Answer:
Step-by-step explanation:
In accordance with the Remainder theorem, the given part means that the given polynomial has the roots of 1, -2 and 2.
So we write these three equations expressing this fact
2A*1^4 - B*1^3 - C*1 - 16 = 0
2A*(-2)^4 - B*(-2)^3 - C*(-2) - 16 = 0
2A*2^4 - B*2^3 - C*2 - 16 = 0
or
2A - B - C = 16 (1)
32A + 8B + 2C = 16 (2)
32A - 8B - 2C = 16 (3)
Adding equations (2) and (3), you get
64A = 32, which implies A = 32%2F64 = 0.5.
Then from (1) and (2), substituting A = 0.5 there, you get
B + C = -15 (4)
8B + 2C = 0 (5)
Expressing B = -15 - C from (4) and substituting it to (5), you get
8*(-15 -C) + 2C = 0, or
-120 - 8C + 2C = 0
- 6C = 120
C = - 20.
Then from equation (4), B = -15 - (-20) = -15 + 20 = 5.
ANSWER. A = 0.5; B = 5, C = -20.
We have three factors: (x-1),(x+2) and (x-2)
However, we have a quartic polynomial, since the degree (largest exponent) is 4
So we need a fourth factor. Let's call that x-p, for some real number p.
Let's expand out the following
(x-1)(x+2)(x-2)(x-p)
(x+2)(x-2)(x-1)(x-p)
(x^2-4)(x^2-px-x+p)
x^2(x^2-px-x+p)-4(x^2-px-x+p)
x^4-px^3-x^3+px^2-4x^2+4px+4x-4p
x^4+(-px^3-x^3)+(px^2-4x^2)+(4px+4x)-4p
x^4+(-p-1)x^3+(p-4)x^2+(4p+4)x-4p
Compare that result to 2Ax^4-Bx^3-Cx-16
Match up the corresponding terms, and we have the following equations
2Ax^4 = 1x^4 which leads to 2A = 1 and solves to A = 1/2 = 0.5
(-p-1)x^3 = -Bx^3 which leads -p-1 = -B and solves to B = p+1
(4p+4)x = -Cx which leads to 4p+4 = -C and solves to C = -4p-4
-4p = -16 which solves to p = 4
Use that value of p to find the other coefficients
B = p+1 = 4+1 = 5
C = -4p-4 = -4*4-4 = -20
The polynomial 2Ax^4-Bx^3-Cx-16 turns into x^4-5x^3+24x-16 after we plug in those A,B, and C values.
Answers:
A = 1/2 = 0.5
B = 5
C = -20
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Which property is illustrated by the statement 13 * 12 = 12 * 13
Answer:Commutative property of multiplication
Step-by-step explanation:
Commutative property of multiplication
Are you able to find the area of the following figure?
A: Yes the area can be found by adding four and the seven and dividing by two
B: No you are not able to find the area because one side length is missing
C: Yes the area can be found by multiplying the 4 and 7 and then dividing the product by two.
D: No you are not able to find the area because the numbers are both irrational numbers
C: Yes the area can be found by multiplying the 4 and 7 and then dividing the product by two.
This is the same as using the formula [tex]A=\frac{1}{2}bh[/tex].The Humber Room advertises two types of entrée, meat and fish. It is known that 70% of all customers order meat, and 30% order fish. All customers are individually asked after their meals if they were satisfied with them. This survey shows that 80% of those who ordered meat and 95% of those who ordered fish were satisfied. Draw a probability tree for this problem to answer the question.
If M represents the event of ordering meat, F is the event of ordering fish, + is the event of being satisfied, and − is the event of not being satisfied, then answer the following questions:
(a) Determine the following probabilities based on the probability tree:
P(M)
P(F)
--------- Determine the conditional probabilities
(iii) P (+ M)
(iv) P (- M)
(v) P (+F)
(vi) P(-F)
(b) Write down the results of calculating the joint probabilities below:
P (M and +)
P (M and -)
P (F and +)
P (F and -)
(c) If a randomly selected customer was satisfied with his/her meal, what is the probability that the customer ordered fish?
