We have shown that for any eigenvalue λ of A, 1-λ is an eigenvalue of -A. So, the eigenvalues of -A are 1-λ1, 1-λ2, ..., 1-λn, where λ1, λ2, ..., λn are the eigenvalues of A.
What do you mean by eigenvalues?Eigenvalues are scalar values that are associated with a linear transformation of a matrix and are used to represent the behavior of a linear system. They represent the factor by which a linear transformation scales the direction of a vector. Eigenvalues play an important role in many areas of mathematics, including linear algebra, physics, engineering, and statistics. If a matrix A has an eigenvector x and an eigenvalue λ, then A can be represented as a scalar multiplication of x by λ: A x = λ x. The eigenvalues of a matrix can be used to determine its stability, to find the diagonalization of the matrix, and to determine the eigenvectors that represent the most important directions of a linear transformation.
The eigenvalues of a matrix A are scalars that satisfy the equation Av = λv, where v is a non-zero eigenvector and λ is the corresponding eigenvalue. If λ is an eigenvalue of A, then 1-λ is an eigenvalue of -A.
To see why this is true, let's consider an eigenvector v of A with eigenvalue λ. Then, Av = λv. We can multiply both sides of this equation by -1 to obtain:
-Av = -λv
Now, we can substitute -A for A and 1-λ for λ:
(-A)v = (1-λ)v
Thus, we have shown that for any eigenvalue λ of A, 1-λ is an eigenvalue of -A. So, the eigenvalues of -A are 1-λ1, 1-λ2, ..., 1-λn, where λ1, λ2, ..., λn are the eigenvalues of A.
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Based on the results of the second stimulation, what is the experimental probability that a group include only boys?
__%
FAKE ANSWERS= REPORT.
The answers for the asked probabilities, are a) P(boys only) = 6/100, b) P(not boys only) = 94/100 and c) 20
What is probability?Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true.
Given that, a random list of 100 numbers and the assignations 0-4 to represent girls and 5-9 to represent boys,
a) Based on the results of the simulation, what is the experimental probability that a group will include only boys?
Answer :- 6 of the numbers simulate groups of all boys: 7579, 6577, 5697, 9675, 5656, 6658. So, the experimental probability of a group being all boys is 6/100 = 0.06
b) Based on the results of the simulation, what is the experimental probability that a group will not contain four boys?
Answer :- The other 94 groups do not include only boys.
The probability that the group will not contain four boys is
1 -6/100 = 94/100 = 0.94
c) Based on the results of the simulation, if 224 groups are formed, about how many of them would you expect to contain all girls?
Answer :- 9 of the groups contain all girls. Based on these results, we would expect,
9/100 × 224 ≈ 20
Therefore, 20 groups to contain all girls.
Hence, the answers are a) P(boys only) = 6/100, b) P(not boys only) = 94/100 and c) 20
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The question is incomplete, so I solved for,
Use the following random list of 100 numbers and the assignations 0-4 to represent girls and 5-9 to represent boys to answer the question below. 3199 9288 1023 1130 0809 1770 6231 7538 8927 4761 7258 7111 0209 0916 1450 9848 4654 7579 6150 3093 9608 0061 4014 9501 0382 3052 2385 9074 1664 6551 6577 1811 3454 5870 1277 5056 1063 5697 9141 4120 9181 1343 0168 3693 0463 4842 1704 3774 4908 4161 6404 9675 2518 3988 4268 6083 0636 9634 5295 5656 1918 3133 6831 8393 6363 2452 1531 1638 1317 2279 9395 0702 2091 5269 0422 0275 3373 1424 1958 0356 5163 0743 6658 6257 2772 0570 4522 2665 0890 3560 5549 2238 2172 9715 9741 4975 6617 9034 4441 8220 Based on the results of the simulation, what is the experimental probability that a group will include only boys? Based on the results of the simulation, what is the experimental probability that a group will not contain four boys? Based on the results of the simulation, if 224 groups are formed, about how many of them would you expect to contain all girls? Round your answer to the nearest number of groups.
HELP MEEEEEE LOOK AT THE LOW FPS PIC
Answer:
14,35,42,63,77
Step-by-step explanation:
Actually how to get the output you follow the rule;
n×7
the first will be;2×7=14
the second will be; 5×7=35
the third will be; 6×7=42
the forth will be; 9×7=63
the fifth will be; 11×7=77
y= 2x + 3
y= -3x + 3
Answer:
Y=5−2y/3
x=1−y/3
hope that helps
Two splice plates are cut from a piece of sheet steel that has an overall length of 18 5/8 in. The plates are 8 1/2 in. and 7 9/16in. long. How much material remains from the
original piece if each saw cut removes
1/16
in.?
in. of material remains from the original piece.
