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4 years ago

What is the solution to the division (You can use long division or synthetic division.) (4x2 + 5x - 6) / (x + 2)

Mathematics

1 answer:

miv72 [106K]4 years ago

3 0

Hello from MrBillDoesMath!

Answer:

4x - 3

Discussion:

Factor 4x^2+5x - 6 = (4 x - 3) (x + 2) => factor lhs

(4x2 + 5x - 6) / (x + 2) = (4x -3) (x + 2) / (x+2)

Cancel the common factor (x+2) to get

(4x2 + 5x - 6) / (x + 2) = 4x - 3

Thank you,

MrB

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The triangle is isosceles because the lengths of the two shorter legs are the same (2 meters). Use the Pythagorean Theorem to find the length of the hypotenuse of this triangle. (AB)^2 = (2 m)^2 + (2 m)^2, or 8 m^2. Thus, AB = sqrt(8 m^2), or 2sqrt(2). This AB is also the base of the triangle. What is the area of the triangle?

Next, noting that the diameter AB of the semicircle is 2sqrt(2) and the radius is just sqrt(2), find the area of the semicircle. The area of a circle of radius r
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4 years ago

6. 5li Rational numbers

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3 years ago

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Parameterize $S$ by

$\vec s(u,v)=x(u,v)\,\vec\imath+y(u,v)\,\vec\jmath+z(u,v)\,\vec k$

where

$\begin{cases}x(u,v)=u\cos v\\y(u,v)=u\sin v\\z(u,v)=(9-u^2)\end{cases}$

with $0\le u\le3$ and $0\le v\le2\pi$ .

Take the normal vector to $S$ to be

$\dfrac{\partial\vec s}{\partial u}\times\dfrac{\partial\vec s}{\partial v}=2u^2\cos v\,\vec\imath+2u^2\sin v\,\vec\jmath+u\,\vec k$

Then by Stokes' theorem we have

$\displaystyle\int_{\partial S}\vec F\cdot\mathrm d\vec r=\iint_S(\nabla\times\vec F)\cdot\mathrm d\vec S$

$=\displaystyle\int_0^{2\pi}\int_0^3(\nabla\times\vec F)(\vec s(u,v))\cdot\left(\dfrac{\partial\vec s}{\partial u}\times\dfrac{\partial\vec s}{\partial v}\right)\,\mathrm du\,\mathrm dv$

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which has a value of 0, since each component integral is 0:

$\displaystyle\int_0^{2\pi}\cos^3v\,\mathrm dv=0$

$\displaystyle\int_0^{2\pi}\sin v\cos^3v\,\mathrm dv=0$

$\displaystyle\int_0^{2\pi}\sin^3v\,\mathrm dv=0$

$\displaystyle\int_0^{2\pi}\cos v\sin^3v\,\mathrm dv=0$

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3 years ago

Rob's school is selling tickets to annual dance competition. On the first day of ticket sales the school sold 10 senior citizen

Inga [223]

Answer:

senior tickets are 12

student tickets are 3

Step-by-step explanation:

s= senior

t = student

10s+5t =135

14s + 3t=177

10s+5t =135

divide by 5

2s+t = 27

multiply by -3

-3(2s+t) = -3*27

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add this to 14s+3t=177

-6s -3t =-81

14s + 3t=177

---------------------

8s = 96

divide by 8

s = 12

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2s+t = 27

2(12) +t = 27

24 +t =27

subtract 24

24+t-24 = 27 -24

t =3

student tickets are 3

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4 years ago