Write a polynomial function f of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros. Write the function in standard form. Show your work.
0, 5, -5+sqrt8
Answers
The polynomial function is f(x) = x(x - 5)(x + 5)² - 8)
How to determine the polynomial from the zeros?From the question, we have the following parameters that can be used in our computation:
Zeros: x = 0, 5, -5 + √8
The polynomial can be repesented as
f(x) = product of (x - zeros)
using the above as a guide, we have the following:
f(x) = x(x - 5)(x - (-5 + √8))(x - (-5 - √8))
This can be expressed as
f(x) = x(x - 5)(x + 5)² - 8)
hence, the polynomial is f(x) = x(x - 5)(x + 5)² - 8)
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Related Questions
This table shows the low and high temperatures in four different regions in a state.
Answers
Answer:
The answer is the east region
determine if the equation is exact. if it is, then solve it. (3x^2y 3)dx (x^3-5)dy=0
Answers
Φ(x) = x^m is a solution for the equation a , when m = -9 or m = 1
for function
Φ(x) = x^m
then
dΦ/dx (x) = m*x^(m-1)
d²Φ/dx² (x) = m*(m-1)*x^(m-2)
then
for a expression
3x^2 (d^2y/dx^2) + 11x(dy/dx) - 3y = 0
3x^2*m*(m-1)*x^(m-2) + 11*x* m*x^(m-1) - 3*x^m = 0
3*m*(m-1)*x^m + 11*m*x^m- 3*x^m = 0
dividing by x^m
3*m*(m-1) + 11*m - 3 =0
3*m² + 8 m - 3 =0
m= [-8 ± √(64 + 4*3*3)]/2 = (-8±10)/2
m₁ = -9 , m₂= 1
then Φ(x) = x^m is a solution for the equation a , when m = -9 or m = 1
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-3³x2-3-5x12÷2²+2x(-21)÷7
HELP
Answers
Answer:
Step-by-step explanation:
THE ANSWEAR IS 58.5 OR 117/2
John drives his car on two roads for a total of 6 hours. On one road, he can drive at 100 km/h and on the other, he drives at a speed of 80 km/h. If he drives a total distance of 530 km, how long does he drive on each road?
Please show steps. :D
Answers
The total distance D traveled by John is 255 miles.
What is meant by distance?A measurement of how far away two things or points are might be quantitative or occasionally qualitative. Distance can refer to a physical length or an estimation based on other factors in physics and ordinary language. The length of the line that connects two places serves as the unit of measurement for distance. By subtracting the different coordinates from the pair if the two points are on the same horizontal or vertical line, the distance can be calculated. To determine how far apart two points on an XY plane are, use the distance formula in coordinate geometry or Euclidean geometry. The term "x-coordinate" or "abscissa" refers to a point's separation from the y-axis.The total distance D traveled by John is given by
D = 45 × 2 + 3 × 55 = 255 miles.
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John travelled 280 kilometres in the first distance and 250 kilometres in the second distance.
How to find the times associated to each road?This question shows the case of John, who drove at constant speed his car on two roads. The travelled distance (s), in kilometers, is equal to the following formula:
s = v × t
Where:
v - Speed, in kilometers per hour.
t - Time, in hours.
The total time (T), in hours, is found by means of the following expression:
T = t₁ + t₂
T = x₁ / v₁ + x₂ / v₂
Where:
x₁ - Distance traveled in the first road
x₂ - Distance traveled in the second road.
v₁ - Speed taken in the first road.
v₂ - Speed taken in the second road.
T - Total time.
If we know that v₁ = 100 km / h, v₂ = 80 km / h, x₂ = 530 km - x₁ and T = 6 h, then the first distance is:
(530 - x₁) / 100 + x₁ / 80 = 6
[80 · (530 - x₁) + 100 · x₁] / 8000 = 6
42400 - 80 · x₁ + 100 · x₁ = 48000
20 · x₁ = 5600
x₁ = 280 km
And the second distance is:
x₂ = 530 km - 280 km
x₂ = 250 km
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I still don`t get it.
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Answer:
Please type or attach a question that you need help with. Currently, all you have is the statement "I still don`t get it."