(Type a whole number, proper fraction, or mixed number.)
The remaining portion of the sheet from the overall length is 10.16 units.
What are fractions?In mathematics, a fraction is used to denote a portion or component of the whole. It stands for the proportionate pieces of the whole. Numerator and denominator are the two components that make up a fraction. The numerator is the number at the top, and the denominator is the number at the bottom. The denominator specifies the total number of equal parts in the whole, whereas the numerator specifies the number of equal parts that were taken.
Given that the overall length of the sheet is 18 5/ 8 = 149 / 8.
The two pieces removed are:
8 1/2 =17/ 2 and
7 9/16 = 121 / 16 inches.
The sawcut removed 1/16.
For two pieces we have two saw cuts thus, 2(1/16) = 1/8 inches.
The remaining portion is:
R = 149 / 8 - 17/2 - 121/6 - 1/8
R = 447 - 204 - 484 - 3 / 24
R = 10.16
Hence, the remaining portion of the sheet is 10.16 units.
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C. How much car can you afford to finance a new car if your proposed monthly payment is $240, for 60 months (5 years), with a credit score between 601-660?
Finance amount: __________________________________
Estimated percentage rate: ____________________
Amount of interest you will pay for the loan: _____________________________
Finance amount: The amount you can finance for a new car with a monthly payment of $240, for 60 months (5 years), depends on several factors, including the loan interest rate, the down payment, and the value of the car.
Estimated percentage rate: The interest rate for a new car loan with a credit score between 601-660 typically ranges from 5% to 10%.
Amount of interest you will pay for the loan: The amount of interest you will pay for the loan can be calculated by multiplying the loan amount by the interest rate and the number of months.
How to calculate the total interest?For example, if you finance $20,000 at a 7% interest rate for 60 months, the total interest paid over the life of the loan would be $3,140.
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can someone tell me how i find this problem?
as you already know, to get the inverse of any expression we start off by doing a quick switcheroo on the variables and then solving for "y", let's do so.
[tex]\stackrel{f(x)}{y}~~ = ~~\cfrac{x+5}{x+7}\hspace{10em}\stackrel{\textit{quick switcheroo}}{x~~ = ~~\cfrac{y+5}{y+7}} \\\\\\ xy+7x=y+5\implies xy-y+7x=5\implies xy-y=5-7x \\\\\\ \stackrel{\textit{common factoring}}{y(x-1)=5-7x}\implies y=\cfrac{5-7x}{x-1}=f^{-1}(x) \\\\[-0.35em] ~\dotfill\\\\ f^{-1}(-8)~~ = ~~\cfrac{5-7(-8)}{(-8)-1}\implies f^{-1}(-8)=\cfrac{61}{-9}\implies f^{-1}(-8)=-6\frac{7}{9}[/tex]
Need help solving!!! ASAP!
Answer:
Step-by-step explanation:
ur mom
Simplify the expressions with rational exponents 25 1/2 / 27 1/3
The value of the equation is A = 5/3
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
A = ( 25 ^ 1/2 ) / ( 27 ^ 1/3 ) be equation (1)
On simplifying the equation , we get
A = √25 / ∛27
The value of √25 = 5
And , the value of ∛27 = 3
Substituting the values in the equation , we get
A = 5/3
So , the value of A = 1.66667
Hence , the equation is A = 5/3
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A decade-old study found that the proportion, p, of high school seniors who believed that "getting rich" was an important personal goal was 70%. A researcher decides to test whether or not that percentage still stands. He finds that, among the 250 high school seniors in his random sample, 154 believe that "getting rich" is an important goal. Can he conclude, at the 0.01 level of significance, that the proportion has indeed changed?
Perform a two-tailed test. Then complete the parts below.
Carry your intermediate computations to three or more decimal places. (If necessary, consult a list of formulas.)
(a) State the null hypothesis H0 and the alternative hypothesis H1.
H0:
H1:
(b) Determine the type of test statistic to use.
▼(Choose one)
(c) Find the value of the test statistic. (Round to three or more decimal places.)
(d) Find the p-value. (Round to three or more decimal places.)
(e) Can we conclude that the proportion of high school seniors who believe that "getting rich" is an important goal has changed?
