The polynomial function g(x) = [tex]x^4 - x^5[/tex] has two zeroes, which are x = 0 and x = 1. This result is obtained by setting the polynomial equal to zero and solving for x.
Explanation:The given polynomial function is g(x) = [tex]x^4 - x^5[/tex]. To find the zeroes of the polynomial, this function should equal zero. Thus, we have[tex]x^4 - x^5[/tex] = 0.
We can simplify this function by factoring out the common factor, which is [tex]x^4[/tex]. The function thus becomes [tex]x^4[/tex](1 - x) = 0.
A product equals zero when one (or more) of the factors is zero. So, we need to set each factor to zero and solve for x. Setting [tex]x^4[/tex]= 0, yields x = 0. Setting (1 - x) = 0 results in x = 1.
This process gives two values of x that satisfy the equation [tex]x^4[/tex](1 - x) = 0 and therefore, the polynomial function g(x) has two zeroes, specifically x = 0 and x = 1.
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If f(x)=x^2 +3x +5,what is f(a+ h)
[tex]f(a+h)=(a+h)^2+3(a+h)+5\\\\f(a+h)=a^2+2ah+h^2+3a+3h+5\\\\[/tex]
[tex]\bf f(x)=x^2+3x+5~~ \begin{cases}f(a+h)\\x=a+h\end{cases}\implies f(a+h)=(a+h)^2+3(a+h)+5\\\\\\f(a+h)=(a^2+2ah+h^2)+(3a+3h)+5\\\\\\f(a+h)=a^2+2ah+h^2+3a+3h+5[/tex]
What would you divide by ten to get 600000
A missile is fired at an angle of 75 from the horizontal. At one point, its speed was 900 mph. Find its horizontal velocity in miles per minute. (Round to the nearest hundredth.)
Answer:
3.88
Step-by-step explanation:
The horizontal velocity in miles per minute will be 14.49 miles per minute.
What is a vector?The quantity which has magnitude, and direction, and follows the law of vector addition is called a vector.
A missile is fired at an angle of 75 from the horizontal. At one point, its speed was 900 mph.
Then the horizontal velocity in miles per minute will be
V = 900 x sin 75°
V = 869.33 mph
Then we have
V = 869.33 / 60 miles per minutes
V = 14.488
V ≅ 14.49 miles per minutes
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the question is in the attached below. thank you for your help , Please do not answer if you are not sure or simply doing it just to get points because i will report you and your answer. Thank you
First answer is DE≅ EF
Second answer is DE=EF by the ''segment congruence postulate''
Third answer is DE * EF + DF by the ''segment addition postulate''
The fourth answer is DE + DE = DF
Good luck!!!
Which graph represents the function f(x)=|x+2|+1
Answer:
IV Figure represent the given function f(x)=[tex]\mid x+2\mid[/tex]+1.
Step-by-step explanation:
Given function
f(x)=[tex]\mid x+2 \mid[/tex]+1
The given function can be write as
f(x)=(x+2)+1=x+3 when [tex]x\geq -2[/tex]
f(x)=-(x+2)+1 when [tex]x<-2[/tex]
f(x)=-x-1 when [tex]x<-2[/tex]
Put x= 0 in the function
f(x)=x+3=0+3=3
Hence, the function intersect the y-axis at point (0,3).
Therefore, we can say I figure is false.Because in I figure the function intersect y-axis at point (0,-3).
The function break at x=-2 .
Hence, we can say II figure and III figure are false. Because in II figure the function break at x=2 and in III figure the function break at x=-1.
Put x=-2 in the given function
f(x)= x+3 when [tex]x\geq -2[/tex]
Therefore, f(x)= -2+3=1
Hence, IV figure is correct option.
i like rice with tortillas and beans mmmmmm
same here bro, god loves you
Write a division equation that has a solution of -20
Final answer:
A division equation that has a solution of -20 can be written by dividing a negative number by a positive number, such as -100 divided by 5.
Explanation:
To write a division equation with a solution of -20, you can choose any two numbers such that the division of one number by the other equals -20. For example, if we take -100 and divide it by 5, we get -20 as the solution. Thus, a sample division equation could be:
-100 / 5 = -20.
