The factored form of the equation 9x⁴y - 6x³y² + 3x²y³ is 3x²y(3x²-2xy+y²).
What is factored form?The product of a constant and two linear expressions in factored form. The roots of the function are the parameters and the x-intercepts of the graph. Often Factoring is referred to as the process of converting a quadratic function to factored form.
We need to write the given expression [tex]9x^4y-6x^3y^2 + 3x^2y^3[/tex] in the factored form, therefore, we will take the common terms out of the given expression,
1. Taking 3 as the common term, we will get,
[tex]9x^4y-6x^3y^2 + 3x^2y^3\\\\= 3 (3x^4y-2x^3y^2 + x^2y^3)[/tex]
2. Taking x² as the common term
[tex]= 3 (3x^4y-2x^3y^2 + x^2y^3)\\\\= 3x^2(3x^2y-2xy^2+y^3)\\\\[/tex]
3. Taking y as the common term,
[tex]= 3x^2(3x^2y-2xy^2+y^3)\\\\= 3x^2y(3x^2-2xy+y^2)\\\\[/tex]
Hence, the factored form of the equation 9x⁴y - 6x³y² + 3x²y³ is 3x²y(3x²-2xy+y²).
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Tracy wants to make a cylindrical model. The height of the cylindrical model, H(V), in inches, is modeled by this
equation, where Vis the volume of the cylindrical model, in cubic inches.
H(V) = 2. 6937
What is the average rate of change of the model's height when its volume changes from 512 cubic inches to
1,000 cubic inches?
The model's height increases by approximately 21. 52 inches for every 1-cubic-inch increase in its volume.
The model's height increases by approximately 0. 022 inch for every 1-cubic-inch increase in its volume.
The model's height increases by approximately 0. 011 inch for every 1-cubic-inch increase in its volume.
The model's height increases by approximately 26. 9 inches for every 1-cubic-inch increase in its volume.
The average rate of change of the height function is slope of the height function
The model's height increases by approximately 0.011 inch for every 1-cubic-inch increase in its volume.
How to determine the average rate of change?The height function is given as:
[tex]H(V) = 2.69\sqrt[3]{V}[/tex]
When V = 512, the function becomes
[tex]H(512) = 2.69\sqrt[3]{512}[/tex]
[tex]H(512) = 21.52[/tex]
Similarly;
When V = 1000, the function becomes
[tex]H(1000) = 2.69\sqrt[3]{1000}[/tex]
[tex]H(1000) = 26.9[/tex]
The average rate of change is then calculated as:
[tex]H' = \frac{H(1000) - H(512)}{1000 - 512}[/tex]
This gives
[tex]H' = \frac{26.9 - 21.52}{1000 - 512}[/tex]
[tex]H' = \frac{5.38}{488}[/tex]
Evaluate the quotient
[tex]H' = 0.01102459016[/tex]
Approximate
[tex]H' = 0.011[/tex]
Hence, the model's height increases by approximately 0.011 inch for every 1-cubic-inch increase in its volume.
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Answer:
The model’s height increases by approximately 0.011 inch for every 1-cubic-inch increase in its volume.
Step-by-step explanation:
Plato/Edmentum
The total cost of a pizza and 3 drinks is $19. The price of the pizza is $10 and each drink is the same price, d. What is the prive of the one drink?
Answer:
each of the drinks are $3
Step-by-step explanation:
10 d d d /19 d=3
hope it help
Answer:
$3
Step-by-step explanation:
pizza-p
drink-d
p+3d=19
p=$10
10+3 (d)=19
3 (d)=19-10
3 (d)=9
d=9÷3
d=$3
Find the area of the figure.
Answer: 300 ft^2
Step-by-step explanation:
First, find the area of the rectangle on the bottom:
Area of a rectangle = length * width = 18 * 12 = 216
Now, find the area of the trapezoid:
Area of a trapezoid = (base 1 + base 2) / 2 * height → (10 + 18) / 2 * 6 = 84
Add these together: 216 + 84 = 300 ft^2 :)
n the past you paid $800 per month to rent your apartment. You now pay $900 per month for your rent. What is the percent increase in your rent?
