The value of the variable x for the function f(x) = x² + 4x for which
f(f(x) ) = f(x) is equal to x = -1 or x = -3.
The function f(x) = x² + 4x
Substitute the value in the required function we get,
Right hand side
= f ( f(x))
= f ( x² + 4x )
= ( x² + 4x )² + 4 ( x² + 4x )
= x⁴ + 8x³ + 16x² + 4x² + 16x
= x⁴ + 8x³ + 20x² + 16x
Left hand side
f(x)
= x² + 4x
Equate left hand side is equal to right hand side we get,
x⁴ + 8x³ + 20x² + 16x = x² + 4x
⇒x⁴ + 4x³ + 4x³ + 16x² + 4x² + 16x = x² + 4x
⇒x² ( x² +4x ) + 4x ( x² + 4x )+ 4 ( x² + 4x ) = x² + 4x
⇒( x² + 4x ) ( x² + 4x + 4 ) = x² + 4x
⇒ x² + 4x + 4 = 1
⇒ ( x + 2 )² - 1² =0
⇒ ( x + 2 -1 ) ( x+ 2 + 1) = 0
⇒ ( x+ 1 ) ( x+ 3 ) = 0
⇒ x = -1 or x = -3
Therefore, the value of x = -1 or x = -3 for the condition f(f(x)) = f(x).
The above question is incomplete , the complete question is:
Let function f(x) = x² + 4x for what value of x is f(f(x)) = f(x).
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If the measure of DCE is 28 what is the measure of CED
Answer: Measure of CED is: 212°
How far is 500 meters in miles?
500 m is equal to 0.310686 mi. This is due to the fact that one mile is equal to the errant total of 1,609.344 meters.
What is the time required to walk 500 meters?The average person will need about 6 minutes to walk 500 meters, as 500 meters is equal to 0.31 miles. Data from a 2019 study spanning five decades shows that the majority of people can typically anticipate to walk a mile in 15 to 22 minutes. According to the Centers for Disease Control and Prevention, the typical walking speed is between 2.5 and 4 mph. For women aged 70 to 79, the normative two-minute walk test lengths ranged from 150.3 m to 217.9 m. (men, 20 to 29 tears).These results are comparable to those obtained by other authors (7) who found values of 7.3m for the distance walked during the 3-minute test and 22.25m for the 6-minute test.To learn more about distance, refer to:
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Daniel had promied you a alary of S$50. You only received S$40
in your firt paycheck. What could be the reaon for that?
The government deduct income tax from your alary. You only receive your alary after the employer deduct the tax amount and pay it to the government. The government ue taxe to build road, hopital, chool, and other public facilitie. If Daniel’ alary i S$5000
and he pay an income tax of 35%. How much money will he receive in hi paycheck?
After deducting this tax amount, his take-home pay would be $3250.
How to calculate the taxThe determination of the take-home pay after deducting the income tax can be calculated using the following formula:
Take-home pay = Total salary - (Total salary x Tax rate)
In this case, the total salary is S$5000 and the tax rate is 35%, so the calculation would be:
S$5000 - (S$5000 x 35%) = S$5000 - S$1750 = S$3250
The formula used to calculate the take-home pay (Total salary - (Total salary x Tax rate)) is a general formula that can be applied to calculate the take-home pay for most individuals who have income tax deducted from their salary.
However, it may not be applicable in all cases as the amount of tax deducted and the tax rate may vary based on the individual's salary, country, tax laws, and other factors. It is always recommended to consult with a tax professional or financial advisor for a more accurate calculation of take-home pay.
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If 3x + c = 4, then x equals
We can write {x} as follows -
{x} = (4/3) - (c/3)
What is a function?An function in mathematics defines a relationship between one variable (the independent variable, x) and another variable (the dependent variable, y). Example -
y = f{x} = ax + b
Given is a equation as -
3x + c = 4
The given equation is -
3x + c = 4
3x = 4 - c
x = (4 - c)/3
x = (4/3) - (c/3)
Therefore, we can write {x} as follows -
{x} = (4/3) - (c/3).
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how to calculate standard deviation and variance with 7.2, 7.6, 8.5, 8.7, 9.0, 9.3, 9.4, 10.2, 10.9, 11.3
After determining the mean the variance is 1.5689 and standard deviation is 1.253.
The values are 7.2, 7.6, 8.5, 8.7, 9.0, 9.3, 9.4, 10.2, 10.9, 11.3.
