Mathematics High School

tan(x+pi/2)= negative cot x

Answers

Answer 1
I'm only going to alter the left hand side. The right side will stay the same the entire time

I'll use the identity tan(x) = sin(x)/cos(x) and cot(x) = cos(x)/sin(x)
I'll also use sin(x+y) = sin(x)cos(y)+cos(x)sin(y) and cos(x+y) = cos(x)cos(y)-sin(x)sin(y)

So with that in mind, this is how the steps would look:

tan(x+pi/2) = -cot x
sin(x+pi/2)/cos(x+pi/2) = -cot x
(sin(x)cos(pi/2)+cos(x)sin(pi/2))/(cos(x)cos(pi/2)-sin(x)sin(pi/2)) = -cot x
(sin(x)*0+cos(x)*1)/(cos(x)*0-sin(x)*1) = -cot x
(0+cos(x))/(-sin(x)-0) = -cot x
(cos(x))/(-sin(x)) = -cot x
-cot x = -cot x

Identity is confirmed

Related Questions

solve the system by either elimination or substitution
3x-5y=21
2x+y=1
A.2,-3
B.2,3
C.-2,-1
D.-2,1
My guess is c

Answers

The correct answer is A: x=2 and y=-3. Either method would work, but for example, let's use elimination. If you multiply the second equation by 5, you get: 10x +5y = 5. When you add both equations, you can then cross out both y terms. You are left with one equation that reads: 13x=26. Solving for x gives you 2. You can substitute 2 in for x in either equation and you will receive -3 for your y value.

Which shows one way to determine the factors of x3 – 9x2 + 5x – 45 by grouping?

Answers

Factoring by grouping usually pairs up the first 2 sets of expressions with the second 2 sets.  Ours looks like this, then:  [tex](x^3-9x^2)+(5x-45)=0[/tex].  If we factor out the common x-squared in the first set of parenthesis, along with factoring out the common 5 in the second set, we get this:  [tex]x^2(x-9)+5(x-9)[/tex].  Now the common expression that can be factored out is the (x-9).  When we do that, here's what it looks like:  [tex](x-9)(x^2+5)[/tex].  I'm not sure how far you are going with this.  You could set each of those equal to 0 and solve for x in each case.  The first one is easy.  If x - 9 = 0, then x = 9.  The second one involves the imaginary i since x^2 = -5.  In that case,  [tex]x=i \sqrt{5},-i \sqrt{5} [/tex].  Hopefully, in what I have given you, you can find what you're looking for.

Answer:

x(x2 + 5) – 9(x2 + 5)

Step-by-step explanation:

Please help I don’t understand it

Answers

c= number of crickets
g= number of grasshoppers= twice number of crickets= 2c
T= total number of both= 561

If you add the number of crickets and the number if grasshoppers, you'll get a total of 561.

c + g= T
c + g= 561

Now we also know that grasshoppers are 2c (twice the crickets). Substitute 2c for g in the equation to solve for c.

c + g= 561
c + 2c= 561
combine like terms
3c= 561
divide both sides by 3
c= 187 crickets

Substitute number of crickets back in equation to find g.

c + g= 561
187 + g= 561
subtract 187 from both sides
g= 374 grasshoppers

CHECK:
Since grasshoppers are twice the number of crickets, then multiplying the number of crickets by two should equal the number of grasshoppers.
187 * 2= 374
374= 374

ANSWER: 187 crickets and 374 grasshoppers

Hope this helps! :)

Triangle ABC has vertices at A(4, 7) , B(13, 7) , and C(9, 11) .

Triangle FGH has vertices at F(1, 1) , G(10, 1) , and H(6, 5) .

Which sequence of transformations shows that triangle ABC and triangle FGH are congruent?

Select each correct answer.




A Translate ​ triangle FGH ​ down 6 units, and then translate ​ triangle FGH ​ left 3 units. ​

B Translate ​ triangle FGH ​ up 6 units, and then translate ​ triangle FGH ​ right 3 units. ​

C Translate ​ triangle ABC ​ up 6 units, and then translate ​ triangle ABC ​ right 3 units.

