Answers
Therefore , the solution of the given problem of polynomial comes out to be (x-4)²(x-1)(x+2) is a four degree polynomial.
Describe polynomials.A polynomial is a mathematical statement with coefficients or uncertainty that uses only additions, erasures, multiplications, and powers of positive integer variables. There is just one indeterminate x polynomial identified by the formula x2 4x + 7. The term "polynomial" refers to a phrase in mathematics that consists of variables (sometimes referred to as "indeterminates") and coefficients that can be added, deducted, multiplied, then raised to negative number powers of non-variables.
Here,
Given :
=> (x-4)(x-1)(x+2)
=>(x-4)²(x-1)(x+2)
So,
=> (x-4)²(x-1)(x+2) is a four degree polynomial.
The two zeros of the degree four polynomial presented are x = 2 and x = 4. The two components of the above polynomial are (x - 2) and since x = 2 and x = 4 are its two zeros (x - 4).
The quadratic expression with the coefficients 1, 8, and 15 can be factored to find additional components. This equals x2 + 8x + 15.
To learn more about polynomial refer to:
brainly.com/question/1600696
#SPJ1
Related Questions
What is the value of x?
X =
X-38°=90°
Answers
Answer:
This is the answer you want
X=90°-38°
X=52°
Answer:
128°
Step-by-step explanation:
X-38°=90°
X=90°+38°
X=128°
the diagram shows two joined rectangles the total area of the compound shape ABCDEF is 36cm^2
Answers
Note that given the diagram showing joined Rectangles with the total area of the compound shape given as: ABCDEF = 36cm², the value of length AB = 4.5 or 9/2
What is a compound shape?A compound form is created by combining simple shapes. It's also known as a "composite" or "complex" form.
To solve for the value of AB, lets start form the given:
Given that:
The area of the shape ABCDEF is 36 square centimeters.
From the given figure:
In the smaller rectangle, length of sides AB is x and BC is (2-4) cm.
In the larger rectangle, length of the sides DE is (x-2) and EF is 3x cm.
thus the area if the Smaller Rectangle is:
A(Small) = x(x-4)
= x² - 4x
The area of the larger rectangle will be:
A(Large) = 3x(x-2)
= 3x² -6x
The total area of the shape will be:
A(Small) + A(Large) = 36
X²-4x+3x²-6x = 36
⇒ 4x² - 10x - 36 = 0; Divide both sides by 2
⇒2x² - 5x - 18 = 0
solving the above using the factoring method, we have:
⇒2x2-5x-18=0
⇒2x2-9x+4x-18=0
⇒x(2x-9)+2(2x-9)=0
⇒(2x-9)(x+2)=0
⇒(2x-9)=0or(x+2)=0
⇒ 2x = 9or x= -2
Thus, x = 9/2 or -2
Since the value of AB cannot be a negative value, thus the correct answer is: 9/2 or 4.5
Learn more about Compound Shapes:
https://brainly.com/question/16890298
#SPJ1
Full Question:
See image attached
Hi can someone check my work for me! im unsure of my answers, please tell me if get any wrong! please someone
Answers
1. The number of possible outcomes are 12
2. The probability of getting head and rolling a 5 is 1/12.
3. The probability of getting a tail as rolling 1 is 1/12.
4. The probability of getting head and rolling any number on the die is 1/2.
5. The probability of getting tails and rolling an odd number is 1/4.
6. The probability of getting heads and rolling a number greater than 3 is 1/4.
How to calculate the probability?The probability of getting head and rolling a 5 is:
= 1/2 × 1/6
= 1/12.
The probability of getting a tail as rolling 1 is:
= 1/2 × 1/6
= 1/12.
The probability of getting head and rolling any number on the die is:
= 1/2 × 1
= 1/2.
5. The probability of getting tails and rolling an odd number is:
= 1 /2 × 3/6
= 1/4.
Learn more about probability on:
brainly.com/question/24756209
#SPJ1
What is 4=3/5b
Can you send help?