Firstly we find the mean of the numbers.
Mean = Sum of the Numbers/Total numbers
Mean = (7.2 + 7.6 + 8.5 + 8.7 + 9.0 + 9.3 + 9.4 + 10.2 + 10.9 + 11.3)/10
Mean = 92.1/10
Mean = 9.21
Now we determine the variance.
The formula of variance is:
x x - Mean (x - Mean)^2
7.2 (7.2-9.21) = -2.01 4.0401
7.6 (7.6-9.21) = -1.61 2.5921
8.5 (8.5-9.21) = -0.71 0.5041
8.7 (8.7-9.21) = -0.51 0.2601
9.0 (9.0-9.21) = -0.21 0.0441
9.3 (9.3-9.21) = 0.09 0.0081
9.4 (9.4-9.21) = 0.19 0.0361
10.2 (10.2-9.21) = 0.99 0.9801
10.9 (10.9-9.21) = 1.69 2.8561
11.3 (11.3-9.21) = 2.09 4.3681
Total = 15.689
Variance = ∑(x - Mean)^2/10
Variance = 15.689/10
Variance = 1.5689
Standard Deviation = √Variance
Standard Deviation = √1.5689
Standard Deviation = 1.253
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Factor the expression to fill in the blank.
21 + 39 = ? (7 + 13)
The factorization of 21+39 is 3(7+13)
What is factorization of expression?The process of finding two or more expressions whose product is the given expression is called the factorization of algebraic expressions. Thus, the factorisation of algebraic expressions is the reverse process of multiplication.
to factorize, we find a common factor between the two terms
The common factor between 21 and 39 is 3 .
3 in 21 is 7 and 3 in 39 is 13
therefore 21+39 can be written as 3(7+13)
we can therefore be say that 21+39 = 3(7+13) and 3 is the missing number in the question
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Determine, for the typical algorithms that you use to perform calculations by hand, the running time to do the following: a. Add two N-digit integers. B. Multiply two N-digit integers. C. Divide two N-digit integers
The running time of the algorithms of addition, multiplication and division of two numbers are O(N), O(N^2), and O(N^2) respectively.
For the typical algorithms used to perform calculations by hand:
A. Adding two N-digit integers typically takes O(N) time. This is because each digit of the larger number needs to be added to the corresponding digit of the other number and the carry over needs to be taken into account.
B. Multiplying two N-digit integers typically takes O(N^2) time. This is because each digit of one number needs to be multiplied by each digit of the other number, and the intermediate results need to be summed.
C. Dividing two N-digit integers typically takes O(N^2) time. This is because the process of long division involves repeatedly dividing, multiplying, and subtracting the digits of the dividend and the divisor until the result is obtained.
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solve the systen of linear equations by elimintion x-2y=-7 3x+2y=7
The solution to the equation is (0, 7/2)
How to solve the systen of linear equationsFrom the question, we have the following parameters that can be used in our computation:
x-2y=-7 3x+2y=7
Add the two equations to elimiate y
4x = 0
So, we have
x = 0
This means that
0 - 2y = -7
So, we have
y = 7/2
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Complete the sentence. Then, use the laws of exponents to write an equivalent expression for the given expression.
To divide powers that have the same base and different exponents, keep the ___ and ___ the exponents.
To divide powers that have the same base and different exponents, keep the base and subtract the exponents.
How to divide exponents with same baseWhen dividing two powers that have the same base but different exponents, you keep the base and subtract the exponents.
For example, if you want to divide a^m by a^n,
you can write it as a^m / a^n
= a^(m-n).
The new exponent is the result of subtracting the exponents of the two powers.
hence the division will result to a^(m-n).
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if a variable x is normally distributed with a mean of 60 and a standard deviation of 15, what is
For a normally distributed variable x with a mean of 60 and a standard deviation of 15, theprobability P(x < 75) is 0.3173
Here, a variable x is normally distributed a mean of 60 and a standard deviation of 15.
This means, mean (μ) = 60
and the standard deviation (σ) = 15
To find: P(x < 75) .
First we find the z-score.
Using the formula for the z-score,
[tex]z=\frac{75-60}{15}[/tex]
z = 1
Using standard normal table, the p-value corresponding to z = 1 is:
p = 0.3173
Thus the probability P(x < 75) is 0.3173
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The complete question is:
if a variable x is normally distributed with a mean of 60 and a standard deviation of 15, what is the probability P(x < 75) .
d) what percentage of the data falls between q1 and q3?