This is because when you divide a negative number by a positive number, the result is negative, and -100 \/ 5 leads to the desired solution of -20.
Mrs. Dimas has $130 to but basketballs for Edison Middle School. How many can she buy at $15 each
The number of yeast cells in a laboratory culture increases rapidly initially but levels off eventually. the population is modeled by the function n = f(t) = a 1 + be−0.5t where t is measured in hours. at time t = 0 the population is 20 cells and is increasing at a rate of 8 cells/hour. find the values of a and
b.
The values of a and b in the population function n = f(t) = a(1 + be-0.5t) are a = -40 and b = -1.5.
Explanation:The population of yeast cells in a laboratory culture can be modeled by the function n = f(t) = a(1 + be-0.5t). Given that at time t = 0 the population is 20 cells and is increasing at a rate of 8 cells/hour, we can find the values of a and b.
First, substitute the given values into the equation:
20 = a(1 + be0)
Next, find the derivative of the function with respect to t to find the rate of change:
f'(t) = -0.5abe-0.5t
Since the population is increasing at a rate of 8 cells/hour, we can set the derivative equal to 8:
8 = -0.5abe-0.5(0)
Now, we have two equations:
20 = a(1 + b)
8 = -0.5ab
Solving these equations simultaneously will give us the values of a and b.
Using the first equation, we can solve for b:
b = (20/a) - 1
Substituting this value of b into the second equation:
8 = -0.5a((20/a) - 1)
Simplifying and solving for a:
a = -40
Substituting the value of a back into the first equation to solve for b:
b = (20/(-40)) - 1 = -1.5
Therefore, the values of a and b are a = -40 and b = -1.5.
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At time t = 0, the population is 20 cells and is increasing at a rate of 8 cells/hour. After solving the equation, we find that a = 20 and b = 16.
Explanation:To find the values of a and b in the function n = f(t) = a(1 + be-0.5t), we can use the given information.
At time t = 0, the population is 20 cells and is increasing at a rate of 8 cells/hour.
This means that the derivative of the function with respect to time is equal to 8 at t = 0.
Using the chain rule, we can differentiate the function f(t) with respect to t and set it equal to 8 to solve for a and b.
After solving the equation, we find that the growth will be a = 20 and b = 16.
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Julie is opening a savings account at a bank that offers new clients 0.1% interest compounded quarterly. She deposits $1,700 when she opens the account.
Write an exponential expression in the form a(b)c, where b is a single value, to find the amount of money, in dollars, that will be in the account after t years. Round any decimals to the nearest hundred-thousandth and do not include dollar signs in the expression.
Initial amount deposited (a) = $1,700.
Rate of interest (c) = 0.1% compounded quarterly =0.001 quarterly = 0.001/4 = 0.00025.
Number of years = t.
Let us assume amount after t years would be = $b.
We know, compund interest formula.
Total balance = Deposited amount (1- rate of interrest)^time.
Plugging values in formula,
[tex]b = a (1+c)^t[/tex]
We have a=$1700, c =0.00025.
Plugging those values, we get
[tex]b=1700(1+0.00025)^t[/tex]
Or
[tex]b=1700(1.00025)^t[/tex]
Which polynomial represents the area of the rectangle?
What is vertex of this function? Is it a maximum or minimum value.
The vertex of the function corresponds to the maximum velocity of the particle.
Explanation:The vertex of a function corresponds to the maximum or minimum value of the function. In this case, the vertex corresponds to the maximum velocity of the particle. The maximum velocity occurs when the slope of the velocity function is zero, which is the point where the acceleration function crosses the x-axis.
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Mr. Boyle is buying pizza for percussion band. The bill is $56.82 for 5 pizzas. If there are 12 members of the band, how much does a pizza cost Per member? Round to the nearest cent
Round 56.82 up to 57 divide that by 5 and your answer should be 11.40 per member
What is the anserw to round to the nerst hunder with 872
900. You round up, because it is above 850. :-)
Simplify 7(x – 2) – 4x + 9.
