Answers
Answer:
The answers are...:
The common ratio is -3
the sequence of the function is 2,-6, 18, -54, 162
and
the sequence of the function model is geometric
I hope this helps ^^"
Step-by-step explanation:
the common ratio is just from the -3 itself
the sequence model is just plugging n for every term so
a(1) would equal to 2, a(2)=-6 , a(3) would equal to -18, etc
and the geometric is bc it has the exponential that has (n-1), thus it is a geometric sequence
Related Questions
Select the two values of x that are roots of this equation x^2-5x+2=0
Answers
The roots of the equation is x = 4.56 OR x = 0.44
Quadratic equationFrom the question, we are to determine the roots of the given equation
The given equation is
x² -5x +2 = 0
Using the formula method,
[tex]x =\frac{-b \pm \sqrt{b^{2}-4ac } }{2a}[/tex]
In the given equation,
a = 1, b = -5, c = 2
Putting the values into the formula,
[tex]x =\frac{-(-5) \pm \sqrt{(-5)^{2}-4(1)(2) } }{2(1)}[/tex]
[tex]x =\frac{5 \pm \sqrt{25-8} }{2}[/tex]
[tex]x =\frac{5 \pm \sqrt{17} }{2}[/tex]
[tex]x =\frac{5 + \sqrt{17} }{2}[/tex] OR [tex]x =\frac{5 - \sqrt{17} }{2}[/tex]
[tex]x =\frac{5 + 4.12}{2}[/tex] OR [tex]x =\frac{5 - 4.12}{2}[/tex]
[tex]x =\frac{9.12}{2}[/tex] OR [tex]x =\frac{0.88}{2}[/tex]
x = 4.56 OR x = 0.44
Hence, the roots of the equation is x = 4.56 OR x = 0.44
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In order to pass an exam, a student must answer 70% of the questions correctly. If answering 42 questions correctly results in a 70% score, how many questions are on the test?
Answers
There are 60 questions on the test
Calculating percentagesTotal number of questions = 42
Percentage equivalent= 70%
Let the total number of questions in the test be represented by x
42 = 70% of x
[tex]42=\frac{70}{100} \times x[/tex]
42 = 0.7x
Divide both sides by 0.7
42/0.7 = 0.7x/0.7
x = 60
Therefore, there are 60 questions on the test
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your restaurant serves 50 bowls of French onion soup daily and each serving has 8 ounces of onion per portion. Do you think it would be better to purchase whole onions at $1.99 per pound, and cut them yourself, or purchase pre-sliced onions at $2.99 per pound?
Answers
I would be better to purchase whole onions at $1.99 per pound, and cut them yourself
Optimization of costNumber of bowls = 50
Weight of each bowl = 8
Total weight of the onion soup = 8 x 50 = 400 ounces
Note that:
1 pound = 16 ounces
Total weight in pounds = 400/16
Total weight in pounds = 25 pounds
If you buy the whole onions and purchase at $1.99 per pound
Total cost = 25 x 1.99 = $49.75
If you purchase pre-sliced onions at $2.99 per pound
Total cost = 25 x $2.99 = $74.75
Since it is cheaper to purchase whole onions at $1.99 per pound, it is the better choice
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Find the interest rate for a principal of $6514 and charged $45415 in interest for 15 years.
Answers
Answer:
the answer is 46.47937775048613
3. Make a conjecture about the sum of two even numbers based on the following pattern:
12 = 4 + 8
26 = 6 + 20
48 = 16 + 32
72 = 24 + 48
88 = 36 x 52
and so on.
Answers
The conjecture we can use is that the sum of all even numbers is an even number.
How to write Mathematical Conjectures?We are given the sum of two even numbers as follows;
12 = 4 + 8
26 = 6 + 20
48 = 16 + 32
72 = 24 + 48
88 = 36 x 52
From the above, we see that they are all even numbers and as such the conjecture we can use is that the sum of all even numbers is an even number.
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A zoo has a black rhinoceros that weighs 18 times as much as an average-size chimpanzee. The rhinoceros weighs 2,250 pounds.
