Answer: (x2 - x - 1) • (2x + 1)
Step-by-step explanation:
((2x3 - x2) - 3x) - 1
STEP
2
:
Checking for a perfect cube
2.1 2x3-x2-3x-1 is not a perfect cube
Trying to factor by pulling out :
2.2 Factoring: 2x3-x2-3x-1
Thoughtfully split the expression at hand into groups, each group having two terms :
Group 1: -3x-1
Group 2: 2x3-x2
Pull out from each group separately :
Group 1: (3x+1) • (-1)
Group 2: (2x-1) • (x2)
Bad news !! Factoring by pulling out fails :
The groups have no common factor and can not be added up to form a multiplication.
Polynomial Roots Calculator :
2.3 Find roots (zeroes) of : F(x) = 2x3-x2-3x-1
Polynomial Roots Calculator is a set of methods aimed at finding values of x for which F(x)=0
Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers x which can be expressed as the quotient of two integers
The Rational Root Theorem states that if a polynomial zeroes for a rational number P/Q then P is a factor of the Trailing Constant and Q is a factor of the Leading Coefficient
In this case, the Leading Coefficient is 2 and the Trailing Constant is -1.
The factor(s) are:
of the Leading Coefficient : 1,2
of the Trailing Constant : 1
Let us test ....
P Q P/Q F(P/Q) Divisor
-1 1 -1.00 -1.00
-1 2 -0.50 0.00 2x+1
1 1 1.00 -3.00
1 2 0.50 -2.50
The Factor Theorem states that if P/Q is root of a polynomial then this polynomial can be divided by q*x-p Note that q and p originate from P/Q reduced to its lowest terms
In our case this means that
2x3-x2-3x-1
can be divided with 2x+1
Polynomial Long Division :
2.4 Polynomial Long Division
Dividing : 2x3-x2-3x-1
("Dividend")
By : 2x+1 ("Divisor")
dividend 2x3 - x2 - 3x - 1
- divisor * x2 2x3 + x2
remainder - 2x2 - 3x - 1
- divisor * -x1 - 2x2 - x
remainder - 2x - 1
- divisor * -x0 - 2x - 1
remainder 0
Quotient : x2-x-1 Remainder: 0
Trying to factor by splitting the middle term
2.5 Factoring x2-x-1
The first term is, x2 its coefficient is 1 .
The middle term is, -x its coefficient is -1 .
The last term, "the constant", is -1
Step-1 : Multiply the coefficient of the first term by the constant 1 • -1 = -1
Step-2 : Find two factors of -1 whose sum equals the coefficient of the middle term, which is -1 .
-1 + 1 = 0
Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored
Final result :
(x2 - x - 1) • (2x + 1)
Which points on this vertical number line best represent the locations of 2.5 and
A: G and J
B: G and K
C: H and I
D: H and J
Use Lagrange multipliers to find the maximum and minimum values of subject to the given constraint. Also, find the points at which these extreme values occur.
f(x, y) xy: 48x+3y2 3456
Enter your answers for the points in order of increasing x-value.
Maximum______
Minimum_______
Answer:
Following are the responses to the given question:
Step-by-step explanation:
Given:
[tex]\to f(x,y)=xy\\\\\to 48x^2+3y^2=3456\\\\[/tex]
let [tex]\phi(x,y)=48x^2+3y^2=3456[/tex]
using the lagrange multiplies:
[tex]\bigtriangledown f=\lambda \bigtriangledown \phi\\\\i)\ \ y=96 \lambda x \to \lambda=\frac{y}{96\ x} \\\\ii)\ \ x=6 \lambda y \to \lambda=\frac{y}{6\ y} \\\\iii)\ \ 48x^2+3y^2=3456\\\\[/tex]
From equation (i) and (ii)\\\\
[tex]\to \frac{y}{96x}=\frac{x}{6y}\\\\\to 6y^2=96x^2\\\\\to 3y^2=48x^2\\\\[/tex]
From equation 3:
[tex]48x^2+48x^2=3456\\\\96x^2 3456\\\\x^2=36\\\\x=\pm 6\\\\\therefore 3y^2=48(36)\\\\3y^2=1728\\\\y^2=576\\\\y=\pm24\\\\(x,y)=(\pm 6,\pm 24)\\\\Maximum \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 144 \ \ \ \ at \ \ (6,24) \ \ \ \ \ \ \ and \ \ \ \ \ \ (-6, -24) \\\\Minimum \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ -144 \ \ \ \ at \ \ (-6,24) \ \ \ \ \ \ \ and \ \ \ \ \ \ (6,-24)\\\\[/tex]
Can someone help me? I’ll reward points + brainalist (btw only need help with number 5)
Answer:
A. 55°
hope it can help you
What is the answer to
8/12 = ?/3
Answer:
2/3 is the answer.