A. –21x + 49
B. –11x – 11
C. 3x – 5
D. 3x + 7
Answer: 3x - 5
Step-by-step explanation:
1. Expand:
7x - 14 - 4x + 9
2. Collect like terms:
(7x - 4x) + (-14 + 9)
3. Simplify:
3x - 5
Hope this helps! :)
The answer is 3x-5.
Hope this helps!
A greenhouse that specializes in growing geraniums is divided into sections. The number of geranium pots in each section depends on the number of sprinklers in that section.
There are x(7x − 2) pots of red geraniums and (x + 3)2 pots of pink geraniums in a section with x sprinklers.
Which simplified expression represents the total number of red and pink geranium pots in a section with x sprinklers? (5 points)
a
8x2 + 4x + 9
b
8x2 + 6x + 9
c
8x2 + 6x + 7
d
8x4 + 4x2 + 9
Answer:
a) 8x^2 + 4x + 9
Step-by-step explanation:
To find the total number of red and pink geranium pots, we need to add the two expressions given for the number of pots for red and pink respectively.
x (7x - 2) + (x + 3)^2
Expanding x (7x - 2) gives (7x^2 - 2x)
Expanding (x + 3)^2 gives (x^2 + 6x + 9)
Adding the like terms in these two expanded expressions:
(7x^2 - 2x) + (x^2 + 6x + 9)
= 7x^2 + x^2 + 6x - 2x +9
8x^2 + 4x + 9
Answer:
A greenhouse that specializes in growing geraniums is divided into sections. The number of geranium pots in each section depends on the number of sprinklers in that section.
There are x(7x − 2) pots of red geraniums and (x + 3)^2 pots of pink geraniums in a section with x sprinklers.
Which simplified expression represents the total number of red and pink geranium pots in a section with x sprinklers? (5 points)
a
8x^2 + 4x + 9
b
8x^2 + 6x + 9
c
8x^2 + 6x + 7
d
8x^4 + 4x^2 + 9
Is that what you mean, Jalenschaefer12? The way you had it made it confusing. If you want to do an exponent just do the carat sign (^), then a number, for example 4^22.
evaluate the expression for the given value of the variuble with step by step explanation
-4b-8 + -1-b^2 +2b^3 b=-2
Substitute the value of b = -2 to the expression
[tex]-4b-8+(-1)-b^2+2b^3=2b^3-b^2-4b-8-1=2b^3-b^2-4b-9\\\\2(-2)^3-(-2)^2-4(-2)-9=2(-8)-4+8-9=-16-4+8-9=-21[/tex]
A family of four spent 104 dollars for tickits at a concert all the tickits were the same price price was the cost of each ticket
To find the cost of each concert ticket for a family of four, divide the total cost, $104, by the number of tickets, which is 4. The resulting cost per ticket is $26.
The student is asking for help with a simple division problem. A family purchased concert tickets for a total of $104, and we know there are four tickets purchased since it's a family of four. To find the cost of each ticket, we have to divide the total cost ($104) by the number of tickets (4).
Step-by-Step Solution:
Determine the total spent: $104.
Determine the number of tickets: 4.
Calculate the cost per ticket: $104 ÷ 4 = $26.
Therefore, the cost of each concert ticket was $26.
JayQuan has decided to make party baskets for the fundraiser. Balloons are sold in bags of 20, party horns are sold in bags of 30. How many baskets can he make so there are an equal number of balloons and horns in each basket, with none left over?
Answer: 10
Step-by-step explanation:
Find the GCF of 20 (balloons) and 30 (party horns)
20: 2 x 5 x 2
30: 2 x 5 x 3
GCF = 10
Note: There will 2 balloons and 3 party horns in each basket.
if f(x)=-4x^2-6x-1 and g(x)=-x^2-5x+3 find (f – g)(x)
[tex]f(x)=-4x^2-6x-1\\\\g(x)=-x^2-5x+3\\\\(f-g)(x)=f(x)-g(x)=(-4x^2-6x-1)-(-x^2-5x+3)\\\\=-4x^2-6x-1+x^2+5x-3=(-4x^2+x^2)+(-6x+5x)+(-1-3)\\\\=-3x^2-x-4\to\boxed{B.}[/tex]
At the end of 1994 Walter was half as old as his grandmother. The sum of the years in which they were born is 3838. How old will Walter be at the end of 1999?
he will be 55 in 1999
Which of the following equations represents the line with a slope of 2/3 and a y-intercept of 9?
y = 3/2x + 9
y = 2/3x - 9
y = 3/2x - 9
y = 2/3x + 9
Solution
The general form of the equation is y = mx + b, where m is the slope and b is the y-intercept.