Yes No
Therefore , the solution of the given problem of test statistics comes out to be Since the p-value is less than the level of significance of 0.01, we reject the null hypothesis.
What is the test statistic?The Z-statistic, which demonstrates that the ordinary normal balanced hypothesis is true, has been used as the statistic for anything resembling a Z-test. Let's say you run two separate X-y tests with a 0.05 level of significance, and the results show that you got a 2.5 R t. (also a Z-value). The p-value variable for this Z-value is 0.0124.
Here,
a) State the null hypothesis [tex]H_{0}[/tex] and the alternative hypothesis H1.
[tex]H_{0}[/tex]: p = 0.70 (proportion has not changed)
H1: p ≠ 0.70 (proportion has changed)
(b)
Since we are testing for a proportion and have sample size n = 250, we can use the normal distribution to approximate the sampling distribution of the sample proportion. Therefore, we will use the z-test statistic.
(c)
z = (p' - p) / √(p(1-p)/n)
p' = 154/250 = 0.616
z = (0.616 - 0.70) / √(0.70(1-0.70)/250)
z = -2.759
(d)
The p-value is the probability of observing a z-score as extreme as -2.759 or more extreme under the null hypothesis. Since this is a two-tailed test, we need to find the area in both tails of the standard normal distribution.
p-value = P(Z ≤ -2.759) + P(Z ≥ 2.759)
p-value = 0.0058 + 0.0058
p-value = 0.0116
(e)
Since the p-value is less than the level of significance of 0.01, we reject the null hypothesis. We can conclude that there is sufficient evidence to suggest that the proportion of high school seniors who believe that "getting rich" is an important goal has changed.
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Learning aids, listed along the bottom of the window, are available for most problems on homework assignments and study plan practice but are not available on tests and quizzes. Identify the learning aid described in each part below.
One learning aid that provides an interactive walk-through for solving the particular problem you are working on is "view an example"
What does learning aid offer student?It is also known as teaching aids, which are an essential part of any classroom. Teaching aids can help students improve their reading comprehension skills, illustrate or reinforce a skill or concept, differentiate instruction, and relieve anxiety or boredom by presenting information in a new and exciting way.
Teaching aids also engage students' other senses because there are no restrictions on what aids can be used to supplement a lesson. As technology advances, so do teaching aids, which are now classified as audio aids, visual aids, mechanical teaching aids, audio-visual aids, and more.
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What number should go in the space?
Multiplying by 0.65 is the same as decreasing by _____%.
Answer:
35%
Step-by-step explanation:
For each value of x, evaluate f(x).
f(x)=x-4
X
-2
-1
0
1
2
Just enter each value of x into the formula f(x) = x - 4. For example, f(x) = 2 - 4 = -2 when x = 2.
How do you find the value of x?A general rule is that the algebraic expression should take any of the following forms: addition, subtraction, multiplication, and division. to ascertain x's value.
Finding the value of f(x) =... or y =... that corresponds to a given value of x is the definition of function evaluation. Simply swap out all instances of x with the value that has been allocated to x to do this. For instance, if f(4) is to be evaluated, then x has been given the value of 4.
Separate the variable. In this instance, you transfer the constant term across the equal sign by doing the reverse operation on both sides and adding 1 to isolate the variable term. Isolate the variable further, then simplify.
Given,
f(x)=x-4
⇒ when x = -2,
⇒ f(x) = -2 -4 = -6
When x = -1,
⇒ f(x) = -1 -4 = -5
When x = 0
⇒ f(x) = 0 -4 = - 4
When x = 1
⇒ f(x) = 1 -4 = -3
When x = 2
⇒ f(x) = 2 -4 = - 2
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The expenditure of a family is represented in the table below. Draw a pie chart to illustrate the information. Item Rent Transport Food Medical Savings School fees Expenditure 2000 1000 2500 2000 12,000 10,000
The pie chart for the data representing the expenditures of the family is given by the image presented at the end of the answer.
How to construct a pie chart?A pie chart is constructed in pizza format, considering the percentages of each input data in the problem.
A percentage is calculated as the division of the number of desired outcomes by the number of total outcomes, and then multiplied by 100%.
The total expenditures for the family are given as follows:
2000 + 1000 + 2500 + 2000 + 12000 + 10000 = 29500.