Florida has about 66 tornadoes each year, which is approximately 5.7% of all tornadoes in the United States annually. Estimate how many tornadoes occur in the United States each year
Answers
The number of tornadoes that occur in the United States each year is 1158
How to determine the tornadoes each yearLet's call the number of tornadoes in the United States each year "x".
The number of tornadoes in Florida each year is 5.7% of this total
So we can write:
66 = x * 5.7%
Divide both sides by 5.7%
x = 66/5.7%
Evaluate
x = approximately 1158
So, approximately 1162 tornadoes occur in the United States each year.
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MODELING WITH MATHEMATICS You push your younger cousin on a tire swing one time and then allow your
cousin to swing freely. On the first swing, your cousin travels a distance of 14 feet. On each successive swing,
your cousin travels 75% of the distance of the previous swing. What is the total distance your cousin swings?
Answers
56 feet is the total distance your cousin swings. This can be solved by using the concept of explicit formula.
What is explicit formula?From the term of the series, it is simple to get the explicit formula for the arithmetic sequence. For the mathematical series a, a + d, a + 2d, a + 3d,.......a + (n - 1)d, and the nth component in the sequence provides the explicit formula. Consequently, a = a + (n - 1)d serves as the explicit formula for the arithmetic series.
Given that,
You push your younger cousin on a tire swing one time and then allow your cousin to swing freely. On the first swing, your cousin travels a distance of 14 feet.
So, a₁ = 14 feet
the second swing the person travels a distance that is 75% of the first, hence, a₂ = 0.75 a₁
On the third swing it is a₃ = 0.75 a₂
since, a₂ = 0.75 a₁ and a₃ = 0.75 a₂
Now, using explicit formula we find that,
a₂ = 0.75 a₁ = 14 × 0.75
a₃ = 0.75 a₂ = 0.75 × (14 × 0.75) = 14 × (0.75)²
a₄ = 0.75 a₃ = 0.75 × 14 × (0.75)³
Thus, the general formula becomes: a(n) = 14 × (0.75)ⁿ
Now use formula for the Sum of infinite geometric series to calculate the total distance: S = a₁ / (1 - r)
S = 14 / ( 1 - 0.75)
S = 14 / 0.25
S = 56 feet
56 feet is the total distance your cousin swings.
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suppose there are ten five- and six-year-olds attending a birthday party. when a 30-year-old mother walks into the room with an infant in her arms, what happens to the standard deviation of ages in the room? (changes or stays approximately the same) changes what happens to the median of ages in the room? (gets bigger; gets smaller; stays approximately the same
Answers
The standard deviation of ages in the room increases, while the median of ages stays approximately the same.
Standard deviation is a measure of the variability of a set of data points. The addition of a 30-year-old mother and an infant to the group of ten five- and six-year-olds increases the spread of the ages, thus increasing the standard deviation.
The median, on the other hand, is the middle value in a set of data points. Since the median only depends on the order of the values, not their magnitude, adding a mother and an infant to the group of children does not significantly affect the median age in the room, which would still be close to 5 or 6 years old.
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How can you calculate the terms of pi if the total surface area of a solid cylinder of radius is 3 cm and height is 4 cm?
Answers
Answer:
yes. see below
Step-by-step explanation:
area of a cylinder = top circle + bottom circle + lateral
lateral = perimeter of the circle * height = 2π*4 * 10 =80π
area of a circle = πr² = 9π
top & bottom =18π
total = 80π+18π =98π
An electrician leans an extension ladder against the outside wall of a house so that it reaches an electric box 27 feet up. The ladder makes an angle of 62 degrees with the ground. Find the length of the ladder. Round your answer to the nearest tenth of a foot if necessary.
Answers
The length of the ladder is given as 30.58 ft using Trigonometry.
What is Trigonometry ?In the field of mathematics known as trigonometry, correlations between angles and length ratios are studied. The field was created in the Hellenistic era in the third century BC as a result of the use of geometry in astronomical research.
Distance is the measurement of an object's horizontal distance from a certain point, whereas height is the measurement of an object's height in the vertical direction.
Trigonometry includes heights and distances, and it has many uses in practical daily life. It is used to determine the distance between any two objects, including celestial bodies or other objects, as well as the height of towers, buildings, mountains, etc. Astronauts, surveyors, architects, and navigators are the main users.
