under which of the following operations are the polynomials 3x+2 and 4y-11 not closed
Answers
A. subtraction:
(3x+2)-(4y-11)=3x+2-4y+11=3x-4y+13
similarly, (4y-11)-(3x+2)=-3x+4y-13
both are polynomials (of 2 variables)
B. (3x+2)(4y-11)=12xy-33x+8y-22, which is a polynomial
C. (3x+2)+(4y-11)=3x+2+4y-11=3x+4y-9, which is a polynomial
D.
both [tex] \frac{3x+2}{4y-11} [/tex] and [tex] \frac{4y-1}{3x+2} [/tex] are rational expressions in 2 variables, not polynomials
Answer: D
Related Questions
If (h, •) and (k, •) are subgroups of (g, •), prove that (h n k, •) is a subgroup of (g, •). can the same be said for the union, hu k? prove or give a counterexample.
Answers
[tex]\eta\in H\cap K\implies\begin{cases}\eta\in H\\\eta\in K\end{cases}\implies\eta\in G[/tex]
Because both [tex]H,K[/tex] are subgroups of [tex]G[/tex], then [tex](H\cap K,\bullet)[/tex] contains the identity element [tex]e[/tex]. Furthermore, there must be some element [tex]\eta^{-1}\in H[/tex] and [tex]\eta^{-1}\in K[/tex], i.e. [tex]\eta^{-1}\in H\cap K[/tex], such that [tex]\eta\bullet\eta^{-1}=e[/tex].
Now let [tex]\eta_1,\eta_2,\eta_3\in H\cap K[/tex]. By the same reasoning as above it follows that each of these belong in [tex]G[/tex], and since [tex](G,\bullet)[/tex] is a group, we have [tex]\eta_1\bullet(\eta_2\bullet\eta_3)=(\eta_1\bullet\eta_2)\bullet\eta_3[/tex], so [tex]H\cap K[/tex] is associative under [tex]\bullet[/tex].
So [tex]H\cap K[/tex] contains the identity, is closed with respect to inverses, and is associative under [tex]\bullet[/tex]. Therefore [tex]H\cap K[/tex] must be a subgroup of [tex]G[/tex].
In the case of union, this is not always the case. Consider the group [tex](\mathbb Z,+)[/tex] with subgroups [tex](H,+)[/tex] and [tex](K,+)[/tex] where [tex]H[/tex] is the set of all integer multiples of 2 and [tex]K[/tex] is the set of all integer multiples of 3.
It's easy to show that [tex]H[/tex] and [tex]K[/tex] are indeed subgroups, but this is not the case for [tex]H\cup K[/tex]. We have
[tex]H\cup K=\{0,\pm2,\pm4,\ldots\}\cup\{0,\pm3,\pm6,\ldots\}[/tex]
Take the elements [tex]2\in H[/tex] and [tex]3\in K[/tex]. Addition yields [tex]2+3=5[/tex], but [tex]5\not\in H\cup K[/tex], so [tex]H\cup K[/tex] is not closed under [tex]+[/tex].
Ohm’s Law states that the electrical current, I in amperes, through a resistor is given by the formula 644-14-04-00-00_files/i0210000.jpg where V is the voltage in volts and R is the resistance in ohms. If the current is 6 amperes and the resistance is 18 ohms, what is the voltage?
Answers
Your Answer is 108 volts
Answer:
The correct answer is D., or "108 volts".
How many minutes does it take an athlete to run a 10.0 kilometer race? assume the athlete's pace is 6.50 minutes per mile. (1 mi = 1.609 km)?
Answers
To find out how many minutes it takes an athlete to run a 10.0 kilometer race using a pace of 6.50 minutes per mile, we can set up a proportion and solve for x. The athlete takes approximately 40.33 minutes to run the race.