How much does an average-size chimpanzee weigh?
Enter the answer in the box. [_]
Answers
Answer: 125 pounds
Step-by-step explanation:
Let's first represent the weight of the black rhinoceros and chimpanzee with variables. We will assign r for the rhinoceros and c for the chimpanzee.
In the question, we were given that the weight for a black rhinoceros is 18 times as much as an average-size chimpanzee. This makes 18 times the chimpanzee's weight equal to the rhinoceros' weight.
Let's put this into an equation.
[tex]r=18*c[/tex]
Now, let's put in the values we know to find the weight of the chimpanzee (i.e., c). We know the weight of a rhinoceros (represented by r) is 2250 pounds, so we can replace it for r in the equation.
[tex]2250=18*c[/tex]
To solve this equation, we can divide both sides by 18 to get c by itself and know what it's value is.
[tex]\frac{2250}{18}=\frac{18*c}{18}[/tex]
We can remove the [tex]\frac{18}{18}[/tex] from the right side to be left with c. We can also divide 2250 by 8 to get the weight of an average-size chimpanzee.
[tex]c=\frac{2250}{18}\\ c=125[/tex]
Hence, an average-size chimpanzee weighs 125 pounds.
Find the first 10 terms of the sequence below :
g) the sequence whose terms are constructed sequen tially as follows: start with 1, then add 1, then mul
tiply by 1, then add 2, then multiply by 2, and so on
h) the sequence whose nth term is the largest integer k
such that k!
Answers
The first ten terms of the sequence are 1, 2, 8, 33, 148, 765, 4626, 32431, 259512, 2335689.
The n-th term of the sequence is aₙ ₊ ₁ = (aₙ + 1) · n.
How to generate the elements of a sequence
A sequence is a set of elements generated by at least one condition, usually an equation. In this case, the sequence is generated by a recurrence formula:
a₁ = 1, aₙ ₊ ₁ = (aₙ + 1) · n (1)
The first ten terms of the sequence are:
n = 1
a₂ = (a₁ + 1) · 1
a₂ = 2
n = 2
a₃ = (a₂ + 2) · 2
a₃ = 4 · 2
a₃ = 8
n = 3
a₄ = (a₃ + 3) · 3
a₄ = 11 · 3
a₄ = 33
n = 4
a₅ = (a₄ + 4) · 4
a₅ = 37 · 4
a₅ = 148
n = 5
a₆ = (a₅ + 5) · 5
a₆ = 153 · 5
a₆ = 765
n = 6
a₇ = (a₆ + 6) · 6
a₇ = (765 + 6) · 6
a₇ = 4626
n = 7
a₈ = (a₇ + 7) · 7
a₈ = 4633 · 7
a₈ = 32431
n = 8
a₉ = (a₈ + 8) · 8
a₉ = 32439 · 8
a₉ = 259512
n = 9
a₁₀ = (a₁₀ + 9) · 9
a₁₀ = 259521 · 9
a₁₀ = 2335689
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The graph of f(x) = x3 − 7x − 6 is shown.
Based on the graph, what are all of the solutions to f(x) = x3 − 7x − 6?
x = −6
x = −2, −1
x = −2, −1, 3
x = −6, −2, −1, 3
Answers
In accordance with the graph of the cubic function, the roots are - 2, - 1, 3.
What are the roots of a cubic equation according to a graph?
In this question we have a graph of a cubic equation, the roots are the points of the curve that pass through the x-axis. Cubic equations have at least a real root and at most three. In accordance with the graph of the cubic equation, the roots are - 2, - 1, 3.
