Part A: describe the type of function
Part B: what are the standard and factored form of the function
Part C: what are the zeros of the function
Part D: use the zeros to find all of the linear factors
Part E: write the equation of the graphed function
Part F: Use the Y intercept of the graph and your equation from part E to calculate the value of a
Part G; write the equation for the function shown in graph
Answers
The type of function of the given graph is polynomial in nature.
Each element of X receives exactly one element of Y when a function from one set to the other is used.
The sets X and Y are collectively referred to as the function's domain and codomain, respectively.In mathematics, a polynomial is an expression made up of coefficients and indeterminates that solely uses the operations of multiplication, addition, and non-negative integer exponentiation.A) The given function is a polynomial of the third degree.
B) The factored form of the polynomial is: [tex]-\frac{1}{1500} (x+20)(x+5)(x-15)[/tex]
The standard form is: [tex]p(x)=-\frac{x^3}{1500} -\frac{x^2}{150} +\frac{11x}{60} +1[/tex]
C) The zeroes of the polynomial function are -20, -5 and 15
D) The linear factors are (x+20)(x+5) and (x-15)
E) The equation of the function is [tex]y=-\frac{1}{1500} (x+20)(x+5)(x-15)[/tex]
F) From the graph it is seen that the factors of the polynomial function are (x+20)(x+5) and (x-15).
Now at x=0, y=1.
Substituting these values we get:
1=a(0+20)(0+5)(0-15)
or, a = [tex]-\frac{1}{1500}[/tex]
So the value of a for the equation is [tex]-\frac{1}{1500}[/tex] .
G) The equation for the function in the graph is
[tex]y=-\frac{1}{1500} (x+20)(x+5)(x-15)[/tex]
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Related Questions
Adsila and Carlos volunteer to fill gift boxes for soldiers serving overseas. Both work at a constant rate. They work together for 4 hours and fill 108 boxes, Adsila fills 11 boxes every hour. How many boxes does Carlos fill every hour?
Answers
Answer:
Carlos fills 16 boxes per hour.
Step-by-step explanation:
Given that:
Adsila and Carlos are working together to fill the gift boxes for soldiers.
Number of boxes filled while working together in 4 hours = 108 boxes
Number of boxes filled while working together in 1 hour = [tex]\frac{108}{4} = 27[/tex] boxes per hour
Number of boxes filled by Adsila every hour = 11 boxes
To find:
Number of boxes filled by Carlos every hour = ?
Solution:
Number of boxes filled every hour while working together = Number of boxes filled every hour by Adsila + Number of boxes filled every hour by Carlos
Number of boxes filled every hour while working together = 27 = 11 + Number of boxes filled every hour by Carlos
Number of boxes filled every hour by Carlos = 27 - 11 = 16
find the compound interest on 30,000 for 2years at 7 percent per annum
Answers
Answer:
34347
Step-by-step explanation:
Use the formula s=p(1+r/k)^kt
p=30000
r=7% (interest)
k=1 (because of per annum)
t= 2 (years)
Hence: 30000(1+0.07/1)^1(2) = 34347
How do I solve this
Answers
Answer: 0.10 I think
Step-by-step explanation:
i am not 100 percent sure consider looking it up
8
Given the summation E (3 + 2n),
n=1
a. Write the first four terms of the sequence.
Answers
Answer:
(e^3 / e^2n)
Step-by-step explanation:
Amani's calculator weighs 7/25 pound. \tVhat is the weight of her calculator expressed as a
decimal?
Answers
Answer:
0.28 pounds
Step-by-step explanation:
Here, we want to get the weight of the calculator expressed as a decimal
Mathematically, what we have to do is to divide 7 by 25
The answer is 0.28 pounds
The wholesale cost of a bicycle is $98.75.
The markup for the bicycle is 33.3%. Find
the selling price of the blcycle. Round to
the nearest cent. (Answer please)
Answers
Answer:
$131.60
Step-by-step explanation:
For the promotion, markup is 33.3% of the selling price.
Now, Selling Price = Cost price + Cost price*Markup
Selling Price = $98.75 + $98.75*33.3%
Selling Price = $98.75 + $32.88375
Selling Price = $131.63375
Selling Price = $131.60
Thus, the selling price of the bicycle after calculating the markup is $131.60.
Help me out:( Don’t forget to explain pls :(
Answers
Answer:
When you find the volume of a triangle, remember to do this:
Step-by-step explanation:
Multiply the base times the height, then divide by two.
:)
The mistake is in the second triangle and is noticeable at first because the length of the leg is longer than the length of the hypotenuse.
