Form a polynomial whose zeros and degree are given. Use a leading coefficient of 1. Zeros: -1, 1, - 5; degree 3Af(x) = x3 + 5x2 - x - 5Bf(x) = x3 + 5x2 + x + 5Cf(x) = x3 - 5x2 + x - 5Df(x) = x3 - 5x2 - x + 5
Answers
By definition:
- The zeros of a function are also called roots and x-intercepts.
- The highest exponent of the variable of the function indicates the degree of the function.
In this case, knowing that the zeros of the function are:
\(\begin{gathered} x=-1 \\ x=1 \\ x=-5 \end{gathered}\)You can write it in the following factored form:
\(f(x)=(x+1)(x-1)(x+5)\)Simplifying it, you get:
\(\begin{gathered} f(x)=(x+1)(x-1)(x+5) \\ f(x)=(x^2-1)(x+5) \\ f(x)=(x^2)(x)+(x^2)(5)-(1)(x)-(1)(5) \\ f(x)=x^3+5x^2-x-5 \end{gathered}\)Hence, the answer is: Option A.
Related Questions
In 2004 Colin had a salary of $7200
This was an increase of 20% on his salary in 2002. Calculate his salary in 2002.
Answers
Answer:
I think it would be $3400
Step-by-step explana
Solve the quadratic equation by using a numeric approach. x squared + 8 x + 16 = 0 a. x = 1 c. x = 5 b. x = -4 d. x = -8 Please select the best answer from the choices provided A B C D
Answers
Answer:
The answer is b. x = -4
" If $6000 is borrowed at 7.5% simple interest for 2 yr, then the amount of interest is "
Answers
Answer:
u
Step-by-step explanation:
Which point could not be part of a function that includes (3, -1), (4, 2), (5, 4), (-2, 0), and (8, -3)?
(6, -7)
(2,2)
(3, -2)
(7, 4)
Answers
Answer:
(3, -2) is the correct choice.
help plz i need help
Answers
*group like terms*
3y+6y+y+5-4
=10y+1
The volleyball team bought 12 new volleyballs. The price for each volleyball was $26. How much did the team spend? Select the choice that shows all of the partial products of 12 × 26.
A.
12, 70, 4, 400
B.
12, 90, 14, 200
C.
12, 62, 4, 260
D.
12, 60, 40, 200
Answers
========================================================
Explanation:
Imagine a rectangle that is 12 by 26. Multiplying the length and width will get us the area.
We can break the 12 into 10+2
Also, break the 26 into 20+6
Check out the diagram below. We have 4 smaller rectangles. Finding the product of those sub-areas will then get us the partial products needed.
In the bottom right corner we have a 2 by 6 rectangle, so it has area 2*6 = 12 square units. This is one of the four partial products. The other partial products are found the same way.
Once you determine the four partial products, we then add them up
12+60+40+200 = 12+100+200 = 12+300 = 312
Therefore, 12*26 = 312 which we can use a calculator to confirm.
Which statement is false?
ОА.
The inequality sign always opens up to the larger number.
OB
The greater number in an inequality is always above the other number on the vertical number line.
P.S: Plato user and no links please people send them for no reason
Ос.
The smaller number in an inequality is always located to the left of the other number on the horizontal number line.
OD. The inequality Chign always opens up to the smaller number.
Answers
Answer:
D. The inequality sign always opens up to the smaller number.
Step-by-step explanation:
Well if A says sign always opens up to larger number and D says sign always opens up to smaller number so 1 of them must be false. Inequality signs always open up to greater number so the answer is D.
A clothing eCommerce company has an Average Order Value of USD 65. It costs the company USD 35 to produce the clothes in the average order and USD 15 to ship it to the customer. What is the Average Order's Gross Profit?
USD 65
USD 30
USD 15
USD 50
Answers
The Average Order's Gross Profit for the clothing eCommerce company in this scenario is USD 15.
For the Average Order's Gross Profit for the clothing eCommerce company in this scenario, we need to subtract the cost of production and shipping from the Average Order Value as;
⇒ Gross Profit = Average Order Value - Cost of production - Cost of shipping Gross Profit
⇒ Gross Profit = USD 65 - USD 35 - USD 15
⇒ Gross Profit = USD 15
Therefore, the Average Order's Gross Profit for the clothing eCommerce company in this scenario is USD 15.
