Show that the equation has no rational root. 11. x3 + 3x2 - 4x + 6 = 0 12. 3x3 - 4x2 + 7x + 5 = 0 13. 5x4 + 3x2 - 5 14. x4 - 9x + 7 15. x5 – 3x3 + 4x2 + x - 2 = 0 16 2x5 + 3x3 + 7 = 0
Answers
To show that an equation has no rational root, we can apply the Rational Root Theorem.
The theorem states that if a rational number p/q (where p and q are integers and q≠0) is a root of a polynomial with integer coefficients, then p must be a factor of the constant term, and q must be a factor of the leading coefficient.
11. x³ + 3x² - 4x + 6 = 0
Leading coefficient: 1, Constant term: 6
Possible rational roots: ±1, ±2, ±3, ±6
None of these roots satisfy the equation, so there are no rational roots.
12. 3x³ - 4x² + 7x + 5 = 0
Leading coefficient: 3, Constant term: 5
Possible rational roots: ±1, ±5, ±1/3, ±5/3
None of these roots satisfy the equation, so there are no rational roots.
13. 5x⁴ + 3x² - 5
This is not an equation, so we cannot determine the roots.
14. x⁴ - 9x + 7
Leading coefficient: 1, Constant term: 7
Possible rational roots: ±1, ±7
None of these roots satisfy the equation, so there are no rational roots.
15. x⁵ – 3x³ + 4x² + x - 2 = 0
Leading coefficient: 1, Constant term: -2
Possible rational roots: ±1, ±2
None of these roots satisfy the equation, so there are no rational roots.
16. 2x⁵ + 3x³ + 7 = 0
Leading coefficient: 2, Constant term: 7
Possible rational roots: ±1, ±7, ±1/2, ±7/2
None of these roots satisfy the equation, so there are no rational roots.
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Related Questions
parallelogram calc: find p, b=n/a, a=n/a
Answers
Therefore, the perimeter can be calculated by adding up all four sides: p = 2b + 2n.
To find the perimeter (p) of a parallelogram, you need to know the length of all four sides. However, in this case, you are given the ratio of the base (b) to one of the sides (a), which is n/a.
Since a parallelogram has two pairs of parallel sides, the opposite sides are equal in length. Therefore, if the base is b, then the opposite side is also b. Using the given ratio, you can find the length of the other side (n) by multiplying a by n/a, which is n.
So, the length of the other side is also n, and the perimeter can be calculated by adding up all four sides: p = 2b + 2n.
However, if given the ratio of the base to one of the sides, you can use this to find the length of the other side. For this problem, if the base is b, then the opposite side is also b, and the length of the other side is n (where n/a = b/a).
Therefore, the perimeter can be calculated by adding up all four sides: p = 2b + 2n.
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2.1.3 8-23 + 110 - √64
Answers
I don’t know if it is 2.138 or 21.38
Let f be the function with derivative given by f ' (x) = sin (x^2 +1). How many relative extrema does f have on the interval 2< x < 4?
a. One
b. Two
c. Three
d. Four
e. Five
Answers
The function f(x) has at most one relative extremum on the interval 2 < x < 4, based on the behavior of its derivative f'(x) = sin(x^2 + 1). Therefore, the correct option is a. One.
To determine the number of relative extrema of the function f(x) on the interval 2 < x < 4, we need to analyze the behavior of its derivative f'(x).
We have that f'(x) = sin(x^2 + 1), we need to examine where the derivative changes its sign within the interval (2, 4) to identify the relative extrema.
Since the sine function oscillates between -1 and 1, we can observe that sin(x^2 + 1) will also oscillate between -1 and 1 as x^2 + 1 varies.
However, since the interval (2, 4) is relatively small, the value of x^2 + 1 will not vary significantly, and the sine function will not complete multiple oscillations within this interval.
