The price of new car is reduced by $825 from the original price $12,500 which implies the price of car after reduction is $11,625 i.e
The percentage reduction is 7 .
Percentage is calculated by dividing the value by total value and then multiply with 100.
We have given that,
The price of a new car = $12,500
After the some reduction in price
then the price of car = $11,625
The reduction in total price of car = original price - price after reduction
= $12,500 - $11,625
= $875
Now, we have to calculate the reduction of price in percentage.
Using the percentage reduction formula,
P% = (original price - price after reduction )× 100 /original price
=> percentage reduction = ( 875/12500)×100
=> percentage reduction = 875/125 = 7
Hence, the reduction is 7% .
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A ball i drawn randomly from a jar that contain 5 red ball, 2 white ball, and 1 yellow ball. Find the probability of: Find P(red ball): Find P(NOT Yellow): Find P(white or yellow)
Following are all of the subparts' solutions using the probability formula:
Red ball (A) P: 5/8
(B) P: 7/8 (NOT Yellow)
(C) P(yellow or white): 3/8
What is probability?
Probability is a branch of mathematics that deals with numerical representations of the likelihood of an event occurring or of a proposition being true.
What is an event?The probability of an event is a number between 0 and 1, with 0 approximately denoting impossibility and 1 denoting certainty.
Probability formula: P(E) = favorable events/Total events
(A) P(red ball):
P(E) = favorable events/Total events
P(E) = 5/8
(B) P(NOT Yellow)
P(E) = favorable events/Total events
P(E) = 7/8
(C) P(white or yellow)
P(E) = favorable events/Total events
P(E) = 3/8
Therefore, the answers to all the subparts using the probability formula are shown:
(A) P(red ball): 5/8
(B) P(NOT Yellow): 7/8
(C) P(white or yellow): 3/8
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Does lower production cost increase profit?
Yes lower production cost increase profit.
Production costs are expenses, such as labor and materials that your company incurs within the course of producing the product that you simply offer to consumers. In common, the lower your generation cost, the higher your benefit, or the sum you've got remaining after you subtract your costs from your sales revenue. lower production costs generally lead to higher profits. When production costs are lower, companies can charge lower prices and still make a profit, or they can keep prices the same and earn higher profits. Lower production costs also reduce the amount of money spent on materials, labor, and other expenses, leaving more of the revenue as profit.
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The weights of a pack of chewing gum for a certain brand have a mean of 47. 1 grams and a standard deviation of 2. 4 grams. What is the weight of a randomly selected pack of gum that has a z-score of 3. 11? 39. 6 grams 44. 7 grams 49. 5 grams 54. 6 grams.
The weight of a randomly selected pack of gum that has a z-score of 3.11 is 54.6 grams
What is Z-score?Z-score aids in determining how much the data deviates from the mean. It represents the frequency with which the data is above or below the mean.
How do you calculate the z-score?Z-scores are calculated using the formula z = (x-)/, where x represents the raw score, the population mean, and the population standard deviation. The z-score is just the raw scoreless population mean, divided by the population standard deviation, as the calculation demonstrates.
According to the formula,
Z = ( X - μ ) / σ
Z being the Z-score,
The data point is X,
The standard variable is, and the mean is.
The z-score of the weight of a randomly chosen pack of gum is 3.11. As a result, this pack of gum weighs 3.11 standard deviations more than the average.
Z = ( X - μ ) / σ
3.11 X 2.4 = X - 47.1
X = 54.6 g
Therefore, choice B is the right one.
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Each craft box has 8 crayons Which equation represents the relationship between the total number of craft boxes, b, and the total number of crayons, c? O b = 8c b = c +8 Oc=b+8 Auto saved at c = 8b
HELP asap
Answer:
c=8b
Step-by-step explanation:
The number of crayons is equal to 8 times the number of boxes.
albert purchased a tract of land for $140,000 in 2019 when he heard that a new highway was going to be constructed through the property and that the land would soon be worth $200,000. highway engineers surveyed the property and indicated that he would probably get $180,000. the highway project was abandoned in 2022 and the value of the land fell to $100,000. what is the amount of loss albert can claim in 2022?
If the value of the land fell to $100000 , then the amount of loss albert can claim in 2022 is $0 .
In the question ,
it is given that ,
the value of the tract land in 2019 that Albert purchased = $140000
and he heard that after the new highway project the property and land would soon be worth of $200,000 .
after survey the value of the project will be = $180000 ,
after the abandoning of highway project , the value = $100000 .
but Albert cannot claim any loss because there was no transaction.
