Without using mathematical tables or calculator, find, in surd form(radicals) the value of tan22.5​

Answers

Answer 1

Answer:

Step-by-step explanation:

tan 45=1

[tex]tan 2\alpha =\frac{2tan\alpha}{1-tan^2\alpha } \\put~\alpha =22.5\\2\alpha =2 \times 22.5=45\\tan~2\alpha =tan~45=1\\1=\frac{2tan \alpha }{1-tan^2\alpha} \\1-tan^2\alpha =2 tan\alpha \\ tan^2\alpha +2tan \alpha -1=0\\tan\alpha =\frac{-2 \pm\sqrt{4+4} }{2} \\=-1\pm\sqrt{2} \\\alpha =22.5\\so ~tan~\alpha ~is~positive.\\so ~tan~\alpha =\sqrt{2} -1[/tex]


Related Questions

the money in a bank account increased from $400 to $1000.
copy and complete these sentences.

a) $1000 is ........% of $400.

b) the money has increased by .......%​

Answers

Answer:

a).1000/400*100

= (1000*100)/400

= 100000/400 = 250

b).600

Step-by-step explanation:

a). Percentage solution with steps:

Step 1: We make the assumption that 400 is 100 % since it is our output value.

Step 2: We next represent the value we seek with x.

Step 3: From step 1, it follows that 100 % = 400.

Step 4: In the same vein, x % = 1000 .

Step 5: This gives us a pair of simple equations:

100 % = 400(1).

x % = 1000(2).

Step 6: By simply dividing equation 1 by equation 2 and taking note of the fact that both the LHS

(left hand side) of both equations have the same unit (%); we have

100 % / x % = 400/1000

Step 7: Taking the inverse (or reciprocal) of both sides yields

x/100 = 1000/400

x = 250 %

Therefore, 1000 is 250 % of 400.

b) $1000-$400= 600

= $400+$600=$1000

what is 52 + 6 × (5 − 3) − 10⁄2 =

Answers

Answer: 59

Step-by-step explanation:

Order of operations.

52+6x(2)-5

52+12-5

64-5

59

Step-by-step explanation:

52+6×2-10/2

52+6×2-10÷2

52+6×2-5

52+12-5

64-5 =59

my answer is 59.

what is the solution to the system of equations below?
3x+y+2z=8
8y+6z=36
12y+2z=12

A. x=2, y=1, z=6
B. x=3, y=0, z=4
C. x=2, y=0, z=6
D. x=3, y=1, z=4

Answers

The solution to the system of equation are x=2, y=0, z=6

System of equations

System of equations are equations that contains unknown variables.


Given the equations

3x+y+2z=8

8y+6z=36

12y+2z=12

From equation 2 and 3

8y+6z=36 * 1

12y+2z=12 * 3

______________

8y+6z=36

36y+6z= 36

Subtract

8y - 36y = 36 - 36

-28y =0

y = 0

Substitute y = 0 into equation 2

8(0)+6z=36

6z = 36

z = 6

From equation 1

3x+y+2z =8

3x + 0 + 2(6) = 8

3x = 8 - 12

3x = 6

x = 2

Hence the solution to the system of equation are x=2, y=0, z=6

Learn more on system of equation here: https://brainly.com/question/14323743

#SPJ1

The sum of ten and eight times a number is 162. What is the number?

Answers

9. The sum of ten and eight is 18, 18 time 9 is 162

Answer:

9

Step-by-step explanation:

10x + 8x = 162

18x = 162

x = 9

What is the net percent gained or lost on a stock with goes up 30% on monday and then drops 30% on tuesday? use a negative sign to indicate percentage lost.

Answers

Answer:

0 is the answer to the question

Which table represents a proportional relationship? A 2-column table with 3 rows. Column 1 is labeled x with entries 4, 8, 18. Column 2 is labeled y with entries 6, 12, 26. A 2-column table with 3 rows. Column 1 is labeled x with entries 5, 20, 60. Column 2 is labeled y with entries 7, 28, 84. A 2-column table with 3 rows. Column 1 is labeled x with entries 12, 18, 26. Column 2 is labeled y with entries 5, 7, 9. A 2-column table with 3 rows. Column 1 is labeled x with entries 3, 9, 15. Column 2 is labeled y with entries 2, 8, 14.

Answers

Answer:

X     Y

5      7

20   28

60   84

This table shows the proportional relationship.

Step-by-step explanation:

The equivalent ratios of two variables known as proportional relationship.