The median divides the data into half so that 50% of the measurement lies below the median and 50% lies above it, the quartile breaks down the data into quarters so that 25% of the measurements are less than the lower quartile, 50% are less than the median, and 75% are less than the upper quartile.
Now, According to the question:
The interquartile range and semi-interquartile range give a better idea of the dispersion of data. To calculate these two measures, you need to know the values of the lower and upper quartiles. The lower quartile, or first quartile (Q1), is the value under which 25% of data points are found when they are arranged in increasing order. The upper quartile, or third quartile (Q3), is the value under which 75% of data points are found when arranged in increasing order. The median is considered the second quartile (Q2). The interquartile range is the difference between upper and lower quartiles. The semi-interquartile range is half the interquartile range.
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The complete question is this:
What percent of data is between Q1 and Q2?
If AB = 9 and AB ∣∣∣∣ DC, what is the perimeter of ABCD?
Answer:
38
Step-by-step explanation:
Since the figure shown of ABCD has two pairs of parallel lines, it can be classified as a parallelogram.
Opposite sides are congruent in a parallelogram, so:
AB = CD = 9
BC = AD = 10
To find the perimeter you sum together all the sides. Therefore the perimeter of ABCD would be AB + BC + CD + AD. This is equal to:
9 + 10 + 9 + 10 = 38
The length of a cell phone is 1.21.2 inches and the width is 3.43.4 inches. The company making the cell phone wants to make a new version whose length will be 1.141.14 inches. Assuming the side lengths in the new phone are proportional to the old phone, what will be the width of the new phone?
Assuming the side lengths in the new phone are proportional to the old phone, the width of the new phone would be equal to 3.23 inches.
What is a proportion?In Mathematics, a proportion simply refers to an equation which is typically used to represent the equality of two (2) ratios. This ultimately implies that, proportions can be used to establish that two (2) ratios are equivalent and solve for all unknown quantities.
By applying direct proportion to the given information, we have the following mathematical expression:
1.2 inches = 3.4 inches
1.14 inches = w inches
Cross-multiplying, we have the following:
1.2w = 3.4 × 1.14
1.2w = 3.876
w = 3.876/1.2
w = 3.23 inches.
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Given p(x) = -37 +2/5(x²-14), what is the value of p(-9)?
The value of p(-9) is -10.2.
What is an Equation?An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side.
Given is an equation,
p(x) = -37 + (2/5) (x² - 14)
To find the value of p(-9), substitute -9 in the place of x.
p(-9) = -37 + (2/5) ((-9)² - 14)
= -37 + (2/5) (81 - 14)
= -37 + (2/5) × 67
= -37 + 26.8
= -10.2
Hence the value of the function when x = -9 is -10.2.
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(3) I'm stuck pls help me with my algebra work show all ur steps
x=2y-7
3x-8y=-27
Answer:
x = -1
y = 3
Step-by-step explanation:
Equation 1: x=2y-7
Equation 2: 3x-8y=-27 ==> isolate x
Equation 3: 3x = 8y - 27 ==> isolate 3x by adding 8y on both sides
3 * (x = 2y - 7) ==> multiply 3 by equation 1 to get 3x
Equation 4: 3x = 6y - 21
3x = 8y - 27
- (3x = 6y - 21)
3x-3x = 8y-6y - 27-(-21) ==> subtract equation 4 from equation 3 to cancel x
0 = 2y - 27 + 21 ==> simplify
0 = 2y - 6 ==> solve for y
6 = 2y ==> add 6 on both sides to isolate y
y = 3 ==> divide 2 into both sides
Solve for x:
x=2(3) - 7 ==> plug in 3 for y in x=2y-7
x = 6 - 7
x = -1
Write these ratios in their simplest form
a 9:18
Answer:
1 : 2
Step-by-step explanation:
9 : 18
Both numbers are divisible by 9, thus:
9/9 : 18/2
[1 : 2]
Does an electric motor turn faster if you increase the voltage? 3. What is the Independent variable in example B?
Yes, increasing the voltage of an electric motor will cause it to turn faster. Voltage is the difference in electrical potential between two points, and is measured in volts.
When voltage is increased, the electric motor is able to draw more power from the power source, which will result in a faster rotation speed. The independent variable in example B is the voltage supplied to the electric motor.
