10 => x =-2\\\\Therefore \ the \ coordinates \ of \ the \ points \ p \ and \ q\ are \ (0, 2) \ and \ (-2, 0)[/tex]
Solve the proportion then around your answer to the nearest hundredth
Answer:
[tex] \frac{6.3}{x} = \frac{2.56}{9.3} \\ x = \frac{6.3 \times 9.3}{2.56} \\ x = 22.89[/tex]
Answer:
x = 22.89
Step-by-step explanation:
6.3 / x = 2.56 / 9.3
Cross multiply
58.59 = 2.56x
Divide both sides by 2.56
22.88671875 = x
Round
x = 22.89
Given lim f(x) = 4. What is lim
X-0
X-0
x5 [F(x)]* ?
оо
O 4
O 64
128
Answer:
64
Step-by-step explanation:
We are given the limit of f(x) as x approaches 0 is 4.
We are asked to find the limit for 1/4 times (f(x))^4 as x approaches 0.
Let's use limit laws by bringing the limit inside the power.
So we have 1/4 * 4^4.
This equals 4^3=64.
The solution is : 64 is limit.
What is limit?In mathematics, a limit is the value that a function approaches as the input approaches some value. Limits are essential to calculus and mathematical analysis, and are used to define continuity, derivatives, and integrals.
here, we have,
Given lim f(x) = 4.
We are given the limit of f(x) as x approaches 0 is 4.
We are asked to find the limit for 1/4 times (f(x))^4 as x approaches 0.
Let's use limit laws by bringing the limit inside the power.
So we have 1/4 * 4^4.
This equals 4^3=64.
Hence, The solution is : 64 is limit.
To learn more on limit click:
https://brainly.com/question/24169952
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What is the length of AC?
a length of 25 meters.cindy cut the string in 4 pieces of equal length.how was each piece
Answer:
6.25 meters
Step-by-step explanation:
25/4 = 6.25
Length of each cut piece is 6.25 m.
What is division?The division is one of the basic arithmetic operations in math in which a larger number is broken down into smaller groups having the same number of items.
Given
A length of 25 meters cut the string in 4 pieces of equal length.
= [tex]\frac{25}{4}[/tex]
= 6.25
Length of each cut piece is 6.25 m.
Find more information about division here
https://brainly.com/question/5805897
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