Table 1:  X     Y                                        Table 3: X     Y

              4     6                                                       12    5

              8     12                                                      18    7

              18    26                                                     26   9

Ratio = 4:6 = 8:12 ≠ 18:26                       Ratio = 12:5 ≠ 18:7 ≠ 26:9

Table 2: X     Y                                       Table 4: X     Y

              5     7                                                       3      2

              20   28                                                    9      8

              60   84                                                    15     14

Ratio = 5:7 =20:28=60:84                       Ratio = 3:2 ≠ 9:8 ≠ 15:14

Here we see table 2 shows the proportional relationship.

Learn more about proportional relationship here - https://brainly.in/question/17614286

#SPJ10

How does simplifying a square root expression differ from simplifying a cube root expression?

Answers

The square root contains two same numbers and the cubic root contains three same numbers.

What is an expression?

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

The square root contains two same numbers and the cubic root contains three same numbers.

For an example:-

√9 = [tex]\sqrt{3\times 3}[/tex] =  3 as we can see in the example the value of the square root of 9 is 3 it consists of two threes in the roots.

∛27 = [tex]\sqrt[3]{3\times 3\times 3}[/tex] = 3 here we have found that 27 contains 3 times 3 so the cube root of 27 will be equal to 3.

Therefore square root contains two same numbers and the cubic root contains three same numbers.

To know more about Expression follow

https://brainly.com/question/723406

#SPJ1

\How could Brent use a rectangle to model the factors of x2 – 7x + 6?

He could draw a diagram of a rectangle with dimensions x – 3 and x – 4 and then show the area is equivalent to the sum of x2, –3x, –4x, and half of 12.
He could draw a diagram of a rectangle with dimensions x + 7 and x – 1 and then show the area is equivalent to the sum of x2, 7x, –x, and 6.
He could draw a diagram of a rectangle with dimensions x – 1 and x – 6 and then show the area is equivalent to the sum of x2, –x, –6x, and 6.
He could draw a diagram of a rectangle with dimensions x – 4 and x + 3 and then show the area is equivalent to the sum of x2, –4x, 3x, and half of –12.

Answers

Option third "He could draw a diagram of a rectangle with dimensions x – 1 and x – 6 and then show the area is equivalent to the sum of x², –x, –6x, and 6' is correct.

What is the area of the rectangle?

It is defined as the area occupied by the rectangle in two-dimensional planner geometry.

The area of a rectangle can be calculated using the following formula:

Rectangle area = length x width

We have a quadratic expression to model the area of the rectangle:

= x² – 7x + 6

[tex]\rm =\left(x^2-x\right)+\left(-6x+6\right)[/tex]

[tex]=\rm x\left(x-1\right)-6\left(x-1\right)[/tex]

= (x - 1)(x - 6)

Thus, option third "He could draw a diagram of a rectangle with dimensions x – 1 and x – 6 and then show the area is equivalent to the sum of x², –x, –6x, and 6' is correct.

Learn more about the rectangle here:

https://brainly.com/question/15019502

#SPJ1

Here is the histogram of a data distribution. All class widths are 1.

Which of the following numbers is closest to the mean of this distribution?

A. 7
B. 5
C. 9
D. 4
E. 3

Answers

Considering the given histogram, the mean of the data-set is closest to:

B. 5.

What is an histogram?

An histogram is a graph that shows the number of times each element of x was observed.

What is the mean?

The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations.

Hence, considering the histogram, the mean is given by:

M = (1x1 + 2x2 + 3x3 + 4x1 + 5x1 + 6x2 + 7x3 + 8x1 + 9x1)/(1 + 2 + 3 + 1 + 1 + 2 + 3 + 1 + 1) = 4.87.

Which is closest to 5, hence option B is correct.

More can be learned about histograms at https://brainly.com/question/26622630

#SPJ1

i need help asappppp

Answers

Answer:

a = 11, b = 7

Step-by-step explanation:

See picture

Which is the graph of the equation y-1=2/3(x-3)?

Answers

Answer:

The right graph

Step-by-step explanation:

Because the equation is in point slope form, we know it passes through (3,1) and has a slope of 2/3.

