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Please simplify, 50 points.<br><br> (sin Θ - cos Θ) - (sin Θ + cos Θ)^2

Amanda [17]

Answer:

Using x for Θ:

(sinx - cosx)^2 - (sinx + cosx)^2

= (sin^2 x - 2sinxcosx + cos^2 x) - (sin^2 x + 2sinxcosx + cos^2 x)

= - 2 sinx cosx - 2 sinx cosx

= - 4 sinx cosx

= - 2sin(2x)

Step-by-step explanation:

8 0

3 years ago

Write the equation for a horizontal line that passes through the point (-2,8)

Rudik [331]

Answer:

$y=8$

Step-by-step explanation:

we know that

A horizontal line is parallel to the x-axis

The slope of a horizontal line is equal to zero

The equation of a horizontal line is equal to the y-coordinate of the point that passes through it

The line passes through the point (-2,8)

so

The y-coordinate is 8

therefore

The equation is equal to

$y=8$

5 0

4 years ago

The lengths of the sides of a square are multiplied by 1.2. How is the ratio of the areas related to the ratio of the side lengt

bekas [8.4K]

(1.2)^3=1.73 (for cube with 1 unit length)

3 0

3 years ago

Abby's school is 6 blocks west of her house. Her mother works at a store that is 4 blocks east of her school. Use a number line

faltersainse [42]

Answer:

Step-by-step explanation:

Let us give a proper illustration in the number line

let H be Abby's house

and S be the school

let W be her mother's work.

kindly find attached a rough sketch of the number line for your reference

Question:<em> What value represents the difference in position between Abby's house and her mother's store?</em>

basically, the distance between two points on a number line is the difference between the points.

So the value that represents the position between Abby's house and her mother's store is the distance between the two points.

= 4-(-6)

=4+6

=10

7 0

3 years ago

One of the vertices of an equilateral triangle is on the vertex of a square and two other vertices are on the not adjacent sides

Elina [12.6K]

<h2>Answer:</h2>

<em> The side of the triangle is either 38.63ft or 10.35ft</em>

<h2>Step-by-step explanation:</h2>

This problem can be translated as an image as shown in the Figure below. We know that:

The side of the square is 10 ft.
One of the vertices of an equilateral triangle is on the vertex of a square.
Two other vertices are on the not adjacent sides of the same square.

Let's call:

Since the given triangle is equilateral, each side measures the same length. So:

x: The side of the equilateral triangle (Triangle 1)

y: A side of another triangle called Triangle 2.

That length is the hypotenuse of other triangle called Triangle 2. Therefore, by Pythagorean theorem:

$\mathbf{(1)} \ x^2=100+y^2$

We have another triangle, called Triangle 3, and given that the side of the square is 10ft, then it is true that:

$y+(10-y)=10$

Therefore, for Triangle 3, we have that by Pythagorean theorem:

$(10-y)^2+(10-y)^2=x^2 \\ \\ 2(10-y)^2=x^2 \\ \\ \\ \mathbf{(2)} \ x^2=2(10-y)^2$

Matching equations (1) and (2):

$2(10-y)^2=100+y^2 \\ \\ 2(100-20y+y^2)=100+y^2 \\ \\ 200-40y+2y^2=100+y^2 \\ \\ (2y^2-y^2)-40y+(200-100)=0 \\ \\ y^2-40y+100=0$

Using quadratic formula:

$y_{1,2}=\frac{-b \pm \sqrt{b^2-4ac}}{2a} \\ \\ y_{1,2}=\frac{-(-40) \pm \sqrt{(-40)^2-4(1)(100)}}{2(1)} \\ \\ \\ y_{1}=37.32 \\ \\ y_{2}=2.68$

Finding x from (1):

$x^2=100+y^2 \\ \\ x_{1}=\sqrt{100+37.32^2} \\ \\ x_{1}=38.63ft \\ \\ \\ x_{2}=\sqrt{100+2.68^2} \\ \\ x_{2}=10.35ft$

<em>Finally, the side of the triangle is either 38.63ft or 10.35ft</em>

5 0

4 years ago

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