The angle made by the ladder is 62°
Length of the ladder is x ft (say)
Height of the Electric Box is 27 ft
Now ,
sinθ = height of Electric box/ length of ladder
sin62° = 27/x
⇒x = 30.58 ft.
The length of the ladder is given as 30.58 ft using Trigonometry.
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Find the product of the solutions for which [tex]\frac{x-5}{9} = \frac{5}{x+7}[/tex]
A. -80
B. 80
C. 60
D. -60
Answers
The product of the solutions of the algebraic equation is -80
How to solve algebraic equations?An algebraic equation is any equation that contains unknown values, usually represented with alphabets or letter
(x-5)/9 = 5/(x+7)
(x-5)(x+7) = 5 * 9
(x-5)(x+7) = 45
x² - 5x + 7x - 35 = 45
x² + 2x - 35 = 45
x² + 2x - 35 -45 = 0
x² + 2x - 80 = 0
(x − 8)(x + 10) = 0
x−8=0 or x+10=0
x=8 or x=-10
Product of the solutions = 8 * (-10) = -80
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For a normally distributed population with μ-300 and σ-25, determine the standardized z-value for each of the x-values below. a. x 325 b, x=295 c. x 350 a. z= □ (Round to two decimal places as needed.) b. z= □ (Round to two decimal places as needed.) c. z= □ (Round to two decimal places as needed,)
Answers
a. z= 0.80, b. z= -0.60, c. z= 1.40, The z-value is calculated by subtracting the population mean (μ) from the given x-value, and then dividing the result by the population standard deviation (σ).
The standardized z-value is used to measure the number of standard deviations away from the mean a given value lies. To calculate the z-value, we subtract the mean (μ) from the given x-value, and divide the result by the standard deviation (σ) of the population. For example, to calculate the z-value for x=325:
z= (325 - 300)/25 = 0.80
Similarly, for x=295:
z= (295 - 300)/25 = -0.60
And for x=350:
z= (350 - 300)/25 = 1.40
Therefore, the z-value for each of the x-values given is 0.80, -0.60 and 1.40 respectively.
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a circular mirror is surrounded by a square metal frame. the radius of the mirror is 2x. the side length of the metal frame is 12x what is he area of the metal frame?
Answers
The total area filled by a flat (2-D) surface or an object's form is referred to as the area and the required area of the metal frame is 93.76x² unit square.
What is Area?The area is the total area occupied by a flat (2-D) surface or the form of an object.
Create a square on paper by using a pencil.
Two dimensions make it up.
A form's area on paper is the space it takes up.
So, given, a square metal frame encircles a circular mirror.
The mirror has a 4x radius.
The metal frame's side length is 12x.
According to the basic formula for the area of a circle and a square:
area of a circle = pi * radius * radius
Square Area = Side * Side
In the given situation:
Mirror's Area = pi * 4x * 4x = pi * 16x² = 50.24x
Squared mirror's Area = 12x * 12x = 144x²
The area of the metal frame is the sum of the areas of the squared and round mirrors.
Metal frame area = 144x² - 50.24x²
Metal frame size = 93.76x²
Therefore, the total area filled by a flat (2-D) surface or an object's form is referred to as the area and the required area of the metal frame is 93.76x² unit square.
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Correct question:
A circular mirror is surrounded by a square metal frame. The radius of the mirror is 4x. The side length of the metal frame is 12x. What is the area of the metal frame?
Hong deposits $4000 into an account that pays simple interest at an annual rate of 5%. He does not make any more deposits. He makes no withdrawals until the end of 6 years when he withdraws all the money.
Answers
Simple interest formula-
Amount Received = Principle*[1 + Rate.(Time)]
A= 4000*[1+ 5 (6)]
A= 4000*(1+30)
A= 4000*31
A= $124000
Final Answer - $124000
prove that for every vector spacee, iff:e→eis an idempotentlinear map, i.e.,f◦f=f, then we have a direct sum
Answers
Every vector spaces, iff:e→eis an idempotent linear map as E= Kcr(f) + Im(f)
What is Linear Map?