Therefore, there will be at most one sign change for sin(x^2 + 1) within the interval (2, 4), indicating that f(x) may have at most one relative extremum within this interval.
Hence, the correct answer is: a. One.
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the following results on summations will help us in calculating the sample variance s2. for any constant c,
Answers
In the context of calculating sample variance (s²), the following results on summations can be helpful.
These results state that for any constant c, the sum of the squared deviations from c is equal to the sum of the squared values minus 2c times the sum of the values, plus c squared times the count of values.
To calculate the sample variance (s²), which measures the variability of a set of values, it is necessary to compute the sum of the squared deviations from the mean. The following results on summations can aid in this calculation:
Sum of Squares: The sum of the squared values is equal to the sum of each value squared.
∑(x²) = (x₁)² + (x₂)² + ... + (xₙ)²
Deviation from a Constant: If we have a constant value c, the sum of the squared deviations from c is obtained by subtracting 2c times the sum of the values from the sum of the squared values and adding c squared times the count of values.
∑((x - c)²) = ∑(x²) - 2c∑(x) + c²n
These results can be utilized in calculating the sample variance (s²) by considering c as the mean of the values. By applying these formulas, we can efficiently compute the necessary summations and obtain the desired variance measurement for the given dataset.
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the perimeter of a rectangular garden is 84 feet. write and solve the system of equations that can be used to find the dimensions of the garden if its length, l, is 3 feet longer than its width, w.
Answers
Answer:
The length is 22.5 and the width is 19.5
Step-by-step explanation:
2L + 2W = P
\/
2L + 2W = 84
\/
W + 3 + W + 3 + W + W= 84
\/
4W + 6 = 84
\/
4W = 78
\/
W = 19.5 L = 19.5 + 3 = 22.5
I hope this helps, have a nice day! :D
There are 14 dogs at the dog park on a busy Saturday. 2 of them are springer spaniels.
What is the probability that a randomly selected dog is a springer spaniel?
Write your answer as a fraction or whole number.
Answers
Answer:1/7
Step-by-step explanation: You take the amount that are springer spaniels and you put them with the whole of the dogs in the park 14 so you would have 2/14. You can reduce this fraction to 1/7 by dividing both the top and bottom of the fraction by 2.
2. When was the dollar worth more than it was today?
A. 1990
B. 1880
C.1960
D. 2016
Answers
Answer:
1960
Step-by-step explanation:
1880 unknown
1990 $1.23
2016 $1
1960 $8
C.1960
But I’m not 100% positive
SOMEONE HELP ME PLS
I ATTACHED A PIC
Answers
Answer:
\(A=54.95\ ft^2\)
Step-by-step explanation:
The angle of shaded sector = 360-332 = 28°
The radius of sector, r = 15 ft
We need to find the area of the shaded sector. The formula for the area of the sector is given by :
\(A=\dfrac{\theta}{360}\times \pi r^2\\\\=\dfrac{28}{360}\times 3.14\times (15)^2\\\\A=54.95\ ft^2\)
So, the area of the shaded sector is equal to \(54.95\ ft^2\).
In one month, Jillian made 36 local phone calls and 20 long distance calls.
What was her ratio of local calls to long distance calls for that month?
A. 2:1
B. 3:2
C. 9:4
D. 9:5
Answers
Answer:
D.
Step-by-step explanation:
Because 36:20 simplified is 9:5.
Answer:
It is D 9:5
Step-by-step explanation:
Beacuse 9x4= 36
and 5x4= 20
so 36:20 or 9:5
In the past month, Kala rented 3 video games and 7 DVDs. The rental price for each video game was $3.30. The rental price for each DVD was $3.80. What is
the total amount that Kala spent on video game and DVD rentals in the past month?
Answers
Answer:
$24.20
Step-by-step explanation:
Find the volume of a sphere with a radius of 5 in. Round to the nearest hundredth.