The percentages for the data-set in this problem is given as follows:
Rent: 2000/29500 x 100% = 6.78%.Transport: 1000/29500 x 100% = 3.39%.Food: 2500/29500 x 100% = 8.47%.Medical Savings: 2000/29500 x 100% = 6.78%.School fees: 12000/29500 = 40.68%.Expenditure: 10000/29500 = 33.9%.More can be learned about pie charts at https://brainly.com/question/26851221
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in 2-3 paragraphs, summarize your findings. support your statements with references that verify the uncertainty inherent in measurements.
The greater the magnitude of the measurement, the greater the uncertainty in the measurement.
The accuracy of these measurements is often of great importance, but it is important to keep in mind that there is always some degree of uncertainty inherent in any measurement.
This uncertainty can arise from a number of sources, including the limitations of the measuring tools, the skill and experience of the person making the measurement, and the conditions under which the measurement is taken.
One way to describe the relationship between measurement uncertainty and the magnitude of the measurement is through the use of exponential functions.
An exponential function is a mathematical relationship between two variables, in which one variable changes at a rate that is proportional to its current value.
In the case of measurement uncertainty, the exponential function describes the relationship between the uncertainty in a measurement and the magnitude of the measurement.
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The following data set represents the age of a random sample of cars on the road today. 1 3 3 7 10 12 The standard deviation of this sample is A. 4.382 B. 8.802 C.7.143 D. 9.063
The required standard deviation for the given data set is 4.38.
What is Standard deviation?
The standard deviation reveals the degree of data skewedness. It gauges how far away from the mean each observed value is. Approximately 95% of values in any distribution will be within two standard deviations of the mean.
According to question:To calculate the standard deviation of this sample, we'll follow these steps:
Find the mean of the sample:
mean = (1 + 3 + 3 + 7 + 10 + 12) / 6 = 6
Subtract the mean from each value in the sample to find the deviations:
deviations: -5, -3, -3, 1, 4, 6
Square the deviations:
squared deviations: 25, 9, 9, 1, 16, 36
Sum the squared deviations:
sum of squared deviations = 25 + 9 + 9 + 1 + 16 + 36 = 96
Divide the sum of squared deviations by the number of values minus one:
sum of squared deviations / (n - 1) = 96 / (6 - 1) = 96 / 5 = 19.2
Take the square root of the result from step 5 to get the standard deviation:
standard deviation = [tex]\sqrt{(19.2)}[/tex] = 4.38
So, the standard deviation of this sample is 4.38.
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Which equation best describes the relationship between the corresponding
values of x and y shown in the table?
A. y = x - 10
B. y = 2x - 8
C. y = 3x - 6
D. y = x2 - 8
The equation y = 2x - 8, best describes the relationship between the corresponding values of x and y shown in the table.
What is the Linear equation?A linear equation is defined as an equation in which the highest power of the variable is always one.
The table is given in the question, as follows:
x : -2 0 1 4
y : -12 -6 -3 6
Option C, y = 3x - 6, best describes the relationship between the corresponding values of x and y shown in the table. This can be seen by plugging in the x values from the table into the equation and observing that it yields the corresponding y values.
So substitute the values of x = 4 and y = 6 in the equation y = 3x - 6, and we get
6 = 3(4) - 6
6 = 12 - 6
6 = 6
Hence, the correct answer would be option (C).
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The question seems incomplete, the missing part has been below:
Which equation best describes the relationship between the corresponding values of x and y shown in the table?
x : -2 0 1 4
y : -12 -6 -3 6
A. y = x - 10
B. y = 2x - 8
C. y = 3x - 6
D. y = x2 - 8
Rotate the triangle through 180' about the origin.
y
51
4
3
2
11
ܘܝ ܚ ܚ ܬ
-5 -4 -3 -2 -10
-1
-2
-4
L
1
2 3 4 5
X
The coordinates of the vertex points of the triangle rotated through 180° about the origin, are (-1, -2), (-4, -2), and (-4, -4)
The drawing of the image of the triangle rotated through 180°, created using MS Excel is attached
What is a rotation transformation?A rotation transformation is one in which points on the figure to be rotated are turned about a center of rotation, following a circular path.
The coordinates of the vertices of the triangle are; (1, 2), (4, 2), and (4, 4)
The coordinates of the image following rotation of a point (x, y) 180°, about the origin is the point (-x, -y)
Therefore, the coordinates of the image of the triangle following the rotation are;
Rotation of the point (1, 2) 180° ⇒ (-1, -2)
Rotation of the point (4, 2) 180° ⇒ (-4, -2)
Rotation of the point (4, 4) 180° ⇒ (-4, -4)
Please find attached the graph of the image of the triangle with the vertex points (-1, -2), (-4, -2), and (-4, -4) following the rotation through 180° about the origin, created with MS Excel
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A straw is placed inside a rectangular box that is 9 inches by 6 inches by 8 inches, as shown. If the straw fits exactly into the box diagonally from the bottom left corner to the top right back corner, how long is the straw? simplest radical form
If the straw fits exactly into the box diagonally from the bottom left corner to the top right back corner, then the straw is √181 inches long.