A linear map is a mapping in mathematics, more specifically in linear algebra. It is also known as a linear transformation, vector space homomorphism, or, in some cases, a linear function. that maintains the operations of vector addition and scalar multiplication between two vector spaces
Given that,
F : E → E is an idempotent linear map i.e FoF =F
F is an idempotent, then for any W in the image of F statistics
W = F(x)
for some x = E
Then F(w) = FoF(x)
F(x)=(W)----- (A)
So F is indeed a projection to Im(F) as a subspace of v
also , Kcr(F) + Im(F) =0
Because if x∈Kcr(f) + Im------(B)
then f(x) = 0 and
f(t)=x for some x∈E
FoF (t) = 0
f(t)=x
x=0
also from A we have
f(x)-w=0
f(x) -f(w)=0
f(x-w)=0
x-w=t
where t∈Kcr (F)
X = W+T
here x is arbitrary
E = Kcr + Im f ------(C)
From (B) and (C) we have E = Kcr(f) + Im (f)
Since E= Kcr(f) + Im, every vector space is an idempotent linear map (f)
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on a recent trip to the beach, jaya collected seashells. the lengths of the seashells were measured, in inches. the 5 number summary of seashell lengths are shown below min median max 2 3.5 5 6.2 7 a) % of the length of seashells collected by jaya were between 3.5 and 7 inches b) 25% of the length of seashells collected by jaya were between 2 and inches. c) % of the length of seashells collected by jaya were more than 5 inches. d)* the range of lengths of seashells collected by jaya was inches.
Answers
a) Not possible to determine the percentage of the length of seashells collected by Jaya that were between 3.5 and 7 inches.
b) 25% of the length of seashells collected by Jaya were between 2 and 3.5 inches.
c) It is not possible to determine the percentage of the length of seashells collected by Jaya that were more than 5 inches based on the information provided.
d) The range of lengths of seashells collected by Jaya was = 4.2 inches.
In statistics, the range is the difference between the highest and lowest values for a particular data collection.
For instance, if the provided data set is 2,5,8,10,3, the range is 10 - 2 = 8.
As a result, the range may alternatively be defined as the difference between the highest and lowest observations.
a) It is not possible to determine the percentage of the length of seashells collected by Jaya that were between 3.5 and 7 inches based on the information provided.
b) 25% of the length of seashells collected by Jaya were between 2 and 3.5 inches.
c) It is not possible to determine the percentage of the length of seashells collected by Jaya that were more than 5 inches based on the information provided.
d) The range of lengths of seashells collected by Jaya was 6.2 - 2 = 4.2 inches.
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(a) A straight duct extends in the z direction for a length L and has a square cross section, bordered by the lines x = plusminus B and y = plusminus B. A colleague has told you that the velocity distribution is given by v_z = (P_0 - P_1)B^2/4 mu L [1 - (x/B)^2] [1 - (y/B)^2] (3B.3-1) Since this colleague has occasionally given you wrong advice in the past, you feel obliged to check the result. Does it satisfy the relevant boundary conditions and the relevant differential equation?
Answers
A straight duct extends in the z direction for a length L and has a square cross section, bordered by the lines x = plus minus B and y = plus minus B
z direction
f(x,y) = x² - y² subject to x² + y² = 1 g(x,y) = x² + y²- 1
δf(x,y)/ δx = 2*x δg(x,y)/ δx = 2*x
δf(x,y)/ δy = - 2*y δg(x,y)/ δy = 2*y
δf(x,y)/ δx = λ* δg(x,y)/ δx
2*x = λ*2*x
δf(x,y)/ δy = λ* δg(x,y)/ δy
- 2*y = λ*2*y
Then, solving
2*x = λ*2*x x = λ*x λ = 1
- 2*y = λ*2*y y = - 1
x² + y²- 1 = 0 x² + ( -1)² - 1 = 0 x = 0
Point P ( 0 ; -1 ) ; then at that point
f(x,y) = x² - y² f(x,y) = 0 - ( -1)² f(x,y) = - 1 minimum
b) f( x, y ) = 3*x + y g ( x , y ) = x² + y² = 10
δf(x,y)/ δx = 3 δg(x,y)/ δx = 2*x
δf(x,y)/ δy = 1 δg(x,y)/ δy = 2*y
δf(x,y)/ δx = λ * δg(x,y)/ δx ⇒ 3 = 2* λ *x (1)
δf(x,y)/ δy = λ * δg(x,y)/ δy ⇒ 1 = 2*λ * y (2)
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Graph this inequality y>-x
Answers
Answer:
I have graphed it and attached an image in the explanation.
