Polynomial function of least degree with integral coefficients that has the given zeros imaginary [tex]\\f(x) & =x^4+5 x^2-6[/tex]
As per the given data:
[tex]\sqrt{6} i$[/tex] is a zero.
Therefore [tex]$-\sqrt{6} i$[/tex] is also a zero.
[tex]$(x+1),(x-1),(x-\sqrt{6} i)$[/tex] and [tex]$(x+\sqrt{6} i)$[/tex] are factors
[tex]$$\begin{aligned}f(x) & =(x+1)(x-1)(x-\sqrt{6} i)(x+\sqrt{6} i) \\& =\left(x^2-1\right)\left(x^2-(\sqrt{6} i)^2\right) \\& =\left(x^2-1\right)\left(x^2-6 i^2\right) \\& =\left(x^2-1\right)\left(x^2+6\right) \\& =x^4+6 x^2-x^2-6 \\f(x) & =x^4+5 x^2-6\end{aligned}$$[/tex]
Therefore the polynomial function is [tex]\\f(x) & =x^4+5 x^2-6[/tex]
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Write a polynomial function of least degree with integral coefficients that have the given zeros of-1, 1, and i times square root of 6.
Please help read text on image.
Answer: -4 < n [tex]\leq[/tex] 5
Step-by-step explanation:
Arturo was comparing the price of apple juice at two stores. The equation y=0.29x represents what Arturo would pay in dollars and cents, y, for x bottles of apple juice at store A. Arturo can buy 13 bottles of apple juice at Store B for a total cost of $8.84. How much more is a bottle of apple juice at Store B than at Store A?
Answer:
$0.39
Step-by-step explanation:
First find the unit rate for store B ( $8.84/13)
At store B Artuto spends $0.68 for one bottle of apple juice
At store A they spent $0.29
0.68-0.29= 0.39
Solve for m.
m/2 = m+5/4
Answer:
m = -5/2 or -2.5
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Craig collect coin, He collected a total of 175 coin. If 72% of the coin he collected were foreign, how many other coin did he collect?
The number of coins which Craig collected as calculated from the given data is 49.
Given ,
percentage of foreign coin = 72%
Therefore the percentage of normal coins will be 28%.
Hence , the number of normal coins which he collected can be found out as ,
28% of 175
= 28% × 175
= 28/100 × 175
= 0.28 × 175
= 49
When we divide a given number by 100 as a fraction , the result we get is known as percentage .
It is represented by the percentage sign which is "%".
The percentage is denoted by the letters "pct" or "pc," respectively. In other words, the percent or % is calculated at a value of around 100 and represents the proportion of one quantity made up of another.
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The speed of sound, S, in meters per second, is a linear function of the temperature of the air through which
the sound travels. Air temperature, T, is measured in degrees Celsius and S=0.6T+331.4. Which of the
following is the best interpretation of the number 331.4 in the context?
a) The speed of sound in meters
per second at 0.6 degrees Celsius
c) The speed of sound in meters
per second at 0 degrees Celsius
b) The increase in speed of sound at 331.4 degrees
per degree of temperature
d) none of the above
Answer:
C
Step-by-step explanation:
S = .6T + 331.4
When S = 331.4:
331.4 = .6T + 331.4 <=====you should be able to see this is true when T= 0
Find the measure of <1
A. 77 degree
B. 38 degree
C. 65 degree
D. 142 degree
Please help!!!!
(Picture provided)
Answer:
D. 142 degree
Step-by-step explanation:
A triangle has 180 degree
77 + 65 = 142 degree
180 - 142 = 38 degree
38 degrees is the missing angle of the triangle. This angle must add with angle 1 outside equal to 180
180 - 38 = 142 degree
So, the answer is D
Write the equation of the line with
slope -3 that goes through the point (-1,3).
Switch the equation to slope y intercept form.
Answer:
y = -3x
Step-by-step explanation:
You want the slope-intercept equation of the line with slope -3 through the point (-1,3).
