Answer: 5.474 m
Step-by-step explanation:
first jump = 4.25
best jump = first jump * 1.12
winning jump = best jump *1.15
A bag contains 10 pieces of paper, numbered 1 through 10with a different number on each piece of paper. A second bag contains 8 pieces of paper, numbered 20 through 27with different number on each piece of paper. One piece of paper is drawn random from each bag. What is the expected value of the sum of the numbers on the two selected pieces of paper
To find the expected value of the sum of the numbers on the two selected pieces of paper, we need to calculate the probability of each possible outcome and then multiply that probability by the value of the outcome. The expected value of the sum of the numbers on the two selected pieces of paper is 6.1625.
Therefore the answer is 6.1625.
The possible outcomes for the first bag are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, each with a probability of 1/10.
The possible outcomes for the second bag are 20, 21, 22, 23, 24, 25, 26, 27, each with a probability of 1/8.
The possible outcomes for the sum of the numbers on the two selected pieces of paper are:
(1,20) ,(1,21) ,(1,22) ,(1,23) ,(1,24) ,(1,25) ,(1,26) ,(1,27)
(2,20) ,(2,21) ,(2,22) ,(2,23) ,(2,24) ,(2,25) ,(2,26) ,(2,27)
(3,20) ,(3,21) ,(3,22) ,(3,23) ,(3,24) ,(3,25) ,(3,26) ,(3,27)
...
(10,20) ,(10,21) ,(10,22) ,(10,23) ,(10,24) ,(10,25) ,(10,26) ,(10,27)
The expected value of the sum of the numbers on the two selected pieces of paper is the sum of the products of each possible outcome and its corresponding probability.
The probability of each outcome is (1/10) * (1/8) = 1/80
So the expected value of the sum of the numbers on the two selected pieces of paper is
(1 + 21)×(1/80) + (1 + 22)×(1/80) + (1 + 23)×(1/80) + (1 + 24)×(1/80) + .... + (10 + 27)×(1/80) = (21 + 22 + 23 + 24 + ... + 37)/80
= (20×17 + 1 + 2 + ... + 17)/80
= (340 + 17×(17 + 1)/ 2)/ 80
= (340 + 17×9)/ 80
= 6.1625
So the expected value of the sum of the numbers on the two selected pieces of paper is 6.1625
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What is similarity example?
When two figures have the same shape but differ in size, they are said to be similar figures. In other words, two figures are said to be comparable when they have many characteristics but aren't necessarily identical.
For instance, despite appearing to be the same size, the sun and moon are actually different sizes. However, because both of our figures are circular in shape, we are comparable figures. This phenomenon is seen as a resemblance property while taking shape and distance into consideration.
When two shapes, such triangles, polygons, or quadrilaterals, have the same dimension or common ratio but a different size or length, they are referred to as comparable figures in geometry.
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Given: △ACE,BD¯¯¯¯¯∥AE¯¯¯¯¯ Prove: BACB=DECD A triangle with vertices labeled as A, C, and E, with base A E. Sides C A and C E contain midpoints B and D, respectively. A line segment parallel to base A E is drawn from point B to D. Angle C A E is labeled as 4 and angle C E A is labeled as 3. Angle C B D is labeled as 1 and angle C D B is labeled as 2. Drag an expression or phrase to each box to complete the proof. Statement Reason △ACE,BD¯¯¯¯¯∥AE¯¯¯¯¯ Given Response area Corresponding Angles Postulate △ACE∼△BCD Response area CACB=CECD Definition of similar triangles CA=CB+BACE=CD+DE Segment Addition Postulate CB+BACB=CD+DECD Substitution Property of Equality CBCB+BACB=CDCD+DECD Addition of fractions 1+BACB=1+DECD Simplification of fractions Response area Subtraction Property of Equality
For triangle ACE, if BD ∥AE , then BA/CB = DE/CD is proved.