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!!GIVING BRAINLISET!! HELP IF ANYONE CAN
SOLVE THIS FOR ME 1-7 JUST ANSWERS
Answers
The solution to the given polynomial in their degree are:
5m²p³ + 6 - binomial5q^-4 + 6q - binomial7ab + 6b² - 2a³ - TrinomialPolynomial5m²p³ + 6 - binomial5q^-4 + 6q - binomial7ab + 6b² - 2a³ - Trinomial2a + 4a³ - 5a² - 1
= 4a³ - 5a² + 2a - 1
The leading coefficient is 4a³
4z - 2z² - 5z⁴
= -5z⁴ - 2z² + 4z
The leading coefficient is -5z⁴
(-3d² - 8 + 2d) + (4d - 12 + d²)
= -3d² - 8 + 2d + 4d - 12 + d²
= -2d² + 6d - 20
(y + 5) + (2y + 4y² - 2)
= y + 5 + 2y + 4y² - 2
= 4y² + 3y + 3
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18. Sam retires in 1996. He has an amount of R350 000 available to invest. He decides to buy a second house for 50% of the money, which he lets at an amount of R2000 per month. He increases the rent every year by an amount of R300. The balance of R175 000 he invests in the bank at a rate of 12%. He uses the interest every month to supplement his income, so the interest is not compounded. He also gets a pension of R3000 per month, which is increased by R300 per month every year. What was his monthly income in 1996? (1)
Answers
If Sam had Rs. 350000 and invested Rs.175000 in house, in bank Rs.175000 and getting 3000 pension then the monthly income was Rs. 6750.
Given that Sam had Rs.350000,investment in house Rs.175000 at a rent of Rs.2000 per month and Rs.175000 in bank at rate of 12%, getting pension of Rs.3000 per month.
We are required to find the monthly income in 1996.
We have assumed that Sam was retired on 1st January, 1996 so the amount of rent, investment in bank and pension did not increase because they had to be increase in a year and we have to calculate the monthly income in which he was retired.
Monthly income=Rent of 1 month+Simple interest of 1 month+Pension per month
=2000+175000*1/100+3000
=2000+1750+3000
=Rs.6750
Hence if Sam had Rs. 350000 and invested Rs.175000 in house, in bank Rs.175000 and getting 3000 pension then the monthly income was Rs. 6750.
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How much should be invested now at an interest rate of 6.5% per year, compounded continuously, to have $1500 in two years?
Do not round any intermediate computations, and round your answer to the nearest cent.
If necessary, refer to the list of financial formulas.
Answers
Answer:
$1317.14
Step-by-step explanation:
compounded continuously formula is A=Pe^rt
given that you want to have $1500 in 2 years while the rate is 6.5%, you have A, r, and t of the formula and you are just looking for the P.
plugging everything in...
1500=P (e)^2x0.065
P=1500/1.139
P=1317.14
Question
n⃗ =⟨−2, −1⟩ and D=[−4423].
What is D⋅n⃗ ?
Enter your answer as a vector by filling in the boxes.
Answers
The dot product of the D⋅n is 32.
According to the statement
We have given the value of n vector and d matrix and we have to find the dot product of these.
So, For this purpose,
The given values:
n = {-2,-1} and D = [−4423].
The dot product or scalar product is an algebraic operation that takes two equal-length sequences of numbers, and returns a single number.
So, The d matrix become
[tex]D = \left[\begin{array}{cc}-4&4&\\2&3&\\\end{array}\right][/tex]
Now solve it with the help of multiplication then the matrix become
D = (-12, -8)
and n = {-2,-1}
Now multiply both terms with the dot product.
So, the dot product of the both terms will become
D.n = 24 +8
Then
The output of the dot product of both terms is 32.
So, The dot product of the D⋅n is 32.
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lim x→-1 x^m + 1/x^n + 1
Answers
I assume [tex]m,n[/tex] are integers to avoid (ir)rational powers of -1.
If [tex]m,n[/tex] are both even, or if [tex]m=n[/tex], then
[tex]\displaystyle \lim_{n\to-1} \frac{x^m+1}{x^n+1} = \frac{1+1}{1+1} = 1[/tex]
If [tex]m,n[/tex] are both odd and [tex]m\neq n[/tex], then we can factorize
[tex]\dfrac{x^m+1}{x^n+1} = \dfrac{(x+1)(x^{m-1} - x^{m-2} + \cdots - x + 1)}{(x+1)(x^{n-1}-x^{n-2}+\cdots-x+1)}[/tex]
Note that there are [tex]m[/tex] terms in the numerator and [tex]n[/tex] terms in the denominator.