A square its diagonal length = 12cm then its area =

Answers

Answer:

72  sq cm

Step-by-step explanation:

For any rectangle, the diagonal is the hypotenuse of the right triangle formed by the base of the rectangle(b) and the height (h) of the rectangle

By the Pythogorean formula

[tex]d^{2} = b^{2} + h^{2}[/tex]

where d is the diagonal

For a square, all sides are equal so b = h = a and we get the formula

[tex]d^{2} = a^{2} + a^{2} = 2a^{2}[/tex]

[tex]a^{2} = d^{2} /2[/tex]

In this case we have d =12 so

[tex]a^{2} = 12^{2} /2 = 144/2 = 72[/tex]

But for a square of side a, the area is [tex]a^{2}[/tex] so 72 is the area

Answer:

72 square cm

Step-by-step explanation:

Area of square:

       [tex]\sf \boxed{\bf Area = \dfrac{d^{2}}{2}}[/tex]  , here d is the length of the diagonal

                  [tex]\sf =\dfrac{12* 12 }{2}\\\\ = 6*2\\\\= 72 \ cm^2[/tex]

in an isosceles triangle, the perimeter is 75 cm and one of the sides is 25 cm. Find all its sides. can you find all angles of the triangles?

Answers

Answer:

all angles of the triangles is 60

Step-by-step explanation:

the perimeter = 2*side of an isosceles triangle + bottom edge

----> bottom edge = the perimeter - 2*side of an isosceles triangle  =25

----> This is an equilateral triangle ----> all angles of the triangles is 60

In a group of 42 students, 9 study both Art and Biology.
10 study Biology but not Art.
7 study neither subject.
Given that a randomly selected student studies Art, what is the probability the student studies Art and Biology?

help asap

Answers

Answer:
The probability the student studies Art and
Biology is 0.2143.
Step-by-step explanation:
Denote the events as follows:
A = a students studies Art
B= a students studies Biology
The information provided is:
N = 42
n (An B) = 9
n (A' n B) = 10
n (A' n B') =7
Then the number of students who study Art
but not Biology is:
n(An B') = N -n (An B) -n (A' nB) - n (A'n B')
= 42 - 10 - 7 - 9
= 16
The number of students who study Art but
not Biology is 16.
Compute the probability the student studies
Art and Biology as follows:
P(ANB)
n(ANB)
= 0.2143
Thus, the probability the student studies Art
and Biology is 0.2143.

Help... will give you 20 points if you answer

Answers

Answer:

(-3,5) (-3,3) (-8,3)

Step-by-step explanation:

Answer:

(-3,5) , (-3,3) , (-8,3)

Step-by-step explanation:

bye, bye!!

The mean height of 20 boys and 14 girls is 161 cm. The mean height of 14 girls is 151 cm. Find the sum of the heights of 14 girls.

Answers

Answer: 2114

Step-by-step explanation:

m = sum of the terms / number of terms

151 = a/ 14

14 x 151 = a

2114 = a

Answer:

21.14 m

Step-by-step explanation:

the mean is calculated as

mean = [tex]\frac{sum}{count}[/tex]

here mean is 151 cm and count = 14 , then

[tex]\frac{sum}{14}[/tex] = 151 ( multiply both sides by 14 to clear the fraction )

sum = 14 × 151 cm = 2114 cm = 2114 cm ÷ 100 = 21.14 m

Simplify fully 4d2-6d2+5d2

Answers

Answer:

3d²

Step-by-step explanation:

Hello!

To simplify, we combine the like terms by adding them.

Like terms

Like terms are terms with the same variable and degree. A degree is a power to which the term is raised. Like terms can have numerical coefficients. For example, a coefficient of 4 to x² would mean 4 times x².

We can see that the variable is common throughout the three terms, meaning they are like terms. We can simply add and subtract them.

Simplify4d² - 6d² + 5d²-2d² + 5d²3d²

The simplified form is 3d².

What is the domain and range of the following graph?

Answers

Answer:

Domain is all x-values and range is all y values. See all of the x values and y values that are touching the graph. Also, when there is a circle/ hole, use parenthesis for the interval notation.  Hope it helps!

Area is all x - values and reach is all y - values. See the entirety of the x qualities and y esteems that are contacting the diagram. Likewise, when there is a circle use enclosure for the stretch documentation

Which expression is equivalent to the one below? (x2y)(x4y3) xy2

Answers

The expression which is equal to the expression [tex]x^{2} yx^4} y^{3} xy^{2}[/tex] is as [tex]x^{7} y^{6}[/tex].

Given Expression   [tex]x^{2} yx^4} y^{3} xy^{2}[/tex] and we have to find the expression equal to this.

Two variables are present in the given expression x and y but both are in different form or powers.

x is having power 2 , 4 and 1 so because the base is same for all and they are in multiplied form so we will add the powers to form [tex]x^{4+2+1}\\[/tex]

=[tex]x^{7}[/tex]

Now y is having 1,3,2 powers so because the base is same for all and they are in multiplied form so we will add all the powers to form [tex]y^{6}[/tex]

Now multiply both to get the required expression which is [tex]x^{7} y^{6}[/tex].