Can someone please explain how to resolve this ?
The probability of ordering meat is 0.7 and the probability of ordering fish is 0.3.
P(+ | M) = 0.8 and P(- | M) = 0.2,
P(+ | F) = 0.95 and P(- | F) = 0.05.
P(M and +) = 0.56 and P(M and -) = 0.14,
P(F and +) = 0.285 and P(F and -) = 0.015.
C: the probability that the customer ordered fish is 0.3.
What is probability?Probability is a way to gauge how likely something is to happen. According to the probability formula, the likelihood that an event will occur is equal to the proportion of positive outcomes to all outcomes. The probability that an event will occur P(E) is equal to the ratio of favorable outcomes to total outcomes.
Given The Humber, Room advertises two types of entrée, meat and fish,
70% of all customers order meat, and 30% order fish,
M represents the event of ordering meat, F is the event of ordering fish,
probability of M and F,
p(M) = 70% = 0.7
p(F) = 30% = 0.3
and 80% of those who ordered meat and 95% of those who ordered fish were satisfied,
+ is the event of being satisfied, and − is the event of not being satisfied,
probability of satisfied customers with meat,
p(+) = 80% = 0.8
not satisfied with meat,
p(-) = 1 - 0.8 = 0.2
probability of satisfied customers with fish,
p(+) = 95% = 0.95
not satisfied with fish,
p(-) = 1 - 0.95 = 0.05
B: calculating the joint probabilities,
P (M and +) = P(M ∩ +) = p(M)*p(+)
P (M and +) = 0.7*0.8
P (M and +) = 0.56
P (M and -) = P(M ∩ -) = p(M)*p(-)
P (M and -) = 0.7*0.2 = 0.14
P (F and +) = P(F ∩ +) = p(F)*p(+)
P (F and +) = 0.3*0.95
P (F and +) = 0.285
P (F and -) = P(F ∩ -) = p(F)*p(-)
P (F and -) = 0.3*0.05
P (F and -) = 0.015
C: Determine the conditional probabilities,
P (+ | M) = P(M ∩ +)/p(M)
substitute the values
P (+ | M) = 0.56/0.7
P (+ | M) = 0.8
P (- | M) = P(M ∩ -) /p(M)
P (- | M) = 0.14/0.7
P (- | M) = 0.2
P (+ | F) = P(F ∩ +)/p(F)
substitute the values
P (+ | F) = 0.285/0.3
P (+ | F) = 0.95
P(- | F) = P(F ∩ -)/p(F)
P(- | F) = 0.015/0.3
P(- | F) = 0.05
D: If a randomly selected customer was satisfied with his/her meal, what is the probability that the customer ordered fish,
to find P (F | +) = P(F ∩ +)/p(+)
substitute the values
P(F | +) = 0.285/0.95
P (F | +) = 0.3
Hence the probabilities are as followed.
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Brady is making snack bags with 18 juice boxes and 27 cookies. He wants each bag to have the same number of juice boxes and the same number of cookies. (a) What is the maximum number of snack bags he could make? (b) How many juice boxes and (c) how many cookies could he put in each bag?
(a) The maximum number of snack bags he could make,
= 18 snack bags.
(b) 18 juice boxes.
(c) 18 cookies in each bag.
What is greatest common factor?The greatest number that can divide the numbers in equal parts.
It is called as greatest common factor.
Given:
Brady is making snack bags with 18 juice boxes and 27 cookies.
He wants each bag to have the same number of juice boxes and the same number of cookies.
(a) The maximum number of snack bags he could make,
= GCF(18, 27)
= 18 snack bags.
(b) 18 juice boxes.
(c) 18 cookies in each bag.
Therefore, all the required values are given above.
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help help help
pleas3e
Answer: 3
Step-by-step explanation:
Dan organized his books and DVDs into boxes. He has 88 books and 76 DVDs. What is the greatest number of boxes he could have used if he put the same number of books and the same number of DVDs into each box?