Explanation:To convert the athlete's pace from minutes per mile to minutes per kilometer, we will use the conversion factor 1 mile = 1.609 kilometers. Therefore, the athlete's pace is 6.50 minutes per 1.609 kilometers. To find out how many minutes it takes the athlete to run a 10.0 kilometer race, we can set up a proportion:
6.50 minutes / 1.609 kilometers = x minutes / 10.0 kilometers
Using cross multiplication, we can solve for x:
x = (6.50 minutes × 10.0 kilometers) / 1.609 kilometers
x = 40.33 minutes (rounded to two decimal places)
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For an analysis of variance, the term “one-way” refers to
Answers
Let c be the curve of intersection of the parabolic cylinder x2 = 2y, and the surface 3z = xy. find the exact length of c from the origin to the point 4, 8, 32 3 .
Answers
[tex]x^2=2y\implies t^2=2y\implies y=\dfrac{t^2}2[/tex]
[tex]3z=xy\implies3z=\dfrac{t^3}2\impiles z=\dfrac{t^3}6[/tex]
Then the length of the path is
[tex]\displaystyle\int_{t=0}^{t=4}\sqrt{\left(\frac{\mathrm dx}{\mathrm dt}\right)^2+\left(\frac{\mathrm dy}{\mathrm dt}\right)^2+\left(\frac{\mathrm dz}{\mathrm dt}\right)^2}\,\mathrm dt[/tex]
[tex]=\displaystyle\int_0^4\sqrt{1+t^2+\frac{t^4}4}\,\mathrm dt[/tex]
[tex]=\displaystyle\frac12\int_0^4\sqrt{4+4t^2+t^4}\,\mathrm dt[/tex]
[tex]=\displaystyle\frac12\int_0^4\sqrt{(t^2+2)^2}\,\mathrm dt[/tex]
[tex]=\displaystyle\frac12\int_0^4(t^2+2)\,\mathrm dt[/tex]
[tex]=\dfrac{44}3[/tex]
To find the exact length of the curve c from the origin to a given point, we can parameterize the curve and use the formula for arc length. In this case, we need to solve for x, y, and z in terms of a parameter t. Then, we can integrate the arc length formula to obtain the exact length.
Explanation:To find the exact length of the curve c from the origin to the point (4, 8, 32/3), we need to first parameterize the curve. Given that x2 = 2y and 3z = xy, we can solve for x, y, and z in terms of a parameter t. Then, we can use the formula for arc length to calculate the length of the curve using integration.
Let's begin by solving for x, y, and z in terms of t:
From x2 = 2y, we have x = √(2t) and y = t2/2.Substituting these values into 3z = xy, we get 3z = √(2t) * (t2/2) or z = (t3√2)/6.Now, we can calculate the arc length using the formula:
L = ∫ sqrt((dx/dt)2 + (dy/dt)2 + (dz/dt)2) dt
Plugging in the values of x, y, and z in terms of t, we can evaluate the integral to find the exact length of curve c.
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Solve the following inequality: 2(x + 1) – (–x + 5) ≤ –18. A. x ≤ –9 B. x ≤ –20 C. x ≤ –37 D. x ≤ –5
Answers
2x + 2 + x - 5 < = -18
3x - 3 < = -18
3x < = -18 + 3
3x < = -15
x < = -15/3
x < = - 5 <==
Answer:
Solve the following inequality: 2(x + 1) – (–x + 5) ≤ –18. A. x ≤ –9 B. x ≤ –20 C. x ≤ –37 D. x ≤ –5
Step-by-step explanation:
2 (x + 1) - (-x + 5) ≤ -18
2x + 2 + x - 5 ≤ - 18
3x - 3 ≤ - 18
3x ≤ - 15
x ≤ - 15/3 ≤ - 5
The answer is: D. x ≤ - 5
A given line has the equation 2x + 12y = −1.
What is the equation, in slope-intercept form, of the line that is perpendicular to the given line and passes through the point (0, 9)?