It is not given that Albert sold the land so neither did he gain or make a loss.
Therefore , the correct option is (e)None of these choices are correct .
The given question is incomplete , the complete question is
Albert purchased a tract of land for $140,000 in 2019 when he heard that a new highway was going to be constructed through the property and that the land would soon be worth $200,000. highway engineers surveyed the property and indicated that he would probably get $180,000. the highway project was abandoned in 2022 and the value of the land fell to $100,000. what is the amount of loss albert can claim in 2022 ?
(a) $100,000
(b) $60,000
(c) $40,000
(d) $80,000
(e) None of these choices are correct.
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Trish is paying $15 for a meal. She has a 10% off coupon for the meal. After the discount, a 6% sales tax is applied. What is the final cost of the meal?
Answer:
$9.01
Step-by-step explanation:
10 percent off of 15 is 8.5 and since sales tax is 6%, that means it adds 0.51 cents to the total, bringing the total to $9.01
Answer:
17.49
Step-by-step explanation:
15x0.10= 1.5
15+1.5= 16.5
16.5x0.06=0.99
16.5+0.99=
find the distance from a vector (2; 3; 1)t to the subspace spanned by the vectors (1; 2; 3)t , (1; 3; 1)t .
By using Gram Schmidt process of orthogonalization, it can be calculated that-
Distance from a vector (2; 3; 1)t to the subspace spanned by the vectors [tex](1; 2; 3)^T , (1; 3; 1)^T[/tex] IS 2.51 units
What is Gram Schmidt process of orthogonalization?
In an inner product space, the set of mathematical operations which converts a set of linearly independent vectors into an orthonormal vector that spans the same set as spanned by the original vectors is called Gram Schmidt process of orthogonalization.
Distance from [tex]b=(2,3,1)^T[/tex] to W= [tex]Span\left \{u_1= (1,2,3)^T,u_2=(1,3,1)^T \right \}[/tex]
Here, Gram Schmidt process of orthogonalization is used
[tex]v_1=u_1=(1,2,3)^T\\ v_2=u_2-\frac{ < u_2,v_1 > }{||v_1||^2}v_1[/tex]
[tex]=(1,3,1)^T-\frac{(1,2,3)^T.(1,3,1)^T}{(1,2,3)^T.(1,2,3)^T}(1,2,3)^T\\ =(1,3,1)^T-\frac{1+6+3}{1+4+9}(1,2,3)^T\\ =(2/7,11/7,-16/14)^T[/tex]
[tex]v_2 =(2/7,11/7,-8/7) ^T[/tex]
[tex]proj_bW=\frac{(2,3,1)(1,2,3)}{(1,2,3)(1,2,3)}(1,2,3)+\frac{(2,3,1)(2/7,11/7,-8/7)}{(2/7,11/7,-8/7)(2/7,11/7,-8/7)}(2/7,11/7,-8/7)[/tex]
=(1.42, 5.11, -0.22)
[tex]b-proj_bW[/tex]=(2,3,1)-(1.42,5.11, -0.22)=(0.58,-2.11,1.22)
Required distance from b onto W=
[tex]||b-pro_bW||=||(0.58,-2.11,1.22)||=\sqrt{(0.58)^2+(-2.11)^2+(1.22)^2}[/tex] = 2.51 units
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Write an equation of the line that passes through the given point and is (a) parallel and (b) perpendicular to the given line.
Answer:
[tex]\textsf{a)} \quad y=-4x+19[/tex]
[tex]\textsf{b)} \quad y=\dfrac{1}{4}x+2[/tex]
Step-by-step explanation:
From inspection of the graph, two points on the line are:
(1, 6)(2, 2)Substitute these points in the slope formula to find the slope of the line:
[tex]\implies \textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{2-6}{2-1}=\dfrac{-4}{1}=-4[/tex]
Part (a)Lines that are parallel have the same slope.
Therefore, a line parallel to the given line has a slope of -4.
To write an equation of the parallel line, substitute the found slope and point (4, 3) into the point-slope formula and rearrange:
[tex]\implies y-y_1=m(x-x_1)[/tex]
[tex]\implies y-3=-4(x-4)[/tex]
[tex]\implies y-3=-4x+16[/tex]
[tex]\implies y=-4x+19[/tex]
Part (b)If two lines are perpendicular to each other, their slopes are negative reciprocals.