Its divided by 4...
Hope it helps!!!
Answer:
2/3(Bolded number is the answer)
Step-by-step explanation:
8/12(divide by 4)
?/3
So, you get 2 as 8 divided by 4 is 2.
Which of the following is a unit rate?
55 miles / 2 hours
2 pounds per 32 ounces
6 miles per minute
21 days in 3 weeks
Answer:
Lets be honest we all come to this website just to get answers but the answer would be either C or A
Step-by-step explanation:
Solve this for me (geometry) ? It asks if it’s yes or no.
Answer:
Yes, it is
Step-by-step explanation:
Given
The attached image
Required
Is AB a tangent to the circle
From the attached circle, we can see that AP is the radius of the circle P.
And by definition, a tangent touches the circle at only one point.
Since AB touches the circle at only point A, then AB is a tangent.
Can anyone help me with my homework
Answer:
A.
1) No
2)yes
3)yes
4)yes
5) it's not a function
Which of the following would be a correct interpretation of a 99% confidence interval such as 4.15.6? Choose the correct answer below. A. We are 99% confident that the interval from 4.1 to 5.6 actually does contain the true value of . B. It means that 99% of sample means fall between 4.1 and 5.6. C. It means that 99% of all data values are between 4.1 and 5.6. D. There is a 99% chance that will fall between 4.1 and 5.6.
Answer:
A. We are 99% confident that the interval from 4.1 to 5.6 actually does contain the true value of population mean.
Step-by-step explanation:
x% confidence interval:
A confidence interval is built from a sample, has bounds a and b, and has a confidence level of x%. It means that we are x% confident that the population mean is between a and b.
In this question:
99% confidence interval means that we are 99% sure that this interval contains the population mean.
Interval between 4.1 and 5.6.
So the correct answer is given by option A.
How many miles are in 506,880 inches?
Explain a method you could use to find 50% out of $24.
Answer:
$12
Step-by-step explanation:
50% means half of something. Like 50% of 20 is 10. 100% means the whole number. So, 50% is half of the number.
24 divided by 2 is 12.
Hope this helps !!
f(x)=-x^2+x-5
What are the coordinates of the vertex of the parabola of the function ?
Answer: I took a screen shot of it hope it helps
Step-by-step explanation:
Shim bougth a pair of shoes fo $600.If she got a discount of 30% ,home much did she paid for the shoes?
Answer:
she paid 420 dollars for it
Step-by-step explanation:
30 percent of 600 is 180
For questions 3 that’s all i need help please !!! For a test and please put your answers below !!!
Answer:
D) 1078
Step-by-step explanation:
If a circle has a circumference of 8.5 cm, what is the diameter of the circle to the nearest 0.1 cm?
Answer:
Step-by-step explanation:
2[tex]\pi[/tex]r = circumference
2[tex]\pi[/tex]r = 8.5 cm
[tex]\pi[/tex]r = 4.25 cm
r = 1.352817 cm
d = 2r
d= 2.705
diameter = 2.7 cm
The tuft bind strength of a synthetic material used to make carpets is known to have a mean of 100 lb and standard deviation of 20 lb. A sample of 40 is randomly selected and the average strength was found as 105lb. Let μ denote the average tuft strength. Could it be that the average tuft strength is above 100 lb? Based on the information, what should be the appropriate null and alternative hypotheses for the purpose of your analysis?