Since this is a 30 60 90 triangle, you can use the properties that apply to them. I'm assuming that the leg with the length of 62ft is the given side. Using the rules, we know that x/2 is 62 (since the properties of a 30 60 90 triangle state that the shortest side is x/2). In order to find the hypotenuse (which is x), we can multiply both sides of the equation x/2 = 62 to get x = 124. To find the second leg, we need to use sqrt(3)*x/2, which when you plug in 124, gives 107.39. Andrea just switched the lengths of the second leg and the hypotenuse on accident.
Question 11 (5 points)
The ordered pair (2,6) is a solution to the system of linear equations.
x + y = 8
3x - y = 0
O True
False
Answers
Answer:
Yes
Step-by-step explanation:
Substitute the x value in the ordered pair for the x in the equation, or 2, and the y-value (6) in for y. So, 2 + 6 = 8, and this is true. Then do 3(2) - 6 = 0, which is also true.
can someone pls help me with this?
15х – бу = 6
Answers
Answer:
x=2/5y+2/5
Step-by-step explanation:
EXPLANATION-
Move all terms that don't contain x to the right side & solve
What is the number that when you multiply by 2 and add 7 to the product you get is 10.8 pls answer
Answers
Answer:
1.9
Step-by-step explanation:
2x+7=10.8
2x=3.8
x=1.9
1.9x2=3.8+7=10.8
The required number is 1.9, when multiply by 2 and add 7 to the product gives 10.8.
What are equation models?The equation model is defined as the model of the given situation in the form of an equation using variables and constants.
Here,
let the number be x,
According to the question,
2x + 7 = 10.8
Simplifying the above expression,
2x = 10.8 - 7
2x = 3.8
x = 1.9
Thus, the required simplified value of the given equation model is 1.9.
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the set of all real numbers less than 50 or greater than 50
helppp
Answers
The set notation of the numbers is {x | x < 50 ∪ x > 50}
How to determine the set notation of the numbers?The set is given as
The set of all real numbers less than 50 or greater than 50
Let the number be represented by x
So, we have
x less than 50 or x greater than 50
When represented as an inequality, we have
x < 50 or x > 50
Using set notation, we have
{x | x < 50 ∪ x > 50}
Hence, the set notation of the numbers is {x | x < 50 ∪ x > 50}
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Find the length of side x in simplest radical form with a rational denominator.
Answers
Answer:
x = 5[tex]\sqrt{2}[/tex]
Step-by-step explanation:
Using the cosine ratio in the right triangle and the exact value
cos45° = [tex]\frac{1}{\sqrt{2} }[/tex] , then
cos45° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{5}{x}[/tex] = [tex]\frac{1}{\sqrt{2} }[/tex] ( cross- multiply )
x = 5[tex]\sqrt{2}[/tex]
Two sides of a triangle have lengths 8 and 16. Which expression describes the length of the third side?
greater than 8 and at most 24
at least 8 and at most 24
at least 8 and less than 24
greater than 8 and less than 24
Answers
Answer:
Based on the given description above, the correct answer would be the second statement. If two lengths of two sides of a triangle are 9 and 15, therefore, the length of the third side must be greater than or equal to 6 and at most 24. Hope this answer helps.
Step-by-step explanation:
Write an equation for the nth term of each arithmetic sequence. Then find the 12th term of the sequence.
as = 14, d = -3
Answers
We need to know about arithmetic sequence to solve this problem. The equation for the nth term of each arithmetic sequence is a+(n-1)d and the 12th term of the sequence is -19.
An arithmetic sequence is a sequence of numbers where the difference between consecutive numbers is constant. If a,b and c are in arithmetic sequence then we can say that 2b=a+c. If the starting value of an arithmetic sequence is a and the difference between every consecutive number is d, then we can write the second number as a+d, the third as a+2d and so on. So for the nth term of an arithmetic sequence the equation is
nth term=a+(n-1)d where a is the starting value, d is the constant difference
We have been given the value of a and d, a=14 and d=-3, we need to find the value of the 12th term of the sequence.
12th term= a+(n-1)d= 14+(12-1)x(-3)=14-33=-19
Therefore we found out using the concept of arithmetic sequence that the equation for the nth term is a+(n-1)d and the 12th term of the sequence is -19.
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Please help!!!! With my Algrebra 2 homework!! i will give brainiest and 60 pts
options are
A. A(x)= 3| x- 6| + 4
B. A(x)= 1/3 |x+6| + 4
C. A(x)= 3 |x+6| + 4
D. A(x)= 1/3|x-6| +4
Answers
Answer: C
Step-by-step explanation: I tested some points from the graph into all of the equations (-8,10) (-4,10) (-6,4) and C is the only one that works for all of them. Plus when you are adding inside an absolute value, it means you are moving to the left by whatever number you added, which automatically eliminates A and D. So B and C were the only ones left and I tested the points to see which one is correct.