Answers
12y = -2x - 1
y = - 1/6x - 1/12...slope here is -1/6. A perpendicular line will have a negative reciprocal slope. All that means is flip the slope and change the sign. So our perpendicular line will need a slope of 6.
y = mx + b
slope(m) = 6
(0,9)...x = 0 and y = 9
sub and find b, the y int
9 = 6(0) + b
9 = b
so ur perpendicular equation is : y = 6x + 9 <==
Answer
the answer is d
Step-by-step explanation:
The infinite sequence –1, –2, –3, –4, –5, ... can be generated with which explicit formula?
Answers
Answer:
An = (-1)* n
Step-by-step explanation:
An = ( -1) * n
A2 = (-1 ) * 2 = -2
A3= ( -1 ) * 3 = -3
A4= ( -1 ) * 4 = -4
A5= ( -1 ) * 5 = -5
An explicit formula also known as an exact formula is a mathematical formula used to find the nth term in a series or sequence . hence the explicit formula used to find the nth term of this sequence can be represented as
An = ( -1 ) * n where n = number of the next term
Answer:
A
Step-by-step explanation:
i got it right
Complete the pattern ___, ___, ___, 0, 2, 4, 6
Answers
Answer:-6, -4, -2, 0, 2, 4, 6. They continue in increments of +2.
Step-by-step explanation:
If a new car is valued at $13,200 and 6 years later it is valued at $3000, then what is the average rate of change of its value during those six years?
Answers
A forest ranger can see for a distance of 12 miles from a firetower how many square miles can he observe?
Answers
using 3.14 for pi
area = pi x r^2
since he can see 12 miles in any direction 12 would be the radius
so 3.14 x 12^2 = 452.16 square miles
round the answer as needed.
Write out the form of the partial fraction decomposition of the function (see example). do not determine the numerical values of the coefficients. (a) x4 + 5 / x5 + 2x3
Answers
Paula has 3 bananas. She wants to divide each of them into sections. How many 's are there in 3 bananas?
Answers
Answer:
B IS 21
Step-by-step explanation:
Simplify: 4x^2+36/4x•1/5x
Answers
Answer:
Step-by-step explanation:
The given equation is:
[tex]\frac{4x^2+36}{4x}{\times}\frac{1}{5x}[/tex]
On solving the above equation, we get
=[tex]\frac{4x^2+36}{(4x)(5x)}[/tex]
=[tex]\frac{4(x^2+9)}{(4x)(5x)}[/tex]
=[tex]\frac{x^2+9}{(x)(5x)}[/tex]
=[tex]\frac{x^2+9}{(5x^2)}[/tex]
which is the required simplified form.
Thus, the simplified form of the given equation [tex]\frac{4x^2+36}{4x}{\times}\frac{1}{5x}[/tex] is [tex]\frac{x^2+9}{(5x^2)}[/tex].
A deposit of $1,295 at 7% for 180 days what is the interest earned
Answers
To find the simple interest on a deposit of $1,295 at a 7% rate for 180 days, we use the formula I = P × r × t. With 180 days being roughly 0.5 years, the interest earned is approximately $45.33.
Explanation:Calculating Simple Interest for a Deposit
To calculate the simple interest earned on a deposit, we can use the simple interest formula which is Interest (I) = Principal (P) × Rate (r) × Time (t).
In this case, a student wants to know the interest earned on a deposit of $1,295 at 7% for 180 days. Since simple interest is usually calculated on an annual basis, we need to adjust the time to reflect a portion of the year. 180 days is equivalent to ½ year (since 180/365 ≈ 0.493). Now we can plug in the values into the formula:
I = P × r × t
I = $1,295 × 0.07 × 0.5
So, the interest earned would be:
I = $1,295 × 0.07 × 0.5I = $45.325
The student will earn approximately $45.33 in interest (rounded to the nearest cent).
Which of the following is not one of the three ways to express a ratio A 3/4 B 3:4 C 3 of 4 D 3 to 4
Answers
For what values of b will f(x)= log b^x be an increasing function?
Answers
This is basically a line with slope [tex]log(b)[/tex]
For this to be an increasing function, the slope has to be greater than 0.
