Answers
Answer:
A
Step-by-step explanation:
Fundamental Theorem of Algebra:
This states that any polynomial with degree n will have n solutions which are real or complex.
Since this function you gave has 4 zeroes, this function has to have at at least a degree of 4. The reason I say at least, is because of something called multiplicity. When a zero has an even multiplicity it will have a turning point at the zero, if it has an odd multiplicity it will pass the x-axis. So assuming each zero only has a multiplicity of 1, then this will have at least a degree of 4. It also might have complex zeroes which still count as zeroes.
End Behavior of Polynomial Functions:
So this is pretty easy to remember, but if the leading coefficient is positive, then the end behavior to the right will go up, if it's negative it will go down. Now the next thing to know is an odd degree means that the end behavior will go in opposite directions. So if the right goes up, then the left side will be going down and vice verse. if it's an even degree then the two opposite sides will go in the same direction.
In this case both ends are going down, in the same direction. This means that the leading coefficient is negative and the degree is even.
Using these two things, we can exclude answers
B can't be the answer, it only has 3 zeroes, this has at least 4.
C can't be the answer, it has an odd degree so the end behaviors would go in opposite directions
D can't be the answer, it has a positive leading coefficient so the right side would be going up
This means the only possible equation is A which has at least a degree of 4, negative leading coefficient, and even degree.
Related Questions
If the mass of the empty container is 250 grams and the final mass of the container with liquid is 1,300 grams, calculate the mass of the liquid by itself.
Answers
Hello!
To find the mass of the liquid by itself, subtract the mass of the container from the mass of the liquid and container.
⇒ 1,300 - 250
⇒ 1,050 grams
∴ The mass of the liquid by itself is 1,050 grams.
(I added the picture needed)
1.Create a sample space and find the product of each combination. What is the probability that a person wins the game? Express your answer as a fraction in lowest terms and as a percent rounded to the nearest tenth.
(answer to this one is 9/28 and 32.1%)
2. You realize a short time into the carnival that you don’t have enough prizes to last the entire event. You call your teacher, and she suggests that you change the winning number so that a participant will win only 25% of the time. What number will that be? Support your answer.
3. Participants achieving a winning score of 36 or higher in four consecutive attempts will receive a large prize! What is the probability of this occurring?
4. After changing the game rules, participants and the crowd are disappointed when the first five games yield scores of 12, 18, 30, 28, and 24. What statement can you recommend the teacher posts to reassure everyone that the game is fair?
Answers
Going by the rules of the game to pick a random card and then multiply it by a roll of a number cube, we can find that:
The probability a person wins a game is 3/8 or 37.5%.For a participant to win 25% of the time, they needs to get 32 or higher. The probability of a score of 36 or higher in 4 consecutive attempts is 1/1,1296.Teacher should tell people that just as the lower numbers could be picked, the products that are 32 or higher can be picked as well.What sample space represents the data?If the die is rolled, it will land on a number between 1 and 6 while there are only four cards that can be picked.
The sample space is:
Dice Card Product
1 5 5
1 6 6
1 7 7
1 8 8
2 5 10
2 6 12
2 7 14
2 8 16
3 5 15
3 6 18
3 7 21
3 8 24
4 5 20
4 6 24
4 7 28
4 8 32
5 5 25
5 6 30
5 7 35
5 8 40
6 5 30
6 6 36
6 7 42
6 8 48
Based on the products, we can come up with the following frequency table:
Frequency table
Product Frequency
5 1
6 1
7 1
8 1
10 1
12 1
14 1
16 1
15 1
18 1
21 1
24 2
20 1
28 1
30 2
32 1
25 1
35 1
40 1
36 1
42 1
48 1
Total 24
The frequency table shows that to get 28 or more, a person will have a relative frequency of:
= 1 + 2 + 1 + 1 + 1 + 1 + 1 + 1
= 9
Probability is:
= 9 / 24
= 3/8
= 37.5%
How can a person win only 25% of the time?The number of products required to win 25% of the time is:
= 25% x 24
= 6
To find the winning number, count down from the highest product 6 times to get 32.
What is the probability that a player wins a large prize?The probability of getting 36 or higher is:
= ∑(Probabability of picking 36 and above numbers)
= 1 / 24 + 1/24 + 1/24 + 1/24
= 1 / 6
The probability of repeating this 4 consecutive times is:
= 1 / 6 x 1 / 6 x 1/ 6 x 1 / 6
= 1 / 1,296
= 0.0007716
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The oven temperature was at 325325325 degrees because my mom just finished baking a pie. i increased the temperature 757575 degrees so i could bake a pizza. after the pizza was cooked, i turned off the oven. the oven cooled to the room temperature of 686868 degrees.