Point-slope formThe equation of the line with slope m through point (h, k) can be written ...
y -k = m(x -h)
For slope -3 and point (-1, 3), the equation is ...
y -3 = -3(x +1)
Slope-intercept formEliminating parentheses gives ...
y -3 = -3x -3
Adding 3 gives the equation ...
y = -3x
__
Additional comment
As you can see, the y-intercept is 0.
a coin is tossed and a die is rolled. find the probability of getting a head and a number greater than 5
The probability of getting a head and a number greater than 5 i.e, independent events is 0.0833.
A coin is tossed and a die is rolled. These are two independent events. Two events are defined as independent if the outcome of one event has no effect on the outcome of another event. The probability is calculated by multiplying two independent probabilities together, i.e, P(A and B) = P(A) x P(B)
We have, Let us assume two independent events be ,
A : A coin is tossed and the head is thrown.
B : A die is rolled, and a number greater than 5 occurs.
Total possible outcomes when a coin tossed = 2 ={ H ,T }
Total possible outcomes when a die rolled = 6 = { 1,2,3,4,5,6} .
We have to determine probability of getting a head and a number greater
than 5.
Probability of getting the head on toss a coin, P(A) = 1/2
Probability of occuring a number greater than 5 on rolling a die = P(B) = 1/6
So, the probability of getting a head on coin and a number greater than 5 on die =P(A)×P(B)
=(1/2)× 1/6 = 1/12=0.0833
Hence, required probability is 0.0833.
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10.1 approximately how many more calories are there in 2 slices of bacon than there are in 3 slices of trasted turkey? why is there a difference?
Therefore, Two slices of bacon had 96 less calories than three slices of roasted turkey.
What does equation mean?a formula that illustrates the connection between two expressions on either side of a sign. It usually only has one variable and an equal sign. like this: 2x – 4 = 2.
Here,
One piece of bacon has 42 calories in it.
There are 60 calories in 1 slice of turkey.
2 slices of bacon are 2 calories each (42)
So 84 calories in 2 slice of bacon
3 slices of roasted turkey have 3 calories each slice (60)
Three slices of roasted turkey have 180 calories each.
180-84 is the difference in the amount of calories.
96 calories are added due to the calorie difference.
Two slices of bacon had 96 less calories than three slices of roasted turkey.
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the radius of a spherical ball is increasing at a rate of . at what rate is the surface area of the ball increasing when the radius is cm?
Although part of your question is missing, you might be referring to this full question: The radius of a spherical ball is increasing at a rate of 2 cm/min. At what rate is the surface area of the ball increasing when the radius is 8 cm? The surface area of a sphere with radius r is given by 4πr².
The rate at which the surface area of the ball increasing when the radius is 8 cm is 128 cm²/min.
Given A = 4πr²
So, we have:
dA/dt = d/dt (4πr²)
= 4π * d/dt * (r²)
= 4π * 2r * dr/dt
= 8πr * dr/dt
Now, we have that dr/dt = 2 cm/min. So, when the radius of the ball is 8 cm, we have that:
dA/dt = 8πr * dr/dt
= 8π * 8 * 2
= 128π
Since we are measuring area, our unit is cm²/min, not cm/min.
Thus, the rate at which the surface area of the ball increasing when the radius is 8 cm is 128 cm²/min.
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it is estimated that 70% of ucf students participate in anti-racist practices. in a sample of 50 ucf students, how many would you expect to participate in anti-racist practices?
35 expect to participate in anti-racist practices.
anti-racist practices=Anti-racism encompasses a range of ideas and political actions which are meant to counter racial prejudice, systemic racism, and the oppression of specific racial groups. Anti-racism is usually structured around conscious efforts and deliberate actions which are intended to provide equal opportunities for all people on both an individual and a systemic level. As a philosophy, it can be engaged in by the acknowledgment of personal privileges, confronting acts as well as systems of racial discrimination, and/or working to change personal racial biases. Major contemporary anti-racism efforts include Black Lives Matter organizing and workplace antiracism.