Therefore, a line perpendicular to the given line has a slope of ¹/₄.
To write an equation of the parallel line, substitute the found slope and point (4, 3) into the point-slope formula and rearrange:
[tex]\implies y-y_1=m(x-x_1)[/tex]
[tex]\implies y-3=\dfrac{1}{4}(x-4)[/tex]
[tex]\implies y-3=\dfrac{1}{4}x-1[/tex]
[tex]\implies y=\dfrac{1}{4}x+2[/tex]
What is the Supremacy Clause government ?
Article IV Clause 2 of the US Constitution is referred to as the Supremacy Clause. It proves that all other laws and international treaties are subordinate to US federal law.
The United States Constitution's Supremacy Clause declares that the Constitution, federal laws adopted in accordance with it, and treaties signed in accordance with its authority are the "supreme Law of the Land" and supersede any conflicting state laws. According to its provisions, state constitutions are subservient to the supreme law and state courts are obligated by it.
Moreover, federal statutes and treaties must be within the bounds of the Constitution, i.e., they must be in accordance with the enumerated powers of the federal government and must not violate other constitutional restraints on federal power that specify that the federal government only has the authority granted to it by the Constitution.
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imagine you are drawing from a deck of 52 cards. determine the number of ways you can achieve the following 5-card hands drawn from the deck without repeats. (5 points each) a) a straight (5 cards of sequential rank). hint: when considering the ace, a straight could be ace, 2, 3, 4, 5 or 10, jack, queen, king, ace, but no other wrap around is allowed (e.g., queen, king, ace, 2, 3 is not allowed) b) a flush (5 cards of the same suit) c) a full house (3 cards of one rank and 2 from a single other rank) d) a straight flush (5 cards of sequential rank from the same suit)
Thus , the probability of that a) a flush (5 cards of the same suit) is .198% and probability of a 3 card of same rank and2 from single other rank is 0.07612 %
Describe probability.The field of mathematics known as probability studies numerical representations of the likelihood that an event will occur or that a statement is true. The probability of an event is a number between 0 and 1, with 0 generally signifying the event's impossibility and 1 generally signifying its certainty.
Here,
a) It doesn't matter what suit the first card is. Any of the suits may be drawn first, provided that the following four cards are taken from the same deck and have the same suit.
The deck contains 13 of each suit, so after the first card is pulled, there are only 12 of that suit remaining. There are then 11 remaining for the third card, 10 remaining for the fourth card, and 9 remaining for the fifth and final card. The deck will also contain one fewer card overall each time.
(ℎ) = (2 ) ∙ (3 ) ∙ (4ℎ )\s∙ (5ℎ )
(ℎ) = [tex]\frac{12}{51} *\frac{11}{50} *\frac{10}{49} *\frac{9}{48}[/tex]
(ℎ) =11880 / 5997600
(ℎ)= 33/16660 = .00198 .198%
c) The probability of a 3 card of same rank and2 from single other rank
Since there are 13 ranks in the cards
So, P = [tex]\frac{13}{52} * \frac{12}{51} *\frac{11}{50} *\frac{13}{52} *\frac{12}{51}[/tex]
P = 267696/351655200
P=0 .0007612 or 0.07612 %
Thus , the probability of that a) a flush (5 cards of the same suit) is .198% and probability of a 3 card of same rank and2 from single other rank is 0.07612 %
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The product of three and a number plus five is 20
Answer:
5
Step-by-step explanation:
3 × 5= 15
15 + 5= 20
Answer: 5
Step-by-step explanation: 20-5 is 15 and then 3 * x must be 5 since 3x5=15.
Ethan buys a video game on sale. if the video game usually costs $39.99, and it was on sale for 20% off, how much did ethan pay? round to the nearest cent.
Amount paid by Ethan to buy a video game on sale of 20% with usual cost of $39.99 is equal to $32 ( nearest cent ).
As given in the question,
Usual cost of Video game bought by Ethan = $39.99
Sale discount received by Ethan on video game = 20%
Let 'x' be the amount paid by Ethan for video game.
Discount amount = 20% of $39.99
= ( 20 / 100 ) × 39.99
= 799.8/100
= $ 7.998
= $7.99
Amount to be paid by Ethan 'x' = $39.99 - $7.99
= $32 ( nearest cent)
Therefore, the amount paid by Ethan to purchase a video game on sale discount of 20% is given by $32.