In the limit, the factors of [tex]x+1[/tex] cancel and
[tex]\displaystyle \lim_{x\to-1} \frac{x^m+1}{x^n+1} = \lim_{x\to-1} \frac{x^{m-1} - x^{m-2} + \cdots - x + 1}{x^{n-1}-x^{n-2}+\cdots-x+1} \\\\ ~~~~~~~~~~~~~~~~~~= \dfrac{1-(-1)+1-(-1)+\cdots-(-1)+1}{1-(-1)+1-(-1)+\cdots-(-1)+1} \\\\ ~~~~~~~~~~~~~~~~~~=\frac{1+1+\cdots+1}{1+1+\cdots+1} = \dfrac mn[/tex]
If [tex]m[/tex] is even and [tex]n[/tex] is odd, then we can only factorize the denominator and the discontinuity at [tex]x=-1[/tex] is nonremovable, so
[tex]\displaystyle \lim_{x\to-1}\frac{x^m+1}{x^n+1} = \lim_{x\to-1} \frac{x^m+1}{(x+1)(x^{n-1}-x^{n-2}+\cdots-x+1)} \\\\ ~~~~~~~~~~~~~~~~~~= \frac2m \lim_{x\to-1} \frac1{x+1}[/tex]
which does not exist.
If [tex]m[/tex] is odd and [tex]n[/tex] is even, then we can factorize the numerator so that
[tex]\displaystyle \lim_{x\to-1}\frac{x^m+1}{x^n+1} = \lim_{x\to-1} \frac{(x+1)(x^{m-1}-x^{m-2} +\cdots -x+1)}{x^n+1} \\\\ ~~~~~~~~~~~~~~~~~~= \frac{0m}2 = 0[/tex]
1. Quadratics.
The path of the longest shot put by the Women's track team at Sun Devil U is modeled by h(x) = -0.017x² + 1.08x + 5.8, where x represents the horizontal distance from the start and h(x) is the height of the shot put above the ground. (Both x and h(x) are measured in feet.)
a. 4 points. Determine h(24). Round your answer to 2 decimal places. Then explain what your answer means in the context of the problem. ("In the context of the problem" means "in terms of the shot put's horizontal distance from the start and in terms of the height of the shot put above the ground.")
b. 4 points. Determine the numerical value of the vertical intercept and explain what this means in the context of the problem.
c. 4 points. Determine the numerical values of the vertex coordinates and explain what they mean in the context of the problem.
d. 4 points. How far from the start did the shot put strike the ground? Round your answer to 2 decimal places.
Answers
h(24) = 21.93, vertical intercept is 5.8, (31.76,22.95) are the vertex coordinates and the distance traveled by the shot is 73.49 feet given the equation of the path of the longest shot h(x) = -0.017x² + 1.08x + 5.8. This can be obtained by understanding the concepts of graph function.
What is the value of h(24)?Given,
h(x) = -0.017x² + 1.08x + 5.8
Put h = 24,
h(24) = -0.017(24)² + 1.08(24) + 5.8
h(24) = -9.792 + 25.92 + 5.8
h(24) = 21.93
The height of the shot put above the ground is 21.93 feet when the shot is 24 feet horizontally from the start.
What is the value of the vertical intercept?Vertical intercept, x = 0
h(0) = -0.017(0)² + 1.08(0) + 5.8
h(0) = 5.8
The height of the shot put above the ground is 5.8 feet at the start.
What is the values of the vertex coordinates?vertex coordinates,
(h,k) = [(-b/2a),-(b²- 4ac)/4a]
(h,k) = [(-1.08/2(-0.017)),-((1.08)²- 4(-0.017)(5.8))/4(-0.017)]
(h,k) = [(1.08/0.034),(1.5608)/0.068)]
(h,k) = (31.76,22.95)
The maximum height attained by the shot is 22.95 feet when it is horizontally 31.76 feet away from the start.