A) 53.05 in3
B) 104.72 in3
C) 392.70 in3
D) 523.60 in3
Answers
Answer:
D
Step-by-step explanation:
it's D I don't have a full step by step
What is the sum of 42÷9198?
Answers
Answer: 219
Step-by-step explanation: hope this helps!!!!
Round 0.698 to the nearest hundredth.
PLZ PLZ HELP
Answers
Answer:
0.70
Step-by-step explanation:
The nine is in the hundreths place, and it is over five, so you would round the number to the left of it up (the six). Basically, ignore the 8.
The number 0.698, when rounded off to the nearest hundredth, will become 0.70.
For the Rounding, some number to a specific value is making its value, mostly done for better readability or accessibility.
We need to round 0.698 to the nearest hundredth.
The hundredth place in the number is 9, that is greater than or equal to 5.
Since, we round up the tenths place to 7 + 1 = 8 and drop all other digits after the hundredth place and replace them with zeros.
0.698 rounded to the nearest hundredth is 0.70.
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Evaluate -4a+8b-6c
What is the value of the expression
Answers
-2(2a-4b+3c)
determine the convergence or divergence of the series. (if you need to use or –, enter infinity or –infinity, respectively.) [infinity] (−1)n 1 n 3
Answers
Based on the computation, the series \(\sum \frac{(-1)^n}{n^3}\) converges
How to determine the convergence or divergence of the series.From the question, we have the following parameters that can be used in our computation:
\(\sum \frac{(-1)^n}{n^3}\)
From the above series, we can see that:
The expression (-1)ⁿ implies that the sign of each term of the series would change from + to - and vice versaThe denominator n³ has no impact on the sign of the termUsing the above as a guide, we have the following:
We can conclude that the series converges
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how many pattern block rhombuses would create 2 hexagons
Answers
To determine the number of pattern block rhombuses needed to create 2 hexagons, we need to understand the relationship between the two shapes.
A pattern block rhombus is a rhombus-shaped tile commonly used in geometry and math education. It is composed of two equilateral triangles joined together.
A hexagon, on the other hand, is a polygon with six sides. Each side of a regular hexagon is congruent to the others, and all its angles are equal.
In order to create a hexagon using pattern block rhombuses, we need to consider the arrangement of the rhombuses. Let's assume that the hexagons we want to create are regular hexagons.
A regular hexagon can be divided into six equilateral triangles. Each equilateral triangle can be formed using two pattern block rhombuses. Therefore, to create one regular hexagon, we need a total of 6 equilateral triangles x 2 rhombuses per triangle = 12 pattern block rhombuses.
Since we want to create 2 hexagons, we multiply the number of rhombuses required for one hexagon by 2:
12 pattern block rhombuses per hexagon x 2 hexagons = 24 pattern block rhombuses.
Therefore, we would need 24 pattern block rhombuses to create 2 regular hexagons.
Does anybody know the answer. 51 - 3 + 5k = 58
Answers
Answer:
k=2
Step-by-step explanation:
1. 48+5k=58
2. 5k=58-48
3. 5k=10
4. k=10/5
5. k=2
express the radical using the imaginary unit i
Answers
Answer:
27
Step-by-step explanation:
Systems of equations are often used to model real-life situations. List 2 examples where a system of equations could describe a real-life situation. Elaborate on why you think a system of equations would be useful for each example.
Answers
2 examples where a system of equations could describe a real-life situation are given below.
What is equation?Equation is a physical and mathematical statement that describing physical phenomena and the relationship between different physical quantity typically consist of variable simple presenting physical quantity and then it personal variable may be pointed such as your energy.
1.Modeling a business’s profit: A business can be represented by a system of equations to find the maximum profit. The equations can include the cost of the product, the price of the product, the number of units of the product sold, and other variables such as taxes and shipping costs. By representing the business with a system of equations, a business can optimize the equation to achieve the maximum profit.