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Given h of x equals negative 2 times the square root of x minus 3 end root, which of the following statements describes h(x)?
The function h(x) is increasing on the interval (–∞, 3).
The function h(x) is increasing on the interval (–3, ∞).
The function h(x) is decreasing on the interval (–∞, 3).
The function h(x) is decreasing on the interval (3, ∞).
Answers
Answer:
The function h(x) is decreasing on the interval (3, ∞).
Step-by-step explanation:
Please take a look at the attached image.
You will see a graph of the given function h(x) = -2\(\sqrt{x-3}\). The function is decreasing.
The function starts at 3 and starts to go towards negative infinity on the x-axis. Therefore the function is decreasing on the interval (3, ∞).
The Tucker Gym charges a one time fee of $50 plus a $25 monthly membership
charge.
THe NoFo Health Club charges a one time fee of $80 plus a $15 monthly
membership fee.
Represent the situation as a system of two equations in two variables.
Solve the equation algebraically using substitution or elimination.
Answers
Answer:
y = 50 + 25x.............(i)
y = 80 + 15x.............(ii)
x = 3
y = 125
Step-by-step explanation:
The tucker Gym charges a one time fee of $50 plus a $25 monthly membership charge.
The NoFo health club charges a one time fee of $80 plus a $15 monthly membership fee.
Let
number of month = x
total cost = y
Tucker Gym
y = 50 + 25x.............(i)
NoFo Gym
y = 80 + 15x.............(ii)
combining the equation
y = 50 + 25x.............(i)
y = 80 + 15x.............(ii)
y - 50 = 25x
y/25 - 2 = x
insert x in equation (ii)
y = 80 + 15(y/25 - 2)
y = 80 + 3y/5 - 30
y = 50 + 3y/5
y - 3y/5 = 50
5y - 3y/5 = 50
2y/5 = 50
cross multiply
2y = 250
y = 250/2
y = 125
insert y in equation (i)
125 = 50 + 25x
125 - 50 = 25x
75 = 25x
x = 75/25
x = 3
Madison read 1/2 of a book in the morning, and she read some more at night. By the end of the day she still had 2/5 of the book left to read. How much of the book did Madison read at night?
Answers
Answer: 1/10
Step-by-step explanation:
At the end of the day, she still had 2/5 of the book to read. Which meant that she had read 3/5 of the book. Since she read 1/2 of the book in the day, we would read 3/5 - 1/2 = 6/10 - 5/10 = 1/10 of the book at night.
A pole that is 3 m tall casts a shadow that is 1.55 m long. At the same time, a nearby tower casts a shadow that is 49.25 m long. How
tall is the tower? Round your answer to the nearest meter.
m
Answers
The tower is approximately 95 meters(m) tall.
What is a meter?
A meter is the basic unit of length in the International System of Units (SI). It is defined as the distance light travels in a vacuum in 1/299,792,458 of a second.
What kind of unit is meter?
The meter is a unit of measurement for length or distance. It is commonly used in science, engineering, and daily life to measure the size or distance between objects.
According to the given information
Let's call the height of the tower h. We can use similar triangles to set up a proportion:
3 / 1.55 = h / 49.25
Simplifying this expression gives:
h = (3 * 49.25) / 1.55
h = 95.48
Rounding this answer to the nearest meter gives:
h ≈ *95 meters*.
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Identify the domain of the function represented below:y= 2√x4-3x ≥ 4O x ≥ 3Ox≥-3Ο x > 0
Answers
Solution
Step 1
Write the function
\(y=2\sqrt{x-4}-3\)Step 2
\(\begin{gathered} \mathrm{Domain\:definition} \\ The\:domain\:of\:a\:function\:is\:the\:set\:of\:input\:or\:argument\:values \\ \:for\:which\:the\:function\:is\:real\:and\:defined. \end{gathered}\)Step 3
To find the function domain, equate the expression in the square to at least zero.
\(\begin{gathered} x\text{ - 4 }\ge\text{ 0} \\ \\ x\text{ }\ge\text{ 4} \end{gathered}\)Final answer
\(\)Alisha has some number cards that each have a whole number on them. If she chooses a card at random, the probability that the number on it is even is. Work out the ratio of even cards to odd cards that Alisha has. Give your answer in its simplest form.