This is the variable that will be changed in order to test the effect on the motor's speed. By increasing the voltage supplied to the motor, we can see how the speed of the motor changes in relation to the change in voltage. By doing this, we can determine the motor's speed at various voltages, and can determine how the voltage affects the motor's speed.
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I need both questions , help
Use the information in provided in each part of the question to analyze the probability is 42.
What mathematical equation is used to probability calculate the of a compound event?Use the information in provided in each part of the question to analyze the probability.
A dealer deals a hand consisting of 3 spades, 4 diamonds. 6 clubs and 5 hearts. If two cards are picked at random from that hand without replacement,
The two types of compound events are calculated using several formulas: If two occurrences, A and B, are mutually exclusive, then P(A or B) = P (A) + P (B). P (A or B) = P(A) + P(B) - P for mutually inclusive occurrences (A and B).
Once the first event has occurred, multiply the likelihood of the subsequent event by the previous event's probability to arrive at the compound probability of dependent events.
P (A) + P (B)
3(4) + 6(5) = 12 + 30 = 42.
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in a survey, the of respondents are identified as for for for and for anything else. the average (mean) is calculated for respondents and the resu
What number must you multiply the second equation by so that the sum of the x-coefficients is zero?
7x−y=55
x+3y=33
1. -7
2. 1/3
3. -1/3
4. 7
-7 must you multiply the second equation by so that the sum of the x-coefficients is zero.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The system of equations are
7x−y=55..(1)
x+3y=33..(2)
We have to multiply with -7 second equation by so that the sum of the x-coefficients is zero
-7x-21y=-231..(3)
Add equation 1 and equation 2
7x−y-7x-21y=33-231
-22y=-198
Hence, -7 must you multiply the second equation by so that the sum of the x-coefficients is zero.
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Write the augmented matrix for each of the following systems of linear equations. a. x – 3y=5 b. x+2y=0 x+y=1 c. x - y + z=2 x - z=1 d. y + 2x=0 y+z=0
The augmented matrix for the given systems of linear equations are obtained. a. x – 3y=5 b. x+2y=0 x+y=1 c. x - y + z=2 x - z=1 d. y + 2x=0 y+z=0
Explain the term augmented matrix?Two matrices are combined to form enhanced matrices.
A augmented matrix is often one in which the matrices have been merged so that they are next to one another. A divider which expresses the "border" of each matrix connects the last column of the initial matrix to the initial column of a second matrix. Augmented matrices can be used to visualize systems of equations.Thus, augmented matrix for the given systems of linear equations are obtained as:
a. x – 3y = 5 : [1 - 3 : 5]
b. x+2y=0 x+y=1 : [1 2 : 0]
[1 1 : 1]
c. x - y + z=2 and x - z=1 : [1 -1 1 : 2]
[1 0 -1 : 1]
d. y + 2x=0 y+z=0 : [2 1 0 : 0]
[0 1 1 : 0]
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The mean salary at Ivy's store is $850 per week with a standard deviation of $120. Ivy earns $1,000 per week. Calculate the z-score of her salary
Dividing the sum above by the total number of values in the data set.
How do you calculate the data’s mean absolute deviation?Take the absolute value of each integer in the data collection and remove the mean. Then add the absolute values together. Divide the total number of values in the data set by the sum above to get the mean absolute deviation. Finally, round up to the tenth.
A collection of data’s Mean Absolute Deviation (MAD) is the average distance between each data item and the mean. The mean absolute deviation is the “average” of each point’s “positive distances” from the mean. The bigger the MAD, the greater the variability in the data (the data is more spread out).
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Write the decimal expansion for 5 9.
Answer:We got 0.56 as the answer when you convert 5/9 to a decimal.
15. The Atlanta Braves had a run differential of +134 in the 2021 season. What does this mean?
O A. They scored a total of 134 runs
O B. They scored 134 more rurks than they allowed their opponents to score.
O C. They allowed their opponents to score a total of 134 runs.
OD. They allowed their opponents to score 134 more runs than they scored.
They allowed their opponents to score 134 more runs than they scored.
What is the differential equation?
A differential equation is an equation that contains at least one derivative of an unknown function, either a normal differential equation.
A differential equation is an equation that contains at least one derivative of an unknown function, either a normal differential equation or a partial differential equation.