Hence the expression which is equal to the given expression is [tex]x^{7} y^{6}[/tex].

Learn more about expression at https://brainly.com/question/723406

#SPJ10

raios of 3 The ratboys to 5 girls

Answers

5/3 = g/24 where g is the number of girls for 24 boys. Typing 5/3 = g/24 into the math tutoring calculator gives us g = 40.

label the vertices and all the elements needed. find x

Answers

The value of x would be 30 degrees.

What is the angle sum property?

The angle sum property of a triangle states that the sum of the interior angles of a triangle is 180 degrees.

Let's consider an angle CAD be t.

In a triangle ABD

x + 90 + t = 180

t = 180 -x - 90

t = 90 - x ( by angle sum property)

Now, we know that the sum of the corresponding angle on a transversal is 180

So,

Angle A + angle D = 180

2x + t + x + x = 180

substitute the t value

2x + 90 - x + 2x = 180

3x + 90 = 180

3x = 90

x = 30 degree

Hence, the value of x would be 30 degrees.

Learn more about the triangles;

https://brainly.com/question/2773823

#SPJ1

Find y in terms with x
Help me pleaseee thank uu:)​

Answers

Answer:

y = 90 -5/2 x

Step-by-step explanation:

The angle on the left equals x+3x+x = 5x

The angle on the right equals 2y

The two angles are same side interior angles which are supplementary because the lines are parallel

5x+2y = 180

Solving for y

2y = 180-5x

Divide by 2

2y/2 = 180/2 -5x/2

y = 90 -5/2 x

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\tt y = 90 \degree - \cfrac{5x}{2} [/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

The two lines are parallel, henceforth we can apply Angle pair rules.

[tex]\qquad \tt \rightarrow \:(x + 3x + x) + 2y = 180[/tex]

[ Co - interior angles ]

[tex]\qquad \tt \rightarrow \:5x + 2y = 180[/tex]

[tex]\qquad \tt \rightarrow \:2y = 180 - 5x[/tex]

[tex]\qquad \tt \rightarrow \:y = \dfrac{180 - 5x}{2} [/tex]

[tex]\qquad \tt \rightarrow \:y = \cfrac{180 }{2} - \cfrac{5x}{2} [/tex]

[tex]\qquad \tt \rightarrow \:y = 90 \degree - \cfrac{5x}{2} [/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

-35÷6=

-350÷6-350-6=

350 - 60 =

Answers

Answer:

The first one is 5.83 or -5 5/6

The second one is -414 1/3

The last one is 290

Find the value of x ??
A. 31
B. 5
C. 11
D. 25

Answers

I believe the answer is C

PLEASE ANSWER ASAP!!!!!!!
A cheesecake has equally sized slices. Each slice is a different flavor. The diameter of the cheesecake is 10 inches, and the area of the slice of blueberry cheesecake is 25π16 square inches.

How many slices does the cheesecake have?

Answers

A cheesecake has equally sized slices. Each slice is a different flavor. The cheesecake has 12 slices.

What is the area of the circle?

The area of the circle is defined as the product of the pie and the square of the radius.

The area of the circle = πr²

In order to calculate the total area of the cheesecake, since it's a circle its area is given by:

cheesecake area =  πr²

cheesecake area =  π(10/2)² =  π(5)²

cheesecake area = 25 π square inches

Therefore the number of slices is the ratio of the cheesecake total area by the area of each slice:

The number of slices = 25 π/(25 π/12)

The number of slices = 12

The cheesecake has 12 slices.

Learn more about circle;

brainly.com/question/12512221

#SPJ1

Answer: 12 slices

Step-by-step explanation:

im a year late woo hoo

Help needed
a hunid points :)

Answers

Answer:

the answer is C, 5a^6b

Step-by-step explanation:

Question 3 of 10 A Assume EFG = JKL. If mLJ = 90°, mL K = 26°, and m< L = 64°, what is the measure of < E?

Answers

The measure of angle E will be 90 degrees as well.

Assume EFG = JKL.

If mLJ = 90°, mL K = 26°, and m< L = 64°,

What is the congruent triangle?

Two triangles are said to be congruent if the length of the sides is equal, a measure of the angles are equal and they can be superimposed.

We have been given an image of two congruent triangles.