Solve the formula V = s²h for s.
Answers
Answer: [tex]s=\sqrt{Vh}[/tex]
Step-by-step explanation:
[tex]V = s^2h\\[/tex]
divide both sides by h to isolate s
[tex]Vh=s^2[/tex]
since s is squared, square root both sides to make s not squared
[tex]\sqrt{Vh}=\sqrt{s^2}[/tex]
Vh isn't a numerical value so no need to simplify anything just leave everything as is, so you should get:
[tex]s=\sqrt{Vh}[/tex]
What are the five positions of classical ballet?
Answers
Answer:
1st, 2nd, 3rd, 4th, and 5th position.
Step-by-step explanation:
Please help meee……………..
Answers
Answer by pythagorean theorem
Answer:
Step-by-step explanation:
redraw the diagrams separately now you have a rectangle and a trianglebc=12 inchesAttached is the whole processHOPE THIS HELPS30 POINTS! PLATO HELP! NUTRITION CLASS!
The Egyptians invented _____ , which they used to store ______ for many years.
Storage silos
Wooden baskets
Glass bottles
Wines
Grains
Vegtables
Answers
Answer:
30 points where ???
Step-by-step explanation:
Answer:
The answer is The Egyptians invented storage silos, which they used to store grains for many years.
Step-by-step explanation:
Hope this helps!! :)
Solve the equation: f(x) = 3r - 2x +5
Answers
what is a solutions of x^2-2x+10=0?
Answers
Answer:
x = 1± 3i
Step-by-step explanation:
x^2-2x+10=0
We can complete the square to solve by subtracting 10 from each side
x^2-2x+10-10=-10
x^2 -2x = -10
We need to add (2/2) ^2 to each side or 1
x^2 -2x+1 = -10 +1
x^2 -2x+1 = -9
The left side factors into (x- (2/2) ) ^2
(x-1) ^2 = -9
Take the square root of each side
sqrt((x-1) ^2 =± sqrt(-9)
x-1 = ±sqrt(-1) sqrt(3)
Remember the sqrt(-1) = i
x-1 = ± 3i
Add 1 to each side
x-1+1 = 1± 3i
x = 1± 3i
pls help thank you very much:)
Answers
A (4,7) B(7,8) C (22,30)
Chloe is deciding between two landscaping companies for her place of business. Company A charges $70 per hour and a $150 equipment fee. Company B charges $55 per hour and a $300 equipment fee. Let AA represent the amount Company A would charge for tt hours of landscaping, and let BB represent the amount Company B would charge for tt hours of landscaping. Write an equation for each situation, in terms of t,t, and determine the number hours, t,t, that would make the cost of each company the same.
Answers
The equations are AA = 150 + 70t and BB = 300 + 55t.
It is 10 hours which make the cost of each company the same.
Given,
Company A:
Charge for an hour =$ 70
Equipment fee = $ 150
Charge for ' t ' hours = 70 x t = 70t
Total cost = Equipment fee + charge for t hours
AA = 150 + 70t
Company B:
Charge for an hour =$ 55
Equipment fee = $ 300
Charge for 't' hours = 55 x t = 55t
Total cost = Equipment fee + charge for t hours
BB = 300 + 55t
Now, we have to find
BB = AA
300 + 55t = 150 + 70t
300 – 150 = 70t – 55t
150 = 15t
t = 150 / 15
t = 10
That is,
The equations are AA = 150 + 70t and BB = 300 + 55t.
It is 10 hours which make the cost of each company the same.
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Which expression represents the correct form of the partial fraction decomposition of StartFraction 19 x + 20 Over x squared minus 64 EndFraction? StartFraction A x + B Over x squared minus 64 EndFraction StartFraction A Over x minus 8 EndFraction + StartFraction B Over x + 8 EndFraction StartFraction A x + B Over x squared minus 64 EndFraction + StartFraction C over x minus 8 EndFraction StartFraction A Over x minus 8 EndFraction + StartFraction B x + C Over (x minus 8) squared EndFraction
Answers
Answer:
A
Step-by-step explanation:
I got it right, Edg2020
Answer:
It's B!
Right On Edge
Step-by-step explanation:
Bob and Alice have designed and created a website for their high school. The first week they had 5 visitors to the site; the second week, they had 10 visitors; and during the third week, they had 20 visitors. If the trend continues, how many visitors can they expect in the fifth week? Explain your answer.