[tex]log(b) \ \textgreater \ 0\\ b \ \textgreater \ 10^0\\ b \ \textgreater \ 1[/tex]
So f(x) will be an increasing function for all b > 1
Using logarithmic function concepts, it is found that for values of b > 1, [tex]f(x) = \log_b{x}[/tex] will be an increasing function.
What is an logarithmic function?A logarithmic function is modeled by:
[tex]f(x) = \log_b{x}[/tex]
The coefficient b determines the behavior of the function, as follows:
b > 1: The function is increasing.b < 1: The function is decreasing.Hence, for values of b > 1, [tex]f(x) = \log_b{x}[/tex] will be an increasing function.
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A kitchen assistant knocked over a cooling rack and spilled 12% of the cookies onto the floor Francesca had
to bake 36 more cookies to replace them.
how many cookies were ordered in total
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How many degrees would the hour hand move in 4hrs?
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a complete circle is 360 degrees, there are 12 numbers on a clock
360/12 = 30 degrees between each number
30 * 4 = 120 degrees in 4 hours
In the figure below, segment AC is congruent to segment AB:
Triangle ABC with a segment joining vertex A to point D on side BC. Side AB is congruent to side AC
Which statement is used to prove that angle ABD is congruent to angle ACD?
Answers
the answer is A. segment AD bisects angle CAB. I just took the exam and I got it right. hope this helps!
Answer: Isosceles triangle theorem
Step-by-step explanation:
In the given picture, there a triangle whose two sides are equal AB=AC.
Therefore it is an isosceles triangle.
Now, the isosceles theorem says that the angles opposite to the equal sides of a triangle are equal.
Therefore by isosceles triangle theorem in ΔABC we have
[tex]\angle{B}=\angle{C}[/tex]
Since [tex]\angle{ACD}=\angle{C}[/tex] [Reflexive]
[tex]\angle{ABD}=\angle{B}[/tex] [Reflexive]
Therefore, [tex]\angle{ACD}=\angle{ABD}=[/tex]
Whats the quotient of 2 1/4 and 5/8
Answers
Evaluate the surface integral. ∫∫s (x2 + y2 + z2) ds s is the part of the cylinder x2 + y2 = 16 that lies between the planes z = 0 and z = 5, together with its top and bottom disks.
Answers
[tex]\mathbf r_1(u,v)=\begin{cases}x(u,v)=4\cos u\\y(u,v)=4\sin u\\z(u,v)=v\end{cases}[/tex]
where [tex]0\le u\le2\pi[/tex] and [tex]0\le v\le5[/tex],
[tex]\mathbf r_2(u,v)=\begin{cases}x(u,v)=u\cos v\\y(u,v)=u\sin v\\z(u,v)=0\end{cases}[/tex]
where [tex]0\le u\le4[/tex] and [tex]0\le v\le2\pi[/tex], and
[tex]\mathbf r_3(u,v)=\begin{cases}x(u,v)=u\cos v\\y(u,v)=u\sin v\\z(u,v)=5\end{cases}[/tex]
where [tex]0\le u\le4[/tex] and [tex]0\le v\le2\pi[/tex].
