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]
Which ratio is equivalent to 1:3 and 12:36? (A) 2:18 (B) 4:9 (C) 4:12 (D) 6:6
Answer:
I think the right answer is c 4:12
Answer:
(C) - C for Correct!
Step-by-step explanation:
We can look at ratios as a fraction, so 1:3 = 1/3 and 12:36 = 12/36. We can simplify the second fraction into 12/36 = 1/3 by canceling 12 from the numerator and denomerator. We can do this with all of the answer choices:
(A) Wrong - 2/18 = 1/9
(B) Wrong - 4/9
(C) Correct - 4/12 = 1/3
(D) Wrong - 6/6 = 1
I hope this helps!!! :)
A farmer needs to pack 2,903 apples into crates to ship to supermarkets. Each crate can hold only 30 apples. How many crates does the farmer need to ship all of the apples? Explain your answer.
Answer:
97
Step-by-step explanation:
Afla suma a trei numere ,stiind ca primul este succesorul numarului 999 ,al doilea este cu 1.872 mai mare ,iar al treilea cat primele doua la un loc.
Answer:
7744
Step-by-step explanation:
Din informațiile furnizate:
Succesorul primului număr 999 = 1000
Al doilea este cu 1872 mai mare= 1872 + 1000 = 2872
Al treilea care sunt primele două împreună = 1000 + 2872 = 3872
∴
Suma celor trei numere = 1000 + 2872 + 3872
= 7744
Express the area of the entire rectangle.
Your answer should be a polynomial in standard form.
Answer:
x^2 + 11x + 24
Step-by-step explanation:
x^2 + 3x + 8x + 24 =
= x^2 + 11x + 24
A group of 8 students was asked, "How many hours did you watch television last week?" Here are their responses: 7, 14, 12, 13, 14, 6, 9, 16 Find the mean and median number of hours for these students. If necessary, round your answers to the nearest tenth.
Answer:
11.4- average
12.5 - median
Step-by-step explanation:
AVERAGE:
Add them up and divide by 8
MEDIAN:
1. Arrange the set from least to greatest.
6,7,9,12,13,14,14,16
2. Start from the first and last numbers and cross them out until you are left with the 2 in the middle. If there was an odd set of numbers, you would end up with one number.
7,9,12,13,14,14
9,12,13,14
12,13
3. Add the remaining two numbers and divide by 2.
12+13/2 = 12.5
Car x travels 162 miles in 3 hours: write an equation of the line that describes the relationship between distance and time. Use x for the time in hours and y for the distance in miles
Answer:
A:The equation y=54x describes the relationship
B: y as 216 and x being 4
If a car travels for 0 hours, it will travel 0 mile(s). This means it will pass through the point (0,0)
.Use the slope to move 3 units to the right of the origin and
162 unit(s) up to find the point
(3,162) that can be used to graph the relationship. Step-by-step explanation:
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!! :)
Answer:
36
Step-by-step explanation:
Since the 3 numbers have a ratio of 2:3:7, that means it simplifies to that. So, there must be a common factor, let’s say x, for each of the numbers. Thus, the numbers are 2x, 3x, and 7x. To find the mean, we add up all of the numbers and divide by the number of numbers: (2x + 3x + 7x)/3 = 12x/3 = 4x = 48. Dividing by 4 on both sides gets x = 12. The median of the numbers is the number in the middle which is 3x. Substituting x = 12, we get: 3(12) = 36.
I hope this helps!!! :)
What is the solution to the System of Equations graph below?
2
y = -3x + 2
0
0
3
6
-2-
v=x-6
(2, 4)
B (2,-4)
C (-4, 2)
D) (4,2)
Answer:
D?
Step-by-step explanation:
HELP PLEASE FAST ILL MARK BRAINLIEST IF CORRECT 20 points!!
Answer:
8.49
Step-by-step explanation:
6^2 + 6^2 = 72
√72 = 8.485... = 8.49
Pls helpooooooooo indeddhelpillgovebrqinlyidkwkek
Answer:
3-7×14 12946.-40
Step-by-step explanation:
mark me as brainliest
Find an equation of the parabola with vertex (2, -1) and directrix y=-7.
Answer:
the answer to this is y=7x-15
Please help guys!!!!!!
Answer:I think its 68
Step-by-step explanation:
Answer:
The measure of angle N is 68 degrees.
Step-by-step explanation:
Since this shape is a parallelogram, opposite angles will be equivalent. So to start, set (6x - 2) equal to (4x + 36).
— 6x - 2 = 4x + 36
Next, subtarct the 4x from both sides of the equation as well as add 2 to both sides of the equation an simplify.
— 6x - 4x - 2 + 2 = 4x - 4x + 36 + 2
— 2x = 38
Now, divide both sides of the equation by 2 to find the value of x.
— 2x/2 = 38/2
— x = 19
Finally, substitute 19 for every x in the original equation. Simplify.
— 6(19) - 2 = 4(19) + 36
— 114 - 2 = 76 + 36
— 112 = 112
We now know that these two angles are 112 degrees. If a parallelogram's angles must add up to 360 degrees, then subtract 112 twice from 360 to find the combined total angle measure of N and Q. Then divide that number by 2 to find the measure of N.
— 360 - 112 - 112 = 136
— 136/2 = 68
The measure of angle N is 68 degrees.
Find the area of the region under the graph of the function f on the interval [1, 8].
f(x) =3/x
square units
Answer:
[tex]\displaystyle \int\limits^8_1 {\frac{3}{x}} \, dx = 9 \ln 2[/tex]
General Formulas and Concepts:
Calculus
Integration
IntegralsIntegration Rule [Fundamental Theorem of Calculus 1]: [tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]
Integration Property [Multiplied Constant]: [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]
Area of a Region Formula: [tex]\displaystyle A = \int\limits^b_a {[f(x) - g(x)]} \, dx[/tex]
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle f(x) = \frac{3}{x} \\\left[ 1 ,\ 8 \right][/tex]
Step 2: Integrate
Substitute in variables [Area of a Region Formula]: [tex]\displaystyle \int\limits^8_1 {\frac{3}{x}} \, dx[/tex][Integral] Rewrite [Integration Property - Multiplied Constant]: [tex]\displaystyle 3 \int\limits^8_1 {\frac{1}{x}} \, dx[/tex][Integral] Logarithmic Integration: [tex]\displaystyle 3 \int\limits^8_1 {\frac{1}{x}} \, dx = 3 \ln \big| x \big| \bigg| \limits^8_1[/tex]Evaluate [Integration Rule - Fundamental Theorem of Calculus 1]: [tex]\displaystyle 3 \int\limits^8_1 {\frac{1}{x}} \, dx = 3 \ln 8[/tex]Simplify: [tex]\displaystyle \int\limits^8_1 {\frac{3}{x}} \, dx = 9 \ln 2[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Integration
1/9 x (1/2)^3 (solve please!)
9514 1404 393
Answer:
1/72
Step-by-step explanation:
[tex]\dfrac{1}{9}\times\left(\dfrac{1}{2}\right)^3=\dfrac{1}{9}\times\dfrac{1}{8}=\boxed{\dfrac{1}{72}}[/tex]
What is 3 3/8 divided by 9
Answer:
0.375
Step-by-step explanation:
Answer:
3/8
Reason:
I just did a question exactly like this, and this was the answer.
Jacob stated that he solved the equation 2x + 3 = 5 using the addition and multiplication property of equality. Which statement is true
Answer: First one
Step-by-step explanation:
PLEASE HELP 6TH GRADE
Can someone please help me I dont understand this at all i need help thank you
Answer:
See below
Step-by-step explanation:
The formula for the perimeter of a rectangle is 2(L+W).
We know the perimeter is 12, so we first need to divide.
12=2(L+W)
6=L+W
It's asking for possible value
so it can be anything
1+5
2+4
3+3
4+2
5+1
it's whatever adds up to 6
I'm actually not 100 percent sure...
Which set of ordered pairs is made up of points on the graph of the function below? y=2x+3
Factor the expression using the GFC 44-11
The set of integers greater than -1
Need help this is math keep in mind this is round your answer to the nearest 10
Answer:
The amount of acid in the solution will be: 55.4 millimeters
Step-by-step explanation:
The total amount of solution of acid and water = 342 milimeters
The percentage of acid included in the solution = 16.2%
The amount of acid in the solution:
[tex]16.2\%\:\times 342[/tex]
[tex]=\frac{16.2}{100}\times \:342[/tex]
[tex]=\frac{162}{1000}\times \:342[/tex]
[tex]=0.162\times \:342[/tex]
[tex]=55.4[/tex] millimeters
Thus, the amount of acid in the solution will be: 55.4 millimeters
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?
Answer:
its 547632
Step-by-step explanation:
cuz yeeeeeeeeee
10 ( y - 2)
what is the answer
Answer:
10y-20
Step-by-step explanation:
sorry if I am incorrect
What is the value of 3.5 (11) + 1.9 (11) + 1.6 (11)? 40 77 4,096 9,317
Answer:
77
it right on Edg......
Answer:
77
Step-by-step explanation:
got it right on edge
7
Complete the statement. Round to the nearest hundredth if necessary.
39 ft
yd
Answer:
1.7 mi
Step-by-step explanation:
Solve the equation - [tex]\frac{w}{5}[/tex] +9=13. What is w?
Answer:
w = -20
Step-by-step explanation:
-[tex]\frac{w}{5}[/tex] + 9 = 13
Shift the (+9) to the other side of the equation. (+9) will turn into (-9).
-[tex]\frac{w}{5}[/tex] = 13 - 9
= 4
Shift the (÷5) to the other side of the equation. (÷5) will turn into (×5).
-w = 4 × 5
= 20
Multiply both sides of the equation by (-1) so that -w will turn into w.
w = (-1) × 20
w = -20
how long will it take for 95% of a sample to decay
I searched up the entire problem. I solved it and got 129.7 seconds but I'm not sure it's right.
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!!!!!!!!
Nate's package is 8 kilograms. This is because, if there are 1,000 grams in 1 kilogram, 8,000/ 1,000= 8 Therefore, the mass of his package is 8 kilograms.
Have a Merry Christmas!