Step-by-step explanation:
do waiters or waitresses earn larger tips? to answer this question, a restaurant consultant undertook a preliminary study. the study involved measuring the percentage of the total bill left as a tip for one randomly selected waiter and one randomly selected waitress from each of 50 restaurants during a 1-week period. what conclusions can be drawn from these data?
Answers
From these data, it is difficult to draw any meaningful conclusions about which waiters and waitresses earn larger tips.
The data only measure the percentage of the total bill left as a tip for one randomly selected waiter and one randomly selected waitress from each of the 50 restaurants during a 1-week period, which does not provide a large enough sample size to draw any meaningful conclusions. In order to draw more reliable conclusions, a larger, more comprehensive study should be conducted that measures the tips for multiple waiters and waitresses from each restaurant over a longer period of time.
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Pls help me what is 5.849
Answers
Answer:
it's significant figure it have 4 significant figure
it have other value also percentage, rational and whole number
Solve
5a + 3-3a = 31
Paragraph V
BI U A/
▶11
OF
00
+ v
...
PLEASE HELP ASAP I NEED HELP PLEASE AND THANKS SO MUCH
Answers
After solving the equation we know that the resultant value of a is 14.
What are equations?A mathematical statement that has an "equal to" symbol between two expressions with equal values is called an equation.
As in 3x + 5 Equals 15, for instance.
Equations come in a variety of forms, including linear, quadratic, cubic, and others. In this tutorial, let's study more about math equations.
The point-slope form, standard form, and slope-intercept form are the three main types of linear equations.
So, we have the equation:
5a + 3-3a = 31
No, solve the equation as follows for 'a:
5a + 3-3a = 31
5a - 3a = 31 - 3
2a = 28
a = 28/2
a = 14
Therefore, after solving the equation we know that the resultant value of a is 14.
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Question in picture. Pls answer soon 30 points!
Answers
Answer: 25.13cm
Step-by-step explanation:
Answer:
31.4 cm
Step-by-step explanation:
C=2πr
Plug in numbers: C= 2 * 3.14 * 5
one of the two equations in a linear system is given. if the system has no solution, which equation could be the second equation in the system?
Answers
The second linear equation will be linearly dependent to the first equation. The graphs of the two linear equation will be parallel to each other.
When two systems of linear equation is given and they do not have a solution that means the first one is depended on the second one or the second equation is depended on the first set of equations.
The system of linear equations that does not posses a solution is called inconsistent form of linear equation where the multiples of the variables are multiples of each other but the constant is completely different.
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Help? (FILL IN THE BLANKS) GIVING BRAINLY
Answers
By evaluatin a proportional relationship we will find the complete table:
grams: 11.4 | 22.8 | 68.4 | 114
packages: 1 | 2 | 6 | 10
How to complete the table?We assume there is a proportional relation between the number of grams y and the number of packages x.
y = k*x
Using the second pair of the table (22.8, 2) we will get:
22.8 = k*2
22.8/2 = k
11.4 = k
So the proportional relation is:
y = 11.4*x
Now let's complete the table, when x = 1
y = 11.4*1 = 11.4
When x = 6
y = 11.4*6 = 68.4
when y = 114
114 = 11.4*x
114/11.4 = x
10 = x
Then the complete table is:
grams: 11.4 | 22.8 | 68.4 | 114
packages: 1 | 2 | 6 | 10
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if given y=45x+2 what is the coefficient and what is the constant
Answers
Answer:
Coefficient: 45
Constant: 2
Hope this helped!
Step-by-step explanation:
what is the value of (x - y) (x - y) if xy = 3 and x2 y2 = 25?
Answers
The value of (x - y)(x - y), if xy = 3 and x² + y² = 25, is 19.