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8(−5x−8)=-3x-4−3x−4
Find for X
8(−5x−8)=-3x-4−3x−4
-40x-64=-3x-4-3x-4
-40x-64=-6x-8
-36x=-56
[tex]x=\frac{56}{36}[/tex]
[tex]x=\frac{14}{9}[/tex]
Halona walks 1. 931. 93 kilometers to a neighbor's house in 2323 minutes. Assuming she walks at a constant speed, write a proportion that represents how many kilometers, yy, halona can walk in xx minutes. Then solve your proportion for yy.
The required proportional ratio is y = 0.08 x. gives Halona 23 minutes to move her 1.93 kilometers to her neighbor's house. As long as you move at a steady pace.
How many kilometers Halona can run in x minutes y expressed as a ratio. Then find y in percentage. The relationship between two or more proportional or inversely proportional sets of values, whether they are directly related or not, is called proportionality.
Here we have
yxxy = kxwhere k is the proportionality constant ofand at x = 23 y = 1.931.93 = 23k4 k = 2 444k = 1.93k = 0.08Substitute k into the proportional equation.
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Given f(x)=−x−1, find f(0)
Answer: -1
Step-by-step explanation: If you plug in 0 as x, the equation will become f(0)=-0-1. If you solve this, then f(0)=-1
Answer now please……………….
The measure of angle 2 is 61 degrees.
The measure of angle 4 is 119 degrees.
What is triangle?
A triangle is a polygon with three vertices and three sides. The angles of the triangle are formed by the connection of the three sides end to end at a point. The triangle's three angles add up to 180 degrees in total.
In the given triangle the measure of two triangles is given which is 61° and 58°.
We have to solve for the measure of angle 2.
Since, the sum of three angles of triangle's is 180 degrees.
⇒ 61° + 58° + ∠2 = 180°
119 ° + ∠2 = 180°
∠2 = 180° - 119°
∠2 = 61°
Hence, the measure of angle 2 is 61 degrees.
Now to find measure of angle 4.
Here ∠2 and ∠4 are planer angles and their addition is 180°.
⇒ ∠2 + ∠4 = 180°
61° + ∠4 = 180°
∠4 = 180° - 61°
∠4 = 119°
Hence, the measure of angle 4 is 119°.
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Can the following question be considered as stactical question, and why?
Answer:Yes
Step-by-step explanation: It came because your asking questions that you have to gather data for.
Following the route shown, what is the total distance traveled by the architectural tour if it ends where it started? What properties and theorems did you use to find the distance?
Using (SAS,CPCTC, and SSS) , it can be shown that the two triangles formed are congruent. Then using (SSS, SAS and CPCTC) the length of the road from the intersection to the first turn can be found to be ----------------- feet. Thus, the total length of the tour is-------------------- feet.
Using SAS, it can be shown that the two triangles formed are congruent. Then using SSS the length of the road from the intersection to the first turn can be found to be 200ft. Thus the total length of the tour is 1700ft.
What is congruent triangles?
If the three sides and the three angles of both angles are equal in any orientation, two triangles are said to be congruent.
The SAS formula states that if two sides and one angle of two triangle are the same then the triangles are congruent to each other.
Two lines AD, EC intersects each other at the point B . Therefore, ∠ABC = ∠DBE .
The length of the sides AC = DE, BC = BE .
The triangles ΔABC, ΔBDE are congruent to each other by the SAS formula.
The SSS formula states that two triangles are congurent to each other if the ratio of corresponding sides of two triangles are the same and vice-versa.
Use the SSS formula in the triangles ΔABC, ΔBDE and simplify to calculate the length of BD.
BD/200 = 300/300
BD/200 = 1
BD = 200
Therefore, using SSS the length of the road from the intersection to the first turn can be found to be 200ft.
Add the lengths of AB, BD, DE, EB, BC, CA to calculate the total length of the tour.
200 + 200 + 300 + 350 + 350 + 300 = 1700
The total length of the tour is 1700ft.
Hence, using SAS, it can be shown that the two triangles formed are congruent. Then using SSS the length of the road from the intersection to the first turn can be found to be 200ft. Thus the total length of the tour is 1700ft.
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if every possible code between 000-999 has equal chance of being chosen, how long (approximate time) will it take, in the average case, to guess the code?