Answer:
The null hypothesis is: [tex]H_{0}: \mu = 100[/tex]
The alternative hypothesis is: [tex]H_{a}: \mu > 100[/tex]
Step-by-step explanation:
At the null hypothesis, we test if the mean is equal to a certain value.
At the alternate hypothesis, we test if the mean is less than, more than, or different from the value tested at the null hypothesis.
The tuft bind strength of a synthetic material used to make carpets is known to have a mean of 100 lb and standard deviation of 20 lb.
This means that the null hypothesis is: [tex]H_{0}: \mu = 100[/tex]
Could it be that the average tuft strength is above 100 lb?
The world above means that the appropriate alternative hypothesis is: [tex]H_{a}: \mu > 100[/tex]
I’m not sure how I do this. Plz help me
Answer:
y = 3/4x - 2
Step-by-step explanation:
Given:
m = 3/4
b = -2
y = mx + b
m = slope
b = y-intercept
y = 3/4x - 2
find the solution of the system of equations
Answer:
( -2 , 1 )
Step-by-step explanation:
••••••••
sorry no explanation for today
Which equation is NOT equivalent to p – 7 = 22? Select all that apply.
A. p – p – 7 = 22 – p
B. p – 7 – p = 22 – p
C. p – 7 + 22 = 22 – 7
D. p – 7 + 7 = 22 – 22
E. p – 7 + 7 = 22 + 7
Answer:
C. p - 7 + 22 = 22 - 7
D. p - 7 + 7 = 22 - 22
Step-by-step explanation:
p - 7 = 22
Add 7 to both sides
p = 29
An equivalent equation could be;
-7 = 22 - p
Find a formula for a geometric sequence that begins with 11, -33, 99
Answer:
17
Step-by-step explanation:
if c and d vary inversely, and d=5/3 and c=5. write a function that models inverse variation and find d when c=10
Answer:
xy = k
solve for k...
(8) * (8/3) = (64/3) = k
y = k / x
when x = 4,
y = (64/3) * (1/4) = (16/3)
Step-by-step explanation:i g o o g l e it
The circumference of a circle is 7π m. What is the area, in square meters? Express your answer in terms of π.
Answer:
12.25π m²
Step-by-step explanation:
Circumference = Diameter x pi
Area = radius squared (^2) x pi
7 divided by 2 = 3.5
3.5^2 = 12.25
12.25π
Answer:
A ≈ 3.9
Step-by-step explanation:
How to solve
Using the formulasA=πr2
C=2πr
Solving for AA=C2
4π = 72
4·π ≈ 3.8993
Therefore, the circle in square meters in the nearest tenths is A ≈ 3.9
A rectangular print on the Smiths living room wall is 4 feet long and 2 feet 6 inches wide. How many inches longer is the print than it is wide?
Answer:
The print is 18 inches longer then it is wide
Step-by-step explanation:
I multiplied 12 x 4 becuase there are 12 inches in a foot to get 48 inches. So the print is 48 inches long. Then I multiplied 2 times 12 to get 24 and then 24+6 + 30 so the rug is 30 inches wide. Finally I subtracted 30 from 48 to get the diffrence in inches. Which is 18 :)
Factor out the greatest common factor
15x^2-21x
^=exponent
Answer:
3x
Step-by-step explanation:
3x(5x-7)
brainliest!