Expect value= n*p=0.70*50
=35
Answer=35
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Which of the following represents 1 amu?AMass of a Câ12 atomBMass of a hydrogen atomC1/12th of the mass of Câ12 atomDMass of Oâ16 atom
option c) = [tex]\frac{1}{12}[/tex]th of the mass of C - 12 atom is correct.
First, let us study the definition of Atomic Mass,
Atomic mass -
The total weight of any matter perceived in an atom or any element.1 atomic mass is equal to [tex]1.660539040 * 10^{-24}[/tex] grams.The atomic mass that is derived is slightly lesser than that of the masses of neutrons, protons, and electrons.This slight difference in masses is termed as mass defect.The number of protons and neutrons decides the atomic mass of any particle.The standard unit to measure atomic mass is called Dalton.So we can also conclude that the 1 atomic mass unit is equal to 1/12 of the mass of the C-12 atom
Therefore, option c) = [tex]\frac{1}{12}[/tex]th of the mass of C - 12 atom is correct.
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for the polynomial below -3 is a zero g(x)= x^3+5x^2+56x+150 express g(x) as a product of linear factors
The product of linear factors of the given polynomial are;
(x + 3 )*(x² + 2x + 50 + (−100/(x + 3)))
How to find the linear factor of a polynomial?We are given the polynomial expression as;
g(x)= x³ + 5x² + 56x + 150
Now, we are told that -3 is a zero. Thus, if -3 is a zero that means x = -1
and x + 3 is a factor.
Using online polynomial division calculator, the the polynomial is divided by (x + 3) to get;
(x³ + 5x² + 56x + 150)/(x + 3) = x² + 2x + 50 + (−100/(x + 3))
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Evaluate the Expression P(7, 5)?
Responses:
35
2,520
21
3,500
Based on the values you've listed, it appears that the expression P(7, 5) represents a combination calculation. In combinatorics, the notation P(n, k) represents the number of ways to choose a subset of k items from a set of n items, without regard to the order in which the items are chosen. This is also known as the number of k-permutations of n items.
In this case, the expression P(7, 5) would represent the number of ways to choose a subset of 5 items from a set of 7 items. Using the formula for combinations, this would be calculated as follows:
P(7, 5) = 7! / (5! * (7 - 5)!)
= 7! / (5! * 2!)
= 7 * 6 * 5 * 4 * 3 / (5 * 4 * 3 * 2 * 1 * 2 * 1)
= 7 * 6 / 2
= 21
Therefore, the correct answer for the expression P(7, 5) is 21.
Warner received 7 letters. Each letter weighed between 3.92 ounces and 4.1 ounces. Warner estimates a reasonable weight of all the letters to be 30 ounces.
Is this a reasonable estimate?
The estimate made by Warner is 95% reasonable.
What is inequality? What is a mathematical function, equation and expression?function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.equation : A mathematical equation is used to equate two expressions.Given is that Warner received 7 letters and each letter weighed between 3.92 ounces and 4.1 ounces.
If the we take the maximum possible weight of each letter, which is 4 ounces, then the total weight of 7 letters will be equal to (4 x 7) = 28. But since the weights are weighted between 3.92 ounces and 4.1 ounces, let us assume that the weight of each letter is equivalent to -
w(a) = (3.92 + 4.10)/2 = 8.02/2 = 4.01
So, the weight of 7 letters would be -
W{7} = w(a) x 7 = 7 x 4.01 = 28.7
28.7 = 29 (round off) ≈ 30
So, yes the estimate of the Warner is reasonable.
Therefore, the estimate made by Warner is 95% reasonable.
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The cost a sofa set is $9352. how much will 125 such sofa sets cost?