For the cylinder, we have
[tex]\dfrac{\partial\mathbf r_1}{\partial u}\times\dfrac{\partial\mathbf r_1}{\partial v}=\langle4\cos u,4\sin u,0\rangle\implies\left\|\dfrac{\partial\mathbf r_1}{\partial u}\times\dfrac{\partial\mathbf r_1}{\partial v}\right\|=4[/tex]
and the integral over this surface is
[tex]\displaystyle\iint_{\text{cyl}}(x^2+y^2+z^2)\,\mathrm dS=4\int_{v=0}^{v=5}\int_{u=0}^{u=2\pi}((4\cos u)^2+(4\sin u)^2+v^2)\,\mathrm du\,\mathrm dv[/tex]
[tex]=\displaystyle320\int_{u=0}^{u=2\pi}\mathrm du+8\pi\int_{v=0}^{v=5}v^2\,\mathrm dv[/tex]
[tex]=640\pi+\dfrac83\pi(125)[/tex]
[tex]=\dfrac{2920\pi}3[/tex]
Bottom disk:
[tex]\dfrac{\partial\mathbf r_2}{\partial u}\times\dfrac{\partial\mathbf r_2}{\partial v}=\langle0,0,u\rangle\implies\left\|\dfrac{\partial\mathbf r_2}{\partial u}\times\dfrac{\partial\mathbf r_2}{\partial v}\right\|=u[/tex]
and the integral over the bottom disk is
[tex]\displaystyle\iint_{z=0}(x^2+y^2+z^2)\,\mathrm dS=\int_{v=0}^{v=2\pi}\int_{u=0}^{u=4}u((u\cos v)^2+(u\sin v)^2)\,\mathrm du\,\mathrm dv[/tex]
[tex]=\displaystyle2\pi\int_{u=0}^{u=4}u^3\,\mathrm du[/tex]
[tex]=128\pi[/tex]
The setup for the integral along the top disk is similar to that for the bottom disk, except that [tex]z=5[/tex]:
[tex]\displaystyle\iint_{z=5}(x^2+y^2+z^2)\,\mathrm dS=\int_{v=0}^{v=2\pi}\int_{u=0}^{u=4}u((u\cos v)^2+(u\sin v)^2+5^2)\,\mathrm du\,\mathrm dv[/tex]
[tex]=\displaystyle2\pi\int_{u=0}^{u=4}(u^3+25u)\,\mathrm du[/tex]
[tex]=528\pi[/tex]
Finally, the value of the integral over the entire surface is the sum of the integrals over the component surfaces:
[tex]\displaystyle\iint_S(x^2+y^2+z^2)\,\mathrm dS=\frac{2920\pi}3+128\pi+528\pi=\dfrac{4888\pi}3[/tex]
Evaluate the given surface integral by parameterizing the surface and computing the integral on each surface separately. Take the antiderivatives of both dimensions defining the area, from the bounds of the integral for an accurate solution.
Explanation:The problem you've presented is a surface integral in the field of calculus, specifically relating to multivariable calculus. To solve this, we need to evaluate the integral over the specified parts of the cylinder and the top and bottom disks. We start by parameterizing the surface. Given that our cylinder is x² + y² = 16 between z = 0 and z = 5, we can use cylindrical coordinates with the parameterization: r(θ, z) = <4cos(θ), 4sin(θ), z> for 0 ≤ θ ≤ 2π and 0 ≤ z ≤ 5. With this parameterization, you can derive the equation for the surface integral and solve it.
When working with surface integrals, it's essential to remember that you are totaling up the quantity across the entire surface of an object. In such a situation, we could handle this problem by separating it into three parts: the side of the cylinder, the top disk, and the bottom disk, and compute the integral on each surface separately.
The integral can be solved by taking the antiderivatives of both dimensions defining the area, with the edges of the surface in question being the bounds of the integral. You can apply this approach to all the separate parts of this question.
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If sin θ = 2 over 7 and tan θ > 0, what is the value of cos θ?