For given triangle ACE,
BD || AE ...............(Given)
∠4 ≅ ∠1 and ∠3 ≅ ∠2 ..............(Corresponding Angles Postulates)
ΔACE ~ ΔBCD .............(Angle-Angle Similarity Postulate)
CA/CB = CE/CD ............(Definition of similar triangles)
CA = CB + BA, CE = CD + DE ..........(Segment Addition Postulate)
(CB + BA)/CB = (CD + DE)/CD ..........(Substitution Property of Equality)
CB/CB + BA/CB = CD/CD + DE/CD .........(Addition of Fractions)
1 + BA/CB = 1 + DE/CD .............(Siplification of fractions)
BA/CB = DE/CD ...............(Subtraction Property of equality)
Hence proved.
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What are the angles of a 5 12 13 triangle?
The angles of a 5-12-13 triangle are A = 81.19°, B = 48.76°, and C = 9.98°.
The angles of a triangle are determined by the triangle's side lengths. This is known as the Law of Cosines. To determine the angles of a 5-12-13 triangle, we can use the Law of Cosines formula:
Cos(A) = (b² + c² - a²) / 2bc
In this equation, A is the angle opposite side a, b is the angle opposite side b, and c is the angle opposite side c. In a 5-12-13 triangle, a = 5, b = 12, and c = 13.
Using the Law of Cosines formula, we can calculate the angle A:
Cos(A) = (12² + 13² - 5²) / 2(12)(13)
Cos(A) = (144 + 169 - 25) / 156
Cos(A) = 278 / 156
Cos(A) ≈ 1.78
Using a calculator, we can calculate the angle A:
A = cos-1 (1.78)
A ≈ 81.19°
Using the same Law of Cosines formula, we can calculate the other two angles of the triangle:
Cos(B) = (a² + c² - b²) / 2ac
Cos(B) = (5² + 13² - 12²) / 2(5)(13)
Cos(B) = (25 + 169 - 144) / 65
Cos(B) = 50 / 65
Cos(B) ≈ 0.77
Using a calculator, we can calculate the angle B:
B = cos-1 (0.77)
B ≈ 48.76°
We can also calculate the angle C:
Cos(C) = (a² + b² - c²) / 2ab
Cos(C) = (5² + 12² - 13²) / 2(5)(12)
Cos(C) = (25 + 144 - 169) / 60
Cos(C) = 10 / 60
Cos(C) ≈ 0.17
Using a calculator, we can calculate the angle C:
C = cos-1 (0.17)
C ≈ 9.98°
Therefore, the angles of a 5-12-13 triangle are A = 81.19°, B = 48.76°, and C = 9.98°.
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Distribute and then combine the like terms to simplify each expression.
5(-6 +4q) - 2q
please help
Answer:
-30+18q
Step-by-step explanation:
First, distribute the five to the terms in the parenthesis.
5x-6 and 5x4q
so -30+20q-2q
20q-2q equals 18q
so we are left with -30+18q.
When you use substitution What are the steps used to find the solution to a system of linear equations?
In one of the equations, separate one of the two variables. In the other equation, replace the expression with the value of the isolated variable from Step 1. Consequently, a linear equation with just one variable ought to emerge.
What constitutes the substitution system's solution?The one y-value in the substitution method is replaced with the other. We'll give an example to illustrate this. Since y = y, we can replace y in the second equation with y from the first equation. The linear system's solution is (1, 6).
What are the three possible types of solutions for a linear equation?Numerous solutions, no solutions, and a singular solution.
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Nathan had 58 pieces of gum that he wants to make last six days how much can he chew each day so that the gum last him six days between what two whole numbers does your answer lie
Natha can chew between 9 to 10 chewing gum each day so that it could last for 6 days.
What is a unitary method?A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.
Given, Nathan had 58 pieces of gum that he wants to make last six days.
Therefore, The number of chewing gums he can chew is the total number of chewing gums he has divided by the total number of days which is,
= (58/6).
= 9.66 chewing gums but it should be a whole number.
So, Nathan can chew between 9 to 10 chewing gums each day.
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Toss a coin 10 times and record how many times you tossed heads.
a) What is your experimental probability of tossing heads?
b) What is the theoretical probability of tossing heads?
c) Compare the two probabilities and determine if you are considered to be
"lucky" at tossing heads.
d) If you were to toss the coin 100 times, what would you expect the
experimental probability of heads to be? Defend your answer.
