Pleaseeeee helpppppp
Please help me evaluate this in terms of sin/cos/sec etc. (trigonometric form)

tan2θ-(1-tan2θ)=?

Answers

Answer 1

The evaluation is (2sin2∅-cos2∅)sec2∅.

What are trigonometric functions?

Trigonometric functions are functions used to relate the sides of a triangle with its angles.

Analysis:

2tan2∅ -(1- tan2∅)

2tan2∅ - 1 + tan2∅

3tan2∅ - 1

3([tex]\frac{sin2\alpha }{cos2\alpha }[/tex]) - 1

(3sin2∅/cos2∅) - 1

(3sin2∅ - cos2∅)/cos2∅

but 1/cos2∅ = sec2∅

(3sin2∅ - cos2∅)/sec2∅

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Related Questions

Use the hundredth grids to model the question.

Two 10 by 10 grids are shown. In the first grid, 8 columns and 9 squares are shaded brown and 1 column and 1 square are shaded blue. The second grid is entirely shaded blue.

Which is the sum of 0.89 and 1.11?

A.
1.00

B.
1.89

C.
1.90

D.
2.00

Answers

The sum of 0.89 and 1.11 will be 2. Then the correct option is D.

What is Algebra?

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

Two 10 by 10 grids are shown.

In the first grid, 8 columns and 9 squares are shaded brown and 1 column and 1 square is shaded blue.

The second grid is entirely shaded blue

Then the sum of 0.89 and 1.11 will be

⇒ 0.89 + 1.11

⇒ 2.00

Then the correct option is D.

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Compute the indicated power by using de Moivre's theorem.
[tex]\sqrt[4]{1-i\sqrt{3} }[/tex]
please hurry

Answers

I assume you know that there are n total n-th roots for any non-zero complex number.

(If you're looking for "the" principal root, you'll have to specify which branch you're calling the principal branch of the n-th root function.)

Start by writing [tex]1 - i\sqrt3[/tex] in exponential form. We have modulus/magnitude

[tex]|1 - i\sqrt3| = \sqrt{1^2 + (-\sqrt3)^2} = \sqrt4 = 2[/tex]

and [tex]1-i\sqrt3[/tex] lies in the fourth quadrant of the complex plane, so its argument is

[tex]\arg(1-i\sqrt3) = \tan^{-1}\left(-\sqrt3\right) = -\dfrac\pi3[/tex]

Then the exponential form is

[tex]1 - i \sqrt3 = 2 \exp\left(-i\dfrac\pi3\right)[/tex]

(where [tex]\exp(x) = e^x[/tex], if you're not familiar with the notation)

By de Moivre's theorem, we have the fourth roots

[tex]\sqrt[4]{1 - i\sqrt3} = \sqrt[4]{2} \exp\left(i \dfrac{-\frac\pi3+2k\pi}4\right)[/tex]

where [tex]k\in\{0,1,2,3\}[/tex], so that we have a choice of

[tex]\sqrt[4]{1 - i\sqrt3} = \begin{cases} \sqrt[4]{2} \exp\left(-i\dfrac\pi{12}\right) \\\\ \sqrt[4]{2} \exp\left(i\dfrac{5\pi}{12}\right) \\\\ \sqrt[4]{2} \exp\left(i\dfrac{11\pi}{12}\right) \\\\ \sqrt[4]{2} \exp\left(i\dfrac{17\pi}{12}\right) = \sqrt[4]{2} \exp\left(-i\dfrac{7\pi}{12}\right) \end{cases}[/tex]

(I rewrote the exponent to the last root just to be consistent about having each argument between -π and π radians)

If you want these in rectangular form (a + bi), sorry, that's where I draw the line; it can be done with simple trigonometry and algebra, but it's rather tedious, and the exponential forms are far more compact.

What is 8 times the sum of x and 15 as an algebraic expression (written answer)

Answers

Answer:

8x+120 is the answer

Step-by-step explanation:

8(x+15)

=8x + 8×15

=8x+120

Factorise completely
12y² + 4y

Answers

Step-by-step explanation:

[tex]12y^{2} + 4y \\4y( \frac{12y^{2} }{4y} + \frac{4y}{4y} ) \\ 4y(3y + 1)[/tex]

Step-by-step explanation:

12y²+4y

divide both sides by 4

therefore,

3y²+y

y(3y+1)

Question 25 of 25
Over what interval is the function in this graph increasing?
AV
M
<-10
10
A. 6≤x≤ 10
B. -4≤x≤1
C. -10≤x≤-4
D. 1≤x≤6

NEED HELP ASAP

Answers

The correct option is option B :    -4 ≤ x ≤ 1

What is Increasing and decreasing function?