How far from the start did the shot put strike the ground?Put h(x) = 0,
-0.017x² + 1.08x + 5.8 = 0
Use quadratic formula for solving x,
x = (-b±√b²- 4ac)/2a
Here a = -0.017, b=1.08, c=5.8
x = [-1.08±√1.08²- 4(-0.017)(5.8)]/(2×-0.017)
x = [-1.08±√1.5608]/-0.034
x = [-1.08-1.2493]/-0.034 and x = [-1.08+1.2493]/-0.034
x = 68.509 and x = - 4.98
Distance between (68.509,0) and (- 4.98,0) = √[68.509 -(- 4.98)]² + (0-0)²
= √73.49²
= 73.49 feet
Hence h(24) = 21.93, vertical intercept is 5.8, (31.76,22.95) are the vertex coordinates and the distance traveled by the shot is 73.49 feet given the equation of the path of the longest shot h(x) = -0.017x² + 1.08x + 5.8.
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Click to select points on the graph.
104
-10
-8
The solution is
-6
-4
-2
8
6
4
2
-2
4
6
-8
-104
2
4
y = -2x + 1
6
8
10
ha
Answers
Answer: [tex](-2, 5)[/tex]
Step-by-step explanation:
The graphs are shown in the attached image.
The solution is where they intersect.
The solution to the system of equations is x = -2 and y = 5.
i.e
The solution is = (-2, 5)
We have,
To find the solutions, you need to set the two equations equal to each other because they both represent the same variable "y."
So, you'll have:
(-7/2)x - 2 = -2x + 1
Now, let's solve for x:
Step 1:
Get rid of the fractions by multiplying both sides by 2:
2 * ((-7/2)x - 2) = 2 * (-2x + 1)
This simplifies to:
-7x - 4 = -4x + 2
Step 2:
Isolate the x terms on one side of the equation.
Let's move the -4x to the left side by adding 4x to both sides:
-7x - 4 + 4x = -4x + 4x + 2
This simplifies to:
-3x - 4 = 2
Step 3:
Now, isolate the constant term by moving the -4 to the right side by adding 4 to both sides:
-3x - 4 + 4 = 2 + 4
This simplifies to:
-3x = 6
Step 4:
Finally, solve for x by dividing both sides by -3:
x = 6 / -3
x = -2
Now that you've found the value of x, plug it back into either of the original equations to find the corresponding y value.
Let's use the first equation y = (-7/2)x - 2:
y = (-7/2) * (-2) - 2
y = 7 - 2
y = 5
Thus,
The solution to the system of equations is x = -2 and y = 5.
i.e
(-2, 5)
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!!!!!!!!!!!!!!!!!!!!!!helpppppppo
Answers
Answer:
(3x3+3)*2
Step-by-step explanation:
Can you please help me with this?
Answers
Solving for the area.
Answers
Area
1/2(sum of parallel sides)height1/2(50+65)(30)1/2(115)(30)15(115)1150+5751725ft²Answer:
1725 ft²
Step-by-step explanation:
The formula to find the area of a trapezoid is :
Area = [tex]\frac{1}{2}[/tex] × ( sum of the parallel sides ) × height
Let us solve it now.
Area = [tex]\frac{1}{2}[/tex] × ( sum of the parallel sides ) × height
Area = [tex]\frac{1}{2}[/tex] × ( 65 + 50 ) × 30
Area = [tex]\frac{1}{2}[/tex] × ( 115 ) × 30
Area = [tex]\frac{1}{2}[/tex] × 3450
Area = 1725 ft²
Find the integrals:
∫30x^2/√(x-4) dx
u=x-4 and u=√(x-4)
Answers
I assume you're asked to compute
[tex]\displaystyle \int \frac{30x^2}{\sqrt{x-4}} \, dx[/tex]
using both of the substitutions provided.