What is Pythagoras' theorem?In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem.
Given:
A straw is placed inside a rectangular box that is 9 inches by 6 inches by 8 inches, as shown.
So, the diagonal of the base by the Pythagorean theorem,
c = √{(9)² + (6)²}
c = √117
Now, to find the value of d,
d = √{(√117)² + (8)²}
d = √181
Therefore, the straw is √181 inches long.
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what is the slope of the line determined by any two solutions to the equation ( 2 / x ) + ( 3 / y ) ?
The slope of the given line ( 2 / x ) + ( 3 / y ) = 0 which is calculated by solving the equation is equal to ( - 3 / 2).
Slope Definition:A line's slope is defined as the ratio of the change in y coordinate to the change in x coordinate.
The net change in y-coordinate is represented by Δy and the net change in x-coordinate is represented by Δx.
Hence, the expression for the change in y-coordinate with respect to the change in x-coordinate is,
m = y/x = y/x = change in y/change in x
where "m" represents a line's slope.
Furthermore, the slope of the line can be shown as
tan θ = Δy/Δx
So, tan θ to be the slope of a line.
As given in the question,
Given equation of the line is equal to ( 2 / x ) + ( 3 / y ) = 0
Simplify the given equation to get the slope intercept form :
( 2 / x ) + ( 3 / y ) = 0
⇒ ( 2 / x ) = - ( 3 / y )
⇒ 2y = -3x
⇒ y = ( - 3 / 2 ) x + 0 __(1)
Standard slope intercept form of the line is given by :
y = mx + c __(2)
Where m is the slope of the line
Compare (1) and (2) to get the slope of the line we get,
Slope of the line 'm' = ( - 3 / 2 )
Therefore, the slope of the given line by simplify the equation
( 2 / x ) + ( 3 / y ) = 0 in slope intercept form is equal to ( - 3/2).
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Find a quadratic polynomial with integer coefficients which has the following zeros
A quadratic polynomial with integer coefficients is,
p(x) = x² + 6x + (17√21)/49.
A quadratic equation is an algebraic expression in the form of variables and constants.
A quadratic equation has two roots as its degree is two.
Given, The roots of the quadratic equation is x = 2/7, ± √21/7.
Let, p(x) = x² + bx + c.
p(x) = (x + 2/7 + √21/7)(x - 2/7 + √21/7).
p(x) = x² - (2/7)x + (√21/7)x + (2/7)x - (4/49) + 2√(21/49) + (√21/7)x - 2√21/49 + 21/49.
p(x) = x² + 2(√21/7)x + 21/49 - 4/49.
p(x) = x² + {(2√21)x}/7 + 17/49.
p(x) = x² + (42/7)x + (17√21)/49.
p(x) = x² + 6x + (17√21)/49.
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Using the chart above, find the state withholding tax for the following unmarried person.
Mary Smith, salary $342, 2 exemptions.
O 17.82
O 18.91
O 6.76
5.68
The state withholding tax for the unmarried person Mary Smith is 6.76.
What is the withholding tax for the unmarried person?When paying rent, commissions, or fees for professional services at rates specified by current tax laws, the taxpayer is required to withhold tax, which is also known as retention tax.
A tax determined using the tables or computation methods prescribed by the Secretary must be deducted and withheld from all wages paid by an employer, unless otherwise specified in this section.
Withholding taxes are paid by employers to the IRS on behalf of the employee. The amount collected is applied as a credit to the employee's yearly income tax liability. If too much money is withheld, the employee gets a tax refund; if not enough, the employee might have to pay the IRS.
So that the state withholding tax for the unmarried person Mary Smith is 6.76.
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Describe the dilation in each function as it relates to the graph of f(x) = x.
g(x) = (9x)
Answer:
A is the correct answer
Step-by-step explanation:
graph show it If you put a number in for x then you can see the different
What quadrant will the complex number (2i-10) be in?
Answer:
Quadrant II
Step-by-step explanation:
[tex]2i-10[/tex] can be written as [tex]-10+2i[/tex], which shows a 10-unit transformation to the left of the real axis and a transformation of 2 units up on the imaginary axis. Hence, this would be in Quadrant II.