Answers
Answer:
80 visitors
Step-by-step explanation:
From the above question, we can see that:
The trend is explained using geometric sequence
The formula for Geometric sequence is given as:
an = ar ^n - 1
Where a = first term
r = common ratio
n = number of terms
an = nth term
From the above question, let the number of term be equal to the number of weeks.
First week = First term = 5
Second week = Second term = 10
Third week = Third term = 20
Common ratio = a2/a1 = a3/a2 = 10/5 = 20/10 = 2
We are to find the number of visitors for the Fifth week = fifth term,
Hence:
a5 = 5 × 2^5 - 1
a5 = 5 × 2^4
a5 = 80 visitors
The number of visitors we can expect for the fifth week = 80 visitors
17. Carole Winer deposits the following in her checking account: 7 five-
dollar bills, 3 two-dollar bills, 18 one-dollar bills, 9 half dollars, 15
quarters, 99 dimes, 48 nickels, 16 pennies, and a check for $28.32.
What is her total deposit?
Answers
In 2010, a major coffee store chain had 137,239 employees across the world. About how many employees did they have, if they rounded to the nearest thousand?
Answers
Answer: 137,00
Step-by-step explanation:
please help due in an hour!!!
Answers
Answer:
The answer is C
Step-by-step explanation:
which is the best estimate of -14 1/9 (-2 9/10)?
-42
-28
28
42
Answers
Answer:
-42
Step-by-step explanation:
Makayla and John are selling cookie dough for a school fundraiser. Customers can buy chocolate chip or gingerbread cookie dough. Makayla sold 8 packages of chocolate chip and 12 packages of gingerbread cookie dough for a total of $364. John sold 1 package of chocolate chip and 4 packages of gingerbread cookie dough for a total of $93. Find the cost each of one package of chocolate chip cookie dough and one package of gingerbread cookie dough.
The cost per package is $---- for chocolate chip and $----- for gingerbread.
Answers
Answer:
Step-by-step explanation:
Lets give a letter value for the chocolate chip and gingerbread cookies. Lets let C= Chocolate chip and G= Gingerbread For Makayla we can set her equation as 8c+12g=364
For John we can leave it as c+4g=93
To solve the equation we would have to substitute the second one into the first one to solve for gingerbread. Lets isolate C to make C=(93-4g)
We can do this because we know that C=93-4g so we can replace the C variable in the first equation with C=93-4g
8(93-4g) + 12g = 364
744 - 32g + 12g = 364
-32g + 12g = 364 - 744
-20g = -380
g = -380/-20
So we know that g=19 dollars. So one gingerbread cookie dough is $19
So now we can plug in the answer of g which was 19 then solve for C
c = 93 - 4(19)
c = $17 for the chip dough
Answer:
The cost per package is $17 for chocolate chip and $19 for gingerbread.
Step-by-step explanation:
Define the variables:
Let x = cost of chocolate chip cookie dough (in dollars)Let y = cost of gingerbread cookie dough (in dollars)Given information:
Makayla sold 8 packages of chocolate chip and 12 packages of gingerbread cookie dough for a total of $364. John sold 1 package of chocolate chip and 4 packages of gingerbread cookie dough for a total of $93.Create two equations using the defined variables and the given information:
[tex]\textsf{Equation 1}: \quad 8x+12y=364[/tex]
[tex]\textsf{Equation 2}: \quad x+4y=93[/tex]
Multiply Equation 2 by 3:
[tex]\implies 3 \cdot x + 3 \cdot 4y=3 \cdot 93[/tex]
[tex]\implies 3x+12y=279[/tex]
Subtract from Equation 1 to eliminate the term in y:
[tex]\begin{array}{lrl}& 8x+12y =&364\\- & (3x+12y =&279)\\\cline{1-3} & 5x \phantom{+12y)} =& \:\:85\end{array}[/tex]
Solve for x:
[tex]\implies 5x=85[/tex]
[tex]\implies \dfrac{5x}{5}=\dfrac{85}{5}[/tex]
[tex]\implies x=17[/tex]
Substitute the found value of x into Equation 2 and solve for y:
[tex]\implies x+4y=93[/tex]
[tex]\implies 17+4y=93[/tex]
[tex]\implies 17+4y-17=93-17[/tex]
[tex]\implies 4y=76[/tex]
[tex]\implies \dfrac{4y}{4}=\dfrac{76}{4}[/tex]
[tex]\implies y=19[/tex]
Conclusion
Cost per package of chocolate chip cookie dough = $17.Cost per package of gingerbread cookie dough = $19.Learn more about systems of equations here:
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