The greatest number of boxes is 4
How to determine the greatest number of boxesFrom the question, we have the following parameters that can be used in our computation:
88 books and 76 DVDs
To do this, we simply calculate the GCF
So, we have the following representation
88 = 2^2 * 11
76 = 2^2 * 19
This gives
GCF = 2^2
GCF = 4
The greatest number of boxes he could have used is 4 boxes.
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This shape is made using three semicircles.
The smaller semicircles have diameters of 10 cm.
10 cm
Calculate the shaded area.
Take to be 3.142 and write down all the digits given by your calculator.
The shaded area is 157.1 square cm
How to determine the shaded areaFrom the question, we have the following parameters that can be used in our computation:
Diameter = 10 cm
So, the area of the small semicircles is
Area = 1/2π(d/2)²
This gives
Area = 1/2π(10/2)²
Evaluate
Area = 25/2π
For the big semicircle, we have
Area = 1/2π(D/2)²
Area = 1/2π(20/2)²
So, we have
Area = 50π
i.e.
Area =50 * 3.142 = 157.1
This represents the shaded area because the small semicircles cancel out
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Which of these numbers in NOT divisible by 3?
300
321
241
8,910
Answer:
Step-by-step explanation:
241 is divisible by 3
A gas station sells regular gas for $2.15 per gallon and premium gas for $2.90 a gallon. At the end of a business day 300 gallons of gas had been sold, and receipts totaled $690. How many gallons of each type of gas had been sold?
Answer: Let's call the number of gallons of regular gas sold "x". Then, the number of gallons of premium gas sold would be 300 - x.
The total revenue from regular gas would be 2.15 * x dollars. The total revenue from premium gas would be 2.90 * (300 - x) dollars.
We know that the total receipts for the day were $690, so we can set up the following equation:
2.15x + 2.90(300 - x) = 690
Expanding the second term, we get:
2.15x + 870 - 2.90x = 690
Combining like terms, we get:
0.25x = -180
Dividing both sides by 0.25, we get:
x = 720
So, 720 gallons of regular gas and 300 - 720 = -420 gallons of premium gas were sold. However, since it is not possible to sell a negative number of gallons of gas, this solution is not valid.
If we try another value of x that is less than 300, we will find a valid solution. Let's try x = 200:
2.15 * 200 + 2.90 * (300 - 200) = 690
Expanding and simplifying, we get:
430 + 90 = 520
So, 200 gallons of regular gas and 300 - 200 = 100 gallons of premium gas were sold.
Step-by-step explanation:
16. AQRS is an equilateral triangle. If QR is seventeen more than twice x, RS is 19 less than six times x,
and QS is one less than four times x, find x and the measure of each side.
Topic 4: Congruent Triangles
18. Write three valid congruency statements given the triangles below.
P
17. In AJKL, if JK = JL, m/J = 23x - 4, m/K = 4x - 1, and m/L = 9x - 31, find x and the
measure of each angle.
¥
Q
R
S
|||
T
U
19. If AKPLAACM, complete each part.
a) KL =
d)
The value of x is 9 ,
The measure of each side of the equilateral i.e QR , RS , QS is 35
What is a Triangle?A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes.
Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a singular triangle and a singular plane.
Given as :
Triangle QRS is an equilateral triangle
The side of the triangles are, QR , RS, QS
Now, According to the question
QR = 2 x + 17
RS = 6 x - 19
QS = 4 x - 1
If the Triangle is equilateral, then all sides are equal
So , QR = RS = QS
Or, 2 x + 17 = 6 x - 19 = 4 x - 1
Now, 2 x + 17 = 6 x - 19
So, 17 + 19 = 6 x - 2 x
Or, 36 = 4 x
x =
I.e x = 9
So, the measure of side QR = 2 x + 17 = 2 × 9 + 17
Or, the measure of side QR = 35
The measure of side RS = 6 x - 19 = 6 × 9 - 19
Or, The measure of side RS = 35
The measure of side QS = 4 x - 1 = 4 × 9 - 1
Or , The measure of side QS = 35
Hence the value of x is 9,
And the measure of each side of the equilateral i.e QR , RS, QS is 35 . Answer
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Find an angle θ that is coterminal with an angle measuring −490∘, where 0∘≤θ<360∘. Do not include the degree symbol in your answer. For example, if your answer is 20∘, you would enter 20.