To solve this we must be knowing each and every concept related to probability and its calculations. Therefore, the probability of tossing heads is 0.000976.
What is probability?Probability is the branch of mathematics concerned with the outcomes of random occurrences. Probability refers to the chance or potential of an outcome. It describes the likelihood of a specific occurrence occurring.
Probability denotes the possibility of something happening. It is a statistical discipline that deals only with probability of such a random event. The number ranges from 0 to 1, with 0 being an improbable event and 1 representing a certain event.
P(getting heads on one toss) = 1/2
P(getting all heads in 10 tosses)=(1/2)¹⁰
=1/1024
=0.000976
Therefore, the probability of tossing heads is 0.000976.
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A drum of oil has a height of 4 feet and a radius of 1.2 feet. The oil cost $22 per cubic feet. What is the cost to fill the drum of oil
The cost of oil to fill the drum with height of 4 feet and a radius of 1.2 feet will be $397.90.
What is cubic feet?An understanding of the different dimensions is necessary to truly understand cubic feet, how big a cubic foot is, and how to measure cubic feet. There are three known dimensions which include a foot measurement. The dimensions expand to include additional measurements with each new dimension.
The cubic foot is an imperial and US customary unit of volume, used in the United States and the United Kingdom. It is defined as the volume of a cube with sides of one foot in length. Its volume is 28.3168 L. At 60 °F, a cubic foot of water weighs 62.37 pounds. A cubic foot (abbreviated as cu ft. or cubic ft.) is an imperial unit of measurement for the volume of a space or three-dimensional object.
Given: A drum of oil has a height of 4 feet and a radius of 1.2 feet. Oil cost has been given as $22 per cubic feet.
We have to calculate the cost to fill the drum with oil.
Since formula to get the volume of the drum is V = πr²h
V = 3.14×(1.2)²×4 = 18.09 feet³
Now the cost of oil to fill the drum will be
Cost = Volume × cost = 18.09×22 = $397.90
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What number should be added to the polynomial 2x³ − 3x² − 8x so that the resulting polynomial leaves the remainder 12 when divided by 2x 1?
The number that should be added to the polynomial 2x³ - 3x² - 8x is 12x
When a polynomial is divided by a linear factor, the remainder is equal to the constant term of the polynomial multiplied by the reciprocal of the linear factor.
In this case, the polynomial is 2x³ - 3x² - 8x, and the linear factor is 2x-1.
To find the remainder when this polynomial is divided by 2x-1, we need to multiply the constant term of the polynomial, which is -8, by the reciprocal of 2x-1, which is 1/(2x-1).
So the remainder should be -8*(1/(2x-1)) = -8/(2x-1) = -4/(x-0.5)
To make the remainder 12, we will add 12x to the polynomial so that the new constant term is 12.
The polynomial 2x³ - 3x² - 8x + 12x will have a remainder of 12 when divided by 2x-1.
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Which represents the solution set of 5(x+5) <85?
Ox< 12
O x> 12
O x < 18
O x> 18
Answer: O x<12
Step-by-step explanation:
Step 1: Simplify both sides of the inequality.
5x+25<85
Step 2: Subtract 25 from both sides.
5x+25−25<85−25
5x<60
Step 3: Divide both sides by 5.
5x/5 < 60/5
x<12
A gallon of gasoline carries with it about 1.3 x 108 J of energy. Given a price of $3 per gallon, how many Joules can you get for a dollar
By unitary method, you can get joules by $1.
What is the unitary percentage method?When given a percentage of an amount, the unitary method can be used to determine the full amount. For instance, if $23 represents 10% of a sum of money, then $10 times $23 equals $230. $6000 is equal to 8% of a sum of money.
Price of 1 Gallon= $3
Energy produced by 1 gallon = joules
by $1 , you can get 1/3 gallon
energy produced by 1/3 gallon = = joules
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Find the area of a square with a length of ((n ^ 3 * m ^ 4)/(nm)) ^ 2 inches.
The area of a square with a length of ((n ^ 3 * m ^ 4)/(nm)) ^ 2 inches is n^6*m^8/(nm)^4.