Given: m = 2/3 and b = 9
y = 2/3x + 9
The answer is y =2/3x + 9.
A basketball player that shoots 80% from the free throw line attempts two free throws. The notation for conditional probability is P(made 2nd attempt|made 1st attempt) .
Which notation is the probability of the two events being independent?
P(made 2nd attempt|made 1st attempt)=P(made 1st attempt and made 2nd attempt)P(made 1st attempt)
P(made 2nd attempt|made 1st attempt)=P(made 2nd attempt)P(made 1st attempt)
P(made 2nd attempt|made 1st attempt)=P(made 1st attempt)P(made 2nd attempt)
P(made 2nd attempt|made 1st attempt)=P(made 2nd attempt)
Answer:
P(made 2nd attempt|made 1st attempt)=P(made 2nd attempt)
Step-by-step explanation:
Here given that a basketball player that shoots 80% from the free throw line attempts two free throws.
If x is the no of shoots he makes (say) then we find that each throw is independent of the other.
In other words, because he made successful first attempt, his chances for second attempt will not change
Prob for success in each attempt remains the same as 0.80
Hence I throw is independent of II throw.
When A and B are independent,then we have
P(A/B) = P(A)
Hence answer is
P(made 2nd attempt|made 1st attempt)=P(made 2nd attempt)
Find the product 1.9(8.43)
help! What does this mean??
A collection of nickels and quarters is worth 2.85 . There are 3 more nickels than quarters how many nickels and quarters are there
A nickel is equal to 5 cents or 0.05 dollars.
A quarter is equal to 25 cents or 0.25 dollars.
Let number of nickels be = n
Let number of quarters be = q
[tex]0.05n+0.25q=2.85[/tex] ...........(1)
As it is given, there are 3 more nickels than quarters so equation becomes,
[tex]n=q+3[/tex] ................(2)
Plug in the value of 'n' from (2) in (1)
[tex]0.05(q+3)+0.25q=2.85[/tex]
= [tex]0.05q+0.15+0.25q=2.85[/tex]
[tex]0.30q=2.70[/tex]
[tex]q=9[/tex]
As [tex]n=q+3[/tex] we get, [tex]n=9+3=12[/tex]
Hence, there are 12 nickels and 9 quarters.
Gary mails 10^3 flyers in one week so how many did he mail
Fred spins a spinner with five equal spaces numbered 1 thru 5 and draws a card from a standard 52-card deck. What is the probability he spins a 3 or draws a king?
The probability of spinning a 3 or drawing a king is approximately 0.2769231, or around 27.69%.
Explanation:The question is asking us the probability that Fred spins a 3 from a spinner numbered 1 to 5 or draws a king from a standard 52-card deck. This involves the concept of probability, which requires us to look at the total possibilities and the outcome we are interested in.
Probability of spinning a 3 from the spinner numbered 1 to 5 is 1/5 or 0.2 because there is one favorable outcome (spinning a 3) out of 5 total outcomes (the numbers 1 to 5).
A standard 52-card deck has four kings (one from each suite; clubs, diamonds, hearts, and spades). So, the probability of drawing a king is 4/52, which also simplifies to 1/13 or approximately 0.0769231.
In this problem, we're looking at Fred spinning a 3 or drawing a king, hence we use the principle of addition in probability. The total probability will be the sum of the two individual probabilities, which is 0.2 + 0.0769231 = 0.2769231.
So, the probability that Fred spins a 3 or draws a king is approximately 0.2769231 or 27.69% when expressed as a percentage.