Write an inequality for the statement:
negative two thirds is a minimum of the product of a number and negative seven eighths
negative seven eighths ≤ negative two thirdsw
negative seven eighths ≥ negative two thirdsw
negative two thirds ≥negative seven eighthsw
negative two thirds ≤ negative seven eighthsw
The required linear inequality is [tex]-\frac{2}{3} \geq -\frac{7}{8}x[/tex]
What is linear inequation?
A linear inequation is an equation that contains one or more variables, such as x, and involves linear functions. Unlike a linear equation, its solution set is not a single point, but a range of values. Linear inequations are used to represent situations where the exact value of a variable is not known, but a range of values can be determined based on certain conditions. For example, if x represents the amount of money a person makes in a year and we know that it must be greater than $50,000, then we can write the linear inequation x > 50,000.
Let the number be x
[tex]-\frac{2}{3}[/tex] is a minimum of the product of a number and [tex]-\frac{7}{8}[/tex]
[tex]-\frac{2}{3} \geq -\frac{7}{8}x[/tex]
This is the required linear inequality
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What is the center of dilation? How do you know?
Answer:
A
Step-by-step explanation:
You want the center of dilation when ∆ABC is dilated by a factor of 1/2 to get ∆AED.
Center of dilationIn any dilation, the center of dilation is invariant. It doesn't move.
Since point A is common to both triangles, it didn't move. Point A is the center of dilation.
Select the correct answer. What is the end behavior of the radical function represented by this graph? The graph shows the square root function. The function starts at the point (minus 3, 0) and extends upwards and to the right. Some major points on the graph are (0, 3), (2, 4), and (5, 5). A. As x decreases in value, increases in value. As x increases in value, decreases in value. B. As x decreases in value, increases in value. As x increases in value, increases in value. C. As x decreases in value, decreases in value. As x increases in value, decreases in value. D. As x decreases in value, decreases in value. As x increases in value, increases in value.
The end behavior of the function is that;
D. As x decreases in value, f(x) decreases in value.
As x increases in value, f(x) increases in value.
What is the end behavior of the radical function?
The end behavior of a function f(x) describes the behavior of the graph of the function at the "ends" of the x-axis.
Now, in the graph attached, at the end point of the curve on the left of the x-axis, we see that the coordinate is (-3, 0) and to the right which is when x has increased to 9 and now has a coordinate point of (9, 6).
Thus, we conclude that we see that as the value of x increased from left to right, f(x) also increased and as the value of x decreased from right to left, f(x) also decreased.
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in an experiment designed to measure the distance a golf ball is hit by clubs made of different material, the independent variable would be:
In studies intended to measure the distance a golf ball is struck with weapons made of various materials, the material of the golf ball and the direction of the wind at the moment the experiment was done become standardized variables.
In tests intended to assess the distance a golf ball is struck with clubs made of various materials, the kind of material the club is composed of is an independent variable.
Independent variables are those that a researcher tries to manipulate or control to observe how they impact the dependent variable. In this experiment, the effect of different club construction materials on golf ball distance is investigated.
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Write 0.302 repeating as a fraction. show your work.
Answer:
x = 302/999
HERE THE ANSWER
Step-by-step explanation:
A circle with a radius of 1 cm sits inside a 3 cm x 4 cm rectangle.
What is the area of the shaded region?
Round your final answer to the nearest hundredth.
Answer:
below
Step-by-step explanation:
Area of rectangle ( 3 x 4 ) minus the area of the circle (pi * 1^2) =
= shaded area = 8.86 cm^2
question 7 a data analyst adds labels to their line graph to make it easier to read even though they already have a legend on their visualizations. how does labeling the data make it more accessible?
Labels on a line graph can make the visualization more accessible in a few ways:
Labels can provide additional context for the data. For example, if the y-axis of the line graph represents the temperature in degrees Celsius, labeling each line with the location or type of temperature measurement can help the viewer better understand the data.Labels can help the viewer more quickly identify the data they are interested in. If the line graph has many lines and a legend, it can be time-consuming to locate the specific line of interest. By labeling each line directly on the graph, the viewer can more easily find the data they are looking for.Labels can improve the clarity and readability of the graph. If the lines on the graph are close together or overlap, labels can help the viewer distinguish between the different lines.Overall, labels can help make a line graph more accessible by providing additional context, improving readability, and helping the viewer quickly find the data they are interested in.
