Find all zeros of ƒ(x)=x4–22x3+121x2.Then determine the multiplicity at each zero. State whether the graph will touch or cross the x-axis at the zero.
Answers
Answer:
0, 11, both multiplicity 2touch, not cross, at each 0Step-by-step explanation:
The function factors as ...
f(x) = x^4 -22x^3 +121x^2
f(x) = x^2(x^2 -22x +121)
f(x) = x^2(x -11)^2
The zeros are x=0 and x=11, each of multiplicity 2.
Because the multiplicity is even, the graph will touch at each zero, not cross.
Related Questions
The cost in dollars of making x items is given by the function C(x)=10x+800. a. The fixed cost is determined when zero items are produced. Find the fixed cost for this item. Fixed cost =$ Number b. What is the cost of making 25 items? C(25)=$ Number c. Suppose the maximum cost allowed is $2300. What are the domain and range of the cost function, C(x)? When you enter a number in your answer, do not enter any commas in that number. In other words if you want to enter one thousand, then type in 1000 and not 1,000. It's not possible to understand what the interval (1,000,2,000) means, so you should write that as (1000,2000). Domain: Preview Range: Preview
Answers
Answer:
1. Fixed cost is $800
2.Cost of 25 bags is $1025
3. (170,2300)
Step-by-step explanation:
Given
[tex]c(x) = 10x + 800[/tex]
Solving (a): Fixed cost
From the question, fixed cost is when x = 0;
Substitute 0 for x in [tex]c(x) = 10x + 800[/tex]
[tex]c(0) = 10 * 0 + 800[/tex]
[tex]c(0) = 0 + 800[/tex]
[tex]c(0) = 800[/tex]
Hence, the fixed cost is $800
Solving (b): Cost of making 25 items
Here; x = 25
Substitute 25 for x in [tex]c(x) = 10x + 800[/tex]
[tex]c(25) = 10 * 25 + 800[/tex]
[tex]c(25) = 250 + 800[/tex]
[tex]c(25) = 1025[/tex]
Hence, the cost of 25 bags is $1025
Solving (c): Domain and Range where Maximum cost = $2300
Here; c(x) = 2500
Substitute 25 for c(x) in [tex]c(x) = 10x + 800[/tex]
[tex]2500 = 10x + 800[/tex]
Subtract 800 from both sides
[tex]10x = 2500 - 800[/tex]
[tex]10x = 1700[/tex]
Divide both sides by 10
[tex]x = 170[/tex]
The domain and range of a function is in form of (x,c(x))
Hence, the domain and range is (170,2300)
When did the United States first start to consider adopting the metric system?
Answers
Answer:
1866
In 1866, the U.S. Congress authorized the use of the metric system and almost a decade later America became one of 17 original signatory nations to the Treaty of the Meter. A more modern system was approved in 1960 and is commonly known as SI or the International System of Units.
Answer:
1893
Step-by-step explanation:
In 1893, metric standards, developed through international cooperation under the auspices of BIPM please mark brainliest :)
Lee spent $29 to purchase a combination of drinks, sandwiches, and chips for himself and his friends. A drink costs $1.50, a sandwich costs $5, and chips cost $1.25. Identify the linear equation that represents this situation.
Answers
Answer:
1.5d+5s+1.25c=29
Step-by-step explanation:
let d be the number of drinks, s be the number of sandwich, and c be the number of chips Lee purchased.
1.5×d and 5×s and 1.25×c must total 29, or
1.5d+5s+1.25c=29.
circle the digit is in the tens place
219,358,675
Answers
Answer:
219,358,675
the tens digit is the second digit before decimal point (from right to left)
219,358,675
Hope this helps!! :)
Answer:
Hey!
The 7 in *...675* is in the tens place!!
Step-by-step explanation:
Tens place??
AkA THE SECOND PLACE IN FROM RIGHT
▶hOPE IT HELPED!!◀
Please Help! The base of a triangular prism has a base rent of 7 feet and a height of 3 feet the prism is 4 feet tall a second larger prism has dimensions that are three times the dimensions of the small prism what is the difference between the volumes of the two prisms?
Answers
Answer: 1092
Step-by-step explanation:
Answer:
1092
Step-by-step explanation:
How can i write all the names that apply √36 NEED IT ASAP
Answers
Answer:
square of 36 is 6
or maybe 6²
Write 6.93 repeating a mixed number in simplest form.
6.93 =?