A binomial is an expression represented by the sum or a difference of two algebraic terms. Generally, we can express it as a+b. If we square this binomial, (a + b)², it can be expanded into a² + 2ab + b².
xy = 3
x² + y² = 25
Now, (x - y)(x - y) = x² + y² -xy -xy
(x - y)(x - y) = x² + y² -2xy
Now put the values of x² + y² and xy
(x - y)(x - y) = 25 - 2 × 3
(x - y)(x - y) = 25 - 6
(x - y)(x - y) = 19
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Need this done NOW PLS
Answers
Answer:
dteps
Step-by-step explanation:
answer
consider the function f(x)={2xif x<2if x≥2 evaluate the definite integral ∫6−1f(x)dx
Answers
The value of the given integration is =25, where the function is defined.
Integrals are the values of the function that are discovered through the integration process. Integration is the process of obtaining f(x) from f'(x). When all the little data are combined, problems with displacement and motion, area and volume, and other issues develop. Integrals assign numbers to functions in a way that describes these issues. We can determine the function f given the derivative f' of the function f. Here, the function f is referred to as integral of f' or antiderivative of f.
if the function f(x) defined as
[tex]f(x)=\left \{ {2 \ if \ {x < 2} \atop {x\ if\ x\geq 2}} \right.[/tex]
then find out the-
[tex]\int_{-1}^{6}f(x) dx[/tex]
To find out the integral break it -1 to 2 and 2 to 6, where our function is defined as-
[tex]let\ I=\int_{-1}^{2}f(x)dx +\int_{2}^{6}f(x)dx\\\\I=\int_{-1}^{2}2dx+\int_{2}^{6}xdx\\\\=[2x]_{-1}^{2}+[x^2/2]_{2}^{6}\\\\= [4+1]+[18+2]=5+20\\=25 .[/tex]
Hence, the value of the given integration is =25, where the function is defined.
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Consider the following liquids: d = 0.8146 g/mL 1-pentanol Isopropyl alcohol d=0.7851 g/mL 2-pentanol Hexane You have two unknown samples, each known to be one of the above liquids. a. In determining the density of the first unknown, you weighed a 5.00 mL sample of the d 0.8098 g/mL d 0.660 g/mL liquid, and found the mass to be 3.310 g. What is the identity of the unknown? Explain. b. For the second unknown, a 5.00 mL sample weighed 4.061 g. Based on this data, what can you conclude about the identity of unknown number two? Explain. 3. A perfect cube of jade has a mass of 15.00 g. If jade's density is 3.25 g/ml, determine the edge length of the jade cube.
Answers
The identity of the unknown is hexane, the second unknown is isopropyl alcohol, and the edge length of the jade cube is approximately 1.87 cm.
a. To determine the identity of the first unknown, we can compare the calculated density with the known densities of the liquids. The calculated density can be found by dividing the mass of the sample (3.310 g) by its volume (5.00 mL), giving us a density of 0.6620 g/mL.
Since the calculated density (0.6620 g/mL) is closest to the density of hexane (0.7851 g/mL), it is likely that the first unknown is hexane.
b. To determine the identity of the second unknown, we can use the same approach as in part a. By dividing the mass of the sample (4.061 g) by its volume (5.00 mL), we find the calculated density to be 0.8122 g/mL.
This density is closest to the density of isopropyl alcohol (0.7851 g/mL), so it is likely that the second unknown is isopropyl alcohol.
c. To find the edge length of the jade cube, we can use the formula for the volume of a cube: V = l^3. We know the mass of the cube (15.00 g) and its density (3.25 g/mL), so we can find its volume by dividing the mass by the density:
V = m/d = 15.00 g / 3.25 g/mL = 4.62 mL = 4.62 cm^3
Since the volume is equal to the edge length cubed, we can find the edge length by taking the cube root of the volume:
l = cuberoot(V) = cuberoot(4.62 cm^3) = approximately 1.87 cm.
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an investor is offered a partnership deal on a franchise business. she wants to confirm if franchises can succeed by sampling from the over 500 cases measured by the small business administration. if she examines the first 50 rows of their spreadsheet, what kind of sampling is she doing?
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After examining the first 50 rows of their spreadsheet, the investor is doing a kind of sampling that is called convenience sampling.
Convenience sampling is a type of non-probabilistic sampling method where participants are selected based on their ease of access or availability.
Based on the given situation, the investor has chosen to examine the first 50 rows of the spreadsheet because it is convenient for her, rather than selecting a random sample of the 500 cases measured by the Small Business Administration.
However, convenience sampling can lead to bias and is not considered a rigorous method for estimating population parameters.
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