A run differential of +134 for the Atlanta Braves in the 2021 season means that the team scored 134 more runs than their opponents over the course of the season.
A positive run differential indicates that a team has outscored their opponents, while a negative run differential means that a team has been outscored by their opponents.
Hence, They allowed their opponents to score 134 more runs than they scored.
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Which of the following graphs represents a one-to-one function?
Graphs represents a one-to-one function is graph A.
About graphicGraphics is as a combination of
numbers, letters, symbols, pictures, emblems, sayings, paintings, which are presented in one medium to convey concepts and ideas from the sender to the target in the process of conveying information.
There is also another understanding of graphics, which is a framework for forming table visualization objects. Tables consisting of numbers can be presented or can be displayed in the form of images, can be in the form of lines, circles, bars etc. And the third definition is a description of the ups and downs of a situation or existing data with lines or pictures. Graphs are divided into 3 "three" types, including graphs: bars, lines and circles.
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Write an equation:
"Ehren worked 36 hours last week and earned a total of $500"
Please help me ;-; Thanks!
The correct equation to represent "Ehren worked 36 hours last week and earned a total of $500" is,
⇒ 36x = 500
Where, x represent the amount earn in per hour.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
We have to given that;
The expression is,
"Ehren worked 36 hours last week and earned a total of $500"
Let the amount earn in per hour = x
Hence, For Ehren worked 36 hours last week and earned a total of $500, the correct equation is,
⇒ 36x = 500
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What is ittttttttttttttt
Answer:
1/6 and 1/6^1 so the second and 4th one.
Step-by-step explanation:
Look it up bud
find the plane determined by the intersecting lines.
The equation of the plane determined by the intersecting lines is:
0x + 7y + 9z - 19 = 0
What is the equation of the plane?
In mathematics, a plane is a flat, two-dimensional surface that extends infinitely in all directions. It is defined by an equation of the form Ax + By + Cz + D = 0, where A, B, and C are the coefficients of the normal vector to the plane and D is a constant. The coefficients A, B, and C determine the orientation of the plane in 3-dimensional space, and the constant D determines the distance of the plane from the origin.
The equation of the plane can be found by finding the cross product of the direction vectors of the two lines.
Let's start by finding the direction vectors of the two lines:
For line L1, the direction vector is:
d = <3, 2, -1>
For line L2, the direction vector is:
d = <-3, 1, -2>
Now, we can find the cross product of these two direction vectors:
n = d1 x d2 = <3, 2, -1> x <-3, 1, -2> = <0, 7, 9>
So the normal vector to the plane is <0, 7, 9>.
Next, we can find a point on either line to substitute into the general equation of a plane to find the equation of the plane:
Let's use the point from line L1:
x = -1 + 3 * 0 = -1
y = 2 + 2 * 0 = 2
z = 1 - 0 = 1
Now, we have a point (-1, 2, 1) and the normal vector <0, 7, 9>, which we can substitute into the general equation of a plane:
Ax + By + Cz + D = 0
where A, B, C are the components of the normal vector, and D is a constant.
Plugging in the values, we get:
0x + 7y + 9z - 19 = 0
So, the equation of the plane determined by the intersecting lines is:
0x + 7y + 9z - 19 = 0
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let a and b be two possible events when a random number generator is used once. suppose you are told that a and b are mutually exclusive. this implies that the probability that either A. A happens or B happens is equal to theproduct of the probabilities of A and B B. the probability that A and B both happen is equal to the sum ofthe probabilities of A and B C. the probability that either A happens or B happens is equal to thesum of the probabilities of A and B D. the probability that A happens given that B happens is equal tothe probability that A happens E. the probability that A and B both happen is equal to the productof the probabilities of A and B
The probability that either A happens or B happens is equal to the sum of the probabilities of A and B. Option C is the answer.
What is a probability?Probability is a measure of the likelihood of a particular event occurring, expressed as a number between 0 and 1. A probability of 0 means an event is impossible, while a probability of 1 means an event is certain. A probability of 0.5 means an event has a 50-50 chance of happening.
In the question given, the probability that either A happens or B happens is equal to the sum of the probabilities of A and B.
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What is irreflexive closure?
Answer: The irreflexive closure of a relation R R R cannot contain any elements of the form ( a , a ) ∉ R (a,a)\notin R (a,a)∈/R (by the definition of reflexive).
Step-by-step explanation: