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3 years ago

I need help finding the answers someone plz help

Mathematics

1 answer:

Harlamova29_29 [7]3 years ago

8 0

Happy New Year from MrBillDoesMath!

Answer:

Proof by ASA congruence postulate. See below

Discussion:

Fact 1 : angle A = angle T (given)

Fact 2: The angles on both sides of point X are equal as vertical angles

are equal.

From these facts it follows that angle M = angle H (as all plane triangles have 180 degrees). Also AM = TH (given) so

In the left triangle In the right triangle

(angle M, side AM, angle A) = (angle H, side TH, angle T)

Hence the triangles have two congruent angles, and congruent sides included between the angles, so they are congruent by ASA.

Thank you,

MrB

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Show that cos(3x) = cos3(x) − 3 sin2(x)cos(x). (Hint: Use cos(2x) = cos2(x) − sin2(x) and the cosine sum

otez555 [7]

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

To prove:

$\cos 3x=\cos^3x-3\sin^2 x\cos x$

Identities used:

$\cos(A+B)=\cos A\cos B+\sin A\sin B$ ......(1)

$\sin 2A=2\sin A\cos A$ ........(2)

$\cos 2A=\cos^2A-\sin^2 A$ .......(3)

Taking the LHS:

$\Rightarrow \cos 3x=\cos (x+2x)$

Using identity 1:

$\Rightarrow \cos (x+2x)=\cos x\cos 2x-\sin x\sin 2x$

Using identities 2 and 3:

$\Rightarrow \cos x(\cos ^2x-\sin^2 x)-\sin x(2\sin x\cos x)\\\\\Rightarrow \cos^3x-\sin^2x\cos x-2\sin^2 x\cos x\\\\\Rightarrow \cos^3x-3\sin^2x\cos x$

As, LHS = RHS

Hence proved

4 0

3 years ago

A student solves the following equation and

Phoenix [80]

Answer:

Since the equation is undefined for -2

Therefore, NO SOLUTION for the given equation.

Step-by-step explanation:

Considering the expression

$\frac{3}{a+2}-6\cdot \frac{a}{-4+a^2}=\frac{1}{a-2}$

$\frac{3}{a+2}-\frac{6a}{-4+a^2}=\frac{1}{a-2}$

$\mathrm{Find\:Least\:Common\:Multiplier\:of\:}a+2,\:-4+a^2,\:a-2:\quad \left(a+2\right)\left(a-2\right)$

$\mathrm{Multiply\:by\:LCM=}\left(a+2\right)\left(a-2\right)$

$\frac{3}{a+2}\left(a+2\right)\left(a-2\right)-\frac{6a}{-4+a^2}\left(a+2\right)\left(a-2\right)=\frac{1}{a-2}\left(a+2\right)\left(a-2\right)$

$\frac{3}{a+2}\left(a+2\right)\left(a-2\right):\quad 3\left(a-2\right)$

$-\frac{6a}{-4+a^2}\left(a+2\right)\left(a-2\right):\quad -6a$

$\frac{1}{a-2}\left(a+2\right)\left(a-2\right):\quad a+2$

so equation becomes

$3\left(a-2\right)-6a=a+2$

$-3a-6=a+2$

$-3a-6+6=a+2+6$

$-4a=8$

$\mathrm{Divide\:both\:sides\:by\:}-4$

$\frac{-4a}{-4}=\frac{8}{-4}$

$a=-2$

$\mathrm{Verify\:Solutions}$

$\mathrm{Take\:the\:denominator\left(s\right)\:of\:}\frac{3}{a+2}-6\frac{a}{-4+a^2}-\frac{1}{a-2}\mathrm{\:and\:compare\:to\:zero}$

$\mathrm{Solve\:}\:a+2=0:\quad a=-2$

$\mathrm{Solve\:}\:-4+a^2=0:\quad a=2,\:a=-2$

$\mathrm{Solve\:}\:a-2=0:\quad a=2$

So the following points are undefined

$a=-2,\:a=2$

Since the equation is undefined for -2

Therefore, NO SOLUTION for the given equation.

4 0

3 years ago

The mean of 4 numbers is 21. calculate the sum of the 4 numbers

Ugo [173]

Answer:

Step-by-step explanation:

The mean is calculated as

mean = $\frac{sum}{count}$ , then

$\frac{sum}{4}$ = 21 ( multiply both sides by 4 )

sum = 84

8 0

3 years ago

A rectangle measures 4 1/2 inches by 2 3/4 inches, what is the area of the rectangle? Answer in fraction form.

makkiz [27]

12 and 3/8 or if you want it entirely in a fraction 99/8.

7 0

3 years ago

What is the LCD of 5/12 and -9/16 ?

Andreyy89

The least common denominator of 5/12 and -9/16

The answer is 48.

Now, we have to change the numerators also to make this a equal fraction to the first ones we had.

5*4 = 20
12*4 = 48

20/48

-9*3 = -27
16*3 = 48

-27/48

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4 years ago

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