Answers
The amount of the temperature decrease will be 332 °C.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
The oven temperature was at 325 degrees because my mom just finished baking a pie.
I increased the temperature, 75 degrees, so I could bake a pizza.
Then the temperature will be
⇒ 325 °C + 75 °C
⇒ 400 °C
After the pizza was cooked, I turned off the oven.
The oven cooled to the room temperature of 68 degrees.
Then the amount of the temperature decrease will be
⇒ 400 °C – 68 °C
⇒ 332 °C
The remaining question is given below.
How much did the temperature decrease?
More about the Algebra link is given below.
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The graphs below have the same shape. What is the equation of the blue
graph?
g(x) =____
f(x) = x² 5
-5
-5
O A. g(x) = (x + 2)²
OB. g(x)=(x-2)²
O c. g(x)²2-2.
OD. g(x)=x² +21
X
g(x) = ?
5
Answers
Answer:
B
Step-by-step explanation:
given f(x) then f(x ± a ) is a horizontal translation of f(x)
• if + a , then a shift left of a units
• if - a then a shift right of a units
here g(x) is the graph of f(x) moved 2 units right , then
g(x) = (x - 2)²
To graph the inequality y> 5x - 4, you would draw a solid line.
A. True
B. False
Answers
Answer:
The answer is B
Step-by-step explanation:
Answer:
False
Step-by-step explanation:
y > 5x-4
This inequality is greater than, so it would be a dotted line
You would have a solid line when it is greater than or equal to ≥ or less than or equal to ≤
Elizabeth, Frank, Gary, and Helen are getting in line to buy lunch in the cafeteria. How many different ways could they line up so that Helen is first in line?
Answers
Helen, Gary, Frank, Elizabeth.
Will give brainliest.
Answers
Answer:
Its a right isosceles triangle
Answer:
right isosceles
Step-by-step explanation:
it has the right at the top
The formula used to convert degrees Celsius to degrees Fahrenheit is
F=C+32.
Convert 59°F to degrees Celsius. Solve the formula for C, and then use it to
convert the temperature.
Which is the correct formula and conversion?
OA. C=F-32; conversion: 59°F = 135°C
OB. C= (F-32); conversion: 59°F = 15°C
OC. C= (F-32); conversion: 59°F = 106°C
OD. C=F-32; conversion: 59°F = 15°C
Answers
The formula to convert degrees Fahrenheit to Celsius is:
[tex]\bf{^{\circ}C=\dfrac{5}{9}(^{\circ}F-32) \ \ \to \ \ \ Formula }[/tex]
Convert 59°F to degrees Celsius.
Add the number 59 in the formula, and solve.
[tex]\bf{=\dfrac{5}{9}(59-32) }[/tex]
Subtract 32 from 59.
[tex]\bf{=\dfrac{5}{9}(27) }[/tex]
Multiply 5 x 9 = 135, then divide 135/9 = 15.
[tex]\bf{=15 \ ^{\circ}C}[/tex]
Therefore 59 °F = 15 °C. The correct option is "D".
{ Pisces04 }please helpppp!!!!!!!
Answers
(3(1) + 9)² - 64
(3 + 9)² - 64
(12)² - 64
= 144 - 64
= 80
Select the correct answer
Answers
Answer:
option b is the answer
Step-by-step explanation:
One factor of f (x ) = 4 x cubed minus 4 x squared minus 16 x + 16 is (x – 2). What are all the roots of the function? Use the Remainder Theorem.
Answers
[tex]f(x) =4 x {}^{3} - 4x {}^{2} - 16x + 16[/tex]
[tex]divide \: by \: x - 2[/tex]
[tex]4x {}^{2} \: into \: (x - 2) = 4x {}^{3} - 8x {}^{2} [/tex]
[tex]g(x) = 4x {}^{2} - 16x + 16[/tex]
[tex]4x \: into \: (x - 2) = 4x {}^{2} - 8x[/tex]
[tex]z(x) = - 8x + 16[/tex]
[tex] - 8 \: into \: (x - 2) = - 8x + 16 \\ no \: remainder[/tex]
[tex]f(x) = (x - 2)(4x {}^{2} + 4x - 8)[/tex]
[tex]f(x) = 0 \\ x - 2 = 0 \: \: \: \: \: \: \: \: \: 4x {}^{2} + 4x - 8 = 0 \\ [/tex]
[tex]x = \frac{ - 4 + \sqrt{4 {}^{2} - 4(4)( - 8) } }{2(4)} = \frac{ - 4 + \sqrt{144} }{8} = \frac{ - 4 + 12}{8} = 1[/tex]
[tex]x = 2[/tex]
[tex]x = \frac{ - 4 - 12}{8} = \frac{ - 16}{8} = - 2[/tex]
Answer: B
Step-by-step explanation:
Edge 2023
the sum of perimeter of two similar polygons is 24cm,and the ratio of their corresponding sides is 1:3, find the perimeter of the larger polygon
Answers
Answer:
18
Step-by-step explanation:
Polygon A : Polygon B = x : 3x
4A = 24
A = 6
B = 18
B is the larger polygon so the perimeter is 18.
