Solve the matrix equation X-A=B for X if a= [1 -4 -7 4 7 6] and b= [-9 4 8 2 5 2].
X=

[tex]\color{red} {{{\Large {\bf{To\:\:Simplify\::\frac{\sin ^4(x)-\cos ^4(x)}{\sin ^2(x)-\cos ^2(x)}}}}}}[/tex]

[tex]\color{green}{{{\large {\bf{Your\:\:Answer\::\frac{\sin ^4(x)-\cos ^4(x)}{\sin ^2(x)-\cos ^2(x)}=1}}}}}[/tex]

[tex]\color{yellow} {\Huge {\sf{Solution:}}}[/tex]

[tex]\color{blue} {\large {\bf{Factor\:\sin ^4(x)-\cos ^4(x)}}}[/tex]

[tex]\tt \color{blue} {\mathrm{Rewrite\:}\sin ^4(x)-\cos ^4(x)\mathrm{\:as\:}(\sin ^2(x))^2-(\cos ^2(x))^2=(\sin ^2(x))^2-(\cos ^2(x))^2}[/tex]

[tex]\color{fuchsia} {\normalsize {\mathrm{Apply\:exponent\:rule}:\quad \:a^{bc}=(a^b)^c}}[/tex]

[tex]\color{fuchsia} {\normalsize \sin ^4(x)=(\sin ^2(x))^2}[/tex]

[tex]\color{fuchsia} {\normalsize =(\sin ^2(x))^2-\cos ^4(x)}[/tex]=

[tex]\color{fuchsia} {\normalsize \mathrm{Apply\:exponent\:rule}:\quad \:a^{bc}=(a^b)^c}[/tex]

[tex]\color{fuchsia} {\normalsize \cos ^4(x)=(\cos ^2(x))^2}[/tex]

[tex]\color{fuchsia} {\normalsize =(\sin ^2(x))^2-(\cos ^2(x))^2}[/tex]=

[tex]\mathrm{Apply\:Difference\:of\:Two\:Squares\:Formula:\:}[/tex]x^2-y^2=(x+y)(x-y)

[tex](\sin ^2(x))^2-(\cos ^2(x))^2=(\sin ^2(x)+\cos ^2(x))(\sin ^2(x)-\cos ^2(x))[/tex]

=[tex](\sin ^2(x)+\cos ^2(x))(\sin ^2(x)-\cos ^2(x))[/tex]=

[tex]\color{blue} {\large {\bf{Factor\:\sin ^2(x)-\cos ^2(x)}}}[/tex]

[tex]\mathrm{Apply\:Difference\:of\:Two\:Squares\:Formula:\:}[/tex]x^2-y^2=(x+y)(x-y)

[tex]\sin ^2(x)-\cos ^2(x)=(\sin (x)+\cos (x))(\sin (x)-\cos (x))[/tex]

(x)=(sin(x)+cos(x))(sin(x)−cos(x))

=(\sin (x)+\cos (x))(\sin (x)-\cos (x))=(sin(x)+cos(x))(sin(x)−cos(x))

[tex]\large=(\sin ^2(x)+\cos ^2(x))(\sin (x)+\cos (x))(\sin (x)-\cos (x))

(x))(sin(x)+cos(x))(sin(x)−cos(x))

\large =\frac{(\sin ^2(x)+\cos ^2(x))(\sin (x)+\cos (x))(\sin (x)-\cos (x))}{\sin ^2(x)-\cos ^2(x)}[/tex]=

[tex]\mathrm{Apply\:Difference\:of\:Two\:Squares\:Formula:\:}[/tex]x^2-y^2=(x+y)(x-y)

[tex]\sin ^2(x)-\cos ^2(x)=(\sin (x)+\cos (x))(\sin (x)[/tex]

[tex] (x)=(sin(x)+cos(x))(sin(x)−cos(x))

=\frac{(\sin ^2(x)+\cos ^2(x))(\sin (x)+\cos (x))(\sin (x)-\cos (x))}{(\sin (x)+\cos (x))(\sin (x)-\cos (x))}[/tex]=

[tex]\mathrm{Cancel\:}\frac{(\sin ^2(x)+\cos ^2(x))(\sin (x)+\cos (x))(\sin (x)-\cos (x))}{(\sin (x)+\cos (x))(\sin (x)-\cos (x))}:\quad \sin ^2(x)+\cos ^2(x)Cancel

(sin(x)+cos(x))(sin(x)−cos(x))[/tex]

[tex]\mathrm{Cancel\:the\:common\:factor:}\:\sin (x)+\cos(x)Cancelthecommonfactor:sin(x)+cos(x)[/tex]

=[tex]\frac{(\sin ^2(x)+\cos ^2(x))(\sin (x)-\cos (x))}{\sin (x)-\cos (x)}[/tex]=

[tex]\mathrm{Cancel\:the\:common\:factor:}\:\sin (x)-\cos[/tex]

[tex]\mathrm{Use\:the\:following\:identity}:\quad \cos ^2(x)+\sin[/tex]

[tex]\huge \boxed{\color{red} {\ \huge =1}}[/tex]

A scientist teacher murdered $3980 worth of microscopes and dissension kits for the new science lab a total of 38 microscopes and 47 dissension kids were ordered a microscope cost four times as much as a Ascension kit write a system of linear equations that represents the situation what is the cost of each item

what is the equation of the line through (2,-1) and (0,5)
A. y= -3x + 5
B. y= 3x - 5
C. y= -3x - 5
D. y= 3x + 5

please please help me!

3) 15x + 4 = 106


Can someone show me the steps ? Pls :)

You eat 80% of your daily calories at breakfast. Does this statement make sense?

Given that f(x) = x2 + 4x – 21 and g(x) = x - 3, find f(x) · g(x) and
express the result in standard form.

PLEASE HELP 6TH GRADE

Which of the following scenarios is not proportional.
a. Getting paid hourly for babysitting.
b. selling lemonade for $1 per cup.
c. Paying $5 per ticket to a baseball game, plus a $7.50 online service fee.
d. Jogging at a rate of 10 minutes per mile.

Find an equation of the parabola with vertex (2, -1) and directrix y=-7.

10 ( y - 2)
what is the answer

Please help guys!!!!!!

Solve the equation - [tex]\frac{w}{5}[/tex] +9=13. What is w?

student 1 y=-3x+x student 2 y=7x/10 student 3 y=4(2-x) Which students write an equation of a nonlinear function?

100 points. Consider functions f and g ​

What is 3 3/8 divided by 9

What is the value of 4+ y if y = 18?

Which ratio is equivalent to 1:3 and 12:36? (A) 2:18 (B) 4:9 (C) 4:12 (D) 6:6

Help with this question please ASAP!! :)

I know the answer is 36 but I need to know the working out and I am unsure how to work the question out.

Plz explain

Thanks in advance!! :)

Combine like terms.
5x – (-10x) - 4 – (-7x) – 8

A curve is defined by parametric functions x (t) and y(t), where dx/dt= 3t^2 and dy/dx= t^7– 2t^4. For what positive value of t is d^2y/dx^2 =1
A
1.079
B
1.149
С
1.202
D
1.525

Write an recursive rule for the sequence 7,14,21,28

A company produces fruity drinks that contain a percentage of real fruit juice. Drink A contains 20% real fruit juice and Drink B contains 10% real fruit juice. How many liters of real fruit juice would be needed to produce 250 liters of Drink A and 150 liters of Drink B? How many liters of real fruit juice would be needed to produce aa liters of Drink A and bb liters of Drink B?

What is the midpoint of line segment
A (-3,-5)
B (1,-9)
‾
start overline, A, B, end overline?

There are 1,000 grams in 1 kilogram. Nate is mailing a package that has a mass of 8,000 grams.
He wants to know the mass of the package in kilograms.
1.000
8,000
12,000
grams
kilograms
0
1
12
Multiply or divide?
What is the unit rate. ?
I give brainless!!!!!!!!

HELP PLS
A) 16
B) -4
C) -16

The sum of 2 times p and 2 is 48. What is p?

sharice is putting jars of jam into boxes. she puts 8 jars into each box, and she has a total of 144 jars. sharice wants to know how many boxes she needs.

Given the function f(x) = x2-2, find the average rate of change over the interval -2 sxs 4​

11) (-x - 3) + (3x + 8)
i don’t understand these