With [tex]u=x-4[/tex], we have [tex]x=u+4[/tex] and [tex]dx=du[/tex]. Then
[tex]\displaystyle \int \frac{30x^2}{\sqrt{x-4}} \, dx = \int \frac{30(u+4)^2}{\sqrt u} \, du \\\\ ~~~~~~~~ = 30 \int \frac{u^2 + 8u + 16}{\sqrt u} \, du \\\\ ~~~~~~~~ = 30 \int \left(u^{3/2} + 8u^{1/2} + 16u^{-1/2}\right) \, du \\\\ ~~~~~~~~ = 30 \left(\frac25 u^{5/2} + \frac{16}3 u^{3/2} + 32 u^{1/2}\right) + C \\\\ ~~~~~~~~ = 12 u^{5/2} + 160 u^{3/2} + 960 u^{1/2} + C \\\\ ~~~~~~~~ = 12 (x-4)^{5/2} + 160 (x-4)^{3/2} + 960 (x-4)^{1/2} + C \\\\ ~~~~~~~~ = 4 \sqrt{x-4} \left(3 (x-4)^2 + 40 (x-4) + 240\right) + C \\\\ ~~~~~~~~ = \boxed{4 \sqrt{x-4} \left(3x^2 + 16x + 128\right) + C}[/tex]
With [tex]u=\sqrt{x-4}[/tex], we have
[tex]u^2 = x-4 \implies x^2 = (u^2+4)^2[/tex]
and [tex]2u\,du=dx[/tex]. Then
[tex]\displaystyle \int \frac{30x^2}{\sqrt{x-4}} \, dx = \int \frac{60u \left(u^2+4\right)^2}u \, du \\\\ ~~~~~~~~ = 60 \int \left(u^4 + 8u^2 + 16\right) \, du \\\\ ~~~~~~~~ = 60 \left(\frac15 u^5 + \frac83 u^3 + 16u\right) + C \\\\ ~~~~~~~~ = 12 (x-4)^{5/2} + 160 (x-4)^{3/2} + 960 (x-4)^{1/2} + C \\\\ ~~~~~~~~ = 4 \sqrt{x-4} \left(3 (x-4)^2 + 40 (x-4) + 240\right) + C \\\\ ~~~~~~~~ = \boxed{4\sqrt{x-4} \left(3x^2 + 16x + 128\right) + C}[/tex]
1. There are 50 contestants signed up for a TV show. There are 36 more female contestants than male contestants. How many female contestants have signed up to compete? Show your solution and explain how you plan to explain this to your students.
Answers
Answer:
males = 7
females = 43
Step-by-step explanation:
whilst it may seem intuitive to simply subtract 36 from 50, it is not saying "there are 36 males, how many females?" but instead, "the difference between the number of males and females is 36".
You can solve this equation most easily algebraically. For example:
Number of males = x
number of females = y
the question states that the total number of people = 50
therefore we can say that the total number of males (x) + the total number of females (y) = 50 people
therefore: x + y = 50
similarly, the question says that the number of males (x) + 36 = the total number of females (y)
therefore: x + 36 = y
we now have two equations:
x + y = 50
x + 36 = y
whilst both equations have two unknowns (x and y), therefore we can't simple solve for x or y, with the combination, we can see a pattern.
focusing on the second equation: x + 36 = y
we can add x to both sides, because you can pretty much do anything to the equation as long as you do it to both sides.
x + 36 + x = y + x
now this may seem very random, but you now see that one side of the equation equals y + x, and remember from the other equation, x + y = 50. Therefore we can substitute x + y in the second equation for 50.
our two equations:
x + 36 + x = y + x
x + y = 50
therefore:
x + 36 + x = 50
for the sake of clarity, we can combine like terms...
x + x = 2x
therefore:
x + 36 + x = 50
2x + 36 = 50
solve for x by subtracting 36 from both sides, then dividing both sides by 2
2x + 36 - 36 = 50 - 36
2x = 14
2x / 2 = 14 / 2
x = 7
now remember:
Number of males = 7 (we now know x = 7)
now that we've solved for x, we can go back to our original equation:
x + 36 = y
and substitute x...