Is anyone able to solve this?
Answers
The value of ? and X are 24 and 32 respectively
Similarity theorem of a triangleA triangles is 2D shape with three sides and angles.
From the given diagram, the ratio of similar sides is equal to a constant as shown;
15/20 = 9+15/20+x
Cross multiply
15/9+15 = 20/20+x
15/24 = 20/20+x
Comparing with the given ratio
? = 24
X = 20+x
Find x
15(20+x) = 480
300 + 15x = 480
15x = 180
x =12
X = 20 +x
X= 32
Hence the value of ? and X are 24 and 32 respectively
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Determine whether the ordered pair (1, 1) is a solution of the inequality. y ≤ -3x+1
Answers
-------------------------------------------------------------------------------------------------------------
Answer: [tex]\textsf{(1, 1) is NOT a solution of the inequality}[/tex]
-------------------------------------------------------------------------------------------------------------
Given: [tex]y \le-3x + 1[/tex]
Find: [tex]\textsf{Determine if (1, 1) is a solution of the inequality}[/tex]
Solution: In order to determine if (1, 1) is a solution we need to plug in 1 for the x values and 1 for the y values and see if the equation evaluated to true.
Plug in the values
[tex]y \le-3x + 1[/tex][tex]1 \le-3(1) + 1[/tex]Simplify
[tex]1 \le-3 + 1[/tex][tex]1 \le-2[/tex]As we can see the expression states that 1 is less than or equal to -2 which is false therefore (1, 1) is NOT a solution of the inequality.
Hey there!
Keywords and Concepts:Algebra I
Inequality
Ordered pair
How do we determine whether an ordered pair is a solution of a given inequality?Step 1: Define.y ≤ -3x+1
Step 2: Plug in the given values.1 ≤ -3(1) + 1
Step 3: Multiply (Identity Property of 1).1 ≤ -3 + 1
Step 4: Add.1 ≤ -2
Step 5: Validate. Is the statement true?The statement is NOT true as 1 is not less than or equal to -2.
Therefore, the ordered pair is not a solution of the inequality.
For another example, see:
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A square-based pyramid has a base of area 16 cm² and a volume of 16 cm³. Calculate:
a. The perpendicular height of the pyramid.
b. The height and area of the base of a similar pyramid with a volume of 1024 cm³.
Answers
Answer:
3
Step-by-step explanation:
V=⅓b²h
16=⅓*16*h
16=16h/3
h=3cm
Answer to (b) = height is 12cm, area of base is 16 cm2
Formula for question a
Height = (3)V/a^2
We know v=16, we know a is 4
Height = (3) 16/16
Height = (3)
Formula for question b
If it’s similar, we will first find the ratio of V
We know one pyramid V=16, the other is V=1024
16 to 1024 = 64 cm3, take cube root of that for a ratio of 4
Multiply your known measurements x 4
So height is 3 x 4 = 12
Base edge is 4 x 4 =16
Volume is known at 1024cm3
Susan saw birds and mice eating seeds on the ground. She counted 14 heads. 40 legs in total. how many birds and mice are on the ground
Answers
Answer:
Birds = 8
Mice = 6
Step-by-step explanation:
Conditions
Let the birds = x
Let the mice = y
Equations
x + y = 14
2x + 4y = 40
Solution
Using the top equation solve for x
x = 14 - y
Use this result to substitue for x
2(14 - y) + 4y = 40
Remove the brackets
28 - 2y + 4y = 40
Combine
28 + 2y = 40
Subtract 28 from both sides
28 - 28 + 2y = 40 - 28
2y = 12
Divide by 2 on both sides
2y/2 = 12/2
y = 6
Solve for x
x + y = 14
x + 6 = 14
Subtract 6 from both sides
x + 6 - 6 = 14 - 6
x = 8
Answer:
7 mice and 7 birds
Step-by-step explanation:
14 heads would mean there are 14 animals in total, as each animal has one head.
Birds have two legs, and mice have four.