Answers
Answer:
b=20/3, or b=6.67
Step-by-step explanation:
4=3/5b
20=3b
b=20/3
Or, b=6.67
Answer:
20/3 = b or 6 2/3
Step-by-step explanation:
4=3/5b
To solve for b, multiply each side by 5
4 * 5=3/5b * 5
20 = 3 b
Divide each side by 3
20/3 = 3b/3
20/3 = b
We can change the improper fraction to a mixed number.
3 goes into 20 6 times with 2 left over.
6 2/3
b = 6 2/3
Which statement describes the relationship between x and y in these two equations? y = 4x y=x+4 In y = 4x, the value of y is ________ In y=x+4, the value of y is ________ Answer Bank: four more than the value of x four times the value of x
Answers
Answer:
In y = 4x, the value of y is four times the value of x. In y=x+4, the value of y is four more than the value of x.
Natalie i working two ummer job, making $11 per hour babyitting and $10 per hour landcaping. Lat week Natalie earned a total of $86 and worked 3 time a many hour babyitting a he worked hour landcaping. Determine the number of hour Natalie worked babyitting lat week and the number of hour he worked landcaping lat week
Answers
The number of hours Natalie worked babysitting last week is 6hrs and the number of hours she worked landscaping last week is 2 hrs.
Let x be the number of hours Natalie worked babysitting and y be the number of hours she worked landscaping. Then, the total earnings were 11x + 10y = $86.
Also, x = 3y, because she worked 3 times as many hours babysitting as she did landscaping.
Substitute x = 3y into the first equation:
11(3y) + 10y = $86
Expanding the first term we get,
33y + 10y = $86
Combining terms,
43y = $86
Dividing both sides by 43 we get,
y = $2
So, Natalie worked y = 2 hours of landscaping.
To find the number of hours she worked babysitting, substitute y = 2 into x = 3y as follows -
x = 3(2) = 6
So Natalie worked x = 6 hours babysitting.
Read more equations:
brainly.com/question/29115752
#SPJ4
5. The set V = {(x, y): 0, y ≥ 0}, together with the usual operations in R2, is not a vector space. Of the ten axioms that must hold for a vector space, give specific examples showing that two of them do not hold.
Answers
Two of the axioms that do not hold for the set V with the usual operations in R2 are the existence of additive inverses and distributivity of scalar multiplication over addition.
Additive Inverses: For a vector space, every vector has an additive inverse, meaning that there exists a vector in the set such that their sum is equal to the zero vector. However, in the set V, the vector (0, 0) is not an additive inverse of any vector of the form (x, y) where y > 0, since their sum is (x, y) which is not equal to the zero vector (0, 0).Distributivity of Scalar Multiplication over Addition: For a vector space, scalar multiplication must be distributive over addition, meaning that (a + b)v = av + bv for all scalars a, b and all vectors v. However, in the set V, this property does not hold, since if we take a = 1, b = -1, and v = (0, 1), then (a + b)v = (1 + (-1))(0, 1) = (0, 0), which is not equal to av + bv = 1(0, 1) + (-1)(0, 1) = (0, 1) + (0, -1) = (0, 0).To learn more about axioms here:
https://brainly.com/question/13104788
#SPJ4
Which function describes a transformation that maps trapezoid FGHI to trapezoid F'G'H'I'?
Answers
The function that maps the trapezoid FGHI to trapezoid F'G'H'I' is
B. (x, y) → (1/2 x - 5, 1/2 y)
How to determine the transformation?The change of shape as seen in the two objects was reduction in size and linear movement to the left.
The reduction is size is reduction by half and this is dilation with a scale factor of 1/2. This is represented by the formula
(x, y) → (1/2 x, 1/2 y)
Then linear movement to the left is translation to the left and this id 5 units to the left. The formula to show this as below
(x, y) → (1/2 x - 5, 1/2 y)
This is equivalent to B and hence the correct option
Learn more about translation at:
https://brainly.com/question/12861087
#SPJ1
22. Thomas lists all of the different arrangements of the letters in the word CABOOSE. How many of Thomas's arrangements begin with a C and end with an E?
(A) 100
(B) 120
(C) 80
(D) 90
(E)Other
If a b a♣︎b - a - b - 1, then what is the value of 284♣︎1001?
(A) 282435
(B) 283000
(C) 283283
(D) 282000
(E)Other
What is the product of 4% of 112 and 61% of 375?
(A) 144
(B) 90
(C) 120
(D) 105
(E)Other
. Josh rolls two standard six-sided dice. What is the probability that the product of the numbers shown on the dice is a multiple of six?
(A) 4/9
B) 1/3
(C) 5/12
D) 1/2
(E)Other
What is the remainder when the sum of the terms of the arithmetic series 101 108 + 115 + 290 is divided by 28?
(A) 7
(B) 0
(C) 14
(D) 21
(E)Other
Two right triangles have the same perimeter, and each triangle's side lengths are all whole numbers. One right triangle has legs of length 10 and 24. The other right triangle has a hypotenuse of length 25. What is the area of the second triangle?
A) 150
(B) 112
(C) 120
(D) 144
(E)Other .
A function f is defined for positive integers x as f(x) = 0 if x ≤ 2. Otherwise, f(x) = f(x - 1) if x is not divisible by 3, and f(x) = 2 + f (3) if x is divisible by 3. What is the value of f(2020)?
A) 16
B) 14
C) 12
D) 8
E)Other
Answers
Answer:
(A) 22. Thomas lists all of the different arrangements of the letters in the word CABOOSE. How many of Thomas's arrangements begin with a C and end with an E?
Answer: (C) 80
(B) If a b a♣︎b - a - b - 1, then what is the value of 284♣︎1001?
Answer: (B) 283000
(C) What is the product of 4% of 112 and 61% of 375?
Answer: (B) 90
(D) Josh rolls two standard six-sided dice. What is the probability that the product of the numbers shown on the dice is a multiple of six?
Answer: (C) 5/12
(E) What is the remainder when the sum of the terms of the arithmetic series 101 + 108 + 115 + 290 is divided by 28?
Answer: (A) 7
(F) Two right triangles have the same perimeter, and each triangle's side lengths are all whole numbers. One right triangle has legs of length 10 and 24. The other right triangle has a hypotenuse of length 25. What is the area of the second triangle?
Answer: (A) 150
(G) A function f is defined for positive integers x as f(x) = 0 if x ≤ 2. Otherwise, f(x) = f(x - 1) if x is not divisible by 3, and f(x) = 2 + f(3) if x is divisible by 3. What is the value of f(2020)?
Answer: (A) 16
Daniel has a circular piece of paper with a radius of 13 cm. He cuts a circular hole
with a radius of 5 cm in the centre of his piece of paper to make the shape shown
below.
Calculate the area of this shape.
Give your answer in cm² to 1 d.p.
13 cm
5 cm
Not drawn accurately
Answers
Answer:
Step-by-step explanation: Area of circle = pi.r²
A= pi. 5²
A= pi. 25
A≈78cm²
write down the multiplication tables for z/6zand z/7z. list the elements have multi- plicative inverses.
Answers
For Z/6Z and Z/7Z, the multiplication tables are 1-5 and 0 and 1-6 and 0 correspondingly. The elements 1, 2, 3, 4, 5 and 1, 3, 5, 6 respectively have multiplicative inverses.
The multiplication table is as follows for the group Z/6Z:
1 * 1 = 1\s2 * 1 = 2\s3 * 1 = 3\s4 * 1 = 4\s5 * 1 = 5\s0 * 1 = 0
1, 2, 3, 4, and 5 are the elements with multiplicative inverses.
The multiplication table is as follows for the group Z/7Z:
1 * 1 = 1\s2 * 1 = 2\s3 * 1 = 3\s4 * 1 = 4
5 * 1 = 5\s6 * 1 = 6\s0 * 1 = 0
1, 3, 5, and 6 are the elements with multiplicative inverses.
The group members in a group Z/NZ are the remainders after dividing the integers by N. For instance, the elements in Z/6Z are 0, 1, 2, 3, 4, and 5. The product of each element is shown in the multiplication table.by itself when multiplied. The multiplication table for Z/6Z is as follows: 0 * 1 = 0; 1 * 1 = 1, 2 * 1 = 2, 3 * 1 = 3, 4 * 1 = 4, 5 * 1 = 5. 1, 2, 3, 4, and 5 are the elements with multiplicative inverses. The multiplication table is also the same for Z/7Z: 1 * 1 = 1, 2 * 1 = 2, 3 * 1 = 3, 4 * 1 = 5, 6 * 1 = 6, 0 * 1 = 0. 1, 3, 5, and 6 are the elements with multiplicative inverses.
Learn more about inverse here
https://brainly.com/question/13715269
#SPJ4
A. -4(2t-8)
B. -2(4t+16)
C.-4t(2+8)
D. -4(2t+8)
E.-2(4t-32)
F. -8(t+4)
G. -2(4t-16)
H. -8(t-4)
what’s equivalent to -8t – 32? select all that apply.
Answers
Answer:
BCDF
Step-by-step explanation:
B. -2(4t+16)
C.-4t(2+8)
D. -4(2t+8)
F. -8(t+4)
the cost in dollars, of a three-day car rental can be determined by the expression 70+0.30m, where mis the number of miles drive. use this expresion to find the cost of a rental car driven150 miles.
Answers
Answer:
70+0.30m, where mis the number of miles =
Corrine drives d miles to her office at an average
speed of 50 miles per hour. Returning home, she
travels by the same route and averages 60 miles
per hour. If her trip home is 10 minutes shorter
than her trip to her office, what is the value of d?
Answers
The value of distance d is 240 miles.
How to find the calculation?The length of the shortest path connecting any two places in physical space is known as their distance.
Classical physics, particularly Newtonian mechanics, uses the term "distance" to refer to this.
Euclidean distance is calculated in coordinate geometry by applying the Pythagorean theorem.
This first section is
Distance = Speed * Time
Distance: (in metres (m), kilometres (km), miles, and feet
Distance: 50 multiplied by 4 equals 200 miles (50 mph; 4 hours).
In the following segment
Distance is 20 miles multiplied by two to get 40 miles (at a speed of 20 mph) in two hours.
240 miles are hence the total distance.
Assuming a six-hour trip, the average speed is 240 divided by six, or 40 miles per hour.
To Learn more About Distance Refer To:
brainly.com/question/17273444
#SPJ1
Three tudent that hare a townhoue find that their electric bill for October i le than the September bill. The total of both bill i , and each bill i plit evenly among the roommate. How much did each owe in September?
Answers
Three student that hare a townhouse find that their electric bill for October, each owe in September is amount $20.31.
Let amount that September's bill was, be S
Then October's bill was: S - $2.32
Therefore, we get: S + S - 2.32 = 119.56
2S - 2.32 = 119.56
2S = 119.56 + 2.32
2S = 121.88
S, or September's bill was: 121.88/2 or $60.94
Amount each owed for September: 60.94/3 = $20.31
We consume electricity produced for our use by a corporation whenever we switch on a light, plug in a device, or let our refrigerator run. You can purchase this company's electricity by the Kilowatt-hour to power your home. When the firm requests payment for the electricity you consumed, they send a letter outlining the amount of electricity you consumed, the rates they charge, and the amount owed to the company.
Learn more about Electric consumption:
https://brainly.com/question/28451927
#SPJ4
a rectangular storage container with an open top is to have a volume of 14 cubic meters. the length of its base is twice the width. material for the base costs 13 dollars per square meter. material for the sides costs 6 dollars per square meter. find the cost of materials for the cheapest such container.
Answers
The cost of the side material is $148.91, the cost of the base material is $73.67 and the cheapest cost of material is $222.58 and this can be determined by using the arithmetic operations.
Let the width of the rectangular storage container be 'x' then according to the given data the length is '2x' and let the height of the container be 'h'.
The base area of the rectangular storage container is given by:
Base Area = 2x² -- (1)
The side area of the rectangular storage container is given by:
Side Area = 2(2x)h + 2xh
= 6xh -- (2)
Now, the volume of the rectangular storage container is given by:
Volume = l x b x h
14 = 2x²h
h = 7/x²
Now, the cost is given by:
C(x) = 13(2x²) + 6(6xh)
C(x) = 26x² + 252/x
To minimize C(x), differentiate the C(x) with respect to x.
C'(x) = 52x - 252/x² --3()
52x - 252/x² = 0
x³ = ∛(63/13)
Now, differentiate equation (3) with respect to x.
C''(x) = 52 + 504/x³
C"( ∛(63/13) ) = 156 > 0
Therefore, ∛(63/13) is the point of minima.
Now, the cost of the base material is:
= 13 x 2 (62/13)^(2/3)
= $73.67
Now, the cost of the side material is:
= 252/(∛(63/13))
= $148.91
Therefore, the total cost is given by:
= 73.67 + 148.91
= $222.58
Hence, the cheapest cost of material is $222.58
To know more about arithmetic operations here
brainly.com/question/13585407
#SPJ4
To solve the system of linear equations 3 x minus 2 y = 4 and 9 x minus 6 y = 12 by using the linear combination method, Henry decided that he should first multiply the first equation by –3 and then add the two equations together to eliminate the x-terms. When he did so, he also eliminated the y-terms and got the equation 0 = 0, so he thought that the system of equations must have an infinite number of solutions. To check his answer, he graphed the equations 3 x minus 2 y = 4 and 9 x minus 6 y = 12 with his graphing calculator, but he could only see one line. Why is this? because the system of equations actually has only one solution because the system of equations actually has no solution because the graphs of the two equations overlap each other because the graph of one of the equations does not exist
Answers
The given system of equations have infinitely many solutions.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is the system of equations as -
3x - 2y = 4
9x - 6y = 12
We can write the system of equations as -
3x - 2y = 4
9x - 6y = 12
We can write (9x - 6y = 12) as -
3(3x - 2y) = 3(4)
3x - 2y = 4
So both the lines coincide. We can say that the given system of equations have infinitely many solutions.
Therefore, the given system of equations have infinitely many solutions.
To solve more questions on algebraic expressions, visit the link below -
brainly.com/question/1041084
#SPJ1
8. Value Hardware sells 3-in. finishing nails for 0.99/lb and 2-in finishing nails sell for $1.39/1b. Toni needs 5 lb of nails. If his bill totals $6.15, how many pounds of each size did he buy?
Answers
Answer:
This algebraic problem can be solved by setting up a system of equations. For example, let x be the number of pounds of 3-inch nails that Toni buys, and y be the number of pounds of 2-inch nails that Toni buys. We know that x + y = 5 (since Toni believes a total of 5 pounds of pins) and that 0.99x + 1.39y = 6.15 (since that is the total cost of the nails). We can solve for one of the variables using one equation and then substitute that value into the other equation.
Solving for x in the first equation: x + y = 5
x = 5 - y
Substituting this into the second equation: 0.99(5 - y) + 1.39y = 6.15
4.95 - 0.99y + 1.39y = 6.15
4.95 = 0.4y + 6.15
-1.2 = 0.4y
y = -3
Since the number of pounds of nails cannot be harmful, we know that this solution is not possible. We can check by plugging in y = 3 (possible) into the first equation and seeing that x + 3 = 5, so x = 2.
Hence, Toni bought 2 lb of 3-inch nails and 3 lb of 2-inch nails.
Step-by-step explanation:
a right triangle has a hypotenuse with a length of 10cm. one angle of the three in this triangle is 53.1 degrees. what is the length of the side opposite this angle?
Answers
The length of the side opposite this angle of the hypotenuse is 12.51°.
A right triangle consists of the hypotenuse (longest side), the opposite(length of the leg) and the adjacent.
The angle at the corner is 90degrees
In a right triangle, the hypotenuse is the longest side, an "opposite" side is the one across from a given angle, and an "adjacent" side is next to a given angle. We use special words to describe the sides of right triangles. The hypotenuse of a right triangle is always the side opposite the right angle.
Given that,
Length of the leg = 10cm
angle opposite the side = 53.1 degrees
To get the hypotenuse,
sin θ = opposite/hypotenuse
sin 53.1 = 10/hypotenuse
hypotenuse = 10/sin53.1°
hypotenuse = 10/0.799
hypotenuse = 12.51
Therefore,
The length of the side opposite this angle of the hypotenuse is 12.51°.
To learn more about Hypotenuse problems visit :
brainly.com/question/29120144
#SPJ4
here are the weights (in pounds) of 20 steers on an experimental feed diet: 183 140 136 142 172 153 172 156 70 167 192 166 113 171 159 129 112 135 174 155 where is the center of the distribution of this data set?
Answers
The centre of the distribution of weights of the 20 steers is 149.85 pounds.
The centre of a distribution of data can be described as the central tendency or typical value of the data. The most common measure of central tendency is the mean, which is calculated by summing all the values in a data set and dividing by the number of values.
To calculate the mean weight of the 20 steers, we can use the following formula:
mean = (183 + 140 + 136 + 142 + 172 + 153 + 172 + 156 + 70 + 167 + 192 + 166 + 113 + 171 + 159 + 129 + 112 + 135 + 174 + 155) / 20
mean = 2997 / 20
mean = 149.85
Therefore, the centre of the distribution of weights of the 20 steers is 149.85 pounds.
To know more about distribution, here
https://brainly.com/question/29062095
#SPJ4
Determine the value(s) of the variable for which the expression is undefined.
1)-
5
x-10
A)x= 10, x=-5
12
4)=
2)
Write the rational expression in lowest terms.
8z³
3)
20z6
15
12-4
C)
A).
A)
A) Never undefined-any real number may be substituted for y
B) 15
C) -2, 2
D) 4
+ 5y - 36
1²-16
y + 9
y-4
8
20z³
B)x= -10
5y-36
16
C)x=10
B) 23⁹
2
99-3333
B) cannot simplify
D)
y+9
y+4
D) x=5
D) 2535
1)
3)
4)
Whole page pls
Answers
A rational expression seems to be undefined when ever the denominator is zero.
How does an expression becomes undefined?A rational expression seems to be undefined when its denominator becomes zero. Set the denominator to zero and solve the resulting equation to find the values that make a rational expression undefined.An expression in mathematics that has no meaning and thus does not have an interpretation. In the field of real numbers, for example, division by zero is undefined.Here given expression, 5/(x - 10)
The expression becomes undefined when denominator becomes 0.
So here, if x = 10 then the denominator becomes 0.
That is 5/10-10
= 5/0
which is undefined, when x = 10.
Given expression, 15/(y² + 4)
To a expression to be undefined denominator has to be 0.
But here denominator cannot become zero.
To learn more about undefined expression refer to :
https://brainly.com/question/13464119
#SPJ1
6. (5 pts) consider the following statement: do you agree or disagree , and why ? " if i prove that an algorithm takes o(n2) worst-case time, is it possible that it takes o(n) on some inputs?"
Answers
We Disagree with the statement that "" If i prove that an algorithm takes O(n²) worst-case time, is it possible that it takes O(n) on some inputs" because if the algorithm is proven to take O(n²) time in the worst-case, it is likely to take even more time on many inputs.
The "big-O" notation provides an upper bound on the growth rate of a function, and is used to describe the asymptotic behavior of an algorithm as the size of the input grows to infinity.
If an Algorithm is proven to take O(n²) time in the worst-case, it means that the running time grows quadratically as the size of the input increases.
It is not likely that the same algorithm will take O(n) time on some inputs because the big-O notation provides an upper bound, and O(n) represents a much faster growth rate than O(n²).
Therefore , O(n²) represents the "worst-case" scenario, so any scenario where the algorithm runs faster is not considered .
The given question is incomplete , the complete question is
Consider the following statement: do you agree or disagree , and why ?
" If i prove that an algorithm takes o(n²) worst-case time, is it possible that it takes o(n) on some inputs?"
Learn more about Algorithms here
https://brainly.com/question/14531150
#SPJ4
Plsssssass help me nowwww
Answers
Answer:
- 2
Step-by-step explanation:
Answer:
Step-by-step explanation:
2 i think
Can anyone solve these problems?
Answers
24) The value of factors of the expression 25x² - 64 is, (5x - 8) (5x + 8).