D Translate ​ triangle ABC ​ down 6 units, and then translate ​ triangle ABC left 3 units.
The coordinates of the vertices of triangle XYZ are given in the table.

X Y Z
(0, −6) (−10, 4) (3, −1)


Triangle XYZ is reflected across the y-axis.

What are the vertices of triangle X′Y′Z′ ?



Enter your answers in the boxes.



X′ : (
, ​
​)

Y′ : (
, ​
​)

Z′ : (
, ​
​)



The coordinates of the vertices of triangle XYZ are given in the table.

X Y Z
(0, −6) (−10, 4) (3, −1)


Triangle XYZ is reflected across the y-axis.

What are the vertices of triangle X′Y′Z′ ?



Enter your answers in the boxes.



X′ : (
, ​
​)

Y′ : (
, ​
​)

Z′ : (
, ​
​) The coordinates of the vertices of triangle XYZ are given in the table.

X Y Z
(0, −6) (−10, 4) (3, −1)


Triangle XYZ is reflected across the y-axis.

What are the vertices of triangle X′Y′Z′ ?



Enter your answers in the boxes.



X′ : (
, ​
​)

Y′ : (
, ​
​)

Z′ : (
, ​
​)



































































Answers

1) F - A = (1, 1) -(4, 7) = (-3, -6). Triangle FGH has been translated left 3 and down 6, corresponding to selection D.

2) Reflecting (x, y) across the y-axis changes it to (-x, y).
.. X' = (0, -6) . . . . . the point maps to itself. It is on the line of reflection.
.. Y' = (10, 4)
.. Z' = (-3, -1)

The real part of the complex number –5 + 3i is

Answers

A complex number is a number of the form a + bi, where i = and a and b are real numbers. For example, 5 + 3i, - + 4i, 4.2 - 12i, and - - i are all complex numbers. a is called the real part of the complex number and bi is called the imaginary part of the complex number.

Real part of the complex number [tex]-5 + 3i[/tex] is -5.

What is complex number?

" Complex numbers are such numbers which expressed in form of [tex]a+ i b[/tex], where 'a' represents the real part and b represents the imaginary part containing [tex]i[/tex] . Value of [tex]i = \sqrt{-1}[/tex]."

According to the question,

Given complex number,

 

 [tex]-5 + 3i[/tex]

Compare it with general form of complex number [tex]a+ i b[/tex] we get,

Real value of( [tex]-5+ 3i[/tex])  = -5

Imaginary value of [tex]-5+ 3i[/tex] = 3

Hence, real part of the complex number [tex]-5 + 3i[/tex] is -5.

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If the discriminant of a quadratic equation is greater than zero, which of the following is true of the equation?

A. It has two complex solutions.
B. It has one real solution.
C. It has two real solutions.

Answers

C. It has two real solutions. The discriminant in solving a quadratic equation is b^2-4ac. If this is greater than zero it has two real solutions.

21/80 as a percentage

Answers

21/80 = 0.2625

To get a percentage from a decimal, move the decimal point to the right 2 place values

0.2625 becomes 26.25%

26.25% is your answer

hope this helps

An instructional video is 4.2 minutes long. How long is the video in seconds? How long is it in hours?

Answers

384 seconds, 0.106 hours
252 seconds, and the hours hang on just a sec! 

10 POINTS + BRAINLIEST ANSWER!!

Given the right triangle PQR below, which of the following is equal to y/x?

A. cos P

B. cos Q

C. tan P

D. tan Q

Answers

C. tanP =QR/QP=y/x
p/s : follow me and I will help you more about maths

The value of tan P = y /x , Option C is the right answer.

What is a Right Angled Triangle ?

A triangle in which one of the sides is 90 degree is called a Right angled Triangle.