Answers
[tex]\bf sin(\theta )=\cfrac{2}{7}\cfrac{\leftarrow opposite}{\leftarrow hypotenuse}\qquad \textit{let's find the adjacent side} \\\\\\ \textit{using the pythagorean theorem}\\\\ c^2=a^2+b^2\implies \pm\sqrt{c^2-b^2}=a\qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ \pm\sqrt{7^2-2^2}=a\implies \pm\sqrt{45}=a\implies \pm 3\sqrt{5}=a[/tex]
but.... which is it? the + or the -? well, we know that tan(θ) > 0, is another way to say that the tangent of the angle is positive, now, for the tangent to be positive, since it's opposite/adjacent both opposite and adjacent have to be the same exact sign, now, we know the opposite is +2, so that means the adjacent has to be the same sign, thus is the positive version 3√(5)
thus [tex]\bf cos(\theta)=\cfrac{adjacent}{hypotenuse}\qquad \qquad cos(\theta )=\cfrac{3\sqrt{5}}{7}[/tex]
A mountaineer climbed 1,000 feet at a rate of x feet per hour. He climbed an additional 5,000 feet at a different rate. This rate was 10 feet per hour less than twice the first rate. Which expression represents the number of hours the mountaineer climbed
Answers
Suppose v₁ is the mountaineer's velocity during the 1,000-foot trail. Then, v₂ is his speed for the 5,000-foot trail. The equation relating these two variables is:
v₂ = 2v₁ - 10 ---> equation 1
Then, you find the equation for the total number of hours he climbed. That would be the distance divided by their respective speed.
t = 1000/v₁ + 5000/v₂ ----> equation 2
Substituting equation 1 to equation 2,
t = 1000/v₁ + 5000/(2v₁ - 10)
t = 1000/v₁ + 5000/2(v₁-5)
t = 1,000/v₁ + 2,500/(v₁-5)
The equation that represents the number of hours the mountaineer climbed is t = 1000/V1 + 2600(V1 - 5).
How to compute the equation?Based on the information given, V1 = 1000 and V2 = 2V1 - 10.
The time taken will be:
= 1000/V1 + 5000/V2
Well substitute the equations. This will be:
t = 1000/V1 + 5000//(2V1 - 10)
t = 1000/V1 + 5000/2(V1 - 5)
t = 1000/V1 + 2600(V1 - 5).
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the oringinal cost of a lamp is $18.95. the lamp is on sale for 25% off. how much will you pay?
Answers
so, if 18.95 is the 100%, how much is the 75% of that?
[tex]\bf \begin{array}{ccllll} amount&\%\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 18.95&100\\ x&75 \end{array}\implies \cfrac{18.95}{x}=\cfrac{100}{75}[/tex]
solve for "x".
A population of flies grows according to the function p(x) = 2(4)x, where x is measured in weeks. A local spider has set up shop and consumes flies according to the function s(x) = 2x + 5. What is the population of flies after two weeks with the introduced spider?
Answers
now, after two weeks, x = 2
[tex]\bf P(x)-s(x)\implies 2(4)^2-[2(2)+5]\implies 32-9[/tex]
Answer:
answer is 23
Step-by-step explanation:
what is the equation to solve it
Answers
Please ask your question
Is 703.005 is greater than or less than seven hundred three and five hundredths
Answers
Given the Arithmetic sequence A1,A2,A3,A4A1,A2,A3,A4
29, 39, 49, 59
What is the value of A33A33?
Answers
a₁ = 29
a₂ = 39
a₃ = 49
a₄ = 59
This sequence is an arithmetic sequence. Th first term is a₁ = 29, and the common difference is d= 10.
The n-th term is
[tex]a_{n}=a_{1}+(n-1)d[/tex]
The 33-rd termis
a₃₃ = 29 + (33 - 1)*10
= 29 + 320
= 349
Answer: a₃₃ = 349
John has taken out a loan for college. He started paying off the loan with the first payment of $100. Each month he pays, he wants to pay back 1.1 times the amount he payed the month before. Explain to John how to represent his first 20 payments in sequence notation. Then explain how to find the sum of the first 20 payments using complete sentences.
Answers
month 1: $100
month 2: $100*(1.1)
month 3: $100*(1.1)²
month 4: $100*(1.1)³
...
The payments form the geometric sequence
a, ar, ar², ..., arⁿ
where
a = $100
r = 1.1
The sum of the first n terms is
[tex]S_{n} = \frac{a(1-r^{n})}{1-r} [/tex]
Therefore the sum of the first 20 payments is
S₂₀ = [$100(1 - 1.1²⁰)]/(1 - 1.1)
= $5727.50
John makes a total of $5727.50 in the first 20 payments.