The polynomial function is x²- 3xi + 4
What are polynomial functions ?In mathematics, polynomial function can be defined as the equation which consist of coefficient, variables and exponents. A polynomial equation has positive numbers as their exponent which is also known as its degree. All the equations such as quadratic equation, cubic equation which has non negative number as their powers are part of polynomial equation.
Types of polynomial equations :
Monomial equationBinomial equationCubic EquationsLinear PolynomialQuadratic PolynomialSome examples of polynomial equation are :
2x+53x = 93x² + 5x+19(x-3)³According to question,
roots are -i , 4i
Thus the factors are :
(x - (-i) ) ( x - (4i) )
=> ( x + i )( x - 4i )
=> x²- 4xi + xi - 4i²
=> x²- 3xi + 4 ( as i² = -1)
Thus polynomial function for given roots is x²- 3xi + 4
To know more about polynomial functions, visit:
brainly.com/question/17822016
#SPJ4
You pay $10 to play the following game of chance. There is a bag containing 12 balls, five are red,
three are green and the rest are yellow. You are to draw one ball from the bag. You will win $14 if
you draw a red ball and you will win $12 is you draw a yellow ball. How much do you expect to
win or loss if you play this game 100 times?
After playing 100 times the player will loose $-16.67.
Given the outcomes and the probability is:
Outcome Probability
-$10 1 (cost to play)
$14 draw red 5/12
$12 draw yellow 4/12
therefore, expected probability = ∑x.p(x)
x is no of trials and
p(x) is probability of the results.
E(x) = (14)5/12 + (12)4/12 + (0)3/12 - 10
E(x) = -2/12
E(x) = -10.1667
For 100 games the expected value E(100x) =
E(100x) = E(x) × 100
E(100x) = -10.1667 × 100
E(100x) = -16.67 i.e loss after game.
Hence the player lose $-16.67 after 100 games.
Learn more about Expected value here:
brainly.com/question/24855677
#SPJ9
A manufacturer makes bags of popcorn and bags of potato chips. The average weight of a bag of popcorn is supposed to be 3.03 ounces with an allowable deviation of 0.02 ounces. The average weight of a bag of potato chips is supposed to be 5.08 ounces with an allowable deviation of 0.05 ounces. A factory worker randomly selects a bag of popcorn from the assembly line and it has a weight of 3.06 ounces. Then the worker randomly selects a bag of potato chips from the assembly line and it has a weight of 5.03 ounces. Which description closely matches the findings on the assembly line?
Answer:
The weight of the popcorn is off but the potato chips are safe. Simply determine whether each value is within the limit of deviation from eachother.
A 3-quart container of disinfectant costs $13.56. What is the price per cup?
Answer: The answer is $1.13.
Step-by-step explanation:
There are 12 cups inside a 3-quart container.
f(x)=b x and g(x)=logbx are inverse functions. Explain why each of the following is true.
a. The translation f₁(x)=b x-h of f is equivalent to a vertical stretch or compression of f .
The function f₁(x) can be either vertical stretch or vertical compress: TRUE
What do we mean by Logarithmic Function?The following is the formula for basic logarithmic functions: Where b > 0, f(x) = logbx(r), y = logbx.It is the reciprocal of the exponential function x=b∧y.Log functions are denoted by natural logarithm (ln) and common logarithm (log).Here are a few examples of logarithmic functions:
f(x) = ln (x - 2)g(x) = log2(x + 5)-2h(x) = 2 log x, etc.So,
Given function:
f(x) = bˣg(x) = logbxThen,
f₁(x)=b^(x-h)f₁(x)=b^x/b^hNow, Put bˣ=f(x):
f₁(x)=f(x)/b^hf₁(x)=b^(-h)f(x)f₁(x)=c f(x)We discovered that:
c=b^(-h)So, depending on the values of b and h, c can be greater than or less than one.
Therefore, the statement "the function f₁(x) can be either vertical stretch or vertical compress" is TRUE.
Know more about Logarithmic Function here:
https://brainly.com/question/13473114
#SPJ4
23% of a snack mix is almonds. How much snack mix would you need to get 230 g of almonds?