2. Modeling the housing market: A system of equations can be used to model the housing market. The equations can include variables such as housing prices, the number of houses on the market, the number of buyers, the supply of housing, and the demand for housing. By using a system of equations, economists can better understand the housing market and make predictions about future trends in the market.
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Point G is on line segment
F
H
‾
FH
. Given
G
H
=
8
,
GH=8,
F
H
=
3
x
+
3
,
FH=3x+3, and
F
G
=
2
x
,
FG=2x, determine the numerical length of
F
G
‾
.
FG
.
Answers
The numerical length of the line segment FG is 10 units.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables. An independent variable is a variable that does not depend on other variables while a dependent variable is a variable that depends on other variables.
Point G is on FH, hence:
FH = FG + GH
Given that GH = 8, FH = 3x + 3, FG = 2x, hence:
3x + 3 = (2x) + 8
x = 5
FG = 2x = 2(5) = 10
The numerical length of the line segment FG is 10 units.
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Answer the questions below about Line 1 and Line 2 shown below.
[(-2) +8] +3
(-2) + [8+3]
The expression was rewritten using the
[(-2) +8] + 3 equals
(-2) + [8+3] equals (-2)+
Submit Answer
+3 which equals
which equals
Line 1
Line 2
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![Answer the questions below about Line 1 and Line 2 shown below.[(-2) +8] +3(-2) + [8+3]The expression](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/Zo2cTszm3YJ6AMZZyUecQKCSB2GKT0US.png)
Answers
The expression was written using the associative property of addition.
[(-2) +8] +3 equals 6 + 3 which equals 9.
(-2) + [8+3] equals (-2) + 11 which equal 9.
Given,
[(-2) +8] +3 equals ______ + 3 which equals _____
(-2) + [8+3] equals (-2) + _____ which equal _____
We need to see which operation is used and fill in the blanks.
What is the associative property of addition?It states that (a+ b) + c = a + (b + c).
We have,
[(-2) +8] +3 equals ______ + 3 which equals _____
(-2) + [8+3] equals (-2) + _____ which equal _____
We can write it as:
[(-2) +8] +3 = 6 + 3 = 9
(-2) + [8+3] = -2 + 11 = 9
We see that,
[(-2) +8] +3 = (-2) + [8+3]
This is in the form: (a+b)+c = a+(b+c)
Thus the expression was written using the associative property of addition.
[(-2) +8] +3 equals 6 + 3 which equals 9.
(-2) + [8+3] equals (-2) + 11 which equal 9.
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Evaluate the trigonometric function directly, without first changing to degree measure. tan 0.5936
Answers
Given:
\(tan\theta=0.5936\)Aim:
We need to find the trigonometric function and the quadrant of the angle.
Explanation:
\(tan\theta=0.5936\)Take inverse trigonometry on both sides of the equation.
\(\theta=tan^{-1}0.5936\)\(\theta=30.6934\)\(\text{ The angle 30.6934 lies between 0 and }\frac{\pi}{2}.\)\(0\text{ to }\frac{\pi}{2}\text{ refers to the first quadrant.}\)Final answer:
\(Since\text{ 0.5963 is between 0 and }\frac{\pi}{2}\text{ the angle is in quadrant I.}\)\(tan30.6934^o=0.5936\)\(tan\text{ }0.5936=30.6934^o\)The drawing plan for an art studio shows a rectangle that is 19.2 inches by 8 inches. The scale in the plan is 4 in.: 5 ft. Find the length and width of the actual studio. Then find the area of the actual studio.
Answers
Width: 10 feet
Area: 190 feet
can someone help me with this please?? its due today and i only have an hour to finish. im failing math right now and i really need to get my grade up before monday
Answers
Answer:
C = 18π cm
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightGeometry
Circumference Formula: C = 2πr
r is radiusStep-by-step explanation:
Step 1: Define
Identify variables
r = 9 cm
Step 2: Find C
Substitute in variables [Circumference Formula]: C = 2π(9 cm)Multiply: C = 18π cmWhat is the distance between the following points?