Answer: [tex]230[/tex]
Step-by-step explanation:
To find coterminal angles, add/subtract integer multiples of [tex]360^{\circ}[/tex].
[tex]-490^{\circ}+360^{\circ}=-130^{\circ}\\\\-130^{\circ}+360^{\circ}=230^{\circ}[/tex]
An angle θ that is coterminal with −490∘ and lies between 0∘ and 360∘ is 130∘.
To find an angle θ that is coterminal with −490∘ and lies between 0∘ and 360∘, we can use the concept of coterminal angles.
Coterminal angles are angles that have the same initial and terminal sides when drawn in standard position. To find a positive coterminal angle with a negative angle, we can add 360 degrees to the negative angle until we get an angle within the desired range (0∘ to 360∘).
Let's find the positive coterminal angle:
θ = -490∘ + 360∘
θ = -130∘
So, an angle θ that is coterminal with −490∘ and lies between 0∘ and 360∘ is 130∘.
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Interpret the rate of change and initial value from this graph . I really really appreciate your help! Thank you so much .
Answer:
Initial value=50
Rate of change=12.5
Step-by-step explanation:
The rate of change is just the slope.
Initial value is y-intercept.
Examine the triangle below, what is the length of p = (round to the
tenth)
The length of side p of the triangle rounded to the nearest tenth is 7.5.
What is the length of side p?The cosine rule relates the lengths of the sides of a triangle to the cosine of one of its angles.
It is expressed as;
p = √( n² + m² - ( 2nm × cosθ ) )
Given the figure in the diagram;
m = 13n = 11Angle P = 35°p = ?Plug the values into the above formula and simplify.
p = √( n² + m² - ( 2nm × cosθ ) )
p = √( (11)² + (13)² - ( 2 × 11 × 13 × cos( 35 ) ) )
p = √( 121 + 169 - ( 286 × cos( 35 ) ) )
p = √( 290 - ( 286 × cos( 35 ) ) )
p = √( 290 - 234.27748 )
p = √( 290 - 234.27748 )
p = √55.72252
p = 7.5
Therefore, the value of p is 7.5.
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The solution to the system of equations below is (x, y). What is the value of x?
3x + y = 13
2x - 4y = 18
The system of equations is solved and the value of x = 5
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 first equation be represented as A
Now , the value of A is
3x + y = 13 be equation (1)
Let the second equation be represented as B
Now , the value of B is
2x - 4y = 18 be equation (2)
Multiply equation (1) by 4 , we get
12x + 4y = 52 be equation (3)
Adding equation (2) and equation (3) , we get
14x = 70
Divide by 14 on both sides of the equation , we get
x = 70/14
x = 5
Substitute the value of x in equation (1) , we get
15 + y = 13
Subtracting 15 on both sides of the equation , we get
y = -2
Hence , the value of x and y is 5 and -2 respectively
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Ada left home for school at 6:50am and got to school at 7:15am.
How many minutes does it take him to get to school?
Answer:
25 min
Step-by-step explanation:
60-50=10
10+15=25
Step-by-step explanation:
from 6:50am to reach 07:00 it takes 10min and he reach at 07:15am means another 15 min added10min + 15 min=25minprishna and marc 16 miles per hour and 12 miles per hour
The radius of a sphere is decreasing at a constant rate of 6 feet per second. At the instant when the volume of the sphere is 163 cubie feet, what is the rate of change of the volume? The volume of a sphere can be found with the
cquation V =4/3pi r^3. Round your
The rate of change of the volume is 871.2 ft³/sec
What is rate of change of volume?Rate of change of volume is the change in volume with time.