Answer:
23 times 10 is
230 so your answer is 2 times 10
Is 4/8 equivalent to 7/8
Answer:
is 7 more than 4 or 4 more than 7?
Step-by-step explanation:
JUST USE YOUR BRAIN!
Answer:
no
Step-by-step explanation:
of course not. since the denominators are the same, the numerators have to be equal. since the numerators aren't equal, the answer is no
Solve each equation. If necessary, round to the nearest ten-thousandth.1/2log x+log 4=2
For logarithmic equation 1/2 log x + log 4 = 2, the value of x is 34,040.25
How can a logarithmic equation be solved?Step 1: Using exponentiation principles, isolate a logarithmic expression (with the same base) on both sides of the equation.
Step 2: balance the arguments.
Step 3: Solve the resultant equation.
Step 4: Double-check your answers.
Given,
1/2 log x + log 4 = 2
log x^(1/2) + log 4 = 2
using logₐ(m.n) = logₐ(m) + logₐ(n)
log e (4 (x^1/2)) = 2
e² = 4x^(1/2)
7.38 = 4√x
Squaring on both sides -
54.4644 = 16x
x = 54.4644 / 16
x = 34,040.25
To learn more about logarithmic function from given link
https://brainly.com/question/13473114
#SPJ4
Given t(x)=4x−7,what is t(x)when x=3
Answer:
The correct answer is 4(x-7)²-(x-7)+3.
Step-by-step explanation:
When we have captured (t*s)(x), that is as equivalent as t(s(x)). To solve this, we take the important role of s(x), x-7, and call in an alternative for it in for every x in t(x). Instead of 4x², we have 4(x-7)²; instead of -x, we have -(x-7). This gives us 4(x-7)²-(x-7)+3.
Cadence baked 45 cupcakes on Tuesday. This was 3 more than twice the number of cupcakes she baked on Monday. How many cupcakes did Cadence bake on Monday?
Group of answer choices
25
21
24
14
Considering the definition of an equation and the way to solve it, the correct answer is the third option: Cadence baked 21 cupcakes on Monday.
Definition of equationAn equation is the equality existing between two algebraic expressions connected through the equals sign in which one or more unknown values, called unknowns.
The members of an equation are each of the expressions that appear on both sides of the equal sign.
The solution of a equation means determining the value that satisfies it. To solve an equation, keep in mind:
When a value that is adding, when passing to the other member of the equation, it will subtract.If a value you are subtracting goes to the other side of the equation by adding.When a value you are dividing goes to another side of the equation, it will multiply whatever is on the other side.If a value is multiplying it passes to the other side of the equation, it will pass by dividing everything on the other side.Cupcakes baked on MondayBeing "x" the number of cupcakes baked by Cadence on Monday, and knowing that:
Cadence baked 45 cupcakes on Tuesday. The number of cupcakes baked on Tuesday was 3 more than twice the number of cupcakes she baked on Monday.the equation in this case is:
3 + 2x= 45
Solving:
2x= 45 -3
2x= 42
x= 42 ÷ 2
x= 21
Finally, the correct answer is the third option: Cadence baked 21 cupcakes on Monday.
Learn more about equations:
brainly.com/question/4983716
brainly.com/question/13314678
#SPJ1
the city council of anytown, u.s.a., is reviewing the funding for local sports-related activities. to be better informed, the council commissions a study. place the sample groups in order from best to worst, based on how well they would represent the population of anytown residents with an active interest in sports.
The correct order from best to worst of the sample groups is b→ a→ c.
The study conducted by the City Council of USA incorporates the reviewing for the funding for local sports-related activities.
There are 3 sample groups selected from the population of Anytown residents with an active interest in sports. They are:
a. High-school students at three different schools.
b. People randomly approached at a softball tournament, a swim meet, an athletic supply store, and a sports bar.
c. People randomly approached at a department store and at a shopping mall
All these groups are selected randomly.
But for (b), the people are obviously interested in sports activities, as they are selected from softball tournament, a swim meet, an athletic supply store, and a sports bar.
Next would be (a), because the students being younger is probably more interested in sports than elder ones.
The last would be the (c), people selected from the department store since they would be less aware of local- sports related activities.
So the order of samples from best to worst is b→ a→ c.