Increasing and decreasing functions are functions whose graphs go upwards and downwards respectively as we move towards the right-hand side of the x-axis. Increasing and decreasing functions are also called non-decreasing and non-increasing functions.

Here, from graph

as we can observe from x = -4 graph starts increases upto x = 1 and after that graph becomes constant.

Thus, between x belongs -4 to 1 the graph is increasing.

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In the diagram below, OO is circumscribed about quadrilateral ABCD. What is
the value of x?
B
A
93
O
x+30°
D
OA. 57
OB. 117
OC. 123
OD. 63

Answers

Answer:

Ans = A: 57

Step-by-step explanation:

Because

sum of the angke of opposite side of quardilateral triangle is 180°

x°+30°+93°=180°

x°+123°=180°

x°=180°-123°

x°=57°

Hence proved.

The value of x is option A. 57.

What is Cyclic Quadrilateral?

A cyclic quadrilateral is a polygon with four sides where all of it's four vertices lie on a circle.

The circle thus formed is called circumcircle or circumscribed circle.

We have a property for the cyclic quadrilateral that the opposite angles formed on the quadrilateral is supplementary.

That is, sum of the opposite angles is 180°.

Here B and D are opposite angles.

So,

∠B + ∠D = 180

9x + x + 30 = 180

Solving,

x = 57

Hence the value of x is 57.

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1. What is the difference between the altitude rule and the leg rule?

Answers

Answer:

The altitude to the hypotenuse of a right triangle forms two triangles that are similar to each other and to the original triangle

The Leg Rule (or Leg geometric mean theorem) relates the length of each leg of a right triangle with the segments projected by them on the hypotenuse.

Step-by-step explanation:

The altitude to the hypotenuse of a right triangle is the mean proportional between the segments into which it divides the hypotenuse. Notice the triangle used with this rule. The leg of a right triangle is the mean proportional between the hypotenuse and the projection of the leg on the hypotenuse.


Two times a number x increased by 8 is 20. Which one of the following
Equations represents this statement?

Answers

Considering the definition of equation, the equation that represents the statement "Two times a number x increased by 8 is 20" is: 2x + 8= 20

Definition of equation

An equation is the equality existing between two algebraic expressions connected through the equals sign in which one or more unknown values, called unknowns, appear in addition to certain known data.

The unknown values represents the number (or numbers), if any, that make the equality true. This unknown number is the solution of the equation.

This case

Considering that:

"Twice' simply means "multiply by 2"."increased by 8" means "added or plus 8".

the equation that represents the statement "Two times a number x increased by 8 is 20" is:

2x + 8= 20

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The equation for the statement "two times a number x increased by 8 is 20" is 2x+8=20.

The given statement is two times a number x increased by 8 is 20.

We need to write the equation to represent this statement.

What is an equation?

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Now, two times a number x=2x

Increased by 8 is 20=2x+8=20

Hence, the equation for the statement "two times a number x increased by 8 is 20" is 2x+8=20.

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It's the last second of a playoff basketball game and Bridget has three free throws she must make to seal the win she typically makes about 75% of her free throws what is the probability that Bridget makes all three free throws to win the game

Answers

The probability that Bridget makes all three free throws to win the game is; 42.2%

How to find the probability?

We are told that the probability of Bridget making her free throw correctly is 75%.

Now, if she has to get all three free throws correctly, then the probability for that is;

P(3 free throws correct) = 0.75 * 0.75 * 0.75

P(3 free throws correct) = 0.421875 ≈ 42.2%

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-3x^6(-4x+9)
Simplify please lol

Answers

Answer:

-12X^7-27X^6

Step-by-step explanation:

-3x^6(-4X+9)=(-3X^6*)(4X^1)+-27X^6=-12X^7+-27X^6

DUE TODAY: PLEASE HELP

Use transformations to prove that the two figures are similar. Shape A is the original image

(Show work please, how it is similar or not)

Answers

Answer:

See below ~

Step-by-step explanation:

We need to prove that the figures are similar by applying the various kinds of transformations.

===============================================================

Question A :

⇒ Compare the side lengths of A and B

⇒ 2 : 5 (for all sides)

⇒ 1 : 2.5

⇒ Hence, Shape A has been dilated with a scale factor of 2.5 to form Shape B

=============================================================

Question B :

⇒ Compare the side lengths of A and B

⇒ A : B = 2 : 6

⇒ A : B = 1 : 3

Shape A has been dilated with a scale factor of 1/3 to form Shape B

find the approximate volume of this cone. use 3.14 for pi.