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Consider the function f(x)=sqrt(5x-5)+1 which inequality is used to find the domain?
ANSWER = 5x-5 is greater than or equal to 0
Given function is
[tex]f(x)=\sqrt{5x-5}+1[/tex]
Now we have to find which inequality can be used to find the domain.
Given function is a square root function. We know that square root function is defined only for the positive values including 0. In other words expression inside the square root must be greater than or equal to 0.
In given problem, expression inside the square root is (5x-5) so that must be greater than or equal to 0 which can be written as :
[tex]5x-5\geq 0[/tex]
which is same as your answer.
Hence your answer is correct.
Answer:
Step-by-step explanation:
answer is D
The nation of Swampastan produces only two goods, chips and dip. Calculate the GDP for Swampastan if dip retails for $3.00 a pound and 10 pounds are produced while chips sell for $2.00 a pound and 20 pounds are produced.
A) $1,200.00
B) $150.00
C) $30.00
D) $70.00
Answer:
The answer would be D.) $70.00
Step-by-step explanation: First multiply $3.00 by 10, so 3*10=30. Then you multiply $2.00 by 20, so 2*20=40. Then add those together 40+30=$70.
The probability that a randomly selected box of a certain type of cereal has a particular prize is .2. suppose you purchase box after box until you have obtained two of these prizes.
a. what is the probability that you purchase x boxes that do not have the desired prize?
b. what is the probability that you purchase four boxes?
c. what is the probability that you purchase at most four boxes?
d. how many boxes without the desired prize do you expect to purchase? how many boxes do you expect to purchase?
Here we want to analyze some properties of the probability of getting a prize in a cereal box.
a) p(x) = (0.8)^x
b) 0.0768
c) 0.1808
d) 30 boxes in total, 28 of them without the prize.
We know that the probability for a box of having a prize is 0.2.
a) The probability of not having the prize is p = 1 - 0.2 = 0.8
And this is the probability for each one of the x boxes, remember that the joint probability will be the product of the individual probabilities, then the probability that in x boxes you don't have a prize is:
p(x) = (0.8)^x
b) The probability of only purchasing two boxes is:
p = (0.2)^2*(0.8)^2
So two have the prize and two dont, one of the boxes with a prize must be the last one, and the other box can by any of the first 3. Then we have 3 permutations, and the actual probability is:
P = 3*(0.2)^2*(0.8)^2 = 0.0768
c) This is the probability of purchasing two plus the probability of purchasing 3 plus the probability of purchasing four.
For two boxes the probability is:
p₂ = (0.2)^2 = 0.04
For 3 boxes is:
p₂ = 2*(0.2)^2*(0.8) = 0.064
Where the factor "2" represents the permutations of the first box with the prize.
For 4 boxes we know:
p₄ = 0.0768
The total probability is:
P(4)= = p₂ + p₃ + p₄ = 0.04 + 0.064 + 0.0768 = 0.1808
d) before we got the probability for getting the two prizes in a maximum of four boxes, and we got something around 18%.
We just need to keep adding boxes to that sum, until it reaches the 99.9%.
for x boxes the total probability of getting the prize witin the X boxes is:
P(x) = (0.2)^2*(1 + 2*(0.8) + 3*(0.8)^2 + 4*(0.8)^3 + ... + (x-1)*(0.8)^(x-2))
We must find X such that:
P(x) = 1.
Or, we can just find x such that the last term does not contribute anymore, this means that we can solve:
(x-1)*(0.8)^(x - 2) ≈ 0
Notice that this never does become actually equal to zero, but there is a tendency that we can see graphically below:
In the graph we can see that for x = 30, the tendency to zero starts.
This means that for x = 30 the expression (x-1)*(0.8)^(x- 2) becomes almost zero, we can evaluate that:
(30-1)*(0.8)^(30 - 2) = 0.06
This may be large compared with the numbers we saw before, but remember that this is multiplied by (0.2)^2.
This means that for around 30 boxes you are almost sure to get the two prizes you want (there will always be a really small probability that this does not happen, smaller than 5%.).
So you will get 30 boxes in total, and in 28 without prize.
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