A function y(t) satisfies the differential equation dy dt = y4 − 10y3 + 24y2. (a) What are the constant solutions of the equation? (Enter your answers as a comma-separated list.) y = (b) For what values of y is y increasing? (Enter your answer in interval notation.) y (c) For what values of y is y decreasing? (Enter your answer in interval notation.) y
Answer:
[tex](a)\ y =0\ or\ y=4\ or\ y=6[/tex]
[tex](b) \ (-\infty,4)\ u\ (6,\infty)[/tex]
[tex](c)\ (4,6)[/tex]
Step-by-step explanation:
Given
[tex]\frac{dy}{dt} = y^4 - 10y^3 + 24y^2[/tex]
Solving (a): The constants
This implies that:
[tex]\frac{dy}{dt} = 0[/tex]
So, we have:
[tex]y^4 - 10y^3 + 24y^2 = 0[/tex]
Factorize:
[tex]y^2(y^2 - 10y + 24) = 0[/tex]
Expand and Factorize the expression in bracket
[tex]y^2(y^2 - 6y - 4y + 24) = 0[/tex]
[tex]y^2(y(y - 6) - 4(y - 6)) = 0[/tex]
[tex]y^2(y - 4)(y - 6) = 0[/tex]
Split
[tex]y^2 =0\ or\ y-4=0\ or\ y-6=0[/tex]
Solve for y
[tex]y =0\ or\ y=4\ or\ y=6[/tex]
The above represents the constants
Solving (b): Increasing values
Here
[tex]\frac{dy}{dx} > 0[/tex]
Follow the same process in (a) but replace all = with >
i.e.
[tex]y^2(y - 4)(y - 6) > 0[/tex]
[tex]y >0\ or\ y>4\ or\ y>6[/tex]
Test the values of each inequality
For [tex]y > 6[/tex]; say [tex]y = 7[/tex]
[tex]\frac{dy}{dt} = y^4 - 10y^3 + 24y^2[/tex]
[tex]\frac{dy}{dt} = 7^4 - 10*7^3 + 24*7^2[/tex]
[tex]\frac{dy}{dt} = 147[/tex]
[tex]147 > 0[/tex]
This is true for [tex]\frac{dy}{dx} > 0[/tex]; This implies that: [tex](6, \infty)[/tex]
For [tex]y > 4[/tex] Say [tex]y = 5[/tex]
[tex]\frac{dy}{dt} = y^4 - 10y^3 + 24y^2[/tex]
[tex]\frac{dy}{dt} = 5^4 - 10*5^3 + 24*5^2[/tex]
[tex]\frac{dy}{dt} = -25[/tex]
This is false:
Say [tex]y = 3[/tex] i.e. [tex]y < 4[/tex]
[tex]\frac{dy}{dt} = y^4 - 10y^3 + 24y^2[/tex]
[tex]\frac{dy}{dt} = 3^4 - 10*3^3 + 24*3^2[/tex]
[tex]\frac{dy}{dt} = 27[/tex]
[tex]27 > 0[/tex]
This is true for [tex]\frac{dy}{dx} > 0[/tex]. This implies that: [tex](0,4)[/tex]
For [tex]y > 0[/tex]
[tex]y > 0[/tex] implies that: [tex]y < 4[/tex]
For [tex]y < 0[/tex] say [tex]y = -1[/tex]
[tex]\frac{dy}{dt} = y^4 - 10y^3 + 24y^2[/tex]
[tex]\frac{dy}{dt} = (-1)^4 - 10*(-1)^3 + 24*(-1)^2[/tex]
[tex]\frac{dy}{dt} = 35[/tex]
This is true for [tex]\frac{dy}{dx} > 0[/tex]. This implies that [tex](-\infty, 0)[/tex]
We have: [tex](-\infty,0), (0,4)\ and\ (6,\infty)[/tex]
[tex](-\infty,0)\ and\ (0,4)[/tex] can be combined to give: [tex](-\infty,4)[/tex]
So, the interval is: [tex](-\infty,4)\ u\ (6,\infty)[/tex]
Solving (c): Decreasing values
Here
[tex]\frac{dy}{dx} < 0[/tex]
i.e.