Answers
Answer:
[tex]6\frac{93}{100} = \frac{693}{100}[/tex]
Step-by-step explanation:
Turn 6.93 into a fraction: [tex]6\frac{93}{100}[/tex] To turn into a mixed number, first multiply 6 and 100, then add 93. Put 693 over 100: [tex]\frac{693}{100}[/tex]I hope this helps!
Answer: [tex]6 \frac{31}{33}[/tex]
This is a mixed number where the whole part is 6, and the fractional part is 31/33.
=============================================
Explanation:
The 93 repeats forever, so we can say
x = 6.939393...
100x = 693.939393....
Subtracting the left hand sides leads to 100x-x = 99x
Subtracting the right hand sides leads to 693.939393.... - 6.939393... = 687
Notice how the decimal terms cancel out when we subtract.
We're left with 99x = 687 which solves to x = 687/99
This reduces to 229/33 when you divide both parts by 3.
The last step is to convert to a mixed number
The answer will be in the form [tex]6 \frac{x}{33}[/tex] where 6 is the whole part and x/33 is the fractional part. We know the whole part is 6 from the 6 in the original number given.
229/33 = 6.939393... helps confirm we're on the right track so far
this is another way of saying 229/33 = 6 remainder x, where x is the unknown remainder and the numerator we're after for the fraction x/33.
To get the remainder, we just compute 229-6*33 to get 31
This means 31/33 = 0.93939393...
and that [tex]6 \frac{31}{33} = 6.\overline{93} = 6.93939393...[/tex]
Please help me with the question below
Answers
Answer:
The answer is A.
Step-by-step explanation:
This is because Tia's amount of money minus Dana's amount of money should be at least 5
Principal: $1500.
Annual interest rate: 72%.
What is the interest after
6 months?
Answers
To solve this problem, you us the equation A=P(1+rt)
A stands for the amount of money accumulated after t years
P stands for principal
r stands for annual interest rate
t stands for time (in years)
Next you need to plug it into your formula which should look like this...
A=1500(1+(0.072*0.5))
When you plug in your annual interest rate, you have to move your decimal place 2 places to the left. That is why 7.2% is 0.072 in the formula above.
The reason that I plugged in 0.5 for the time instead of 6 months is because the time in this formula is calculated in years. For example, if the question told you the time was 12 months, 12 months is one year, so you would plug in a 1 for t. Since your question asked for 6 months, 6 months is equal to half a year or 0.5 of a year. That is why t is 0.5 in the formula.
Now that you have your problem, the next step is to solve. I will show you what that looks like down below.
A=1500(1+(0.072*0.5))
A=1500(1+(0.036))
A=1500(1.036)
A=1554
From this problem, we just solved for how much money is in this account after 6 months which is $1554. But we’re not done yet, we are looking for how much interest was earned after 6 months.
To find this, all you have to do is subtract the amount earned after 6 months ($1554) by the principal amount ($1500) using this formula (the I stands for Interest).
A-P=I
1554-1500= 54
The interest earned after 6 months is $54.
(If the annual interest rate is 72% and not 7.2%, you can still use the formulas and my lesson to solve it yourself)
Write each statement as a decimal to two decimal places. $6.00 to 95 cents = 3 hours to 35 minutes = 42 inches to 2 feet = (Hint: there are 12 inches in 1 foot.)
Answers
Answer/Step-by-step Explanation:
The above given statements can be written as decimals by first writing both quantities in a statement in the same unit.
1. $6.00 to 95 cents:
This is same as $6.00 : 95 cents = [tex] \frac{6.00}{95} [/tex]
Convert $6 .00 to cents to make both quantities be in the same unit.
$1 = 100 cents
$6.00 = 6*100 = 600 cents
[tex] \frac{600}{95} = 6.32 [/tex] (to 2 d.p)
2. 3 hours to 35 minutes:
Convert 3 hours to 35 mins
1 hr = 60 mins
3 hrs = 3*60 = 180 mins
[tex] 180mins : 35 mins = \frac{180}{35} = 5.14 [/tex] (2 d.p)
3. 42 inches to 2 feet:
Convert 2 ft to inches
1 ft = 12 inches
2ft = 2*12 = 24 inches
[tex] 42 in:24 in = \frac{42}{24} = 1.75 [/tex]
Complete the equation involving x. Order terms like the physical situation, and don't simplify. A 6 foot wide painting should be centered on a 10 foot wide wall. How many feet (x) should be on each side of the painting?