The question is incomplete. Find the complete question below:
The city council of Anytown, U.S.A., is reviewing the funding for local sports-related activities. To be better informed, it commissions a study. Order the sample groups, best to worst, based on how well they would represent the population of Anytown residents with an active interest in sports.
a. high-school students at three different schools
b. people randomly approached at a softball tournament, a swim meet, an athletic supply store, and a sports bar
c. people randomly approached at a department store and at a shopping mall
Learn more about sample groups at https://brainly.com/question/24466382
#SPJ4
Un coche tarda 9hrs en recorrer un trayecto siendo su velocidad de 85km/h, ¿Cuánto tardará en recorrer el mismo trayecto a 70km/h?
The time taken to travel the distance 70 Km/h is 11 hours.
What is speed distance formula?Speed tells us how fast something or someone is travelling. You can find the average speed of an object if you know the distance travelled and the time it took.
The formula can be rearranged in three ways:
speed = distance ÷ timedistance = speed × timetime = distance ÷ speedGiven:
time = 9 hours
speed = 85 Km/h
Now, distance
=speed * time
=85 * 9
= 765 km
As, the speed is 70 km/h
time = distance/ speed
time = 765 / 70
time = 10.92
time= 11 hours
Hence, the time taken to travel the distance 70 Km/h is 11 hours.
Learn more about speed- distance here:
https://brainly.com/question/25422529
#SPJ1
The translation of the question is:
A car takes 9 hours to travel a distance with a speed of 85km/h, how long will it take to travel the same distance at 70km/h?
Suppose you know the measures of all three angles of a triangle. Can you use the Law of Sines to find the lengths of the sides? Explain.
Answer:
No
Step-by-step explanation:
Without any side lengths, the most three angles can determine is similarity, not congruency. This means you can determine the ratio of the lengths of the sides, but not any of the sides individually.
Multiply. State any restrictions on the variables.
8 y-4 / 10 y-5 . 5 y-15 / 3 y-9
The required product of two rational numbers is 8y² - 28y + 4) / (6y² - 21y + 9).
What is a rational number?
Any real number that can be represented in the form of p/q, where q is not equal to 0 is called a rational number. The decimal expansion of rational numbers is terminating and repeating.
Calculation of the product of two rational numbers
Given two rational numbers,
8y - 4 / 10y - 5 and 5y -15 / 3y - 9
We need to multiply both the numbers i.e.
= (8y - 4 / 10y - 5) × (5y -15 / 3y - 9)
= (8y -4) × (5y - 15) / (10y - 5) × (3y - 9)
= (40y² - 140y + 20) / (30y² - 105y + 45)
= (8y² - 28y + 4) / (6y² - 21y + 9)
= (8y² - 28y + 4) / (6y² - 21y + 9)
The restriction is that the denominator, 6y² - 21y + 9 should not be 0.
Hence, the required product of two rational numbers is 8y2 - 28y + 4) / (6y2 - 21y + 9).
To learn more about rational numbers, visit here:
https://brainly.com/question/12088221
#SPJ4
Can someone please help
And explain why correct
If your gonna be immature just go on with your day
Answer:
AD
Step-by-step explanation:
It is the only segment that meets a side of triangle ABC at a right angle.
Are there any values of x that you cannot substitute into the equation? If so what are they? Same question for y
Answer: The problem asks to solve for x. Equation B gives you the value of y, y = 2, so you can substitute 2 into Equation A for y.
Step-by-step explanation:
I am a 4-digit number larger than 2,500. No two of my digits are the same. The product of the thousands digit and the hundreds digit is equal to the ones digit. The sum of my digit is 16.
Read the clues. Find the number
Step-by-step explanation:
4-digit number abcd
a >= 2
a×b = d
so, 2 <= b <= 4 to allow a single digit result of a×b, and if b would be 1 or 0, the result would be either a copy of a or of b violating the rule that no 2 digits are the same.
that means a >= 3, because with a = 2 and b <= 4 the number can't be larger than 2500.
and that again means 2 <= b <= 3 and 3 <= a <= 4 to allow a single digit result of a×b.
the sum of "my digit" ? I guess you mean the sum of all digits is 16.
a + b + c + d = 16
so, my first guess :
a = 3
b = 2
therefore
d = 3×2 = 6
that means we have already 11 as sum of the digits, that leaves 5 for c.
so, the number would be
3256
the only alternative would start with a = 4 and then b = 2.
but that would make d = a×b = 8. abd 8 + 4 + 2 = 14, and that leaves for c only 2 to sum up to 16, and that would duplicate b.
so, 3256 is the only solution.