Answer:
12.5%
Step-by-step explanation:
900 - 800 = 100
Gotta pay $100 more
100 / 800 = 0.125
Heather has a bag containing 4 marbles: 1 red, 1 blue, and 2 green. she draws 1 marble out of the bag, replaces it, and then draws another marble. what is p(red then blue then green)?
Multiply the probability of each by each other:
Probability of red = 1/4
Probability of blue = 1/4
Probability of green = 2/4 = 1/2
probability of red then blue then green = 1/4 x 1/4 x 1/2 = 1/32
answer: 1/32
In a circle, a 225° sector has area 250pi in^2. What is the radius of the circle?
Answer:
r = 200
Step-by-step explanation:
[tex]Area of sector = (\frac{225}{360})[/tex]×πr² = [tex](\frac{5}{8})[/tex] ×πr²
[tex](\frac{5}{8})[/tex] ×πr² = 250π
[tex](\frac{5}{8})[/tex] ×r² = 250
r² = [tex](\frac{8}{5})[/tex] × 250
r² = 400
r = 200 (r is a length so, it's positive)
Without solving, identify whether this equation has a solution that is positive, negative, or zero: It is positive Solve the equation.
Answer:
Step-by-step explanation:
can someone help please????
2. Tania went to Italy. She changed £325 into euros (€). The exchange rate was £1 = €1.68 (a) Change £325 into euros (E).
Answer:
£325 is €546
Step-by-step explanation:
325 times 1.68 is 546
Does anyone know this? I'm stuck on it.
Answer:
For the first triangle:
Sides xz and xy are of equal length
Angles z and y are of equal measure
For the second triangle:
Sides pr and qr are of equal length
Angles p and q are of equal measure
Step-by-step explanation:
Those tiny line segments intersecting the sides indicate that those sides are equal.
Hope that helps!
Which expression is not equivalent to 2² + 10+12?
Option 3 is not equivalent!
(Hope I could help!)
We want to find the zeros of this polynomial:
p(x) = (x+2) (2x^2 + 3x-9)
Answer:
x = - 2, x = - 3, x = [tex]\frac{3}{2}[/tex]
Step-by-step explanation:
to find the zeros equate p(x) to zero , then
(x + 2)(2x² + 3x - 9) = 0 ← factor the quadratic
(x + 2)(x + 3)(2x - 3) = 0
equate each factor to zero and solve for x
x + 2 = 0 ⇒ x = - 2
x + 3 = 0 ⇒ x = - 3
2x - 3 = 0 ⇒ 2x = 3 ⇒ x = [tex]\frac{3}{2}[/tex]
A sandbox has a volume of 330 cubic feet of sand. If the sandbox is 3 feet tall, and 10 feet wide, what is the length of the sand box?
Answer:
We are given that the total volume of the sandbox is 330 cubic feet.
We are given the side measurements of 3 feet tall and 10 feet wide.
3 x 10 = 30 sq2
V(volume)= 330 ft3
330 ft3 divided by 30 sq2 = 11ft
In conclusion, the length of the box would be:
= 11 ft
Step-by-step explanation:
Have a great rest of your day
#TheWizzer
calculate the value of the marked angle
(4, 6) (-3, -2) Find the slope
Answer:
The value of the slope would be:
8/7
Step-by-step explanation:
Have a great rest of your day
#TheWizzer
Answer:
[tex] slope = \dfrac{8}{7} [/tex]
Step-by-step explanation:
(4, 6) and (-3, -2)
[tex] slope = \dfrac{y_2 - y_1}{x_2 - x_1} [/tex]
[tex] slope = \dfrac{-2 - 6}{-3 - 4} [/tex]
[tex] slope = \dfrac{-8}{-7} [/tex]
[tex] slope = \dfrac{8}{7} [/tex]
what the geometric mean of 18 and 30 as a square root?
The geometric mean of 18 and 30 is the product of 18 and 30 square rooted, so:
[tex]\sqrt{18*30} =\sqrt{540} =\sqrt{9*4*15} =\sqrt{36*15} =6\sqrt{15}[/tex]
Hope that helps!