Answers
Answer:
The space on each side of the painting = 2 feet
Step-by-step explanation:
Attached this answer is a diagram to give you visuals on how the value of x is calculated
Given:
width of wall = 10 feet
width of painting = 6 feet
Since the painting is centred on a wall, there is meant to be an equal space on each side of the painting, from the diagram, the following eaquation can be gotten
x + 6 + x = 10
2x + 6 = 10
2x = 10 - 6
2x = 4
x = 4 ÷2
x = 2 feet
Therefore, the space on each side of the painting = 2 feet
Solve the equation 6x + 2x - 5= 19 x=? Simplify your answer
Answers
Answer:
x = 3
Step-by-step explanation:
6x + 2x - 5= 19
8X -5 = 19
8x = 24
x = 3
Please choose one to answer. Thanks of finished all 3 questions BRILLIANT! I give you Braingood thing
Answers
Answer:
Step-by-step explanation:
11.a=6
b=3
Please help me please
Answers
Answer:
y = 4 (Answer C)
Step-by-step explanation:
We want to find side y. The sine function relates the 30 degree angle, the hypotenuse 8 and the opposite side y:
y
sin 30 degrees = 1/2 = -----------
8
so y = 4 (Answer C)
Find the quotient for 12 ÷ (-4).
Answers
Answer: -3
Step-by-step explanation: To divide 12 by -4, remember that a
positive divide by a negative is a negative.
So (12) ÷ (-4) is -3.
Find each of the following functions and state their domains. (Enter the domains in interval notation.)
f(x) = x3 + 4x2, g(x) = 5x2 − 1
(a) f + g
f + g =
domain =
(b) f - g
f − g =
domain =
(c) fg
fg =
domain =
(d) f/g
f/g =
domain =
Answers
Answer:
Step-by-step explanation:
Given functions are,
f(x) = x³ + 4x²
g(x) = 5x² - 1
(a). (f + g)(x) = f(x) + g(x)
= x³ + 4x² + 5x² - 1
= x³ + 9x² - 1
Since the composite function is defined for all values of x, domain of the function will be (-∞, ∞)
(b). (f - g)(x) = x³ + 4x² - (5x² - 1)
= x³ - x² + 1
Domain of the function : (-∞, ∞)
(c). (f.g)(x) = f(x) × g(x)
= (x³ + 4x²)(5x² - 1)
= 5x⁵+ 20x⁴ - x³ - 4x²
Domain of the function will be (-∞, ∞).
(d). [tex](\frac{f}{g})(x)=\frac{f(x)}{g(x)}[/tex]
= [tex]\frac{x^3+4x^2}{5x^2-1}[/tex]
Since this function is not defined at [5x² - 1 = 0] Or x = ±[tex]\frac{1}{\sqrt{5}}[/tex]
Therefore, Domain of the composite function will be,
(-∞, -[tex]\frac{1}{\sqrt{5}}[/tex]) ∪ [tex](-\frac{1}{\sqrt{5}},\frac{1}{\sqrt{5}})[/tex] ∪ ([tex]\frac{1}{\sqrt{5}}[/tex], ∞)
Which of the following are acceptable weights?
13.5oz
13.8oz
14.15oz
14.2oz
14.3oz
Answers
Answer:
13.8 14.15 14.2
Step-by-step explanation:
Edge 2020
~theLocoCoco
Answer: b, c & d !
Step-by-step explanation:
If you count 14 beats in 6 seconds, what is your approximate rate?
Answers
Answer:
About 2.3 beats per second
Step-by-step explanation:
14 / 6 is approximately 2.3.
Answer: About 2.33 beats per second
Step-by-step explanation:
Divide the number of beats by the seconds and find the approximation rate.
49 divided by 7 get a decimal answer
Answers
Answer:
7.0?
Step-by-step explanation:
49/7 would be 7, If the question was 7/49 the answer would be 0.14285714285 (a decimal)
I NEED HELP Are the two functions inverses? f ( x ) = − 8 x + 5 g ( x ) = − 1 8 x + 5 8 Group of answer choices Yes No
Answers
Answer: No
Step-by-step explanation:
To know if the functions are inverses of each other, it is easiest to just find the inverse of one of the functions. To find the inverse, you want to replace y with x and x with y and solve for y.
y=-8x+5 [switch x with y and y with x]
x=-8y+5 [subtract both sides by 5]
x-5=-8y [divide both sides by -8]
y=(x-5)/-8
f⁻¹(x)=(x-5)/-8
Since we know that the inverse doesn't match g(x), we know that these functions are not inverses of each other.
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Question 11 pts
Is the value of the 1 in 1,440,000 10 times as great as the value of the 4 in the hundred thousands place? Explain
Answers
Answer:
Yes
Step-by-step explanation:
The answer is yes because 1,000,000 ÷ 100,000 = 10.