A right angled Triangle is given in the question

The sides of the triangle is x and y

The trigonometric ratios are given and it has to be determined that x/ y represents which one of the given option.

The value of tan x =  Perpendicular / Base

y/ x =  Perpendicular / Base for angle P

Therefore , The value of tan P = y /x , Option C is the right answer.

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The single equivalent discount rate of 9/5/4 is .17008. True or False?

Answers

i think its true but i may be wrong

the answer is true. i just had it on a quiz.

HELP PLEASE!!?!
5. The half-life of a certain radioactive material is 78 hours. An initial amount of the material has a mass of 790 kg. Write an exponential function that models the decay of this material. Find how much radioactive material remains after 18 hours. Round your answer to the nearest thousandth.,

Answers

The half life is 78 hours and the amount after 78 hours is 395 kg hence time constant is 395 = 790 * e^(p*78) By taking 790 common and natural log on both side ln (395 / 790) = (p*78) -0.6931 = 78*p -0.0088 = p (or -0.88%) Material left after 18 hours is A(18) = 790 * e^(-0.0088*18) A = 673.301 kg

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What is the trigonometric ratio for cosD ?

Enter your answer, as a simplified fraction.

Answers

we know that cosine(cos) is the = adj/hyp
in our case
cos D=21/75=7/25

identify the image of xyz for a composition of two 270 degree rotation and a 90 degree rotation both about point x.

Answers

I believe The Answer is C

Answer:

The answer is D

Step-by-step explanation:


sin 4 theta

hey, how do you simplify sin 4 theta? using double angle theory?

Answers

Yes, you do use double-angle formulas. 
You begin with double-angle formula for sine:

sin(4θ) = sin(2·2θ) = 2·sin(2θ)·cos(2θ)

Then, double-angle formula for sine again:

2·sin(2θ)·cos(2θ) = 2·2·sinθ·cosθ·cos(2θ) = 4·sinθ·cosθ·cos(2θ)

Then double-angle formula for cosine:

4·sinθ·cosθ·cos(2θ) = 4·sinθ·cosθ·(cos²θ - sin²θ)

Last, multiply:

4·sinθ·cosθ·(cos²θ - sin²θ) = 4·sinθ·cos³θ - 4·sin³θ·cosθ




The length of a shadow of a building is 32 m . the distance from the top of the building to the tip of the shadow is 38 m . find the height of the building. if necessary, round your answer to the nearest tenth.

Answers

For this case the first thing you should realize is that you have a rectangle triangle where you have two of the three sides.
 Therefore, to solve the problem, you must find the third side using the
 Pythagorean theorem.
 We have then:
 h ^ 2 + 32 ^ 2 = 38 ^ 2
 We cleared h:
 h = root (38 ^ 2 - 32 ^ 2)
 h = 20.49390153
 round to the nearest tenth
 h = 20.5 m
 Answer: 
 the height of the building is: 
 h = 20.5 m

What is the area of this figure?



Enter your answer in the box.


units²

Answers

Area of top triangle = 1/2(7)(2) = 7
Area of rectangle = 4 x 7 = 28
Area of bottom triangle = 1/2(7)(2) = 7

Area of figure = 7+ 28 + 7 = 42

answer
42 units²

Answer:

The answer to this is 42 units²

Step-by-step explanation:

I don't understand how to do this one, any help??


Is it a.?

Answers

C, because the equation of the table is y=80x. The equation for the graph is y=45x. When x is 11, you have 880 and 495. The difference is 385.
c because you multiply than divide. find the slope for both

Calculate.

0 = x² + 10x + 16

Enter your answers in the boxes.

Answers

x = -2 and x = -8. 

You can get this by factoring the polynomial and solving for x or by using the quadratic formula. 

One day a store sold 29 sweatshirts. White ones cost​ $10.95 and yellow ones cost $ 13.50. In​ all, ​$353.25 worth of sweatshirts were sold. How many of each color were​ sold?

Answers

there would be 10 yellow shirts and 19 white shirts...hope its right...

How much more interest is owed on $900 for 9 months then for 6 months? 6 months = 2.4% rate 9 months = 2.9% rate

Answers

keeping in mind that 6 months is not even a year, since there are 12 months in a year, then 6 months is really 6/12 years, and 9 months is 9/12 years, then


[tex]\bf ~~~~~~ \textit{Simple Interest Earned on 9 months}\\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\to& \$900\\ r=rate\to 2.9\%\to \frac{2.9}{100}\to &0.029\\ t=years\to \frac{9}{12}\to &\frac{3}{4} \end{cases} \\\\\\ I=900(0.029)\left( \frac{3}{4} \right)\\\\ -------------------------------[/tex]

[tex]\bf ~~~~~~ \textit{Simple Interest Earned on 6 months}\\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\to& \$900\\ r=rate\to 2.4\%\to \frac{2.4}{100}\to &0.024\\ t=years\to \frac{6}{12}\to &\frac{1}{2} \end{cases} \\\\\\ I=900(0.024)\left( \frac{1}{2}\right)[/tex]

check their difference, that much.

The interest is $8.77 owed in the amount of $900 for 9 months more than for 6 months.

What is the simple interest?

Simple interest is defined as interest paid on the original principal and calculated with the following formula:

S.I. = P × R × T, where P = Principal, R = Rate of Interest in % per annum, and T = Time, The rate of interest is in percentage r% and is to be written as r/100

To  determine interest on the amount of $900 for 9 months

Here P = $900, R =  2.9% = 2.9/100, and T = 9/12 year

Interest  = P × R × T

Interest  = 900 × 2.9/100 × 9/12

Interest  = $19.57

To  determine interest on the amount of $900 for 6 months

Here P = $900, R =  2.4% = 2.4/100, and T = 6/12 year

Interest  = P × R × T

Interest  = 900 × 2.4/100 × 6/12

Interest  = $10.80

The difference of interest is owed on $900 for 9 months then for 6 months: $19.57 - $10.80 = $8.77

Therefore, the interest is $8.77 owed in the amount of $900 for 9 months more than for 6 months.

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The function y = 41 ? 0.95x models the difference (in minutes) between men's and women's finishing times for the boston marathon. the number of years since women first officially ran the race in 1972 is represented by x.

a. does the exponential function represent growth or decay?

b. estimate the difference between finishing times in 1990.

c. predict the difference between finishing times in 2005.

Answers

We are given a function:
[tex]y=41* 0.95^{x} [/tex]

a. Does the exponential function represent growth or decay?
To find out if this is growth or decay we need to observe number that is connected with x. If number is less than 1 we have decay and if it is greaer than 1 we have growth.
In our case we have number 0.95 which is less than 1 so we have decay.

b. Estimate the difference between finishing times in 1990.
x represents the number of years since 1972.
[tex]x=1990-1972=18[/tex]
Now we insert this number into equation to get solution.
[tex]y=41* 0.95^{18} = 16.29[/tex]

c. Predict the difference between finishing times in 2005.
[tex]x=2005-1972=33[/tex]
[tex]y=41* 0.95^{33} = 7.55[/tex]

Can someone give me the answer to the question?

Answers

(7 cm)*(7 cm) = (10 cm)*(x)
x = 49 cm^2/(10 cm)
x = 4.9 cm

PLEASE ANYONE
HELP
I think its 120 + 15x ≤ 360
IS that Correct!!??

Answers

Hello there! I can help you! So the centerpieces take 15 minutes to make, and x equals the amount of centerpieces. That part makes 15x. Just by looking at the answers, A and C are already eliminated. We are adding up the time. the florst has already spent 2 hours, which equals 120 minutes. She will spend no more than 6 hours or 360 minutes on creating the centerpieces. We add the time, not subtract. B is the only one that shows that. 120 + 15x ≤ 360. The answer is B. Your answer is correct.


Kareem wants to wallpaper the back wall of his bedroom. The wall is in the shape of a rectangle. Its length is
13 feet and its width is 12
feet. The wallpaper costs $8
for each square foot. How much will wallpaper cost for the wall?

Answers

The first step in solving this problem is to compute for the area of the rectangular wall. The formula in computing the area of a rectangle is:

A = LW

Substituting the given measurements in the problem to the formula:

A = 13 (12)

A = 156

Therefore, the area of the wall is 156 square feet. To compute the wallpaper cost of the wall, you have to multiply the cost per square foot to the total area.

$8 per square foot x 156 square feet = $1,248

Therefore, the wallpaper cost for the wall is $1,248

Answer to question 3

Answers

If you repeat this polling process numerous times including computing the confidence interval, the true proportion of the population favoring the amendment will fall within the confidence interval 95% of the time.

IF YOU HELP ME ILL WILL GIVE YOU BRAINLIST AND 50 PONITS HELP ME PLZZZZZ



Which statement or statements are TRUE?

I. The data distribution is skewed
II. The interquartile range is 6
III. The median is 10
A) I only
B) II only
C) I and II only
D) II and III only

Answers

I think the answer is A because the data is skewed to the right 
The median (middle) isn't 10, it's 8 
The interquartile range (IQR) is 7 not 6 because you have to subtract the first and third quartile 13 - 6 = 7 not 6

Hope this helps! ;)

I think the answer is A

Quadrilateral ABCD is inscribed in circle O.

What is ​ m∠B ​ ?



Enter your answer in the box.

Answers

The measure of angle B is 125 degrees in the given quadrilateral inscribed in circle O.

In a quadrilateral inscribed in a circle, opposite angles are supplementary.

Therefore, we can set up the equation:

∠A + ∠C = 180 degrees

Substituting the given values:

(2x-7) + (x+4) = 180

Combining like terms:

3x - 3 = 180

Adding 3 to both sides:

3x = 183

Dividing both sides by 3:

x = 61

Now we can find ∠B:

∠B = 2x + 3

∠B = 2(61) + 3

∠B = 122 + 3

∠B = 125

Therefore, m∠B is equal to 125 degrees.

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Can there be a right triangle with side lenghts of 1,2,3

Answers

Nope, it doesn't follow the Pythagorean Theorem.

What is the value of x

Answers

well i atleast know its not 10 lol
Hello,

Answer A x=5 since

x/(x+5)=(x-2)/(x+1)==>x²+x=x²-2x+6x-10==>2x=10==>x=5

Please show work! Thank you

Answers

Answers:
Factored Form is (x+4)(x+2)
Expanded Form is x^2+6x+8

----------------------------------------------------------
----------------------------------------------------------

Explanation:

The factored form is simply a matter of reading off the values from the given image. There isn't much work to show here.
Along the left side we have x and 4 so x+4 is one of the factors. Along the bottom we have x and 2, so x+2 is another factor
The two factors are (x+4) and (x+2) so that's why the factored form is (x+4)(x+2)

-------------------------------

Let's expand out the factored form

The overall rectangle is broken up into four parts. I'll label the four smaller rectangles as...

Rectangle A in the upper left corner (this rectangle is x by x)
Rectangle B in the upper right corner (this rectangle is 2 by x)
Rectangle C in the lower left corner (this rectangle is x by 4)
Rectangle D in the lower right corner (this rectangle is 2 by 4)

The idea is that adding the areas of rectangles A through D leads us to the overall area for this largest rectangle.

Area of Rectangle A = (length)*(width) = x*x = x^2
Area of Rectangle B = (length)*(width) = 2*x = 2x
Area of Rectangle C = (length)*(width) = x*4 = 4x
Area of Rectangle D = (length)*(width) = 2*4 = 8

Notice we have the like terms 2x and 4x (areas of rectangle C and D respectively). They combine to 2x+4x = 6x

So after adding all the individual areas and combining like terms, we arrive at the fully expanded form of x^2+6x+8

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