7 + 36 = y
43 = y
Now remember:
Number of females = 43 (we now know y = 43)
therefore there are 7 males and 43 females. we can proof this by adding 7 and 43, and you'll see you reach 50, which is the correct total number of people.
hope this helps :)
A wire is stretched from the ground to the top of an antenna tower. The wire is 15 feet long. The height of the tower is 3 feet greater than the distance d from the tower's base to the end of the wire. Find the distance d and the height of the tower.
Answers
The distance d is 9 ft and the height is 12ft.
How to find the distance and the height?
Here we can model the situation with a right triangle, where the length of the wire is the hypotenuse.
The height is one cathetus and the distance is the other catheti.
Let's define:
h = heightd = distance.hypotenuse = 15ftWe know that the height of the tower is 3 ft larger than the distance, then:
h = d + 3ft
Now we can use the Pythagorean theorem, it says that the sum of the squares of the cathetus is equal to the square of the hypotenuse.
Then:
[tex]d^2 + (d + 3ft)^2 = (15ft)^2[/tex]
Now we can solve this equation for d:
[tex]d^2 + d^2 + 6ft*d + 9ft^2 = (15ft)^2\\\\2d^2 + 6ft*d - 216 ft^2 = 0\\\\d^2 + 3ft*d - 108ft^2 = 0[/tex]
Then the solutions are:
[tex]d = \frac{-3ft \pm \sqrt{(3ft)^2 - 4*(-108ft^2)} }{2} \\\\d = \frac{-3ft \pm 21ft }{2}[/tex]
We only take the positive solution:
d = (-3ft + 21ft)/2 = 9ft
And the height is 3 ft more than that, so:
h = 9ft + 3ft = 12ft
The distance d is 9 ft and the height is 12ft.
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solve the equation: z^ +4z+20+iz(a+1)=0 Where A is constant, has complex conjuget root. if one of roots this quadratic is z=B+2i?
Answers
The complex conjugate roots exists A = -1 - 4i or A = -1 + 12i.
How to estimate complex conjugate roots?
If one of the roots exists w = B + 2i, then the other root exists its conjugate w = B - 2i. So we can factorize the quadratic to
[tex]z^2+4z+20+iz(A+1) = (z-(B+2i))(z-(B-2i))[/tex]
Expand the right side and collect all the coefficients.
[tex]z^2+(4+(A+1)i)z+20 = z^2-2Bz+B^2+4[/tex]
From the z and constant terms, we have
[tex]$\left \{ {{4+(A+1)i = -2B} \atop {20 = B^2+4}} \right.[/tex]
From the second equation, we get
[tex]B^2 = 16[/tex]
B = ± 4
Then 4+(A+1)i = ± 8
(A + 1)i = 4 or (A + 1)i = -12
Since [tex]$\frac{1}{i} = -i[/tex], we have
[tex]$\frac{-A+1}{i} =4[/tex] or [tex]$\frac{-A+1}{i} =-12[/tex]
A+1 = -4i or A+1 = 12i
A = -1-4i or A = -1+12i
Therefore, the complex conjugate roots exists A = -1-4i or A = -1+12i.
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Write the slope-intercept form of the line that has a slope of 2 and intersects the line, 2x - 3y = 6 at x = 3. Include
your work in your final answer. Type your answer in the box provided to submit your solution.
Answers
Answer:
y= 2x -6
Step-by-step explanation:
The slope-intercept form of a line is given by y= mx +c, where m is the slope and c is the y-intercept.
To find the equation of a line, two information are needed:
Slope (given/ calculated)A pair of coordinatedGiven that the slope is 2, m= 2. Substitute m= 2 into y= mx +c:
y= 2x +c
Let's find the coordinate in which the line intersects the line 2x -3y= 6. Point of intersection refers to the point at which two lines cuts through each other i.e., the point lies on the graph 2x -3y= 6 and the line of interest.