Since, EFG = JKL

therefore, the corresponding angles will be congruent.

m < J = 90° = m< E = 90

By congruence measure of angle, J will be equal to the measure of angle E.

Hence, The measure of angle E will be 90 degrees as well.

Learn more about congruent;

https://brainly.com/question/10586347

#SPJ1

the slope of the line is 4. which of the following is the point-slope form of the line

Answers

The point slope form of line is y+4 = -4( x+3)

What is point slope of form?

The point slope form is used to find the equation of the straight line which is inclined at a given angle to the x-axis and passes through a given point.

Given:

m=4

We know the general form is

y - b = -4(x - a)

So, from the graph attached below

b= -4, a= -3

So, y-(-4)= -4(x-(-3))

y+4 = -4( x+3)

Hence,  point slope form of line is y+4 = -4( x+3).

Learn more about tis concept here:

https://brainly.com/question/13436232

#SPJ1

the vate rate of a country is 15% ,a woman bought an item with a price tag ghc 300 plus vat .what price did she pay for the item. ​

Answers

Answer:

i think 345 if not sorry

Step-by-step explanation:

Which values of x will make the expression
0-3
0-2
0
02
3
6x²-54
5x²-20
equal to 0? Select two options.

Answers

Answer:

3 and -3

Step-by-step explanation:

Other Questions
What is the value of the blue dot? What is the main point of the conclusion of "a big year"? (5 points) a birding is not only about winning a contest. b birding is a fun activity unless it is a competition. c birding can easily be made into a game. d people who bird have families that bird. Cooling towers are used to remove or expel heat from a process. A cooling tower's walls are modeled by x squared over 324 minus quantity y minus 90 end quantity squared over 1600 equals 1 comma where the measurements are in meters. What is the width of the cooling tower at the base of the structure? Round your answer to the nearest whole number. 36 meters 48 meters 80 meters 89 meters What was the key issue at the Constitutional Convention? whether the new national government should be more or less powerful than the Confederation government. whether or not slavery should be abolished. how to balance the conflicting interests of large and small states. how to convince the general population to support a document written by the elite. when the new government could acquire additional territory. Which word signals a nonrestrictive Which excerpt from Silent Spring best appeals to readers pathos? Why do businesses or individuals who violate regulatory laws (like professional licensingrequirements) find themselves in civil courts, not criminal courts? Find the area of sphere of radius 4 cm PLEASE HELP QUICKLY!!! WILL GIVE BRAINLYEST AWARD TO 1st RIGHT!!! Writing an Equation from a TableA 2-column table with 6 rows. Column 1 is labeled x with entries 8, 12, 16, 20, 25, 28. Column 2 is labeled y with entries 2, 3, 4, 5, 6, 7.Which equation produces the values in the table?y = 4xy = 4 + xy = One-fourthxy = 4 x Why does diversity increase as height above land increases A person drops off a prescription for a beneficiary who is a regular customer. The prescription is for a controlled substance with a quantity of 160. This beneficiary normally receives a quantity of 60, not 160. You review the prescription and have concerns about possible forgery. What is your next step?. If you currently makes 425 What is the gross they will earn If they work every week If the year Which country was the last to join the Allied Powers? O Great Britain O France O United States O China Progressives, such as Woodrow Wilson, supported financial reforms because they believed the nations financial system was overly controlled bylabor unions.state governments.foreign countries.big business. Explain How sunlight is the primary source of energy for you life what started human life on Earth? What is the value of the expression 4 x (2a - 1) if a = 3?16202325 Solve the system of equation for y using Cramer's rule. Hint: The determinant of the coefficient matrix is -23. Counties, municipalities, townships, school districts, and other special districts are all local governments. The largest categories of spending by local governments make up approximately 67% of their total expenditures. Which of the following is not an expenditure of local governments?a) public utilities- because fewer utilities serve people on a statewide basis, state governments spend a much smaller percentage of their budgets on public utilities. [Incorrect]b) Elementary and Secondary Education- expenditures in this category include teachers' and administrators' salaries, textbooks, and construction and maintenance of school buildings. c) public welfare- takes the form of cash assistance, payments for medical care, expenditures to maintain welfare institutions, and other miscellaneous welfare expenditures d) Interest on Debt- State and local governments sometimes borrow money to cover operating costs or capital spending. e) Highways- local governments spend almost as much on highways, roads, and street repairs as they do on police protection. Includes the repair of potholes, street signs, and other street-related items. Which type of essay would be used toconvince readers to brush their teethevery day?A. expository essayB. formal personal essayC. informal personal essayD. persuasive essay