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3 years ago

Simplify (1 - sin x)(1 + sin x). 0 1 O cos^2 x O sin^2 x O tan^2 x

Mathematics

1 answer:

V125BC [204]3 years ago

5 0

This would be cos^2x, because when you foil out the equation you get 1-sin^2(x).

1-sin^2(x)=cos^2(x)

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Y=-1/3x^2-4x-5 in vertex form

grigory [225]

Answer:

$Y=-\frac{1}{3}(x+6)^2+7$ [Vertex form]

Step-by-step explanation:

Given function:

$Y=-\frac{1}{3}x^2-4x-5$

We need to find the vertex form which is.,

$y=a(x-h)^2+k$

where $(h,k)$ represents the co-ordinates of vertex.

We apply completing square method to do so.

We have

$Y=-\frac{1}{3}x^2-4x-5$

First of all we make sure that the leading co-efficient is =1.

In order to make the leading co-efficient is =1, we multiply each term with -3.

$-3\times Y=-3\times\frac{1}{3}x^2-(-3)\times4x-(-3)\times 5$

$-3Y=x^2+12x+15$

Isolating $x^2$ and $x$ terms on one side.

Subtracting both sides by 15.

$-3Y-15=x^2+12x-15-15$

$-3Y-15=x^2+12x$

In order to make the right side a perfect square trinomial, we will take half of the co-efficient of $x$ term, square it and add it both sides side.

square of half of the co-efficient of $x$ term = $(\frac{1}{2}\times 12)^2=(6)^2=36$

Adding 36 to both sides.

$-3Y-15+36=x^2+12x+36$

$-3Y+21=x^2+12x+36$

Since $x^2+12x+36$ is a perfect square of $(x+6)$ , so, we can write as:

$-3Y+21=(x+6)^2$

Subtracting 21 to both sides:

$-3Y+21-21=(x+6)^2-21$

$-3Y=(x+6)^2-21$

Dividing both sides by -3.

$\frac{-3Y}{-3}=\frac{(x+6)^2}{-3}-\frac{21}{-3}$

$Y=-\frac{1}{3}(x+6)^2+7$ [Vertex form]

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3 years ago

After creating a hypothesis, Janis decides how to best measure the impact of her manipulation. This variable that is impacted by

Alexandra [31]

Answer:

This variable that is impacted by manipulating the independent variable is known as dependent variable

Step-by-step explanation:

One of the methods to test a hypothesis is the use of independent variable. The independent variable is manipulated to know if the change will be effective or not.

The variable which will be impacted by the independent variable is called dependent variable. The researcher manipulated the values for independent variable to check if the dependent variable changes or not ..

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2 years ago

If it's $8 for four bottles how much is each bottle?

cluponka [151]

Hi there! $8 per 4 bottles means price/# of bottles will give you the average price per bottle.

8/4=$2

Therefore it is $2 for 1 bottle.

Hope this helps!

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2 years ago

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WITCHER [35]

Sorry, what exactly is the question?

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