2+4=6
40/6=6.67 (recurring)
6.67*2=13.3 (recurring)
6.67*4=26.67 (recurring)
Animal legs can't be in decimal numbers, so we can round the numbers.
13.3 becomes 13, 26.67 becomes 27.
13+27=40
Now we can see that there are 13 bird legs and 27 mice legs.
Divide the bird legs by 2 to get 6.5
Divide the mice legs by 4 to get 6.75
Again, we can't have a decimal of an animal, so we can round.
6.5 becomes 7, and 6.75 also becomes 7.
Therefore, there is 7 of each type of animal.
The population of a small town is decreasing exponentially at a rate of 14.3% each year. The current population is 9,400 people. The town's tax status will change once the population is below 6,000 people.
Create an inequality that can be used to determine after how many years, t, the town's tax status will change, and use it to answer the question below.
Will the town's tax status change within the next 3 years?
Answers
Using an exponential function, the inequality is given as follows:
[tex]9400(0.857)^t < 6000[/tex]
The solution is t > 2.9, hence the tax status will change within the next 3 years.
What is an exponential function?A decaying exponential function is modeled by:
[tex]A(t) = A(0)(1 - r)^t[/tex]
In which:
A(0) is the initial value.r is the decay rate, as a decimal.For this problem, the parameters are given as follows:
A(0) = 9400, r = 0.143.
The population after t years is modeled by:
[tex]A(t) = A(0)(1 - r)^t[/tex]
[tex]A(t) = 9400(1 - 0.143)^t[/tex]
[tex]A(t) = 9400(0.857)^t[/tex]
The tax status will change when:
[tex]A(t) < 6000[/tex]
Hence the inequality is:
[tex]9400(0.857)^t < 6000[/tex]
Then:
[tex](0.857)^t < \frac{6000}{9400}[/tex]
[tex]\log{(0.857)^t} < \log{\left(\frac{6000}{9400}\right)}[/tex]
[tex]t\log{0.857} < \log{\left(\frac{6000}{9400}\right)}[/tex]
Since both logs are negative:
[tex]t > \frac{\log{\left(\frac{6000}{9400}\right)}}{\log{0.857}}[/tex]
t > 2.9.
The solution is t > 2.9, hence the tax status will change within the next 3 years.
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There are four people in the Hayden family.each person always eats 3/4 of a cheese pizza. How whole many pizzas should they order? Solve and draw a picture to match this problem
Answers
The family consumes 3 whole pizzas in total. They should order 3 whole pizzas to have enough for everyone.
How did we arrive at the value?To find out how many whole pizzas the Hayden family should order, we can calculate the total number of pizzas they need.
Since each person always eats 3/4 of a pizza, the total amount they eat can be calculated as follows:
3/4 + 3/4 + 3/4 + 3/4 = 4 × (3/4) = 3
So, the family consumes 3 whole pizzas in total. Therefore, they should order 3 whole pizzas to have enough for everyone.
As for the picture, imagine a circle representing a whole pizza. Divide it into four equal parts to represent each person's portion (3/4). Repeat this division three times to represent the three pizzas needed.
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Which irrational number can be multiplied by –StartRoot 41 EndRoot to get a product that equals 1?
StartRoot StartFraction 1 Over 41 EndFraction EndRoot
Negative StartRoot 41 EndRoot
Negative StartRoot StartFraction 1 Over 41 EndFraction EndRoot
StartRoot 41 EndRoot
Answers
The irrational number that can be multiplied to produce 1 is - √41/41
Irrational numbersLet the following expression
-√41 x = 1
We are to find the value of x that will make the expression true
√41 x = -1
Divide both sides by √41
√41 x/ √41 = -1/ √41
x = - √41/41
Hence the irrational number that can be multiplied to produce 1 is - √41/41
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a number is chosen ar random from 1 to 50. find the probaility of selecting multiplies of 3
Answers
Answer:
16/50 or 32% chance of getting a multiple of 3
Step-by-step explanation:
Starting at 0 and going to 50, there are 16 numbers in the range that are multiples of 3.
3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, and 48
Attached is a chart for reference!
So, 16 of the 50 numbers are multiples of 3, making your odds 16/50 (divide that to get .32 which = 32%!)
step by step explanation:
(multiples of 3)= 3 , 6 ,9, 12 ,15, 18 ,21 ,24, 27, 30, 33, 36 ,39 ,42, 45 and 48
probability (multiples of 3)= nó of required outcome/ nó of possible outcome
16 /50 = 8/25 ( you get this after dividing 16/50)
in percentage 8/ 25 would give you 32%
Which of the following is equivalent to
60 1/2
Answers
Answer:
30 or 120 /4
Step-by-step explanation:
a^p/q here p denotes power raised and q denotes inverse power or root. So, 60^1/2 denotes square root of 60 raised to power 1.
