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2 years ago

Expand and Simplify (2x + 1)(x - 2)(x + 3)

Mathematics

1 answer:

lesantik [10]2 years ago

5 0

Answer:

Answer is =2x^3+3x^2-11x-6

Step-by-step explanation:

First of all multiply first and second bracket.

=x(2x+1) -2(2x+1)

=2x^2+x-4x-2

=2x^2-3x-2

Now multiply 2x^2-3x-2 with (x+3)

=x(2x^2-3x-2) +3(2x^2-3x-2)

=2x^3-3x^2-2x+6x^2-9x-6

=2x^3+3x^2-11x-6

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Help pls asap!!!!! !!!!!

stiv31 [10]

Answer:

It is 40 degrees.

Step-by-step explanation:

You can start off by understanding this is not a right angle (exactly 90 degrees, think of a corner of a room) or and obtuse angle (more than 90 degrees, bigger than a right angle). With that information we know that it is an acute angle (less than 90 degrees, smaller than a right angle). With that we have 40 and 50 degrees left. When you compare the angle with the 40 degrees one, it is the same size. The angle 1 is a reflection of the triangle with the 40 degrees angle. Hope this helps :)

5 0

3 years ago

A store keeper buys a fishing rod for $20 and sells it for $5 more than he bought it for. express this profit or gain as a perce

nataly862011 [7]

25/20 × 100% = 125%

125% - 100% = 25%

25% profit :)

5 0

3 years ago

What is the product of x+2 and x-7? Write your answer in standard form.

Leto [7]

X^2-5x-14
It is the correct answer I think

5 0

3 years ago

A rug is to be centered in a room so that the border around it is of a consistent width on all four sides. If the room is 10 ft

aleksley [76]

Answer:

The width of the border can be 9 feet or 3.5 feet.

Step-by-step explanation:

Let the width be x

Length of room = 10 feet

Breadth of room = 15 feet

Length of rug = 10-2x

Breadth of rug = 15-2x

Area of rug = $(10-2x)(15-2x)$

We are given that the area of the rug is 24 square feet.

So, $(10-2x)(15-2x)=24$ ---A

$150-20x-30x+4x^2=24$

$150-24-50x+4x^2=0$

$126-50x+4x^2=0$

$2(x-9)(2x-7)=0$

$x=9,\frac{7}{2}$

$x=9,3.5$

Substitute x =9 in A

$(10-2(9))(15-2(9))=24$

$24=24$

LHS = RHS

Substitute x = 3.5

$(10-2(3.5))(15-2(3.5))=24$

$24=24$

LHS = RHS

So, The width of the border can be 9 feet or 3.5 feet.

7 0

3 years ago

Given that cot θ = 1/√5, what is the value of (sec²θ - cosec²θ)/(sec²θ + cosec²θ) ?

Bogdan [553]

Step-by-step explanation:

$\mathsf{Given :\;\dfrac{{sec}^2\theta - co{sec}^2\theta}{{sec}^2\theta + co{sec}^2\theta}}$

$\bigstar\;\;\textsf{We know that : \large\boxed{\mathsf{{sec}\theta = \dfrac{1}{cos\theta}}}}$

$\bigstar\;\;\textsf{We know that : \large\boxed{\mathsf{co{sec}\theta = \dfrac{1}{sin\theta}}}}$

$\mathsf{\implies \dfrac{\dfrac{1}{cos^2\theta} - \dfrac{1}{sin^2\theta}}{\dfrac{1}{cos^2\theta} + \dfrac{1}{sin^2\theta}}}$

$\mathsf{\implies \dfrac{\dfrac{sin^2\theta - cos^2\theta}{sin^2\theta.cos^2\theta}}{\dfrac{sin^2\theta + cos^2\theta}{sin^2\theta.cos^2\theta}}}$

$\mathsf{\implies \dfrac{sin^2\theta - cos^2\theta}{sin^2\theta + cos^2\theta}}$

Taking sin²θ common in both numerator & denominator, We get :

$\mathsf{\implies \dfrac{sin^2\theta\left(1 - \dfrac{cos^2\theta}{sin^2\theta}\right)}{sin^2\theta\left(1 + \dfrac{cos^2\theta}{sin^2\theta}\right)}}$