Answers
The ratio is \(\frac{3}{2}\) in its simplest form.
EquationIf the probability of choosing an even card is \(\frac{3}{5}\) , then the probability of choosing an odd card is 1- \(\frac{3}{5}\) = \(\frac{3}{2}\).
Let e be the number of even cards Alisha has, and let o be the number of odd cards. Then, we have:
\(\frac{e}{e+0}\)
which simplifies to:
5e=3(e+o)
Expanding the right side gives:
5e=3e+3o
Simplifying further gives:
2e=3o
Dividing both sides by 2 gives:
e= \(\frac{3}{2}\)o
\(\frac{3}{2}\)
What is probablity?Probability is a branch of mathematics that deals with the study of random events or experiments. It involves the analysis of the likelihood or chance of an event occurring, usually expressed as a number between 0 and 1, where 0 indicates that the event will not occur and 1 indicates that the event is certain to occur.
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please help me out with this
Answers
Answer:
a + 5b
Step-by-step explanation:
Distributive property: a*(b + c) = a*b + a*c3*(a + b). In this multiply each term with 3 and in -2(a- b), multiply each term with (-2).
3*(a +b) - 2*(a - b) = 3*a + 3*b + (-2)*a + (-2)*(-b)
= 3a + 3b - 2a + 2b
= 3a - 2a + 3b + 2b {Combine like terms}
= a + 5b
Like terms have same variable with same power. Here, 3a and (-2a) are like terms. So, combine the coefficients of the like terms
3a + (-2a) = a.
cross section, the ratio of the area of the circle to 4 square, the volume of the cylinder equ ea of the square is ap? or 4 2. Cross section 2 o the volume of the prism or (a I the volume of the prism or (4 O I the volume of the prism or 12 o the volume of the prism or (4 h
Answers
Answer:
ya
Step-by-step explanation:
A three digit number is formed at random using the digits
2, 3 and 4. If no digit can be repeated in any one number, find the probability that the number formed is greater than 300.
Answers
Answer:
2/3, or 66.7%
Step-by-step explanation:
There are 2 options for the first digit (3 or 4).
After the first digit is selected, it cannot be repeated, so there are 2 options left for the second digit.
After the first two digits are selected, there is only 1 option for the third digit.
So there are 4 permutations greater than 300.
The total number of permutations is 3! = 6.
So the probability is 4/6 = 2/3.
In one part of a rainforest 3/5 of the frogs are poisonous. what fraction of the frogs are not poisonous?
Answers
Then 1 - 3/5 = 2/5. This means that 2/5 of the frogs in that particular part of the rainforest are not poisonous. This fraction can also be expressed as 40/100 or 0.4 in decimal form.
In the given scenario, we know that 3/5 of the frogs in a particular part of the rainforest are poisonous. This means that the remaining fraction of the frogs are not poisonous.
To find this fraction, we need to subtract 3/5 from 1 (since the sum of the fractions of poisonous and non-poisonous frogs is equal to 1).
It's important to note that just because a frog is not poisonous, it doesn't mean it's safe to touch or handle them. It's always best to admire these beautiful creatures from a safe distance and leave them alone in their natural habitat.
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On a number line what is the distance between 16 and -25
Answers
The Academic Quiz advisor needs to choose the top member to compete in a final challenge.
When she calculated the team members' scores on qualifying tests over the past year,
she found that Tobin and Yolanda had approximately the same mean score.
The MAD for Tobin's scores is 28.3, and the IQR is 39.8.
The MAD for Yolanda's scores is 9.7, and the IQR is 18.5. Which statement is true?
A
Tobin should compete because his measures of variability show that he is more consistent.
B.
Yolanda should compete because her measures of variability show that she is more consistent.
C.
Both players are equally qualified because their measures of variability are approximately the same.
D.
Both players are equally qualified because their mean scores are about the same and their measures of variability do not provide any additional information.
Answers
please Translate the triangle.
Then enter the new coordinates.
A (-2,4)
(-3,2)
< 9.3 >
A'([?], [])
B'([ ].[])
C'([] [])
![please Translate the triangle.Then enter the new coordinates.A (-2,4)(-3,2)< 9.3 >A'([?], [])B'([](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/hYXbUSqbeilzJwElruWoiMoYt074XMtw.png)
Answers
Answer:
A' (7,7)
B' (10,4)
C' (6,5)
Step-by-step explanation:
Add 9 to every x value and 3 to every y value.