Angle 1 and Angle _____________ are supplementary angles.
Answer: number 2
Step-by-step explanation: so a supplementary Angle adds up to a 180 angle so it would be number 2 I think.
Jayce and Lara each made q bowl of punch. Lara used 6 times as much as much lemonade as Jayce did. if Jayce used 3/4 if a cup of lemonade, how many cups did Lara use?
Answer: 4.5
Step-by-step explanation:
6 x 3/4 = 18/4 divided that and it equals 4.5
Determine whether the following sequence is geometric. If so, find the common ratio,
1.-3.9. - 27,...
Answer:
Yes, the sequence is geometric
common ratio (r) = -3
Step-by-step explanation:
Given:
[tex]a_1=1[/tex][tex]a_2=-3[/tex][tex]a_3=9[/tex][tex]a_4=-27[/tex]If a sequence is geometric, common ratio [tex]r[/tex]:
[tex]r=\dfrac{a_4}{a_3}=\dfrac{a_3}{a_2}=\dfrac{a_2}{a_1}[/tex]
Substituting the given values:
[tex]\implies \dfrac{a_4}{a_3}=\dfrac{-27}{9}=-3[/tex]
[tex]\implies \dfrac{a_3}{a_2}=\dfrac{9}{-3}=-3[/tex]
[tex]\implies \dfrac{a_2}{a_1}=\dfrac{-3}{1}=-3[/tex]
Therefore, as
[tex]\dfrac{a_4}{a_3}=\dfrac{a_3}{a_2}=\dfrac{a_2}{a_1}=-3[/tex]
the sequence is geometric with common ratio of -3
what are the solutions to the equation?
Answer:
x = -2 and 1
Step-by-step explanation:
Given :
f(x) = x+2
g(x) = -x²+4
The solution to the equation f(x) = g(x)
=> x+2 = -x²+4
=> x²+x = 4-2
=> x²+x -2 = 0
By factorisation
=> x²+2x-x -2 = 0
=> x(x+2) -1(x+2)
=> (x+2) (x-1)
x = -2 and 1
Which is an equation of the parabola that intersects the x-axis at points (-1, 0) and (3, 0)? Show your work or explain how you determined your answer. A. y = x2 + 2x - 3 B. y = x2 + 3x + 2 C. y = x2 - 2x - 3 D. y = x2 - 3x + 2
Answer:
[tex]\displaystyle \large{y=x^2-2x-3}[/tex]
Step-by-step explanation:
The given points are (-1,0) and (3,0) to find an equation of parabola. Notice that they say or the given points are x-intercepts, which means they make it easier for us to find an equation of parabola using these x-intercepts.
Quick Note:
x-intercepts are simply the roots or solutions of quadratic equation, so if our root is x = -2 then we can write as (-2,0) and write back to x+2=0.So what we are going to do is to write the roots’ equation back as [tex]\displaystyle \large{x+\alpha =0}[/tex]
Our points or roots are given, therefore:
If x = -1 then x+1=0
If x = 3 then x-3=0
Then multiply x+1 with x-3 because if (x-1)(x+3)=0 then x-1=0 or x+3=0:
[tex]\displaystyle \large{(x+1)(x-3)=0}[/tex]
Convert 0 to y since we want to find a function:
[tex]\displaystyle \large{(x+1)(x-3)=y}\\\displaystyle \large{y=(x+1)(x-3)}[/tex]
Expand the expressions in and simplify to standard form:
[tex]\displaystyle \large{y=x^2-3x+x-3}\\\displaystyle \large{y=x^2-2x-3}[/tex]
Therefore, the equation is [tex]\displaystyle \large{y=x^2-2x-3}[/tex]
__________________________________________________________
Summary
If we are given the points [tex]\displaystyle \large{(\alpha ,0)}[/tex] and [tex]\displaystyle \large{(\beta ,0)}[/tex] with wideness of the graph or a-value = 1 then the parabola equation is:
[tex]\displaystyle \large{y=(x-\alpha )(x-\beta )}\\\displaystyle \large{y=x^2-\beta x-\alpha x+\alpha \beta }\\\displaystyle \large{y=x^2-(\beta +\alpha )x+\alpha \beta }[/tex]
__________________________________________________________
Others
If you have any doubts about my answer, explanation or this question, do not hesitate to let me know in the comment!
