Which of the following are true?
(check all that apply)
If you take any number and multiply it by i-squared the sign(s) will change
Any imaginary number can be written as a real number
If you take any real number and
multiply it by i-squared it will stay a real number
If you take any number and multiply it by i-squared nothing will change
Any real number can be written as an imaginary number
Answers
Statements 1, 3, and 4 are true, while statements 2 and 5 are false.
Among the given statements, the following are true:
1. If you take any number and multiply it by i-squared, the sign(s) will change.
This statement is true. The complex number i is defined as the square root of -1. When we multiply any real or complex number by i-squared, it is equivalent to multiplying it by -1. Multiplying by -1 changes the sign of the number.
3. If you take any real number and multiply it by i-squared, it will stay a real number.
This statement is also true. Multiplying any real number by i-squared is equivalent to multiplying it by -1. Since -1 is a real number, the result will also be a real number.
4. If you take any number and multiply it by i-squared, nothing will change.
This statement is false. Multiplying any number by i-squared results in a change because i-squared is equal to -1. The multiplication by -1 changes the sign of the number.
As for the remaining statements:
2. Any imaginary number can be written as a real number.
This statement is false. Imaginary numbers, which involve the imaginary unit i, cannot be written as real numbers because they do not have a real component. They can only be expressed in the form of a real number multiplied by i.
5. Any real number can be written as an imaginary number.
This statement is false. Real numbers do not have an imaginary component, so they cannot be written as imaginary numbers. Imaginary numbers have a unique form with the imaginary unit i in the expression.
To summarize, statements 1, 3, and 4 are true, while statements 2 and 5 are false.
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Related Questions
What kind of multi step do I have to do to prove a is parallel to b and m parallel to n.
Answers
The proof that line n is perpendicular to both a and b is proved below using definition of right angle and perpendicular transversal theorem.
How to prove Perpendicular and Parallel Lines?
We are given that;
Line a is parallel to line b
Line m is parallel to line n.
A) We want to prove that line a is perpendicular to n.
From the image, we see that there is a right angle sign on the opposite side of ∠1 facing m.
Now, we know that by definition of a right angle that ∠1 will also be a right angle.
Since angle 1 is a right angle, then we can say the line transversal a is perpendicular to line m.
B) We want to prove that line b is perpendicular to n.
The definition of the perpendicular transversal theorem, states that if a line is perpendicular to one of two parallel lines, then it is perpendicular to the other.
Thus, b will be perpendicular to n.
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Ringani worked overtime to raise a total amount R30 000.00 to settle his student debt. If he has deposited R8 500.00 yearly into an account earning 7,04% interest per year compounded annually. How long, rounded to one decimal place did it took her to accumulate the total amount? A. 3.0 years B. 2.4 years C. 2.8 years D. 2.0 years
Answers
It took Ringani 2.8 years to accumulate the total amount of R30,000.00 by depositing R8,500.00 yearly into the account with a 7.04% interest rate Compounded annually.The correct answer choice is C. 2.8 years.
To determine how long it took Ringani to accumulate the total amount of R30,000.00 by depositing R8,500.00 yearly into an account with a 7.04% interest rate compounded annually, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A is the final amount
P is the principal amount (initial deposit)
r is the interest rate (in decimal form)
n is the number of times the interest is compounded per year
t is the time in years
In this case, we have:
P = R8,500.00
A = R30,000.00
r = 7.04% = 0.0704 (in decimal form)
n = 1 (compounded annually)
We want to find the value of t.
Using the formula, we can rearrange it to solve for t:
t = (log(A/P)) / (n * log(1 + r/n))
Substituting the given values, we have:
t = (log(30,000/8,500)) / (1 * log(1 + 0.0704/1))
Calculating this using a calculator, we find that t is approximately 2.8 years.
Therefore, it took Ringani approximately 2.8 years (rounded to one decimal place) to accumulate the total amount of R30,000.00 by depositing R8,500.00 yearly into the account with a 7.04% interest rate compounded annually.