The figure below shows one of the steps used in inscribing a square in a circle.
Answers
Answer:
Step-by-step explanation:
Find the missing side lengths.
AB=
BC=
Answers
Answer:
Step-by-step explanation:
given the equation P=S1t-S2t which equation is solved for t A. t=p(s1-s2) B. t=p-S1+S2 C. t=p/S1+S2
Answers
Answer:
C
Step-by-step explanation:
P = S1t - S2t ← factor out t from each term on the right side
P = t(S1 - S2) ← isolate t by dividing both sides by S1-S2
[tex]\frac{P}{S1-S2}[/tex] = t
What is the area of this triangle? Enter your answer in the box. units²
Answers
Answer:
10u²
Step-by-step explanation:
The formula for area of a triangle is b*h/2. When you plug in the numbers, you get 10. Hope this helps!
Which is the graph of the cube root function f(x) = RootIndex 3 StartRoot x EndRoot?
Answers
The graph of a function f(x) = ∛x is shown in the picture, and the domain of the function will be all real numbers.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
We have a function:
f(x) = ∛x
The domain of the function will be all real numbers.
x ∈(-∞, ∞)
The graph will be curved.
Plug x = 0, y = 0
x = 1, y = 1
The graph is shown in the attached picture.
Thus, the graph of a function f(x) = ∛x is shown in the picture, and the domain of the function will be all real numbers.
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Stan guessed on all 10 questions of a multiple-choice quiz. Each question has 4 answer choices. What is the probability that he got at least 2 questions correct
Answers
The probability that he got at least 2 questions correct is 0.756.
Probability is simply how probably something is to appear. every time we're uncertain approximately the final results of an occasion, we can communicate approximately the possibilities of positive outcomes and how in all likelihood they may be. The analysis of occasions ruled through chance is called data.
Basic Probability Rules
For any event A, 0 ≤ P(A) ≤ 1The sum of the probabilities of all possible outcomes is 1The Complement RuleProbabilities Involving Multiple Events.Addition Rule for Disjoint EventsLearn more about probability here https://brainly.com/question/24756209
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Please include what axioms and theorems were used as well.
Answers
Part (i)
1. ABCD is a quadrilateral in which AD=BC and ∠DAB=∠CBA (given)
2. AB = AB (reflexive property)
3. Triangles ABD and BAC are congruent (SAS)
Part (ii)
4. BD=AC (corresponding sides of congruent triangles are equal)
Part (iii)
5. ∠ABD = ∠BAC (corresponding angles of congruent triangles are equal)
Answer:
Hey!
In △ABD and△BAC,
AD = BC (it's given)
∠DAB = ∠CBA (it's given)
AB = BA (Common)
By SAS congruence rule,
∴△ABD≅△BAC
=> BD = AC (By C.P.C.T) (ii)
And, ∠ABD = ∠BAC (By C.P.C.T) (iii)
Hope it helps, any confusions you may ask.
prove that: (1 +tantheta)^2 + (1 - tantheta)^2 = Sec^2 theta pls answer and God will bless u
Answers
Answer:
Step-by-step explanation:
[tex]=(1 +tan\theta)^2 + (1 - tan\theta)^2\\=(1+2tan\theta+tan^2\theta)+(1-2tan\theta+tan^2\theta)\\=2(1+tan^2\theta)\\=2sec^2\theta.\\[/tex]
Solve for x.
2x² +21x-61 = (x+7)²
Please
Answers
Answer:
[tex]x = \frac{-7 +\sqrt{489} }{2}[/tex]
[tex]x = \frac{-7 - \sqrt{489} }{2}[/tex]
Step-by-step explanation:
2x² +21x-61 = (x+7)²
expand
2x² + 21x - 61 = x² + 14x +49
move everything to one side
x² + 7x - 12 = 0
use quadratic formula
[tex]x = \frac{-b +- \sqrt{b^{2}-4ac } }{2a}[/tex]
plug in the values
[tex]x = \frac{-7 +- \sqrt{7^{2}-4(1)(-110) } }{2(1)}[/tex]
solve
[tex]x = \frac{-7 +- \sqrt{49-4(1)(-110) } }{2}[/tex]
[tex]x = \frac{-7 +- \sqrt{49 + 440 } }{2}[/tex]
[tex]x = \frac{-7 +- \sqrt{489} }{2}[/tex]