Write each rate as a unit rate. 70 miles in 2 hours.
Answer: 35 mph
Step-by-step explanation:
We will write this as a unit rate of miles per hour. To do this, we will divide the miles by the hours.
70 miles / 2 hours = 35 miles per hour
PLEASE HELP THANK YOU!
What is the answer to X
Answer: x = 7
Step-by-step explanation:
The right angle is equal to 90 degrees
Therefore (5x - 8) + (4x + 35) is equal to 90 degrees
5x - 8 + 4x + 35 = 90
5x + 4x + 35 - 8 = 90
9x + 27 = 90
- 27 -27 (subtract 27 from both sides)
9x = 90 - 27
9x/9 = 63/9 (divide both sides by 9)
x = 7
Check
5(7) - 8 + 4(7) + 35 = 90
35 - 8 + 28 + 35 = 90
The population of town X was 220,000 in 2000, and 252,000 in 2010. Project the population in 2020.
The population of the town X in 2020 is given by the equation
A = 2,88,654
What is Percentage?A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, %
The difference between an exact value and an approximation to it is the approximation error in a data value. Either an absolute error or a relative error might be used to describe this error.
Percentage change is the difference between the measured value and the true value , as a percentage of the true value
Percentage change =( (| Measured Value - True Value |) / True Value ) x 100
Given data ,
Let the population of the town X in 2020 be A
Let the percentage of increase be represented as r
Now , the equation will be
The initial population of Town X be A = 220,000
The increased population in 10 years be B = 252,000
So , the percentage change = [ ( B - A ) / A ] x 100
Substituting the values in the equation , we get
The percentage change r = [ ( 252,000 - 220,000 ) / 220,000 ] x 100
On simplifying the equation , we get
The percentage change r = [ 32,000/220,000 ] x 100
The percentage change r = 0.1454545 x 100
The percentage change r = 14.545 %
Now , the population of the town X in 2020 = ( 14.545 + 100 )% x increased population in 10 years
On simplifying the equation , we get
The population of the town X in 2020 A = ( 114.545 )% x 252,000
The population of the town X in 2020 A = 2,88,654.544
Hence , The population of the town X in 2020 A = 2,88,654
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Evaluate. Write your answer as a fraction or whole number.
1/4 (4) =
Answer:
1
Step-by-step explanation:
Evaluate. Write your answer as a fraction or whole number.
1/4 (4) = 1
The graph of a function f is shown below.
Find one value of x for which f(x) = 1 and find f(-1)
Step-by-step explanation:
remember, y = f(x)
so, the question is really for what x is y = 1 ?
and what is the y-value for x = -1 ?
a)
when we imagine a horizontal line through y = 1, at what points (x-value) does this line cross the function graph ?
as we can see, at x = -2 and x = 2.
pick one for your answer.
b)
now we imagine a vertical line through x = -1.
at what point (y-value) does this line cross the function graph ?
as we can see, at y = 4.
f(-1) = 4
Determine what Decartes Rule of Signs says about the number of positive and negative real roots for the polynomial function P(x)=8x^3 +2x^2-14x+5
The solution is, max no. of +ve real roots for is 2. & max no. of -ve real roots is 1.
What is Descartes rule ?Descartes rule of signs says the max no. of +ve real roots
= no. of changes in sign of the coefficients of a polynomial.
here, we have,
the polynomial function P(x)=8x^3 +2x^2-14x+5
now,
so max no. of +ve real roots for
P(x)=8x^3 +2x^2-14x+5, which has 2 changes in sign of coefficients (8,2,-14,5)
i,e, max no. of +ve real roots for is 2.
again, P(-x)=-8x^3 +2x^2+14x+5
which has 1 changes in sign (-8,2,14,5)
i.e. max no. of -ve real roots is 1.
Hence, The solution is, max no. of +ve real roots for is 2. & max no. of -ve real roots is 1.
To learn more on Descartes rule click:
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Hasan plans to choose a book from a section of the store where everything is 25%
off. He writes the expression d−0.25d
to find the sale price of the book if the original price is d
dollars.
Bella correctly writes another expression, 0.75d
, that will also find the sale price of the book if the original price is d
dollars.
Drag each description to explain each part of both expressions.
Answer:
see below
Step-by-step explanation:
d= original price
so d−0.25d = full price less 25%
0.75d is the same - paying (1-25%) = 75% of original price