The correct answer choice is C. 2.8 years.
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m grade> Y.4 Area and perimeter: word problems JFR
A rectangular garage is 6 meters wide and 7 meters long. What is its perimeter?
Answers
Answer:
26 meters
Step-by-step explanation:
To solve the perimeter you need to know the formula which is 6 + 7 x 2 and you get 26 meters
Consider the following matrix 2 0 3 A= 1 3 0 0 0 4 a) Compute the eigenvalues of A b) Compute a basis for each eigenspace associated to each distinct eigenvalue of A c) Determine if A is diagonalizable, if it is, compute a diagonalization of A
Answers
Answer:
c) To determine if A is diagonalizable, we need to check if there are enough linearly independent eigenvectors to form a basis for the vector space. In this case, we have two distinct eigenvalues, λ = 2 and λ = 3.
Step-by-step explanation:
To compute the eigenvalues of matrix A, we need to find the values of λ that satisfy the equation (A - λI)x = 0, where I is the identity matrix.
The matrix A - λI is given by:
A - λI =
2 - λ 0 3
1 3 - λ 0
0 0 0
To find the eigenvalues, we set the determinant of A - λI equal to zero and solve for λ:
det(A - λI) =
(2 - λ)((3 - λ)(0) - (0)(0)) - (0)((1)(0) - (0)(3 - λ))
= (2 - λ)(3 - λ) = 0
Expanding and simplifying the expression, we have:
(2 - λ)(3 - λ) = 0
λ^2 - 5λ + 6 = 0
Factoring the quadratic equation, we get:
(λ - 2)(λ - 3) = 0
Setting each factor equal to zero gives us two eigenvalues:
λ - 2 = 0 --> λ = 2
λ - 3 = 0 --> λ = 3
a) The eigenvalues of matrix A are λ = 2 and λ = 3.
To compute the eigenvectors associated with each eigenvalue, we solve the equations (A - λI)x = 0.
For λ = 2:
(A - 2I)x =
(2 - 2) 0 3
1 3 - 2 0
0 0 0
Simplifying the matrix equation, we have:
0 0 3
1 1 0
0 0 0
From the row reduced echelon form, we can see that x1 and x2 are free variables. Solving the equation, we get:
x1 = -3x3
x2 = x3
Therefore, the eigenvector associated with λ = 2 is:
v1 = [x1, x2, x3] = [-3x3, x3, x3] = x3[-3, 1, 1]
For λ = 3:
(A - 3I)x =
(2 - 3) 0 3
1 3 - 3 0
0 0 0
Simplifying the matrix equation, we have:
-1 0 3
1 0 0
0 0 0
From the row reduced echelon form, we can see that x2 and x3 are free variables. Solving the equation, we get:
x1 = 3x3
x2 = x2
x3 = x3
Therefore, the eigenvector associated with λ = 3 is:
v2 = [x1, x2, x3] = [3x3, x2, x3] = x2[0, 1, 0] + x3[3, 0, 1]
b) A basis for the eigenspace associated with λ = 2 is {[-3, 1, 1]}.
A basis for the eigenspace associated with λ = 3 is {[0, 1, 0], [3, 0, 1]}.
c) To determine if A is diagonalizable, we need to check if there are enough linearly independent eigenvectors to form a basis for the vector
1
2.
3
5 5
6
8
9
12
13
10-
8
6
909
NS
2
-6 -5 -4 -3 -2 -1 1 2 3 4
1 2 3 4 5 6 X
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-141
1 1 1
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f(4) = g(4)
Of(4) = g(-2)
O f2) = g(-2)
Of(-2) = g(-2)
Mark this and return
Answers
Answer: f(-3)=g(-3)
Step-by-step explanation:
The graphs intersect at x = -3.
The correct option is f(-3) = g(-3).
What is function?A function is a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.
Given that two lines are intersecting at point (-3, -4)
Therefore the system of equations of these two have a solution at (-3, -4)
So, if taking the lines as function,
We have f(x) and g(x),
so both of them are intersecting at (-3, -4) so the range when the domain is -3 will be equal.
Hence the correct option is f(-3) = g(-3).
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please help me asapp
Answers
Answer:
C. 12, 8, 5
Step-by-step explanation:Side lengths of any triangle must conform to the triangle inequality theorem, which says that the sum of the lengths of any of the two sides of the triangle is greater than the length of the third side.
This means:
a + b > c
a + c > b
b + c > a
Let's check each of the options to see which set are possible lengths for a triangle:
A. 6, 5, 11
6 + 11 > 5 ===> 17 > 5
5 + 11 > 6 ===> 16 > 6
6 + 5 > 11 ===> 11 > 11 (INCORRECT. Does not confirm to tye theorem)
Therefore, this set cannot be possible side lengths for a triangle.
B. 8, 1, 2
8 + 1 > 2 ===> 9 > 2
1 + 2 > 8 ===> 3 > 8 (INCORRECT)
8 + 2 > 1 ===> 10 > 1
This set cannot be possible side lengths for a triangle.
C. 12, 8, 5
12 + 8 > 5 ===> 20 > 5
8 + 5 > 12 ===> 13 > 12
12 + 5 > 8 ===> 17 > 8
All are correct, therefore these are possible side lengths for a triangle.
10(x + 4) = (2x-1) + 4
Answers
Answer:
x = -4 5/8
Step-by-step explanation:
Solved it and got that answer
Answer:
x = -37/8 or
= -4 5/8 or
= -4.625
Step-by-step explanation:
First use distributive property on the left side. We don't even need the parenthesis on the right side, so we'll disappear those also.
10(x + 4) = (2x-1) + 4
10x + 40 = 2x - 1 + 4
Simplify the right side.
10x + 40 = 2x + 3
subtract 2x from both sides.
8x + 40 = 3
subtract 40 from both sides.
8x = -37
divide both sided by 8
x = -37/8
This is a perfectly good answer. Its neat and exact. But maybe you want a mixed number instead.
x = -4 5/8
(that's negative4 and 5/8s)
then also maybe you want you answer in decimal form
x = -4.625
This is also neat and exact.
the answer for these questions
Answers
The triangles are similar by SSS congruence of triangles.
What is SSS congruence of triangles?
The two triangles are congruent if the three sides of one triangle are the same as the corresponding three sides (SSS) of the other triangle.
We are given two triangle ABC and PQR.
In order to see whether these are similar or not, we will use the SSS congruence of triangles.
The ratio of sides are:
⇒AB : PQ = 8 : 6
⇒AB : PQ = 4 : 3
Similarly,
⇒BC : QR = 12 : 9
⇒BC : QR = 4 : 3
Similarly,
⇒AC : PR = 12 : 9
⇒AC : PR = 4 : 3
Since, the ratio of all the sides is same so, the triangles are similar.
Hence, the triangles are similar by SSS congruence of triangles.
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Since, there are multiple questions so, the question answered above is attached below
How do you solve this??
21 a(little 6) b(little 5)
————————————
7 a(little 3) b
Answers
\((21a^6b^5) / (7a^3b)\) simplifies to \(3a^3b^4.\)
To solve this problemWe can use the rules of exponents and simplify the terms with the same base.
Dividing the coefficients: 21 / 7 = 3.
For the variables, you subtract the exponents: \(a^6 / a^3 = a^(^6^-^3^) = a^3.\)
Similarly,\(b^5 / b = b^(5-1) = b^4\).
Putting it all together, the simplified expression is:
\(3a^3b^4.\)
Therefore, \((21a^6b^5) / (7a^3b)\) simplifies to \(3a^3b^4.\)
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Select the correct answer. Which value of x makes this equation true? -12x - 2(x + 9) = 5(x+4)
Answers
Answer: x= -2/9
Step-by-step explanation:
-12x-2(x+9)=5(x+4)
= -12x-2x+18=5x+20
= -14x+18=5x+20
= -9x+18=20
= -9x=2
/-9 /-9
x= -2/9
300 words in 4 minutes
a. 80 words per minute
b. 75 words per minute
c. 70 words per minute
d. 134 words per minute
Answers
state , giving reasons, which of the following if meaningless:
a. (-12, 0 ]
b. ( 1, -13 ]
Answers
Both of the intervals given are meaningful intervals in mathematics, but they are different types of intervals.Therefore, the interval (1, -13] is meaningless because it does not contain any real numbers.
What is intervals?An interval is a number or range of values between two endpoints.
The endpoints can be included or excluded from the interval, and the interval can be open, closed, or half-open depending on whether the endpoints are included or excluded.
The interval (-12, 0] is a closed interval, which includes the endpoint 0, and all real numbers between -12 and 0.
The square bracket indicates that the endpoint 0 is included in the interval.
The interval (1, -13] is an empty interval, which includes no real numbers, since there is no number that is greater than 1 and less than or equal to -13. This interval is meaningless because it does not contain any numbers.
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In a survey of 2266 adults, 736 say they believe in UFOs. Construct a 90% confidence interval for the population proportion of adults who believe in UFOs. A 90% confidence interval for the population proportion is ( ?, ?).
(Round to three decimal places as needed.)
Part 2
Interpret your results. Choose the correct answer below.
A.
With 90% probability, the population proportion of adults who do not believe in UFOs is between the endpoints of the given confidence interval.
B.
The endpoints of the given confidence interval shows that 90% of adults believe in UFOs.
C.
With 90% confidence, it can be said that the population proportion of adults who believe in UFOs is between the endpoints of the given confidence interval.
D.
With 90% confidence, it can be said that the sample proportion of adults who believe in UFOs is between the endpoints of the given confidence interval.
Answers
The 90% confidence interval for the population proportion of adults who believe in UFOs is (0.309, 0.339).
C. With 90% confidence, it can be said that the population proportion of adults who believe in UFOs is between the endpoints of the given confidence interval.
To construct a 90% confidence interval for the population proportion of adults who believe in UFOs, we can use the formula:
Confidence Interval = Sample Proportion ± Margin of Error
First, we calculate the sample proportion:
Sample Proportion \(\hat{p}\) = Number of adults who believe in UFOs / Total number of adults surveyed = 736 / 2266 ≈ 0.324
Next, we need to calculate the margin of error.
Since we are dealing with a large sample size, we can use the formula for a 90% confidence interval:
Margin of Error\(= Z \times \sqrt{(\hat{p} \times (1 - \hat{p}) / n)}\)
Here, Z represents the z-value for a 90% confidence level, which corresponds to a z-value of 1.645. n represents the sample size.
Margin of Error\(= 1.645 \times \sqrt{(0.324 \times (1 - 0.324) / 2266)}\) ≈ 0.015
Finally, we can construct the confidence interval:
Confidence Interval = 0.324 ± 0.015 = (0.309, 0.339)
Therefore, the 90% confidence interval for the population proportion of adults who believe in UFOs is (0.309, 0.339).
Now, let's interpret the results.
The correct answer is:
C. With 90% confidence, it can be said that the population proportion of adults who believe in UFOs is between the endpoints of the given confidence interval.
This means that we are 90% confident that the true proportion of adults who believe in UFOs falls within the range of 0.309 to 0.339.
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The air temperature, T , is related to the number of times, N , that a cricket chirps in a minute. The equation for that relationship is T=40 +1/4 N, where T is measured in degrees Fahrenheit. When the number of cricket chirps per minute increases by 20, , by how much has the temperature changed?
Answers
Answer:
heart me for answer no scam
Step-by-step explanation:
I need help with this problem
Answers
The value of x and y in the cyclic quadrilateral are 15 and 3 respectively.
How to find the angles of a cyclic quadrilateral?A cyclic quadrilateral is a four sided shape that can be inscribed into a circle. The sum of angles in a cyclic quadrilateral is 360 degrees.
Opposite angles of a cyclic quadrilateral is supplementary.
Hence,
6x - 8 + 31y + 5 = 180
6x + 31y = 183
26y + 5 + 6x + 7 = 180
26y + 6x = 168
6x + 26y = 168
Combine the equation
6x + 31y = 183
6x + 26y = 168
subtract the equation
5y = 15
divide both sides by 5
y = 15 /5
y = 3
6x + 31(3) = 183
6x = 183 - 93
6x = 90
divide both sides by 6
x = 90 / 6
x = 15
Therefore,
x = 15 and y = 3
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Does anyone know this answer??
Answers
Approximately 99.7% of scores lie in the shaded region.
We have,
The empirical rule, also known as the 68-95-99.7 rule, provides an estimate of the percentage of scores that lie within a certain number of standard deviations from the mean in a normal distribution.
According to this rule:
Approximately 68% of scores lie within 1 standard deviation of the mean.
Approximately 95% of scores lie within 2 standard deviations of the mean.
Approximately 99.7% of scores lie within 3 standard deviations of the mean.
Now,
In the given scenario, the shaded region represents the area between -2 and 3 standard deviations from the mean on the x-axis.
This encompasses the area within 3 standard deviations of the mean.
And,
Since 99.7% of scores lie within 3 standard deviations of the mean, we can estimate that approximately 99.7% of scores lie in the shaded region.
Therefore,
Approximately 99.7% of scores lie in the shaded region.
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help me asap. my exam is tomorrow.
Answers
The total surface area of the doghouse is 1452 ft²
What is surface area?The area occupied by a three-dimensional object by its outer surface is called the surface area.
The dog house has many surfaces including the roofs . The total surface area is the sum of all the area of the surfaces.
area of the roof part = 2( 13×11) + 2( 12× 10)×1/2
= 286 + 720
= 1006 ft²
surface area of the building
= 2( lb + lh + bh) -bh
= 2( 10× 11 + 10×8 + 11×8) - 10×11
= 2( 110+80+88)-110
= 2( 278) -110
= 556 -110
= 446ft²
The total surface area = 1006 + 446
= 1452 ft²
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Which of the following is the solution to lx+11| < 17 ?
O A. x<60x>-28
B. < 6 and x>-28
O c. x< 6 and x < -28
OD. *<5
Answers
Answer:
B. x < 6 and x > -28
Step-by-step explanation:
|x + 11| < 17
-17 < x + 11 < 17
Subtract 11 from all 3 sides.
-28 < x < 6
x > -28 and x < 6
if angle poa is a right angle and if measure of angle coa is three times as large as measure angle poc.
Answers
The angles COA and POC are 22.5 and 67.5 degrees respectively as POA is a right angled triangle.
POA is a right angle so it is 90 degrees.
POC +COA = 90 .....(1)
Also, POC is 3 times as large as COA.
Let's take COA, "x"
POC = 3x
Substituting the values in equation (1) as follows:
x + 3x = 90
4x = 90
x= 22.5
Therefore,
COA = 22.5°
POC = 22.5*3 = 67.5°
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A basketball team lost 10% of the games they played. They played 30 games in all. How many games did they win?
Answers
Answer:
They won 27 games
Step-by-step explanation:
10% of 30 is 3,
so 30-3= 27
I NEED HELP ASAP PLEASE GIVING BRAINLIEST!!
Answers
Answer:
35 more video games
Step-by-step explanation:
40 times 3 and then substract 85
120-85=35
Help!! Ya girl is struggling
Answers
the 3 one is the correct answer (1,3) (3
A child care center has three rooms, and the same number of children are in each room. If c children attend the center, write an algebraic expression that represents the number of children in each room.
Answers
Answer:
Number of children in each room = c / 3
Step-by-step explanation:
Given:
Number of rooms in care center = 3
Number of children attend the center = c
Find:
Number of children in each room
Computation:
Number of children in each room = Number of children attend the center / Number of rooms in care center
Number of children in each room = c / 3
Use the Law of Detachment to draw a conclusion from the two given statements. If two angles are complementary, then the sum of their measures is 90°. E and F are complementary.
Answers
Using the law of detachment, the conclusion we can draw from the two given statements is: C. m∠E + m∠F = 90°.
What is the Law of Detachment?The law of detachment states that, if two statements are true, a third statement that is true can be derived also.
From the information given, we have:
First statement: If 2 angles are complementary, then their sum equals 90 degrees (If p, then q).
Second statement: Angles E and F are complementary (p).
The third true statement (q) would be:
m∠E + m∠F = 90°. (option C)
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A software development company is voting to elect a president, a secretary, a treasurer, and three directors. If a total of 11 qualified candidates applied for these positions, in how many ways can the positions be filled?
Answers
The ways to elect the candidates from the total is 462
How to determine the ways of selection?From the question, we have
Total number of candidate, n = 11Numbers to selection, r = 6 i.e. the president, a secretary, a treasurer, and three directorsThe number of ways of selection could be drawn is calculated using the following combination formula
Total = ⁿCᵣ
Where
n = 11 and r = 6
Substitute the known values in the above equation
Total = ¹¹C₆
Apply the combination formula
ⁿCᵣ = n!/(n - r)!r!
So, we have
Total = 11!/5!6!
Evaluate
Total = 462
Hence, the number of ways is 462
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grade 11 2022 June common test mathematics memorandum?
Answers
Note that the roots of the equation Unequal and rational (Option D)
How is this so ?The roots of the equation (x - 3)² = 4 can be found by taking the square root of both sidesof the equation.
x - 3 = ±√4
⇒ x - 3 = ±2
Solve for x
For the positive square root.
x - 3 = 2
x = 2 + 3
x = 5
For the negative square root.
x - 3 = -2
x = -2 + 3
x = 1
Since the equation has two roots, x = 5 and x = 1. These roots are unequal and rational. (Option D)
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Full Question:
Although part of your question is missing, you might be referring to this full question:
The roots of the equation (x - 3)² = 4 are
A.Unequal and irrational.
B.Equal and rational.
C. Equal and irrational.
D. Unequal and rational.
Mount Whitney is 3072m tall. Convert the height to kilometers.
Answers
What is the slope of the line through (2,-2)(2,−2)
Answers
Answer: 0. the line is not determine because both points have the same coordinates.
Step-by-step explanation:
m = (y-y)/(x-x)
m = (- 2 - -2)/(2 - 2)
m = (- 2 + 2)/(2- 2)
m = 0
WILL GIVE BRAINLYEST ALL THE PICURES IM SHOWING IS ALL IN 1 QUESTION 100 POINTS
Answers
Answer:
90
Step-by-step explanation:
AnswerAnswerAnswer:90
Step-by-step explanation:
Which rule explains why these triangles are
congruent?
U
T
V
W
AAS
ASA
SAS
SSS
These triangles
cannot be proven
congruent.
Answers
These triangles can be proven congruent by using ASA RULE.
What is congruent triangles and its rules ?
When two triangles are congruent, their three sides and their three angles match precisely.
If there is a turn or a flip, the equal sides and angles might not be in the same place, but they are still present.
ASA rule stands for Angle-Side-Angle rule which means two angles and a side of both triangles are equal.
Main Body:
In ΔTUV and ΔTWV
VT =VT ----(1)
∠VTU=∠TVW -----(2)
As TUVW is a parallelogram
so, ∠T = ∠U
hence, ∠TVU =∠VTW ----(3)
taking equation 1, 2,3
therefore, ΔTUV ≅ ΔTWV by ASA rule which means by Angle- Side- Angle rule.
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