Martin is buying 400 video games for his entertainment store it's video game cost $20 which of the following could be used to find the total amount he will pay for the video games .
Answers
Answer:
What are the following??
Step-by-step explanation:
Imma try to help tho
soo like 20$ per game and like 400 games
thats 20$*400=8,000 dollars
Simplify 3√-1000 and 3√g6h30
Answers
Answer:
[tex] \sqrt[ ]{1000} [/tex]
Step-by-step explanation:
[tex]3 \sqrt{ - 1000} = 3 \sqrt{1000i {}^{2} } \\ = 3 \times 10i \\ = 30i \\ (in \: complex \: form \: i {}^{2} = - 1)[/tex]
Answer:
1st one = -10
2nd one = g2h10
Step-by-step explanation:
Edge2020!!
Each school day, Aidon wolks 11 blocks to school after school, he wolks 4 blocks to the library
and 12 blocks home. How many blocks does Aidon wolk in a week? *
e
Answers
Answer:
189
Step-by-step explanation:
Aidon walked 11 blocks to begin with than he walks 4 blocks to the library and 12 blocks home. This mean we add 11+4+12=27 and a week has 7 days which means we need to multiply that by 7 which gives us the product of 189.
Also, i double checked
PLEASE HURRY I ONLY HAVE 5MIN TO TURN IT IN!!! A new television set was recently purchased for a common Room and a resident Hall for $446.90 including tax. If the tax rate is 9%, find the price of the television set before taxes.
Answers
Answer:
The price of the tv before tax is 410
Step-by-step explanation:
Let x = price of tv before tax
tax = x* 9%
tax = .09x
The total cost is price of tv before tax plus tax
total cost = x + .09x
total cost = 1.09x
446.90 = 1.09x
Divide each side by 1.09
446.90/1.09 = 1.09x/1.09
410 = x
The price of the tv before tax is 410
1/2(-2x - 12) > 7(3 - 4x)
The solution is____
Answers
Answer:
x > 1
interval (1,∞)
Step-by-step explanation:
1/2(-2x - 12) > 7(3 - 4x)
-x - 6 > 21 - 28x
-x + 28x > 21 + 6
27 x > 27
x > 27 / 27
x > 1
interval (1,∞)
-x - 6 > 21 - 28x if x = 2
-2 - 6 > 21 -28(2)
-8 > 21 - 56
- 8 > - 35
please quickly answer. i cant be waiting for 20 mins.
Answers
Answer:
C ( -2,4)
Step-by-step explanation:
In quadrant II, the x values are negative and the y values are positive
( -, +)
(-2,4) is the only point that meets this
Answer:
[tex]\huge \boxed{\mathrm{\bold{C.}} \ ( -2,4)}[/tex]
Step-by-step explanation:
The x values are negative and the y values are positive in quadrant II.
The point (-2, 4) is in quadrant II.
Determine the rate of change for 3/2x -5/4y = 15
Answers
Answer:
-6/5
Step-by-step explanation:
3/2x - 5/4y = 15
-5/4y = -3/2x + 15
multiply each side by (-4/5)
(-4/5)(-5/4y) = (-4/5)(-3/2x + 15)
y = -6/5x - 12
rate of change: -6/5
which function below is the Inverse of f(x)= 7x-1/2
Answers
Answer:
[tex]f-1(x)= \frac{x}{7} +\frac{1}{14}[/tex]
Step-by-step explanation:
If we have y=7x-1/2, the inverse is where we solve for x instead of y.
We can isolate x to get 7x=y+1/2, then divide by 7 to get x=y/7+1/14.
Therefore,[tex]f-1(x)= \frac{x}{7} +\frac{1}{14}[/tex]
Hope that helped,
-sirswagger21
View Lab
Which of the following functions is most likely to have the smallest value for y if x is large? (Assume k is positive.)
a direct variation function with a small value fork
a direct variation function with a large value fork
an inverse variation function with a small value fork
an inverse variation function with a large value fork
Nexi
Subm
Save and Exit
Mark this and retum
Answers
Answer:
an inverse variation function with a small value for k
Step-by-step explanation:
The attached graph shows the cases described. The function with the smallest function value for large x is ...
an inverse variation function with a small value for k
___
On the graph, it is the green curve. The inverse variation functions both continue to decrease for large x, but the function with the smaller k value has a smaller function value.
Answer:an inverse variation function with a small value for k
Step-by-step explanation:Because i took the test