Define square.In geometry, a square is a flat shape with four equal sides and four right angles (90°). A square is an unique sort of parallelogram as well as an equilateral rectangle (an equilateral and equiangular one).
Write general formula to find area of square.The general formula to find area of square is A=a^2 where is a is length of sides.
The area of a square is given by:
A= l^2 where l is the length
So l= n^3*m^4/(nm)^2
A=l^2= n^6*m^8/(nm)^4
So area of the square is n^6*m^8/(nm)^4.
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Tommy earned $225 washing cars with his mobile car washing business. He charges $30 per appointment and earned $45 in tips, but he also has to pay $10 per appointment for water. Write an equation to represent this situation.
A.
(30 + 10)y + 45 = 225
B.
30y + 45 = 225 - 10y
C.
30y + 45y - 10y = 225
D.
(30 - 10)y + 45 = 225
An equation representing this situation where Tommy earned $225 washing cars per appointment charge of $30 and tips of $45 while paying $10 for water per appointment is D. (30 - 10)y + 45 = 225.
What is an equation?An equation is a mathematical statement that states that two or more mathematical expressions are equivalent or equal.
Equations depict the equality of mathematical expressions using the equation symbol (=).
The total amount earned = $225
Variable charge per appointment = $30
Tips earned = $45
Variable cost per appointment for water = $10
Contribution margin per unit = $20 ($30 - $10)
Let each appointment = y
Total earnings: 225 = (30 - 10y) + 45
Thus, the equation that represents the situation of Tommy's net earnings from washing cars is Option D.
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prove that cos x = sin x cot x.
Answer:
can u give me the brainliest
the answer is in the attached documents
In 2010, the population of a city was 237,000. From 2010 to 2015, the population grew by 7.6%. From 2015 to 2020, it fell by 4.7%. To the nearest whole number, by what percent did the city grow from 2010 to 2020?
The population of the city grew from 2010 to 2020 by 13.37 %
What is percentage?A percentage is a number that tells us how much out of 100 and can also be written as a decimal or a fraction.
Given that, In 2010, the population of a city was 237,000. From 2010 to 2015, the population grew by 7.6%. From 2015 to 2020, it fell by 4.7%.
The population in 2015 =
A = P (1+r)ⁿ
A = final population.
P = Initial population.
r = rate
n = time
The population in 2015 =
A = 237,000(1+0.076)⁵
A = 341829.629
The population in 2020 =
A = P (1-r)ⁿ
A = 341829.629(1-0.047)⁵
A = 268704.047
Percent grow = 268704.047 - 237,000 / 237,000 × 100
= 31704.047 / 237,000 × 100
= 13.37 %
Hence, the population of the city grew from 2010 to 2020 by 13.37 %
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The table shows the gallons of fuel remaining after a car
travels a certain distance in miles
Distance
(miles)
Fuel Remaining
(gallons)
The change in fuel remaining from one row to the next
in the table is gallon(s)
The change in distance from one row to the next in the
table is
mile(s)
The slope of the line that runs through the points given
in the table is
The slope indicates a
13. 50
13. 46
13. 42
3
13. 38
13. 34
5
13. 30
The slope shows a change in the amount of fuel left in each mile. Since the slope is -0.04, the amount of fuel left drops by 0.04 gallons each mile
what is slope ?The slope of a line governs its steepness. Using mathematics, the gradient is expressed as "gradient overflow" (the change in y divided by the change in x). The slope is the ratio of the vertical (rise) to the horizontal (run) change in distance between any two sites. Every time the equation for a straight line is written as y = mx + b, the slope-intercept representation of the equation is utilized. At the location of the y-intercept, the line has a slope of m, b, and c. (0, b). As an example, the y-intercept of the equation y = 3x - 7 has a value of 3. (0, 7).
given
It is evident that with each additional row, the distance is increased by one mile and the fuel level is altered.
From one row to the next in the table, the amount of fuel left changes by -0.04 gallons.
The distance in the table that changes from one row to the next is 1 mile.
The slope is the pace at which the amount of fuel left changes in relation to the change in distance.
The line that passes through the places listed in the table has a slope of -0.04 degrees.
The slope shows a change in the amount of fuel left in each mile. Since the slope is -0.04, the amount of fuel left drops by 0.04 gallons each mile.
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What is the area of a rectangle with a length of 14.4 inches and a width that is one-third of the length?
A. 43.2 in.
B. 51.84 in.
C. 69.12 in.
D. 103.68 in.
If you give the answer, please make sure it is correct and one of the answers on the group of answer choices! Thank you! :)
The area of the rectangle is 69.12 square inches.
What is the area of the rectangle?
We know that for a rectangle of length L and width W, the area is given by the formula:
A = L*W
Here we know that the length is 14.4 inches, then:
L = 14.4 in
And the width is one-third of that length, then we can write:
W = (1/3)*L
Replacing the value of L, we will get:
W = (1/3)*14.4 inches
W = 4.8 inches.
Then the area of the rectangle is:
A= (4.8 in)*(14.4 in) = 69.12 in²
That is the area of the rectangle.
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Can anyone me help PLEASE
Answer: (0, 1), (2,3), (x,x), (-5,x) (I put x's in for the missing numbers)
Step-by-step explanation: Hope this helps!!
Here is the graph:
Analyzing
K
Which statements correctly describe the properties of heat? Select all that apply.
A. Heat is an essential component of life on Earth.
B. Heat is energy that flows from one object to another.
%
4
&
Prt Scna
Thus , Heat moves from a hotter object to a colder one, which accurately sums up the properties of the heat equation. Energy moves from one item to another in the form of heat.
What is equation?An equation is a mathematical formula that expresses equality by joining two expressions together with the equal symbol =. The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions. In the equation 3x + 5 = 14, for instance, the terms 3x + 5 and 14 are separated by an equal sign. An equal sign is a part of all mathematical formulas, including equations. Often, algebra is used in equations. In mathematics, algebra is employed when we don't know the precise quantity to calculate
Here,
Heat's characteristics
The direction of this transmission is always determined by the temperature differential between the bodies.
To achieve an equilibrium temperature, heat is transferred from the hotter to the cooler body.
As a result of the fact that a body and its surrounds are at different temperatures, we can infer that heat is the energy that is transferred between them.
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At summer camp this year, Clare is leading the beadwork class. Each of the 9 craft tables has a bucket of beads. The graph shows the weight of the beads in each bucket.
If Clare distributes all of the beads equally among the 9 buckets, how much will the beads in each bucket weigh?
The beads in each bucket will weigh 1 pound
How to determine the weight of the beads in each bucket?
A fraction is used to represent the portion/part of the whole thing. It represents the equal parts of the whole.
From the graph, we have weights of 0, 1/2, 1 1/2 and 2 pounds.
In order for Clare to distributes all of the beads equally among the buckets, she need to add up weight of the beads and divide by 5.
weight in each bucket = (0 + 1/2 + 1 1/2 + 2)/5 = 5/5 = 1 pound
Thus, each bucket weighs 1 pound
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what is the magnitude of the net electric field at point p due to the particles?
The magnitude of the net electric field at point P due to the particle is 0 . explanation is given as
let us assume that , The charges of the four particles and the distance are given then on understanding the concept of electric field at electrostatics concept. on using the concept of the electric field at any given point, then production of individual electric field by a charge. and we known the concept of superposition law, on applying the law we get the value of the electric field in its direction and this shows the determination of the net electric field at that point.
The magnitude of the electric field,
E = q * R
where R = The distance of field at point from the charge, and q = charge of the individual particle
According to the superposition principle, the electric field at a single point due to more than one charges present ,hence on calculation of net electric field we get the origin of the coordinate system which is placed at point P and the y-axis is situated and oriented in the direction of the charge, (passing through the charge, ). The x-axis which is perpendicular to the y axis, and thus passes through the identical charges, then the individual magnitudes of an electric field is due to the charges are demonstrated by using the absolute signs of the charges. Now let us assume that the point charge which being positive i.e ( q > 0), we can see that the contributions coming from each charge gets cancel to each other. Therefore the net electric field in the direction of the y-axis is given using equation as E= 0
hence the net electric field is zero .
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MEDICINE: Ahmad took 200 mg of a medication. The
function f(t) = 200e 0. 4+ can be used to determine the amount of
medication, f(t), still in his system after t hours. To the nearest hundredth,
after how much time will Ahmad have only 50 mg of medication left in his
system?
A 4. 37 hours
B 7. 47 hours
C
3. 47 hours
D
3. 74 hours
A BH
BO
If Ahmad took 200 mg of medication and the function [tex]f(t) = 200e^{-0.4t}[/tex] can be used to determine the amount of medication, then He will have only 50 mg of medication left in his system after (c) 3.47 hours .
The Function that is used to determine the amount of medication, f(t), still in his system after t hours. is given as [tex]f(t) = 200e^{-0.4t}[/tex] ,
we have to find the after how many hours there will be only 50 mg of medication left ;
we need to substitute f(t) as 50 ;
we get ;
⇒ [tex]50 = 200e^{-0.4t}[/tex] ;
⇒ [tex]\frac{50}{200} =e^{-0.4t}[/tex] ;
⇒ [tex]\frac{1}{4} =e^{-0.4t}[/tex]
On solving further ,
we get ;
⇒ [tex]t=3.4657..[/tex] hours ;
So , t≈ 3.47 hours .
Therefore , After 3.47 hours there will be 50 mg of medication left .
The given question is incomplete , the complete question is
Ahmad took 200 mg of a medication. The function [tex]f(t) = 200e^{-0.4t}[/tex] can be used to determine the amount of medication, f(t), still in his system after t hours. To the nearest hundredth, after how much time will Ahmad have only 50 mg of medication left in his system ?
(a) 4.37 hours
(b) 7.47 hours
(c) 3.47 hours
(d) 3.74 hours
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What is 2 4 reflected across the Y?
The point (2, -4) is reflected across the line y = -1.
The coordinates of the image is (4, -4).
coordinates
Any of a set of numbers used in specifying the location of a point on a line, on a surface, or in space.
Coordinates are a pair of numbers which are used to determine the position of a point or a shape in a 2-dimensional plane. We define the position of a point on a 2D plane using two numbers, called the x-coordinate and the y-coordinate.
Numbers
A number is a mathematical object used to count, measure, and label. The original examples are the natural numbers 1, 2, 3, 4, and so forth. Numbers can be represented in language with number words.
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Fwam went shopping for a new phone. Sales tax where he lives is 9%. The price of the phone is $33. Find the total price including tax. Round to the nearest cent.
Answer:
$35.97
Step-by-step explanation:
33 × .09 = 2.97
33 + 2.97 = $ 35.97
Josiah bought a new car for $25,000. He did some research and found that the value of his car would depreciate at an average rate of $3,750 per year. The table shows data about the value of his car over the next 4 years.
Number of Years Owned 1 2 3 4
Car Value $ 25000 21250 13750 10000
Express the relation as a set of ordered pairs.
Identify the domain and range of this relation.
Is this relation a function?
The domain is the set of years, which is {1, 2, 3, 4}, and the range is the set of values, which is {25000, 21250, 13750, 10000}. The ordered pairs of this function are (1, 25000), (2, 21250), (3, 13750), (4, 10000).
The relation described above can be expressed as a set of ordered pairs by calculating the value of the car for each year based on the depreciation rate. Let's calculate the value of the car for each year:
Year 1: 25000
Year 2: 25000 - 3,750
= 21250
Year 3: 21250 - 3,750
= 13750
Year 4: 13750 - 3,750
= 10000
Therefore, the ordered pairs of this relation are
: (1, 25000), (2, 21250), (3, 13750), (4, 10000).
The domain of this relation is the set of years, which is {1, 2, 3, 4}, and the range is the set of values, which is
{25000, 21250, 13750, 10000}.
This relation is a function because each input (year) is associated with one output (value).
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What is the SHAPE of the 22nd figure?
The color of the 15th figure is green.
The shape of the 40th figure star.
The shape of the 22nd figure triangle.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
We have,
The pattern of shapes we get is:
circle - Triangle - Square - Star
The pattern of color we get is:
Purple - Red - Green
Now,
The color of the 15th figure.