Answer:
A'(7,7)
B'(10,4)
C'(6,5)
Step-by-step explanation:
⭐What is a translation?
a translation is a type of transformation you can do to a figure to shift the figure up/down and left/right.⭐What is the translation notation?
\(T_ < x,y > (ABC) = (A'B'C')\)\(T_ < x,y >\) tells you how much to move the figure left/right and up/down. x = left/righty = up/downThe problem tells us to translate ΔABC 9 units to the right, and 3 units up because it is inside the <>, and the numbers are positive.
To translate the vertices of ΔABC, we have to add the respective x and y coordinates of the translation rule to each vertecie of ΔABC.
A(-2,4):
Add the respective x and y coordinates of the translation rule to the coordinates of the vertecieA'(-2+9, 4+3) = A'(7,7)B(1,1):
Add the respective x and y coordinates of the translation rule to the coordinates of the vertecieB'(1+9, 1+3) = A'(10,4)C(-3,2):
Add the respective x and y coordinates of the translation rule to the coordinates of the vertecieC'(-3+9, 2+3) = A'(6,5)⭐if this response helped you, please mark it the "brainliest"!⭐
fernando charges a flat fee of 4.50 plus 2.00 per mile for his taxi service, when he got to the airport the cab fare was 12.50, how many miles did he cab travel
Answers
Answer:
4 miles, the cab travelled 4 miles.
Step-by-step explanation:
12.50 - 4.50 = 8
8/2.00 = 4
What is the range of the function shown in the graph?
A. -infinity
B. -5
C. -infinity
D. -infinity
Answers
Answer:
c
Step-by-step explanation:
Answer:
(-♾,♾) I'm pretty sure its like that.
This is about scatter plots and association i just need number 1
Answers
The form of association that would be found in the variables would be:
Positive association No association Negative association How to find the association ?As the number of hours spent playing a video game increases, the player is likely to reach higher levels within the game. So positive association.
The number of letters in a person's name and the last digit of their phone number are likely to be unrelated and randomly distributed. There is no association.
As the temperature of the drink decreases, the number of ice cubes in the drink is likely to increase, and vice versa. This is therefore negative association.
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Simplify the algebraic
expression
4(x + 1) + 7(x + 3).
a. 11x + 4
b. 2x + 215
C. 11x + 25
d. 5x + 11
Someone help pleaseeee
Answers
Answer:
C.
Step-by-step explanation:
4(x + 1) + 7(x + 3)= 4*x+4*1 + 7*x+7*3 = 4x+4 +7x +21 = 11x + 25
C
Step-by-step explanation:
4x+4+7x+21
11x+25
you have to combine like terms
Solve kx – 3 = 5 for x.
A. x=2/k
B. X = 8k
C. x=8/k
D. X = 8 - k
Answers
kx - 3 = 5
kx = 8
x = 8/k
Which of the following numbers can be expressed as repeating decimals? (5 points)
4/7,2/5,7/8,4/9
Answers
Answer:
34
Step-by-step explanation:
Show each single-step equation. Show your work. V/8 = 2
Answers
Answer: V = 16
=========================================================
Explanation:
The notation V/8 means we are dividing V over 8.
To isolate V, we undo this division by applying multiplication. We'll multiply both sides by 8 to get V = 2*8 = 16.
Replacing V with 16 will lead to a true equation
V/8 = 2
16/8 = 2
2 = 2
This helps confirm the answer.
If two sides of a triangle are 6 and 16, what is the range of the possible lengths
of the third side?
Answers
The range of the possible length of the third side is between 10 and 22
How to determine the possible length of the third sideFrom the question, we have the following parameters that can be used in our computation:
Lengths = 6 and 16
The possible length of the third side can be calculated using the triangle inequality theorem
For this triangle, the length of the third side must be greater than
16 - 6 = 10
Also, the length of the third side must be less than
16 + 6 = 22
Hence, the possible length of the third sides is between 10 and 22
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What is the answer to 12 plus 12
Answers
Answer:
12 + 12 = 24
12 x 2 = 24
Step-by-step explanation: