Answer:
[tex]\cot(x)+\cot(\frac{\pi}{2}-x)[/tex]
[tex]\cot(x)+\tan(x)[/tex]
[tex]\frac{\cos(x)}{\sin(x)}+\frac{\sin(x)}{\cos(x)}[/tex]
[tex]\frac{1}{\sin(x)}(\cos(x)+\sin(x)\frac{\sin(x)}{\cos(x)})[/tex]
[tex]\csc(x)(\cos(x)+\sin(x)\frac{\sin(x)}{\cos(x)})[/tex]
[tex]\csc(x)[\frac{\cos(x)\cos(x)}{\cos(x)}+\sin(x)\frac{sin(x)}{\cos(x)}][/tex]
[tex]\csc(x)[\frac{\cos(x)\cos(x)+\sin(x)\sin(x)}{\cos(x)}][/tex]
[tex]\csc(x)[\frac{\cos^2(x)+\sin^2(x)}{\cos(x)}][/tex]
[tex]\csc(x)[\frac{1}{\cos(x)}][/tex]
[tex]\csc(x)[\sec(x)][/tex]
[tex]\csc(x)[\csc(\frac{\pi}{2}-x)][/tex]
[tex]\csc(x)\csc(\frac{\pi}{2}-x)[/tex]
Step-by-step explanation:
I'm going to use [tex]x[/tex] instead of [tex]\theta[/tex] because it is less characters for me to type.
I'm going to start with the left hand side and see if I can turn it into the right hand side.
[tex]\cot(x)+\cot(\frac{\pi}{2}-x)[/tex]
I'm going to use a cofunction identity for the 2nd term.
This is the identity: [tex]\tan(x)=\cot(\frac{\pi}{2}-x)[/tex] I'm going to use there.
[tex]\cot(x)+\tan(x)[/tex]
I'm going to rewrite this in terms of [tex]\sin(x)[/tex] and [tex]\cos(x)[/tex] because I prefer to work in those terms. My objective here is to some how write this sum as a product.
I'm going to first use these quotient identities: [tex]\frac{\cos(x)}{\sin(x)}=\cot(x)[/tex] and [tex]\frac{\sin(x)}{\cos(x)}=\tan(x)[/tex]
So we have:
[tex]\frac{\cos(x)}{\sin(x)}+\frac{\sin(x)}{\cos(x)}[/tex]
I'm going to factor out [tex]\frac{1}{\sin(x)}[/tex] because if I do that I will have the [tex]\csc(x)[/tex] factor I see on the right by the reciprocal identity:
[tex]\csc(x)=\frac{1}{\sin(x)}[/tex]
[tex]\frac{1}{\sin(x)}(\cos(x)+\sin(x)\frac{\sin(x)}{\cos(x)})[/tex]
[tex]\csc(x)(\cos(x)+\sin(x)\frac{\sin(x)}{\cos(x)})[/tex]
Now I need to somehow show right right factor of this is equal to the right factor of the right hand side.
That is, I need to show [tex]\cos(x)+\sin(x)\frac{\sin(x)}{\cos(x)}[/tex] is equal to [tex]\csc(\frac{\pi}{2}-x)[/tex].
So since I want one term I'm going to write as a single fraction first:
[tex]\cos(x)+\sin(x)\frac{\sin(x)}{\cos(x)}[/tex]
Find a common denominator which is [tex]\cos(x)[/tex]:
[tex]\frac{\cos(x)\cos(x)}{\cos(x)}+\sin(x)\frac{sin(x)}{\cos(x)}[/tex]
[tex]\frac{\cos(x)\cos(x)+\sin(x)\sin(x)}{\cos(x)}[/tex]
[tex]\frac{\cos^2(x)+\sin^2(x)}{\cos(x)}[/tex]
By the Pythagorean Identity [tex]\cos^2(x)+\sin^2(x)=1[/tex] I can rewrite the top as 1:
[tex]\frac{1}{\cos(x)}[/tex]
By the quotient identity [tex]\sec(x)=\frac{1}{\cos(x)}[/tex], I can rewrite this as:
[tex]\sec(x)[/tex]
By the cofunction identity [tex]\sec(x)=\csc(x)=(\frac{\pi}{2}-x)[/tex], we have the second factor of the right hand side:
[tex]\csc(\frac{\pi}{2}-x)[/tex]
Let's just do it all together without all the words now:
[tex]\cot(x)+\cot(\frac{\pi}{2}-x)[/tex]
[tex]\cot(x)+\tan(x)[/tex]
[tex]\frac{\cos(x)}{\sin(x)}+\frac{\sin(x)}{\cos(x)}[/tex]
[tex]\frac{1}{\sin(x)}(\cos(x)+\sin(x)\frac{\sin(x)}{\cos(x)})[/tex]
[tex]\csc(x)(\cos(x)+\sin(x)\frac{\sin(x)}{\cos(x)})[/tex]
[tex]\csc(x)[\frac{\cos(x)\cos(x)}{\cos(x)}+\sin(x)\frac{sin(x)}{\cos(x)}][/tex]
[tex]\csc(x)[\frac{\cos(x)\cos(x)+\sin(x)\sin(x)}{\cos(x)}][/tex]
[tex]\csc(x)[\frac{\cos^2(x)+\sin^2(x)}{\cos(x)}][/tex]
[tex]\csc(x)[\frac{1}{\cos(x)}][/tex]
[tex]\csc(x)[\sec(x)][/tex]
[tex]\csc(x)[\csc(\frac{\pi}{2}-x)][/tex]
[tex]\csc(x)\csc(\frac{\pi}{2}-x)[/tex]
8x−20
Apply the distributive property to factor out the greatest common factor.
Answer: 4(2x - 5)
Step-by-step explanation:
factors of 8 : (2, 2), 2
20 : (2, 2), 5
Therefore the GCF is 2*2 = 4
8x/4 = 2x and -20/4 = -5
4(2x - 5) = 8x - 20
URGENT !!!!!!!!! Please answer correctly !!!!! Will be marking Brianliest !!!!!!!!!!!!!!!!
It’s due in an hour please help
Find the value of x.
Answer:
10
Step-by-step explanation:
7x+5 = 9x -15
5 = 2x -15
2x = 20
x = 10
-12x + 4y- 6y + 10x - 25 5x - 2(x - 12)
Answer:
=−259x−2y+24
Step-by-step explanation:
Distribute:
=−12x+4y+−6y+10x+−255x+(−2)(x)+(−2)(−12)
=−12x+4y+−6y+10x+−255x+−2x+24
Combine Like Terms:
=−12x+4y+−6y+10x+−255x+−2x+24
=(−12x+10x+−255x+−2x)+(4y+−6y)+(24)
=−259x+−2y+24
Answer:
=−259x−2y+24
Hope this helps emmy! or emma
(sorry I like calling you emmy)
If x = 8 units, y = 3 units, and h = 1 unit, then what is the area of the parallelogram shown above?
Answer:
8unit²
Step-by-step explanation:
The Area of a parallelogram :
Length of base * height
Length of base, x = 8 units
Height, h = 1 unit
Area = Length of base * height
Area = 8 units * 1 unit
Area = 8unit²
Hi can someone help me with my math homework? I just need help with number c.
Answer:
Check pdf
Step-by-step explanation:
Answer:
11/4 pints
Step-by-step explanation:
3¹/² pints of blueberries is equal to 7/2 pints
she ate 3/4pints
7/2is equal to 14/4 because we need same denominator
now we subtract
14/4-3/4
=11/4 pints is left
will mark brainliest and rate 5/5
Answer:
C.) 10,240 cubic feet
Step-by-step explanation:
We have to first find the area of the base by multiplying 32 by 32. 32 * 32 is equal to 1024. Next, we multiply by the height divided by 3. 30/3 is equal to 10, so the total volume is equal to 1024 * 10, which is 10240.
1. x-y=1
x+y=-5
2. x-4y=10
2x+y=2
3. -5x+y=0
x+y=6
4. y=6-2x
y=4
5. 2y=16
4x-y= 4
6. x=y -4
3x+y=12
7. y- 2x=-6
5x-y= 9
8. 3y+x= 2
y-x=-6
Answer:
what is the question write it in thecomments and ill answer
Answer:
1.) (y+1)+y=-5
2y=-6
y=-3
x+(-3)=-5
x=-2
plug in to check if it works
2.) 2(4y+10)+y=2
9y+20=2
9y=-18
y=-2
x-4(-2)=10
x+8=10
x=2
3.) -5(-y+6)+y=0
5y-30=0
5y=30
y=6
x+(6)=6
x=0
4.) 4=6-2x
-2=2x
x=-1
y=6-2(-1)
y=8
5.) 4x-(8)=4
4x=12
x=3
4(3)-y=4
12-y=4
-y=-8
y=8
6.) 3(y-4)+y=12
4y-12=12
4y=24
y=6
x=6-4
x=2
7.) 5x-2x-6=9
3x=15
x=5
5(5)-y=9
25-y=9
-y=-16
y=16
8.)3(x-6)+x=2
4x-18=2
4x=20
x=5
y-5=-6
y=-1
hope this helped :)) also make sure to plug the x and y back into both equations :))
Help please I do not get this problem at all
Answer:
It should be 4. The ratio that AC is equal to DE at should be equal to the ratio of BE to BC. If you want an explanation I'd be happy to add one!
Please help me out!
Evaluate 3 x 2÷4y
Step-by-step explanation:
3 x 2÷4y
3/2y
hope it helps ☺️
NEED TO TURN IN NOW PLEASE HELP ME
Help ASAP!!! Question in pic! Will give brainliest!
Answer:
It is 15.
Step-by-step explanation:
We know the common difference is 2 right?
7
9
11
13
15
Those are 5 times, so its 15.
(Can I get Brainliest)
Answer:
15Step-by-step explanation:
because the common difference is 2, it would look like this: 7,9,11,13,15
Two similar rectangles are shown. Which statement is true? A) The area of rectangle B is 1 3 the area of rectangle A. B) The area of rectangle B is 1 9 the area of rectangle A. C) The area of rectangle B is nine times the area of rectangle A. Eliminate D) The area of rectangle B is three times the area of rectangle A
Answer:
I think it is 19 I not really sure
Step-by-step explanation:
o work it out of my paper and I got 19
Answer: The answer to this math question about finding the statement is very true about 2 similar rectangles are being shown here below is B). B) The area of rectangle B is [tex]\frac{1}{9}[/tex] of the area of rectangle A.
Step-by-step explanation: I'm very sorry about that, but I don't have any step-by-step explanation to this math question about finding the statement is very true about 2 similar rectangles are shown here below, so anyways, I hope that my full short given answer without my given step-by-step explanation to your own math question about finding the statement is very true about 2 similar rectangles are being shown here below, please mark me as Brainliest, take care, always be safe, and have a great rest of the day and good night! :D
Sincerely,
Jason Ta,
The Ambitious of The Brainly And The Role of The TDSB And WHCI Student of The High School.
omg guys imagine sneezing all day and then next thing hourssss later boom you lost your voice has that ever happened to you
Answer:
no lol
Step-by-step explanation:
9. What is the inverse of y = 10x -2?
Answer:
f(x)^-1=x-2/10
Step-by-step explanation:
Surface area question:
Answer:
190π (not part of the answer choices)
Step-by-step explanation:
The surface area of a cylinder can be found using the formula below:
[tex]SA=2\pi r^2+\pi dh[/tex] where [tex]r[/tex] is the radius of the base, [tex]d[/tex] is the diameter of the base and [tex]h[/tex] is the height of the cylinder.
Plug in the given values
[tex]SA=2\pi (\frac{10}{2}) ^2+\pi (10)(14)\\SA=2\pi (\frac{100}{4})+140\pi\\SA=2\pi (25)+140\pi\\SA=50\pi+140\pi\\SA=190\pi[/tex]
Therefore, although this answer isn't one of the choices, the surface area of the cylinder is 190π.
I hope this helps!
1. Find the slope and the y-intercept
of the graph of the linear equation.
y = -7x + 2
A) slope: -3; y-intercept: 2
1
B) slope: 2; y-intercept: -7
C) slope: -7; y-intercept: 2
D) slope: 2; y-intercept: -7
Answer:
c) slope: -7 ; y-intercept: 2
Step-by-step explanation:
Note the slope intercept form:
y = mx + b
y = (x , y)
m = slope
x = (x , y)
b = y-intercept
Note in this case:
y = (-7)x + 2
y = y
m = -7
x = x
b = 2
c) slope: -7 ; y-intercept: 2 is your answer.
~
Find the area of the blue shaded figure.
25 mm
120 mm
I’m begging atp. Please help me
area of blue shaded figure = area of big circle minus small circle
radius of big circle = 60mm
area of big circle= πr² = check pic
PLEASE HELP I DONT UNDERSTAND
Answer:
112
Step-by-step explanation:
Divide 1111 By 999 and you get 1.1121121121121
So 112 is repeating over and over in the decimal.
112 is repeated 4 times and starts to repeat again.
Hope that helps!
What is the value of X
Answer:
11=x
Step-by-step explanation:
since the lines are parallel the distances between each section of line is proportional to each other.
5/6=(x-1)/12
multiply both sides by 12
12(5/6)=(x-1)12/12
10=(x-1)
add 1 to both sides
10+1=x-1+1
11=x
I hope that helps :)
URGENT !!!!!!!!! Please answer correctly !!!!! Will be marking Brianliest !!!!!!!!!!!!!!!!
Answer:
slope is 15/5=3
Step-by-step explanation:
Question 6
Find the slope of the line that passes through the pair of points.
(-3, 2), (7, 2)
Answer:
Slope = 0
Step-by-step explanation:
Given the pair of points: (-3,2) (7,2)
Slope formula: y2-y1/x2-x1
2-2/7-(-3) = 0/10
0/10 = 0
Sketch a graph of the function y = (x + 6)(x- 4)
Step-by-step explanation:
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helllp i really need helpp i hate math
Answer:
C) 10.92
Step-by-step explanation:
A= 1/2bh
A = 1/2(2.8)(7.8)
A= 1/2(21.84)
A = 10.92
Answer:
C. 10.92^2
Step-by-step explanation:
Area of triangles can be solved using: 1/2*b*h
1/2*2.8*7.8=10.92
some one help me with this the highlighted one is the problem
What is the value of x?
Answer:
B
Step-by-step explanation:
Since UV is a tangent then ∠ WUV = 90°
WZ = WU = x - 1 ( both radii of the circle ) , then
WV = x - 1 + 2 = x + 1
Using Pythagoras' identity in the right triangle
WU² + UV² = WV² , that is
(x - 1)² + (2x - 4)² = (x + 1)² ← expand factors using FOIL
x² - 2x + 1 + 4x² - 16x + 16 = x² + 2x + 1
5x² - 18x + 17 = x² + 2x + 1 ← subtract x² + 2x + 1 from both sides
4x² - 20x + 16 = 0 ← divide through by 4
x² - 5x + 4 = 0
(x - 1)(x - 4) = 0 ← in factored form
Equate each factor to zero and solve for x
x - 1 = 0 ⇒ x = 1
x - 4 = 0 ⇒ x = 4
But x ≠ 1 as radius x - 1 = 0
Thus x = 4 → B
HELP!!!
...................
Answer:
Step-by-step explanation:
b
6x - 2x = 16 + 8
4x = 24
x = 6
2
12p^7
I need help on how to get the answer too number 27.
Help me please this is my homework question
512 c2 so A sorry if im wrong
Answer:
384
Step-by-step explanation:
So there are 6 faces in a cube so first you need to know how big is one face then just multiply by 6 for all 6 faces. so 8*8 = 64. that means 64 is the area of one face.
then multiply that by 6 to get the total surface area.
there it is your answer 384 the 3rd option there