You use 4 gallons of water on 30 plants in your garden. At that rate, how much water
will it take to water 45 plants?
Answer:
6 gallons
Step-by-step explanation:
30-----------4
45------------x
30x = 45x4
30x=180
x=6
A shortcut:
45 is ( 30+ half of 30)
( 4 + half of 4) = 4+2 =6
6 gallons
Step-by-step explanation:[tex]Assuming\ that\ it\ will\ take\ x\ gallons\ waters[/tex]
[tex]to\ water\ 45\ plants.[/tex]
[tex]4:30=x:45[/tex]
[tex]30x=4\times 45[/tex]
[tex]30x=18[/tex]°
[tex]x=180\div 3\\ x=6[/tex]
[tex]\left\{If\right.\ a:b=c:d,\ then\ ad=\left.\ bc\right\}[/tex]
I hope this helps you
:)
4.5
3
5
х
Find the length of x
Lethna buys some boxes of pens and some packets of pencils.
There are 40 pens in each box. There are 12 pencils in each packet.
Lethna gives one pen and one pencil to each student in Year 7 of her school.
When she has done this she has no pens left and no pencils left.
Work out how many boxes of pens and how many packets of pencils Lethna could
have bought
Answer:
pen: 3 boxes [pencils : 10 packets
Step-by-step explanation:
40 and 12 4|40/10 12/3 4x3x10=120
pen 120 divided by 40 = 3 boxes
pencils 120 divided by 12 = 10 packets
Ron started the day with a score of +12.
He lost 4 points, gained 3 points, and then
lost 15 points. What was his score then?
+ 12 - 4 + 3 - 15
= 12 + 3 - 4 - 15
= 15 - 19
= - 4
Answer:
He has -4 points. if I'm not mistaken
Step-by-step explanation:
12 - 4 + 3 - 15 = -4
I apologize if I am incorrect
f(x)=−1/2(x−2)^2 −4 Graph it
Answer:
Step-by-step explanation:
Found this when searching on the internet. Hope it helps... Maybe???
Find the 78th term of the arithmetic sequence -4, -2, 0, ...−4,−2,0,...
Answer:
0
Step-by-step explanation:
-4, -2, 0
the 3rd number is always a 0 so if you do the sequence 78 times the 78th term will be a 0
What is the value of y?
у
60°
80°
Answer: 40
Step-by-step explanation:
The angles form a straight angle, so y = 180 - 80 - 60 = 40.
Gobe weighs 53.6 kg. he wears shoes which weigh 450 gm and carries a school bag weighing 4.5 kg. if he stands on the scales in his shoes and carrying the school bag. what weight will be recorded?
Answer:
58.55Kg
Step-by-step explanation:
450 in Kg is 0.45.
0.45 + 4.5 = 4.95. 4.95 + 53.6 = 58.55.
A two-sample t test of the hypothesis H0: mu1 - mu2 = 0 versus HA: mu1 - mu2 > 0 produces a p-value of 0.03. Which of the following must be true? I. A 90 percent confidence interval for the difference in means will contain the value 0. II. A 95 percent confidence interval for the difference in means will contain the value 0. III. A 99 percent confidence interval for the difference in means will contain the value 0.
Considering the p-value of of the test, it is found that the correct option is:
III. A 99 percent confidence interval for the difference in means will contain the value 0.
What is the p-value and the confidence interval?If the p-value is less than the [tex]\alpha[/tex] level, given by 1 subtracted by the confidence level, it does not contain the value tested at the null hypothesis.If it is more, it contains the value tested at the null hypothesis.In this problem, we have that the p-value is of 0.03, hence the confidence interval will contain the value of 0, tested at the null hypothesis, for confidence levels above 97%, hence option III is correct.
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