25) The value of factors of the expression 216x³ - 8 is,
⇒ (6x - 2) (36x² + 12x + 4)
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
We have to given that;
1) The expression is,
⇒ 25x² - 64
2) The expression is,
⇒ 216x³ - 8
Now, We can factors as;
1) The expression is,
⇒ 25x² - 64
⇒ (5x)² - 8²
⇒ (5x - 8) (5x + 8)
2) The expression is,
⇒ 216x³ - 8
⇒ (6x)³ - 2³
⇒ (6x - 2) ((6x)² + 6x × 2 + 2²)
⇒ (6x - 2) (36x² + 12x + 4)
Thus, We get;
24) The value of factors of the expression 25x² - 64 is, (5x - 8) (5x + 8).
25) The value of factors of the expression 216x³ - 8 is,
⇒ (6x - 2) (36x² + 12x + 4)
Learn more about the mathematical expression visit:
brainly.com/question/1859113
#SPJ1
Write the product (2 + 7i)(2 − 7i) in the form a + bi.
A. 4 − 49i
B. 53
C. 4 − 14i2
D. 53 + 14i
Answers
The product of (2 + 7i)(2 − 7i) is (B) 53. It can be written in the form of a + bi as 53 + 0i.
What are Complex Numbers?A complex number is formed by multiplying a real and an imaginary number.
Complex numbers are denoted by the symbol z and have the formula a + ib.
Both a and b are real numbers here.
The real component is denoted by Re(z), while the imaginary component is denoted by Im (z). As a result, 'ib' is an imaginary number.
Here, we have the given expression, (2 + 7i)(2 − 7i) ------(1)
We know that, (a+b)(a-b) = a² - b²
Using the above formula, we get (1) as
(2 + 7i)(2 − 7i) = (2)² - (7i)²
⇒ (2 + 7i)(2 − 7i) = 4 - 49i²
Since, i² = -1, we get
(2 + 7i)(2 − 7i) = 4 - (-49)
Solving, we get
(2 + 7i)(2 − 7i) = 4 + 49
⇒ (2 + 7i)(2 − 7i) = 53
Hence, the product of (2 + 7i)(2 − 7i) in the form a + bi is 53 + 0i.
To learn more about Complex Numbers from the given link
brainly.com/question/5564133
#SPJ1
Raj was selling cricket bats. He sold 8 bats with 20% profit. If the net amount of profit he earned was 560 Rs, what was the selling price of one bat?
Answers
The price of one bat when Aaryan purchased is ₹500
What was the amount of profit?Revenue less costs equals profit. You deduct a few expenses from your earnings. Subtract all costs to determine net profit. The path to net profits is paved with gross and operating profits. The Profit First formula urges you to take the profit from each sale and use the balance for expenses since it places the emphasis on profit.A profit and loss statement (P&L), also known as an income statement, is a financial document that displays the sales and costs incurred by a firm over a specific time period, typically a fiscal quarter or year. Loss = C P - S P (C P > S P) Where C.P. is the item's or commodity's actual price and S.P. is the price at which the item was purchased by the consumer.Let cost price of 1 bat x
Cost price of 8 bats = 8x
He sold 8 bats with 15% profit. If the net amount of profit he earned was ₹ 600
[tex]$\frac{15}{100} \times 8 x=600$[/tex]
[tex]$8 x=\frac{600 \times 100}{15}$[/tex]
[tex]$8 x=40 \times 100$[/tex]
[tex]$x=\frac{40 \times 100}{8}$[/tex]
[tex]$x=500$[/tex]
[tex]$x=500$[/tex]
The price of one bat when Aaryan purchased is ₹500
To learn more about price refer to:
https://brainly.com/question/1153322
#SPJ1
suppose you take a sample of 50 students from your school and measure their height. which one of the following is a random variable?
Answers
If we take a sample of 50 students from your school and measure their height , then (c) The mean of the sample data. will be a Random Variable .
A Random Variable is a defined as a variable whose value depends on the outcome of a random event.
Option (c) : the random event is the selection of 50 students from the school to measure their height. The mean height of this sample of 50 students is a random variable because it can vary depending on the specific students who are selected.
Option (a) : The true mean height of all students from your school is a population parameter and is a fixed value, so it cannot be called as a random variable.
