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3 years ago

(a – b)2 = (a – b)(a – b) = a2 – 2ab + b2

Mathematics

2 answers:

Anni [7]3 years ago

6 0

Answer:

Step-by-step explanation:

satela [25.4K]3 years ago

5 0

It’s k+15 when u division

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Verify the identity

Igoryamba

Answer:

We have to prove

sin⁡(α+β)-sin⁡(α-β)=2 cos⁡ α sin ⁡β

We will take the left hand side to prove it equal to right hand side

So,

=sin⁡(α+β)-sin⁡(α-β) Eqn 1

We will use the following identities:

sin⁡(α+β)=sin⁡ α cos⁡ β+cos⁡ α sin⁡ β

and

sin⁡(α-β)=sin⁡ α cos ⁡β-cos ⁡α sin ⁡β

Putting the identities in eqn 1

=sin⁡(α+β)-sin⁡(α-β)

=[ sin⁡ α cos ⁡β+cos⁡ α sin⁡ β ]-[sin⁡ α cos ⁡β-cos ⁡α sin ⁡β ]

=sin⁡ α cos⁡ β+cos⁡ α sin ⁡β- sin⁡α cos⁡ β+cos ⁡α sin ⁡β

sin⁡α cos⁡β will be cancelled.

=cos⁡ α sin ⁡β+ cos ⁡α sin ⁡β

=2 cos⁡ α sin ⁡β

Hence,

sin⁡(α+β)-sin⁡(α-β)=2 cos ⁡α sin ⁡β

8 0

3 years ago

Identify the interval on which the quadratic function is positive.

Alenkasestr [34]

Answer:

$\textsf{1. \quad Solution: $1 < x < 4$,\quad Interval notation: $(1, 4)$}$

$\textsf{2. \quad Solution: $-2 < x < 4$,\quad Interval notation: $(-2, 4)$}$

Step-by-step explanation:

<h3>Question 1</h3>

The intervals on which a quadratic function is positive are those intervals where the function is above the x-axis, i.e. where y > 0.

The zeros of the quadratic function are the points at which the parabola crosses the x-axis.

As the given quadratic function has a negative leading coefficient, the parabola opens downwards. Therefore, the interval on which y > 0 is between the zeros.

To find the zeros of the given quadratic function, substitute y = 0 and factor:

$\begin{aligned}y&= 0\\\implies -7x^2+35x-28& = 0\\-7(x^2-5x+4)& = 0\\x^2-5x+4& = 0\\x^2-x-4x+4& = 0\\x(x-1)-4(x-1)&= 0\\(x-1)(x-4)& = 0\end{aligned}$

Apply the zero-product property:

$\implies x-1=0 \implies x=1$

$\implies x-4=0 \implies x=4$

Therefore, the interval on which the function is positive is:

Solution: 1 < x < 4
Interval notation: (1, 4)

<h3>Question 2</h3>

The intervals on which a quadratic function is negative are those intervals where the function is below the x-axis, i.e. where y < 0.

The zeros of the quadratic function are the points at which the parabola crosses the x-axis.

As the given quadratic function has a positive leading coefficient, the parabola opens upwards. Therefore, the interval on which y < 0 is between the zeros.

To find the zeros of the given quadratic function, substitute y = 0 and factor:

$\begin{aligned}y&= 0\\\implies 2x^2-4x-16& = 0\\2(x^2-2x-8)& = 0\\x^2-2x-8& = 0\\x^2-4x+2-8& = 0\\x(x-4)+2(x-4)&= 0\\(x+2)(x-4)& = 0\end{aligned}$

Apply the zero-product property:

$\implies x+2=0 \implies x=-2$

$\implies x-4=0 \implies x=4$

Therefore, the interval on which the function is negative is:

Solution: -2 < x < 4
Interval notation: (-2, 4)

3 0

1 year ago

I dont understand this!

DaniilM [7]

Answer:perimeter

Step-by-step explanation:20+20+4=44 and u multiply 3/5x times 2 it equals 6/10x+44

4 0

3 years ago

How to solve 2d-e=7 d+e=5

loris [4]

2d – e = 7 
d + e = 5 

3d=12 

d=4

8 0

4 years ago

zoey made 5 1/2 cups of trail mix for a camping trip. she wants to divide the trail mix into 3/4 cup servings. ten people are go

Andreas93 [3]

A.) Number of 3/4 cup servings in 5 1/2 cups = 5 1/2 / 3/4 = 11/2 / 3/4 = 11/2 x 4/3 = 44/6 = 7 1/3
Therefore, Zoey did not make enough 3/4 cup serving to go round everybody.

b.) For, every one to have a serving, we have 5 1/2 cups which we want to go round ten people, so each person should get 5 1/2 / 10 = 11/2 / 10 = 11/2 x 1/10 = 11/20.
So the serving should be 11/20 cup for every one to get serving.

c.) If she uses the 3/4 cup serving, then she will need 3/4 x 10 = 30/4 = 7 1/2 cups altogether.
Therefore, she will need to make extra 7 1/2 - 5 1/2 = 2 cups of trail mix.

6 0

4 years ago

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