= 15 is a multiple of 3
= 5 x 3
So,
Green will be the color of the 15th figure
Now,
The shape of the 40th figure.
= 40 is a multiple of 4
= 10 x 4
So,
Star will be the shape of the 40th figure.
Now,
The shape of the 22nd figure.
= 22 ÷ 4
We get 2 as the remainder.
So,
Triangle will be the shape of the 22nd figure.
Thus,
The 15th figure color is green.
The 40th figure is a star.
The 22nd figure is a triangle.
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Which polynomial is prime?
x3 + 3x2 -2x - 6
x° - 2x2 + 3x 6
4x4 + 4x3 - 2x - 2
D 2x + x3 -x +2
The final equation is a polynomial of primes [tex]2x^{4} + x^{3} - x + 2[/tex] It can't be factored. Variables are sometimes known as indeterminate in mathematics.
what is polynomial ?An essential component of the "language" of mathematics and algebra are polynomials. They are used to express numbers that are the result of mathematical operations in almost every area of mathematics. Other types of mathematical expressions, such as rational expressions, also use polynomials as "building blocks."
given
Is a base form of a polynomial in other words is a polynomial that can't be factored.
so we have
[tex]A ) x^{3} +3x^{2} - 2x - 6 = ( x +3 ) ( x^{2} - 2 )\\B) x^{3} -2x^{2} +3x - 6 = ( x- 2 ) (x^{2} + 3)\\C)4x^{4} +4x^{3} - 2x - 2 = 2( x +1 )(2x^{2} - 1)\\D) 2x^{4} +x^{3} -x + 2[/tex]
hence, the final equation is a polynomial of primes [tex]2x^{4} + x^{3} - x + 2[/tex] It can't be factored.
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Bella begins to walk from her house toward her friend Ella's house. At the same time, Ella begins to ride her bicycle toward Bella's house. They each maintain a constant speed, and Ella rides 5 times as fast as Bella walks. The distance between their houses is 2 miles, which is 10,560 feet, and Bella covers $2\frac{1}{2}$ feet with each step. How many steps will Bella take by the time she meets Ella
Since Bella takes 4,224 steps, and Ella takes 844.8 steps, they meet at 4,224 steps.
To determine this:
We can start by using the information given to find out how long it takes Bella and Ella to meet.
Since Ella rides 5 times faster than Bella walks, we can use the following equation to find out how long it takes each of them to cover the 2-mile distance:
Time (Ella) = Time (Bella) / 5
We can also use the distance formula to find out how long it takes Bella to cover the 2-mile distance:
Distance = Speed x Time
We know that Bella's speed is [tex]$2\frac{1}{2}$[/tex] feet per step, and the distance between their houses is 10,560 feet. So:
10,560 feet = [tex]$2\frac{1}{2}$[/tex] feet/step x Time (Bella)
Solving for Time (Bella), we get:
Time (Bella) = 10,560 feet / [tex]$2\frac{1}{2}$[/tex] feet/step = 4,224 steps
Now we can use this information to find out how long it takes Ella to meet Bella:
Time (Ella) = Time (Bella) / 5 = 4,224 steps / 5 = 844.8 steps
And since Bella takes 4,224 steps, and Ella takes 844.8 steps, they meet at 4,224 steps.
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Nick mowed about 3.5 of the school lawn yesterday. He mowed another 1/4 of the lawn this morning. How much is left to mow? Answer if you can.
The portion left to mow is 3x+3.5 /4
What are linear equations?Linear equations help in representing the relationship between variables such as x, y, and z, and are expressed in exponents of one degree. In these linear equations, we use algebra, starting from the basics such as the addition and subtraction of algebraic expressions.
Given here:Nick mowed about 3.5 of the school lawn yesterday. He mowed another 1/4 of the lawn this morning. Let the whole lawn be x then on the first day portion left to be mowed is x-3.5 and on the second day he moved 1/4 of this quantity thus portion of lawn left to be mowed is
x-x-3.5/4
=3x+3.5 /4
Hence, The portion left to mow is 3x+3.5 /4
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