What values of x and y satisfy the system of equations {2x+12y=−173x+2y=7?
Enter your answer as an ordered pair, like this: (42, 53)
If your answer includes one or more fractions, use the / symbol to separate numerators and denominators. For example, if your answer is (4253,6475), enter it like this: (42/53, 64/75)
If there is no solution, enter "no"; if there are infinitely many solutions, enter "inf."
The solution to the system where the system contains linear equations is (59/16, -65/32)
What are linear equations?Linear equations are equations that have constant average rates of change. Note that the constant average rates of change can also be regarded as the slope or the gradient
How to determine the solution to the system?A system of linear equations is a collection of at least two linear equations.
In this case, the system of equations is given as
2x + 12y = −17
3x + 2y = 7
Multiply through 3x + 2y = 7 by 6
So, we have
18x + 12y = 42
Subtract the equation 2x + 12y = −17 from 18x + 12y = 42
So, we have
18x - 2x + 12y - 12y = 42 + 17
Evaluate the like terms
So, we have
16x = 59
Divide both sides by 16
So, we have
x = 59/16
Substitute x = 59/16 in 3x + 2y = 7
3 x 59/16 + 2y = 7
This gives
177/16 + 2y = 7
So, we have
2y = 7 - 177/16
Evaluate the difference
2y = -65/16
Divide by 2
y = -65/32
Hence, the solution to the system where the system contains linear equations is (59/16, -65/32)
Read more about linear equations at
https://brainly.com/question/14323743
#SPJ1
m∠W=73°. Find the measure of the complement of ∠W.
115°
15°
17°
107°
The measure of the angle that complements m∠W is 17°. Option C
What are complementary angles?Complementary angles are defined as angles that sum up to 90 degrees.
They are also called angles at right angle.
Example:
If x and y are termed complementary angles, then
x + y = 90°
From the information given, we have that;
m∠W is complementary to another unknown angle x
This is represented as;
x + m∠W = 90°
But m∠W = 73°
Substitute the value into the equation
x + 73° = 90°
collect like terms
x = 90 - 73
x = 17°
Thus, the measure of the angle that complements m∠W is 17°. Option C
Learn more about complementary angles here:
https://brainly.com/question/16281260
#SPJ1
necesito hacer la recta numerica con números negativos y positivos, alguien me ayuda
De acuerdo a la información se puede inferir que su hijo nació en el año 22 antes de Cristo.
¿Qué es una recta numérica?Una recta numérica es una herramienta gráfica de las matemáticas que nos sirve para ubicar números positivos y negativos en un gráfico con el objetivo de organizarlos con respecto al número cero.
¿Cómo funcionan las líneas de tiempo con años Antes de Cristo y Después de Cristo?Las líneas de tiempo con fechas Antes y Después de Cristo se pueden asociar a una recta numérica debido a que los años Antes de Cristo se ubican en la parte negativa de la gráfica (a la izquierda del cero) y los número Después de Cristo se ubican en la parte positiva (a la derecha del cero).
¿Cuál es el año de nacimiento de su hijo?Para identificar el año de nacimiento del hijo debemos tener en cuenta que las fechas que se ubican en la zona negativa de la recta numérica aumentan de forma invertida, es decir que si su hijo nació 28 años después de ella se debe restar este número a su fecha de nacimiento como se muestra a continuación:
50 - 28 = 22
Entonces, el año de nacimiento de su hijo sería el año 22 Antes de Cristo.
Aprenda más sobre rectas numéricas en: https://brainly.com/question/17447899
#SPJ1
help meeeeeeeeeeeee.
Answer:
4:1, 20:5
Step-by-step explanation:
You can determine if a ratio is equivalent by dividing each term with the respective term in the other ratio. If you come out with 1, the ratios are equivalent.
Answer:
4:1 & 20:5
Step-by-step explanation:
These two ratios are equal and true to 12:3!