Option (b) : The mean of the sampling distribution of mean heights for samples of size 50 is a population parameter as well, and it represents the average of all possible sample means of size 50 taken from the population. So, it is a fixed value and not a random variable.
Therefore , The mean of the sample data will be a random variable .
The given question is incomplete , the complete question is
Suppose you take a sample of 50 students from your school and measure their height. Which one of the following is a random variable?
(a) The true mean height of all students from your school.
(b) The mean of the sampling distribution of mean heights for samples of size 50.
(c) The mean of the sample data.
Learn more about Random Variable here
https://brainly.com/question/28942503
#SPJ4
URGENT! WILL MARK BRAINLIEST!!!
A flower kiosk is selling roses and carnations that are either red or white. 3/5 of all the flowers are red, 1/3 of all the flowers are roses, and 9/20 of all the roses are white. What percent of all the flowers are white carnations?
Answers
Answer:
25%
Step-by-step explanation:
If 3/5 of the flowers are red, then 2/5 of them are white. Since 9/20 of the roses are white, then 9/20*2/5=3/20 of all of the flowers are white roses. Subtracting the number of white roses from the total amount of white flowers will give us the fraction of how many of the flowers are white carnations. 2/5-3/20=5/20=1/4 of all of the flowers, which is 25% as a percentage.
The percent of all the flowers are white carnations is 255.
What is Percentage?To determine the quantity or percentage of something in terms of 100, use the percentage formula. Per cent simply means one in a hundred. With the percentage formula, a number between 0 and 1 can be expressed. A number that is expressed as a fraction of 100 is what it is. It is mostly used to compare and determine ratios and is represented by the symbol %.
Given:
3/5 of the flowers are red.
2/5 of them are white.
and, 9/20 of the roses are white.
fraction of white roses of all flower
= 9/20 x 2/5
=3/20
Fraction of Flowers that are white Carnations
= 2/5 - 3/20
= 5/20
= 1/4.
Then, the percent of all the flowers are white carnations is
= 1/4 x 100
= 25%
Learn more about Percentage here:
https://brainly.com/question/29306119
#SPJ2
the backyard of a new home is shaped like a trapezoid with a height of 42 ft and bases of 80 ft and 107 ft. what is the cost of putting sod in the yard, if the landscaper charges $0.25 per square foot for sod
Answers
The cost of putting sod in the yard is $981.75.
What is trapezium?A trapezium is a quadrilateral with four sides where two sides are parallel to each other.
We have,
Area of a trapezium = 1/2 x (sum of the two bases) x height
Now,
Base = 80 ft and 107 ft
Height = 42 ft
Now,
Area = 1/2 x (80 + 107) x 42
Area = 1/2 x 187 x 42
Area = 187 x 21
Area = 3927 ft²
Now,
$0.25 = ft²
Multiply 3927 into both sides.
3927 x 0.25 = 3927 ft²
$981.75 = 3927 ft²
Thus,
$981.75 is the cost of putting sod in the yard.
Learn more about trapezium here:
https://brainly.com/question/22607187
#SPJ1
they are One-fifth of an inch apart. What scale could Lyle include on the map? Select three options.
One-fifth inch = Three-fourths mile
Three-fourths inch = One-fifth mile
Four-fifths inch = 3 miles
3 inches = 12 miles
4 inches = 15 miles
Answers
The scale that Lyle could include on the map is /5 inch = 3/4 mile, 4/5 inch = 3 miles, and 4 inches = 15 miles. Hence, option A, option C and option E is the correct answer.
What is the distance?Distance is calculated as the sum of a person's movement and time.
Let D be the actual distance in miles between any two points, and let d be the distance shown on the map between any two points, measured in inches.
The distance between the location on the map and the real distance is equal to 1/5 of an inch since the scale on the map is 1/5 inch = 3/4 mile.
d/D = (1/5)/ (3/4)
1/5 inch = 3/4 mile
4/5 inch = 3 miles
4 inches = 15 miles
Hence, the scale that Lyle could include on the map is /5 inch = 3/4 mile, 4/5 inch = 3 miles, and 4 inches = 15 miles. Hence, option A, option C and option E is the correct answer.
Learn more about ratio here:
https://brainly.com/question/13419413
#SPJ1