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Write a situation for 4.63 x 9 and a picture that goes with it
A problem that could be solved by multiplying 4.63 x 9 is "the product of 4.63 and 9"
How to determine the productFrom the question, we have the following parameters that can be used in our computation:
4.63 x 9
In the above expression, we can see that
4.63 and 9 are multiplied
This means that the problem is a product expression
And a problem that can represent 4.63 x 9 is "the product of 4.63 and 9"
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Find the distance between the two points rounding to the nearest tenth (if necessary).
(0,7) and (4,9)
Nataha wa thinking of a number. Nataha add 2. 5 to the number, then double the reult to get an anwer of 61. Form an equation with x from the information
The equation with x about the number thought by Natasha is (x + 2.5) × 2 = 61
Let the number thought by Natasha be x. To formulate the equation, we will perform the same operations as done by Natasha. Forming the equation now -
(x + 2.5) × 2 = 61
Performing multiplication on Left Hand Side of the equation
2x + 5 = 61
Rewriting the equation
2x = 61 - 5
Performing subtraction on Right Hand Side of the equation
2x = 56
Rewriting the equation
x = 56/2
Performing division on Right Hand Side of the equation
x = 28
Thus, the equation is (x + 2.5) × 2 = 61 and the number thought by Natasha is 28.
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Tomorrow, Mrs. Wendel's class will be using toothpicks for a science project. Each student must use at least 6 toothpicks for the project.
Mrs. Wendel knows that there is already a bag of 50 toothpicks in the class storage room. She plans to buy x additional toothpicks this afternoon to make sure her class will have enough.
If her class has 28 students, which number sentence represents this situation?
the confidence interval for the mean of y is always narrower than the prediction interval for an individual response y given the same data set, x value, and confidence level. group of answer choices true false
The statement 'the confidence interval for the mean of y is always narrower than the prediction interval for an individual response y given the same data set, x value, and confidence level.' is True.
In this question, we have been given a statement 'The confidence interval for the mean of y is always narrower than the prediction interval for an individual response y given the same data set, x value, and confidence level. '
We need to state whether the given statement is true or false.
We know that the confidence interval = sample mean ± margin of error
The confidence interval for the mean of y is narrower when the x value is close to the mean of all of the x values.
Therefore, the confidence interval for the mean of y is always narrower than the prediction interval for an individual response y given the same data set, x value, and confidence level is True.
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The owner expects to sell 800 snow cones next week. He earns a profit of $2.29 on each snow cone sold. Based on last week's results, how much profit can the owner expect to earn from cherry snow cone sales next week? Cherry was sold 120 times last time.
Based on last week's results, the profit that the owner expect to earn from cherry snow cone sales next week is $1832.
How much profit can the owner expect to earn from cherry snow cone sales next week?From the information, the owner expects to sell 800 snow cones next week and he earns a profit of $2.29 on each snow cone sold. Based on last week's results.
The profit can the owner expect to earn from cherry snow cone sales next week will be:
= Number of cheery × Profit on each
= 800 × $2.29
= $1832
The profit is $1832.
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Find the measures of two complementary angles if the measure of the larger angle is 2 less than 3 times the measure of the smaller angle.
Answer:
Let x be the larger angle and y be the smaller angle
Larger angle is 2 less than 3 times the smaller angle that is x = 3y - 2
As the angles are complementary, their sum equals 90°
or, x + y = 90°
or, 3y - 2 + y = 90°
or, 4y = 92°
or, y = 23°
So, x = 3 * 23 - 2 = 67°
Larger angle = x = 67°
Smaller angle = y = 23°