The rate of change of radius is 6 feet per second.
rate of change in volume = dv/dt
rate of change in radius = dr/dt
to find radius of the sphere;
V = 4/3 πr³
163 = 4/3 x3.14r³
r³ = 163× 3)/4×3.14
r³ = 488/12.56
r³ = 38.85
r = 3.4 feet
therefore
dr/dt = 1/4πr² × dv/dt
= 6 = 1/4×3.14× 3.4² × dv/dt
dv/dt = 6×4× 3.14× 3.4²
dv/dt = 871.2 feet³ per second
therefore the rate of change of the volume is 871.2 feet³ per second
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Please help, very important to me !!
Answer:
36 m
Step-by-step explanation:
It says to use a graph so here is one with the height shown as 36 m
help... ME!!
which boxes have a volume of 96 cubic feet?
Answer:
Option B) A and C
Step-by-step explanation:
what type of help is provide by international organizations to your. community
International organizations provide various types of help to communities around the world.
Some of the common forms of help include:
Humanitarian aid: This includes providing food, water, shelter, and medical assistance during natural disasters, conflicts, and other emergencies.Health programs: International organizations work with local communities to improve health outcomes and prevent the spread of diseases.Economic development: International organizations provide support for job creation, entrepreneurship and sustainable economic growth.Education: Organizations like UNICEF and UNESCO work to improve education opportunities for children and adults in communities around the world.Infrastructure development: International organizations provide funding and technical assistance to build roads, bridges and other infrastructure projects.Environmental protection: International organizations work to protect natural resources and ecosystems in communities around the world.Human rights: Organizations like Amnesty International work to defend human rights and promote equality and justice in communities around the world.Learn more about international organizations here: brainly.com/question/27176025
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A baseball player swings and hits a pop fly straight up in the air to the catcher. The height of the baseball in meters is t seconds after the hit is given by the quadratic function h(t) = −4.9t2 + 34.3t + 1.
How could we calculate how long it takes the baseball to reach its maximum height? How could we calculate the maximum height obtained by the baseball?
61.025 meters is the maximum height obtained by the baseball
What is a function?A relation is a function if it has only One y-value for each x-value.
The length of time and the maximum height can be found by finding the vertex of the parabola.
h(t) = -4.9t² + 34.3t + 1
x = -b/2a
t = -34.3/-9.8
t=3.5
Now plug in t value in the function
h(3.5)= -4.9(3.5)² + 34.3(3.5)+ 1
=-4.9(12.25)+120.05+1
=-60.025+120.05+1
=61.025 meters
Hence, 61.025 meters is the maximum height obtained by the baseball
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Simplify (23+16) . Write the sum in the simplest form.
The simplification of (23+16) is 39
What is addition?Addition is one of the four basic operations of arithmetic, the other three being subtraction, multiplication and division. The addition of two whole numbers results in the total amount or sum of those values combined.
For example of there are 20 mangoes. 50 cashews and 80 oranges in a store. The total number of fruits the store can be obtained by adding the number of oranges, mangoes and cashew.
This means that 80+20+50 = 150 fruits
Similarly to get the value of( 23+16) , we add the two numbers together
23+16 = 39
therefore the value of 23+16 = 39
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What is the estimated product? 93 x .26
Answer:
2418
Step-by-step explanation:
Step 1: Setup
Set up your multiplication problem like this:
9 3
x 2 6
Step 2: Multiply
3 x 6 = 18. Put 8 below the line and 1 as a reminder on top:
1
9 3
x 2 6
8
Step 3: Multiply
6 x 9 = 54. Take 54 and add 1 from the previous step to get 55. Enter 55 at the bottom:
9 3
x 2 6
5 5 8
Step 4: Add 0
Enter a 0 at the bottom right as a place holder, because you now move over one digit:
9 3
x 2 6
5 5 8
+ 0
Step 5: Multiply
2 x 3 = 6. Put 6 below the line and 0 as a reminder on top:
0
9 3
x 2 6
5 5 8
+ 6 0
Step 6: Multiply
2 x 9 = 18. Take 18 and add 0 from the previous step to get 18. Enter 18 at the bottom:
9 3
x 2 6
5 5 8
+ 1 8 6 0
Step 7: Add to get an answer
Add up the bottom two numbers (558 + 1860 = 2418) to get the answer:
9 3
x 2 6
5 5 8
+ 1 8 6 0
= 2 4 1 8
The bottom line is the answer. Therefore, 93 times 26 equals:
2418
Part a:Cell phone usage grew about 23% each year from 2010 to 2016. If cell phone usage in 2010 was 43 million, write a function f(x) to model U.S. cell phone usage over that time period, where x is the number of years since 2010.