[tex]y^2(y - 4)(y - 6) < 0[/tex]
[tex]y <0\ or\ y<4\ or\ y<6[/tex]
Test the values of each inequality
For [tex]y < 6[/tex]; say [tex]y = 5[/tex]
[tex]\frac{dy}{dt} = y^4 - 10y^3 + 24y^2[/tex]
[tex]\frac{dy}{dt} = 5^4 - 10*5^3 + 24*5^2[/tex]
[tex]\frac{dy}{dt} = -25[/tex]
This is true for [tex]\frac{dy}{dx} < 0[/tex]; This implies that: [tex](\infty,6)[/tex]
For [tex]y < 4[/tex]; say [tex]y = 3[/tex]
[tex]\frac{dy}{dt} = y^4 - 10y^3 + 24y^2[/tex]
[tex]\frac{dy}{dt} = 3^4 - 10*3^3 + 24*3^2[/tex]
[tex]\frac{dy}{dt} = 27[/tex]
This is false
Say [tex]y = 5[/tex] i.e. [tex]y > 4[/tex]
This is the same as: [tex]y < 6[/tex]
So, we have the interval to be: [tex](4,\infty)[/tex]
For [tex]y < 0[/tex] say [tex]y = -1[/tex]
[tex]\frac{dy}{dt} = y^4 - 10y^3 + 24y^2[/tex]
[tex]\frac{dy}{dt} = (-1)^4 - 10*(-1)^3 + 24*(-1)^2[/tex]
[tex]\frac{dy}{dt} = 35[/tex]
This is false
Say [tex]y = 2[/tex] i.e [tex]y > 0[/tex]
[tex]\frac{dy}{dt} = y^4 - 10y^3 + 24y^2[/tex]
[tex]\frac{dy}{dt} = 2^4 - 10*2^3 + 24*2^2[/tex]
[tex]\frac{dy}{dt} = 32[/tex]
This is also false
So, the intervals are: [tex](4,\infty)[/tex] and [tex](\infty,6)[/tex].
This can be merged as: [tex](4,6)[/tex]
Hence, the interval for [tex]\frac{dy}{dt} < 0[/tex] is [tex](4,6)[/tex]
bruce’s sock drawer contains 9 black socks, 4 white socks, and 12 Brown socks. Express shoes is a sock at random, what is the probability that he will choose a sock that is not brown.
A. 16/25
B. 13/25
C. 12/25
D. 9/25
Answer:
hdhdjidnd rkdb akkabdbnfjbf
dhideijd
eeijberb
Answer: I think its C (12/25) I'm not completely sure though.
Step-by-step explanation:
PLSSSSSSSSSSSSSSSSSSSSSS HELPPPPPPPPPPPPPPPPPPPPPPPPPPPP
Answer:
17925
Step-by-step explanation:
3(1/4)=3.25
simple interest formula:
PV(1+it)=FV
we will divide the 72 months to convert it into years
72/12=6
15000(1+.0325*6)=17925
Answer:
$17,295 will be in his account after 72 months.
Step-by-step explanation:
G.$17295
1 pts
Your school is having a drawing to give away two prizes to students with
perfect attendance. There are ten total students with perfect attendance in
the drawing and you and your best friend are two of those ten. What is the
probability that you and your friend would win the two prizes that your
school is giving away?
Answer:
20% im guessing bc they are out of ten people
The verticals of ABC are A (-3,4), B (-2,4) and C(-4,2). ABC is reflected across the y-axis and then reflected across the x-axis to produce the image A”B”C. Graph ABC and A”B”C.
WHICH GRAPH SHOWS ABC AND A”B”C
Answer:
A
Step-by-step explanation:
Evaluate the expression if b = -2/3 and c = 1/2.
2bc + 3b^2
Answer:
2/3
Step-by-step explanation:
2 (−2/3) (1/2) + 3 (−2/3)^2
= −4/3 (1/2) + 3 (−2/3)^2
= −2/3 + 3 (−2/3)^2
= −2/3 + 3 (4/9)
= −2/3 + 4/3
= 2/3
Gillian has completed 25% of a bicycle race. If the length of the race is 32 km, how many has she traveled so far?
800
80
8
8000
NO LINKS
Answer:
8 km
Step-by-step explanation:
0.25 x 32 = 8