Hopefully this helps have a great day! :D
Read each question. Then write the letter of the correct answer on your paper.What is an equivalent form of 5/2+2 i ?
(F) 5/4i (H) 5+5 i / 4 (G) 10-10i / 4-4i (I) 5-5i / 4
An equivalent form of 5 / ( 2 + 2 i ) is ( 5 -5 i ) / 4 [ option I ]
Given,
5 / ( 2 + 2 i )
To find its equivalent form we need to simplify the term by using the concept of conjugates.
Conjugate of a term results in opposite power of the imaginary part.
The conjugate of 2 + 2 i = 2 - 2 i
Multiply and divide the term with the conjugate
=> 5 * ( 2 - 2 i ) / ( 2 + 2 i ) * ( 2 - 2 i )
=> 10 - 10 i / 2 ² - ( 2 i ) ² [ ( a + b ) ( a - b ) = a ² - b ² ]
=> 10 - 10 i / 4 - (-4) [ i ² = - 1 ]
=> 10 - 10 i / 8
=> 5 - 5 i / 4
This matches with option I
Therefore, we get an equivalent form of 5 / ( 2 + 2 i ) as ( 5 -5 i ) / 4
Learn more about Conjugate of Complex Numbers here:
https://brainly.com/question/18392150?referrer=searchResults
#SPJ9
The leg of a right triangle is 3 units and the hypotenuse is 11 units. What is the length, in units, of the other leg of the triangle? HURRY PLEASE!!!
a
112 units
b
square root 112 units
c
130 units
d
square root 130 units
The correct option is (b) square root 112 units
Step-by-step explanation:By using Pythagoras theorem,
a² + b² = c²where a & b = legs of triangle and c = hypotenuse
Hence:
3² + b² = 11²9 + b² = 121b² = 121 - 9b² = 112b = √112PLEASE HELP and explain in the answer
The missing numbers are 17,66,13, 9 3 and 15 respectively .
The rules given to us are-
first row consist of a number which is the sum of two numbers of middle row
Third row consist of a number which is the product of two numbers of middle row
The first part
The sum of 6 and 11 is 17 and the product of 6 and 11 is 66
17
6 11
66
The second part
To find the second number of middle row we need to divide 36 by 4 and we get 9 and the sum of 4 and 9 is 13
13
4 9
36
The third part
To find the numbers of middle row we need to find the factors of 45 that sum up to 18
The factors of 45 are 3*3*5
The factor 15 and 3 satisfy both the requirements
18
3 15
45
Hence, The missing numbers are 17,66,13, 9 3 and 15 respectively
To know more about Sum and Product - https://brainly.com/question/21369558
#SPJ1
I need help with this problem, I have been stuck on it for awhile.
After 4 stops both buses will have the same amount of riders that is 27.
What are mathematical operations, exactly?An operation is a function in mathematics that converts zero or more input values (also known as "operands" or "arguments") to a good output value.The operation's arity is determined by the number of operands.So, Bus A: 15 people ( +3 at every stop)
Bus B: 35 people ( -2 at every stop)
Then,
Stop 1: Bus A (15 + 3) = 18; Bus B (35 - 2) = 33Stop 2: Bus A (18 + 3) = 21; Bus B (33 - 2) = 31Stop 3: Bus A (21 + 3) = 24; Bus B (31 - 2) = 29Stop 4: Bus A (24 + 3) = 27; Bus B (29 - 2) = 27Therefore, after 4 stops both buses will have the same amount of riders that is 27.
Know more about mathematical operations here:
brainly.com/question/20628271
#SPJ9
MARKING BRAINLEIST AND 100 POINTS JUST PLS EXPLAIN HOW TO SOLVE!!
What is the length of segment AB when A(-2,2) and
B(5,2)?
Answer:
7
Step-by-step explanation:
You have to do the square root of: (5-(-2)) squared pluse (2-2) squared
Now you have the square root of 7 squared
7 squared is 49, so you have the square root of 49
that equals 7
*Don't forget to mark brainliest
In the following figure, BA≅CA, and D is on BC
If BD = 3, then it means that CD is also equal to 3 by definition of Isosceles triangle.
What is the missing length of the triangle?
We are given a triangle with the condition that BA ≅ CA. This means that side BA has a length equal to that of side CA.
Now, an Isosceles triangle is defined as a triangle that has at least two sides of equal length. This means that the given triangle ABC is an Isosceles triangle.
Now, since Triangle ABC is an Isosceles triangle, it means that when we draw a perpendicular line through the point joining the two equal sides, it bisects the third side of the triangle.
Thus, it means that BD is congruent to CD.
If BD = 3, then it means that CD is also equal to 3 by definition of Isosceles triangle.
Read more about Length of triangle at; https://brainly.com/question/2217700
#SPJ1
y = – 3
y = x – 0.8
A coordinate grid with 2 lines. The first line passes through the points (0, negative 0.1) and (0.8, 0). The second line is horizontal passes through the point (0, negative 3). The lines intersect at a point with a coordinate of slightly to the left of negative 2 and negative 3.
What is the best approximation for the solution to this system of equations?
(–3.2, –3)
(–2.9, –3)
(–2.2, –3)
(–1.9, –3)
The best approximation for the solution to the system of equation is option C) (-2.2 , -3)
According to the question we have been given two system of linear equation which are:
y = -3 (1)
and y = x - 0.8 (2)
Now solving these two equation and find the value of x
Substituting the value of y from equation (1) to the equation (2) we get
-3 = x - 0.8
-3 + 0.8 = x
x = -2.2
Thus the best approximation for the solution to the system of equation is option C) (-2.2 , -3)
Learn more about solution to equation here : https://brainly.com/question/13729904
#SPJ9
Four friends race their bikes down the street. Evan finishes in 6.2 seconds, Devon in 6.0999 seconds, Liza in 6.188 seconds, and Tasha in 6.168 seconds. Which order shows the friends’ times from fastest to slowest?
Answer:
Evan, Liza, Tasha, Devon
Step-by-step explanation:
Brett is joining a new gym. He can join Power Plus or Heavy Hulk. At Power Plus, it will cost $34.04 per month, plus a sign-up fee of $24.00. At Heavy Hulk, it will cost $34.29, plus a sign-up fee of $36.50. Right now, Heavy Hulk is cutting their sign-up fee in half for new members. If Brett signs up at a gym today, after how many months will the cost of the memberships be the same?
If Heavy Hulk is cutting their sign-up fee in half for new members. If Brett signs up at a gym today, the number of months that the cost of the memberships be the same is: 23 months.
Number of monthsLet x represent the number of months
Hence,
Formulate
$34.04x+24= $34.29x+(36.50/2)
Collect like terms
($34.04x -34.29x)= 24-(36.50/2)
0.25x=24-18.25
0.25x=5.75
Divide both side by 0.25x
x=5.75/0.25
x=23 months
Therefore If Heavy Hulk is cutting their sign-up fee in half for new members. If Brett signs up at a gym today, the number of months that the cost of the memberships be the same is: 23 months.
Learn more about number of months here:https://brainly.com/question/1292807
#SPJ1
A florist is arranging a bouquet of daisies and tulips. He wants twice as many daisies as tulips in the bouquet. If the bouquet contains 24 flowers, how many daisies are in the bouquet?
(A) 8 daisies (B) 12 daisies (C) 16 daisies (D) 24 daisies
The correct option is (c) 16 daisies
If the bouquet contains 24 flowers then total 16 daisies are in the bouquet.
What are polynomial functions ?In mathematics, polynomial function can be defined as the equation which consist of coefficient, variables and exponents. All the equations such as quadratic equation, cubic equation which has non negative number as their powers are part of polynomial equation.
Some examples of polynomial equation are :
2x+53x = 93x² + 5x+19(x-3)³Now, for the given question,
let d = number of daisies
t = number of tulips
according to statement polynomial equation is,
d + t = 24 , say equation (i)
Twice as many daisies as tulips:
d=2t
Put the value of d in equation (i)
2t + t = 24
3t = 24
t = 8
As, number of daisies = 2 (number of tulips)
Therefore, d = 2t = 2 (8) = 16
Thus, total 16 daisies are in the bouquet.
To know more about polynomial functions, visit:
brainly.com/question/17822016
#SPJ4