2x -3y= 6
When x= 3,
2(3) -3y= 6
6- 3y= 6
3y= 6 -6
3y= 0
Divide both sides by 3:
y= 0
Coordinate that lies on the graph is (3, 0).
Substitute the point into the equation and solve for c:
y= 2x +c
When x= 3, y= 0,
0= 2(3) +c
0= 6 +c
c= -6
Substitute the value of c back into the equation:
Thus, the equation of the line in slope-intercept form is y= 2x -6.
Additional:
For a similar question on slope-intercept form, do check out the following!
https://brainly.com/question/28007941An equation is shown below: 8x + 2(x – 7) = 7x + 3x – 14 Part A: Solve the equation and write the number of solutions. Show all the steps. (6 points) Part B: Name one property you used to solve this equation. (4 points) Source StylesNormalFontSize
Answers
Answer:
Infinitely ManyDistributive PropertyStep-by-step explanation:
8x + 2(x - 7) = 7x + 3x - 14
8x + 2x - 14 = 7x + 3x - 14 Distributive property.
10x - 14 = 10x - 14 Combine the like terms.
-14 = -14 Subtraction.
0 = 0 Addition.
Since the statement 0 = 0 is true regardless of the value of x, there is infinitely many solutions.
8(x-1) >12-2x
O A. x>-/
X>
3
OB. x>7
OC. x>-5
O D. x>¹
3
Answers
Answer: x>2
Step-by-step explanation:
[tex]8(x-1) > 12-2x\\\\8x-8 > 12-2x\\\\10x-8 > 12\\\\10x > 20\\\\x > 2[/tex]
Use the diagram to determine which statement is true
Answers
The answer is d.
Finding area of ABCD :
Find side lengthside = √3² + 4²side = 52. Apply formula to find area
area = 5²area = 25Finding area of GHIA :
area = 4²area - 16Finding area of DEFG :
area = 3²area = 9Now, let's see whether is true.
Area (ABCD) - Area (GHIA) = Area (DEFG)25 - 16 = 99 = 9∴ Hence, it is proved √
Which figures demonstrate a translation?
Answers
The two bottom graphs demonstrate translations.
Which figures demonstrate a translation?
We will have a translation only if:
The size of the figure does not change (like in option 1, which we can discard).If the "direction" of the figure does not change, like in option 2, where you can see that there is a reflection.The images where the figures are only moved a little bit are the ones that demonstrate just a translation, and these are the two lower ones.
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Consider the diagram shown and answer the following questions; the radius of this circle is 6 inches.
a. Define how lines a, b, c, and d relate to circle P. (What special names do these lines have in relation to the circle?)
b. If the measure of angle OPS is 139°, what extra information would we need to calculate the measure of angle ORS using intersecting chords? Explain how we can use this information to calculate the angle.
c. Segment NS is 14 the length of segment TO. Explain how theorem 65 would allow us to calculate the length of segments RO, RS, RV, and RT.
Answers
The additional information needed to calculate ORS are the measures of SPR and PSR
The special names of the linesThe lines are given as:
Lines a, b, c and d
The special names of the lines are as follows:
Line a: A secant. This is because the line divides the circle into unequal segmentsLine b: A tangent: This is because the line touches the circle at a point on the circumferenceLine c: A diameter. This is because the line divides the circle into equal segmentsLine d: A secant. This is because the line divides the circle into unequal segmentsThe additional information neededThe angle is given as:
OPS= 139 degrees
Start by calculating SPR using
SPR = 180- 139
SPR = 41 degrees
So, the additional information needed to calculate ORS are the measures of SPR and PSR
How to calculate the lengths RO, RS, RV, and RTThe theorem 65 is not stated.
So, the question cannot be answered
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Help me please I’m not the smartest
Answers
x= 4 OR x=-4
The picture attached below is your answer because it’s between 4 and -4.
help!! How do I solve for x and what is x
Answers
Answer:
x=75 degrees
Step-by-step explanation:
since the shape is quadrilateral, all the angles added together should equal 360 degrees so you use 360 to subtract all the given angles on the shape and you can find X
360-131-107-47=75