Part b estimate the cell phone usage in 2013.round to the nearest ten thousand.
Answer:
The function f(x) to model U. S. cell phone usage over the time period of 2010 to 2016 can be expressed as f(x) = 43 * (1.23^x), where x is the number of years since 2010. Part b: The estimated cell phone usage in 2013 can be calculated by substituting x = 3 into the function f(x) = 43 * (1.23^x). This yields an estimated cell phone usage of 68.4 million in 2013, which can be rounded to the nearest ten thousand to 68 million.
Step-by-step explanation:
Please help me with the question.
Answer:
MN = 7x + 3
Step-by-step explanation:
Because MN connects the midpoints M and N of AD and BC respectively
MN is the midsegment of trapezoid ABCD , then
MN = [tex]\frac{AB+DC}{2}[/tex]
AB + DC = 6x + 7 + 8x - 1 = 14x + 6
MN = [tex]\frac{14x+6}{2}[/tex] = [tex]\frac{14x}{2}[/tex] + [tex]\frac{6}{2}[/tex] = 7x + 3
8068/31 as a mixed number
the easiest way is to divide, 8068÷31, since it's a big problem, you should use a calculator! When you do, you should get 260.258065, but once you round all the decimals you just get 260, your remainder should be 8. Use 8 as your numerator and 260 as your mixed number! And your finished, and that's why the answer is 260 8/31.
Here is my question. It's for my 6th Grade ALEKS.
Answer:
Step-by-step explanation:
i do 6th grade aleks too!
The functions f(x) and g(x) are shown on the graph. f(x) = x2 What is g(x)?  A. g(x) = 3x^2  B. g(x) = (1/3x)^2  C. g(x) = (x + 3)^2  D. g(x) = (x – 3)^2 (2,12)
The function g(x) is equal to g(x) = 3x².
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 functions f(x) and g(x) are shown on the graph and f(x) = x².
The function g(x) is equivalent to 3 times function f(x) for every value of {x}. So, we can write - g(x) = 3x²
Therefore, the function g(x) is equal to g(x) = 3x².
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help me algebra value functions and graphs
The definition of the absolute value function for this problem is given as follows:
y = |x - 4| - 2.
What is the absolute value function?The absolute value function of vertex at coordinates (h,k) is defined as follows:
y = a|x - h| + k.
From the graph, the coordinates of the vertex are given as follows:
(4,-2).
Hence the equation is given as follows:
y = a|x - 4| - 2.
When x changes by one, y also changes by one, hence the coefficient a is given as follows:
a = 1.
Thus the function is defined as follows:
y = |x - 4| - 2.
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Determine whether the sequence is an arithmetic sequence, a geometric sequence, or neitherIf it is either arithmetic or geometric, give the next term in the sequence 1,4,25,125,625,...
Therefore , the solution of the given problem of arithmetic mean comes out to be the given sequence is geometric sequence..
Definition of arithmetic mean.The arithmetic average, also referred to as the group's means, is obtained by adding up all the values in a list and multiplying that amount by the total number of list items. Math also has a similar trend of progression. The following equation shows that the median of the actual figures 5, 8, and 9 is 3, while the mean of the actual figures 5, 7, and 9 is 4, and the number 21 multiplied by three (there are now multiple three numbers) equals 7.
Here,
Given :
Sequence = 1, 4,25,125,625
Thus,
from the sequence we can see it is an geometric sequence not an arithmetic sequence.
r = 5/1 = 5
=> 1 ,5 ,5(5) , 5(5)² , 5(5)³
So,
it is an geometric sequence.
Therefore , the solution of the given problem of arithmetic mean comes out to be the given sequence is geometric sequence..
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