Answers

The answer is A
how?: 3.14 * 30^2 * 40/3 (put that in a calculator)

help i need it quick!!

Answers

Answer:

47°

Step-by-step explanation:

45+88= 133

180-133=47

If you use 1/8 lb of ham on each sandwich you make, how many
sandwiches
can you make from a 22 lb ham?

Answers

176 by multiplying 22 by 8
pretend a is how many sandwiches you can make

formula - 1/8 x a = 22

switch numbers to the other side to figure out a

a = 22x8

a (how many sandwiches you can make) = 176

kantabai bought 1/2 kg tea and 5 kg sugar from a shop .she paid rupess 50 as return fare for rickshaw .total expense was rupess 700 .then she realised that by ordering online the goods can be bought with free home delivery at the same price .so next month she placed the order online for 2 kg tea and 7 kg sugar she paid rupess 880 for that .find the rate of sugar and tea per kg

Answers

Answer:

40 Rs per kg.

Step-by-step explanation:

solution

Let the rate of tea be x Rs per kg and that of sugar be y Rs per kg.

When Kantabai bought the items by going to the shop,

3/2x+5y+50=700

⇒3x+10y=1300....(I)

When Kantabai bought the items online then

2x+7y=880......(II)

Multiplying (I) with 2 and (II) with 3 we get

6x+20y=2600......(III)

6x+21y=2640.......(IV)

eq.(IV)−(III)

y=40

Putting the value of y =40 in (II)

2x+7(40)=880

⇒2x=880−280=600

⇒x=300

Thus, tea is at 300 Rs per kg and sugar is 40 Rs per kg.

Find the area of the shaded region in terms of pi

Answers

Answer:

[tex]13\frac{1}{3} \pi[/tex]

Step-by-step explanation:

First, find the area of the small circle whose radius is 3cm.

[tex]A = \pi r^{2} \\A = \pi (3^{2})\\A = \pi (9)\\A = 9\pi \\[/tex]

Next, find the area of the large circle. First, you need to find the radius of the large circle by adding the 3 and 4.

Radius of large circle.

3 + 4 = 7 cm

Area of large circle:

[tex]A = \pi r^{2} \\A = \pi (7^{2})\\A = \pi (49)\\A = 49\pi \\\\[/tex]

Now subtract the area of the small circle from the large circle since the shaded area doesn't include the small circle.

[tex]49\pi -9\pi =40\pi[/tex]

Finally find the shaded area. To do this first find what degree of the circle is shade by dividing 120 by 360.

120/360 = 1/3

Now multiply the area by 1/3, or you can divide it by 3

[tex]\frac{40\pi }{3} =13\frac{1}{3} \pi[/tex]

A perpendicular bisector crosses a line segment.which type of angle does it form with the segment

Answers

Answer: A right angle

Step-by-step explanation:

Perpendicular lines form right angles

Answer:

90 degree

Step-by-step explanation:

if cos a =0.8290 then a < is approximately

Answers

Answer:

34 degrees

Step-by-step explanation:

Just reverse the cos function   ( you will need a calculator)

arc cos (.8290) = 34 degrees

this is sometimes written as   cos^-1 (.8290)   <====it is the same thing

Mika bought 9 rolls of film to take 180 pictures on a field trip. Some rolls had 36 exposures and the rest had 12 exposures. How many of each type did Mika buy

Answers

The number of each type Mika bought =x = 6.8 rolls; y= 2.2 rolls.

Calculation using ratio

The number of rolls of film Mika  bought =  9 rolls

The number of rolls that had 36 exposures = x

The number of rolls that had 12 exposures = y

The total number of exposures = 36 + 12 = 48

To find the exposure by one roll = 48/9 = 5.3

If one roll = 5.3 exposure

    x roll    = 36 exposure

Make x roll the subject of formula,

x roll = 36/5.3 = 6.8 rolls

If one roll = 5.3 exposure

    y roll    = 12 exposure

Make y roll the subject of formula,

y = 12/5.3 = 2.2 rolls

Therefore, the number of each type Mika bought = x = 6.8 rolls; y= 2.2 rolls.

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A family reunion planning committee with 8 members plans to elect 3 officers - a president, treasurer, and historian. if each office is to be held by one person and no person can hold more than one office, in how many ways can those offices be filled

Answers

Using the permutation formula, it is found that these offices can be filled in 336 ways.

There are different roles, hence the order in which the people are chosen is important, hence the permutation formula is used.

What is the permutation formula?

The number of possible permutations of x elements from a set of n elements is given by:

[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]

3 people will be chosen from a set of 8, hence the number of ways is given by:

[tex]P_{8,3} = \frac{8!}{5!} = 336[/tex]

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Use the scenario to answer the question.