10 choose 3 with replacement gives you a mere 220 combinations. A “combination” lock uses permutations, so there would be 1000 possibilities.
What is Combination?
Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of the selection is irrelevant.
Mathematically, a combination is a selection of things without regard for order.
The formula for “combination with replacement” is:
[tex]C^{R} (n,r)=\frac{(n+r-1)!}{r! (n-r)!}[/tex]
10 choose 3 with replacement gives you a mere 220 combinations.
The toss of three identical 10-sided dice would have 220 possible outcomes.
Hence, A “combination” lock uses permutations, so there would be 1000 possibilities.
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Jessica bought two tickets of the same price. She then sold one of the tickets at a profit of 10% and the other
one at a loss of $18. It is given that the difference in the selling prices of these two tickets is $36.
(a) Find the cost of each ticket for Jessica.
(b) Did she make an overall profit or loss? Explain your answer
Please give explanation!!! Will give brainliest ty ty!!
Answer and Step-by-step explanation:
Let the cost of each ticket for Jessica be $x. If she sold one of the tickets at a profit of 10%, she got $x + 0.1*x = $1.1x from selling it. Similarly, if she sold the other ticket at a loss of $18, she got $x - $18 from selling it.
Since the difference in the selling prices of the two tickets is $36, we have $1.1x - ($x - $18) = $36. Solving this equation for x, we get $x = $36 / 0.1 = $360. Therefore, the cost of each ticket for Jessica was $360.
To determine whether Jessica made an overall profit or loss, we need to compare the total amount she received from selling the two tickets to the total cost of the tickets. The total amount she received from selling the two tickets was $1.1x + ($x - $18) = $1.1x - $18 + $x = $1.1x = $396. The total cost of the tickets was 2 * $360 = $720. Since $396 < $720, Jessica made a loss of $720 - $396 = $324 overall.
Given G (3, -1) and H (-9, 7), what is the slope of line GH ?
Answer:-2/3
Step-by-step explanation: the rise is 2 and the run is 3
Lindsey bought a car for $9,000. The sales tax is 6.5%. How much would Lindsey pay in total?
Answer: 9,585
Step-by-step explanation:
Answer:
$9,585.00
6.5x9000 over 100
a 1\$ lottery ticket has the following prizes: 10\$ cash for 3 people; 50\$ cash for 2 people ; 100\$ cash for 1 person. winners are chosen randomly. if 300 people bought this lottery, what is the expected profit of a random person?
If winners are chosen randomly from the 300 people who bought this lottery, the expected profit of a random person is $0.766..
Expected value or profit :The expected profit under a probability demand distribution is calculated by multiplying the profit amount by the probability of achieving that profit.
It is denoted as E(X) . We have given that,
A $1 lottery ticket has a number of prizes.
Probability of winning first prize , $10 = p₁ = 3/300 = 1/100
probability of winning a 2nd prize, $50
= p₂= 2/300= 1/150
probability of winning a 3rd prize, $100
= p₃ = 1/300 = 1/300
E = expectation value = ∑ Vᵢpᵢ where Vᵢ = value of prize, pᵢ = probability of winning prize,
E = $10 ×1/100 + $50×1/150 + $100×1/300
=> E = $10/100 + $50/150 + $100/300
Taking LCM as 300 on right hand side,
=> E =( $30+ $100+$100)/300
=> E = $(230/300) = $0.766
So, expected winnings for a person buying one ticket is $0.766..
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Factor out the coefficient of the variable term 4x-20
The coefficient of the variable term of the equation A = 4x - 20 is 4
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is given as
A = 4x - 20
On simplifying the equation , we get
The value of A = 4x - 20
Taking 4 as the common factor of the equation , we get
The value of A = 4 ( x - 5 )
Therefore , the coefficient of the equation A is 4
Hence , The coefficient of the variable term of the equation A = 4x - 20 is 4
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What is 1/2 of 1/3 ?
Answer:
[tex]\frac{1}{6}[/tex]
Step-by-step explanation:
[tex]\frac{1}{2}[/tex] of [tex]\frac{1}{3}[/tex]
[tex]\frac{1}{2}[/tex] × [tex]\frac{1}{3}[/tex] = [tex]\frac{1}{6}[/tex]
Hope this helps! :)
Answer:
= 1/6
Step-by-step explanation:
1/2 0f 1/3
is:
(1/2) (1/3) = (1*1) / (2*3)
= 1/6
A builder has some red and grey bricks. The red bricks weigh 9 kilograms each, and the grey bricks weigh 8 kilograms each. If the total weight of all 14 bricks is 120 kilograms, how many of each type of brick does Nellie have?