Answers
Answer:
if im not mistaken the andswer is D
how do you find the height of a pyramid if the base and volume are given?
formula: 1/3Bh (B=Base H=Height)
Answers
The height of the pyramid from the base and the volume is h = 3V/B
Finding the height of the pyramid from the base and the volumeFrom the question, we have the following parameters that can be used in our computation:
Volume and base area are known
This means that we make the height the subject of the formula
The volume of a pyramid is calculated as
V = 1/3Bh
Where
B Base area
h - height
So, we have
h = 3V/B
By making the height the subject of the formula
Hence, the height of the pyramid from the base and the volume is h = 3V/B
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I need some help with these math questions.
Answers
Answer:
For the first question, D is the correct answer.
For the second question, B is the correct answer.
Step-by-step explanation:
First question:
\(5.89 + .61(30) = 24.19\)
\(5.89 + .61(35) = 27.24\)
So D is the correct answer.
Second question:
A function is a relation in which each element in the domain corresponds to one and only one element in the range. That said, relations A, C, and D are not functions since in each of these relations, one element in the domain corresponds to two elements in the range. Only relation B is a function.
Classify the triangle based on its angles
Answers
Answer:
Right-angled triangle
Step-by-step explanation:
It has a square angle, meaning it is a right angle, which is \(90^{o}\), making it a right angled triangle
Using the same facts as #16, how long would it take to pay off 60% of the a. About 45 months b. About 50 months c. About 55 months d. About 37 months
Answers
To calculate how long it would take to pay off 60% of the debt,
we can use the same facts as in problem #16. Let's go through the steps:
1. Determine the total amount of debt: Find the original debt amount given in problem #16.
2. Calculate 60% of the debt: Multiply the total debt by 0.6 to find the amount that represents 60% of the debt.
3. Divide the amount obtained in step 2 by the monthly payment: This will give us the number of months it will take to pay off 60% of the debt.
Now, let's apply these steps to the options provided:
a. About 45 months: To determine if this is the correct answer, we need to perform the calculations outlined above using the original debt amount and the monthly payment given in problem #16.
b. About 50 months: Same as option a, perform the calculations using the original debt amount and the monthly payment.
c. About 55 months: Perform the calculations outlined above using the original debt amount and the monthly payment.
d. About 37 months: Perform the calculations outlined above using the original debt amount and the monthly payment.
After performing the calculations for each option, compare the results with the options provided to find the correct answer.
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Please Help! 60 points for a rapid reply- please look at the question below= The Figure of circle A shown has a diameter of PR which intersects with QS at point B and the measurements shown, Calculate the following measures-
Answers
The measures in the circle given in the image above are calculated as:
1. m<PSQ = 130°; 2. m<AQS = 30°; 3. m(QR) = 100°; 4. m(PS) = 110°; 5. (RS) = 70°.
How to Find the Measures in the Circle?In order to find the measures in the circle shown, recall that according to the inscribed angle theorem, the measure of intercepted arc is equal to the central angle, but is twice the measure of the inscribed angle.
1. m<PSQ = m<PAQ
Substitute:
m<PSQ = 130°
2. Find m<PBQ:
m<PBQ = 1/2(m(PQ) + m(RS)) [based on the angles of intersecting chords theorem]
Substitute:
m<PBQ = 1/2(130 + 2(35))
m<PBQ = 100°
m<AQS = 180 - [m<BAQ + m<PBQ]
Substitute:
m<AQS = 180 - [(180 - 130) + 100]
m<AQS = 30°
3. m(QR) = m<QAR
Substitute:
m(QR) = 100°
4. m(PS) = 180 - m(RS)
Substitute:
m(PS) = 180 - 2(35)
m(PS) = 110°
5. m(RS) = 2(35)
m(RS) = 70°
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