The number of red bricks is 6, and there are 8gray bricks.
What is the total number of red and grey bricks?To evaluate an algebraic expression, find the expression's value when the variable is replaced by a given number. To evaluate an expression, we substitute the given number for the expression's variable and then simplify the expression using the order of operations.Here given,
A red brick weighs 9 kg and a gray brick weighs 8 kg. The total number of bricks is 14, with a weight of 120kg.
Let x be a red brick and y be a gray brick.
x + y = 14bricks,
=> x = 14 - y bricks
9x + 8y = 120kg
9(14 - y) + 8y = 120
126 - 9y + 8y = 120
-y = -6
y = 6
14 - 6 = 8
The number of red bricks is 6, and the number of gray bricks is 8.
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hey whats the answer to this?
a) The amount of water in the tank will be 0 after 5 minutes.
b) As time increases, the amount of water decreases at a rate of -60 L/min.
At which time the water reaches 0 liters?Here we can see a graph of a linear function that relates the amount of water in an aquarium (vertical axis) with the time (horizontal axis).
The amount of water in the aquarium will reach the 0 liters mark when the line intercepts the x-axis.
We can see that happens for x = 5 minutes
b) We can see that as we move to the right (time flows to the right in that graph) the line goes downwards. This means that the amount of water on the tank decreases as the time increases.
We can see that in 5 minutes, the amount of water goes from 300 lites to 0 liters, so the rate at which the water comes out of the tank is:
R = 300L/5min = 60 liters per minute.
It should actually be written with a negative sign so we are 100% clear that it means that the water is coming out from the tank, so the rate is:
R = -60 L/min
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A 20-gallon drum i being filled with water at a contant rate of 2 gallon a minute. How many gallon of water have been added to the drum after 4 minute?
With a water flow rate of 2 gallons per minute (gpm), the volume of water after 4 minutes will be 8 gallons of water.
Gallons per minute (gpm) is a measurement of the flow rate of the liquid. Gpm measures how much volume of water is flowing out (in imperial measurement of gallon) of the pipe, shower head, taps, pumps, etc in a given time.
Given that a drum is being filled with a flow rate of 2 gpm and the time given is 4 minutes, we need to figure out the volume of water using a water flow rate gallons per minute (gpm) we will then calculate with the following formula:
Volume = flow rate × time
Volume = 2×4
Volume = 8 gallons
Therefore the drum will be filled with 8 gallons of water after 4 minutes of filling.
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Which of the following is an example of continuous data?
1.The height of a Wolsey Hall student
2.The number of modules in a Wolsey Hall course
3.The number of Wolsey Hall students
4.The number of KS3 courses
5.The number of pages in your course book
The height of a Wolsey Hall student is an example of continuous data. Option 1. is the answer
How to identify examples of continuous data?Continuous data is data that can take any value. An easy way of identifying continuous data is that they are measured and not counted.
For example, height, weight, temperature and length are all examples of continuous data. Over time, some continuous data can change.
Thus, the height of a Wolsey Hall student is an example of continuous data because it is measured and not counted
Note: Other options are NOT continuous data because they include only data that can only be counted in whole numbers or integers, which implies that the data can not be split into fractions or decimals.
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4. P(x) = x³ - 5x² + 2x + 8. We know (x + 1)is a factor of P(x). Find the other two
factors then write P(x) as a product of three linear factors and sketch the graph of P(x).
Answer:
P(x) = (x +1)(x -2)(x -4)
see the 2nd attachment for a graph
Step-by-step explanation:
You want the factors of P(x) = x³ - 5x² + 2x + 8, given that (x+1) is one of the factors. You also want a graph of it.
Synthetic divisionThe quotient from dividing P(x) by the given factor will be a quadratic we can factor to find the other two binomial factors. The first attachment shows that quotient is (x² -6x +8).
FactorsTo factor this quadratic, we look for factors of 8 that have a sum of -6. They are -2 and -4. Hence the remaining binomial factors are (x -2)(x -4).
The desired product is ...
P(x) = (x +1)(x -2)(x -4)
GraphThe second attachment shows a graph of P(x). The y-intercept is the constant in the equation, 8. The x-intercepts are the values of x that make the factors zero.