Bryan is asked to find the interquartile range for the data set {5,6,6,8,10,11,14,16,17}.
His work follows.

Step A: Find the median of the data set. The median, or Q2, is 10.
Step B: Find the value of Q1, or the median of the lower half of the data set, {5,6,6,8}.

Q1=6+62=6

Step C: Find the value of Q3, or the median of the upper half of the data set, {11,14,16,17}.

Q3=14+162=15

Step D: Find the difference between Q3 and Q1.

IQR=15−6=9

At which step did Bryan make a mistake, if he made one?

At Step B, he incorrectly found the value of Q1. He should have found the sum of the values and then divided by 4 to get Q1=6.25.At Step B, he incorrectly found the value of textsf cap q 1. He should have found the sum of the values and then divided by 4 to get

At Step A, he incorrectly found the value of the median. He should not have included both 6 values, so the median is 10+112=10.5.At Step A, he incorrectly found the value of the median. He should not have included both 6 values, so the median is

At Step C, he incorrectly found the value of Q3. He should have included 10 to get Q3=14.At Step C, he incorrectly found the value of textsf cap q 3. He should have included 10 to get

At Step D, he incorrectly found the IQR. He should have found the difference between each quartile to get 10−6=4 and 15−10=5.At Step D, he incorrectly found the IQR. He should have found the difference between each quartile to get 10 minus 6 is equal to 4 and

He did not make a mistake.

Answers

Given the steps used to calculate the interquartile range, Bryan did not make any mistake.

What is the interquartile range?

The interquartile range is the difference between the third quartile and the first quartile.

Third quartile = 3/4(n + 1) : 3/4 x 10 = 7.5 term : (14 + 16) / 2 = 15First quartile = 1/4 x (n + 1) 1/4 x 10 = 2.5th term : (6 + 6) / 2 = 6Interquartile range = 15 - 6 = 9

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Assuming that no denominator equals zero, which is equivalent to? r^2-r-6/(r-2)(r-3)​

Answers

The given expression is [tex]\dfrac{ r^2-r-6}{(r-2)(r-3)}[/tex]. the option C [tex]\dfrac{ (r+2)}{(r-2)}[/tex]is correct.

What is a simplification of an expression?

Usually, simplification involves proceeding with the pending operations in the expression.

Simplification usually involves making the expression simple and easy to use later.

The given expression is

[tex]\dfrac{ r^2-r-6}{(r-2)(r-3)}[/tex]

By solving the numerator

[tex]r^2-r-6\\\\r^2 - (3-2)r- 6\\\\(r-3)(r+2)[/tex]

Put the solution in the above equation

[tex]\dfrac{ (r+2)(r-3)}{(r-2)(r-3)}[/tex]

[tex]\dfrac{ (r+2)}{(r-2)}[/tex]

Therefore, the option C is correct.

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*£ HELP PLS !! URGENT!! AFFECT MY GRADE!! *Problem 5.3
Here are three lines that intersect at
one point.
Laila wrote the equation
x + 18 = 90.
Describe the error that Laila might
have made.

Answers

Answer:

Laila assumed that the lines that formed the angles x and 18° added up to 90. This is in fact false because of the lack of the square marking to signify it as a right or 90 degree angle.

I need help with premetier and area for 7 8 9

Answers

The answers to the three shapes are:

Figure 7; perimeter = 16.2mm, area = 12.64 square mm

Figure 8; perimeter = 15.2inches, area = 9.61 square inches

Figure 9; perimeter = 21.47yards,  area = 16.81 square yards

What is the perimeter of a shape?

Perimeter is the outside boundary of a plane shape.

Analysis:

for figure 7, perimeter = s + s + s = 3s = 3(5.4) = 16.2mm

                   Height of triangle = [tex]\sqrt{((5.4)^{2} - (2.7)^{2} }[/tex] = 4.68

            Area of triangle = 1/2 base x height = 1/2 x 5.4 x 4.68 = 12.64[tex]mm^{2}[/tex]

For figure 8, perimeter = b + b + a = 5.9 + 5.9 + 3.4 = 15.2 inches

                     Height of triangle = [tex]\sqrt{(5.9)^{2} - (1.7)^{2} }[/tex] = 5.65inches

           Area of triangle = 1/2 base x height = 1/2 x 3.4 x 5.65 = 9.61[tex]inches^{2}[/tex]

For figure 9, perimeter = b + a + c = 8.2 + 4.1 + 9.17 = 21.47yards

           Area of triangle = 1/2 x base x height = 1/2 x 8.2 x 4.1 = 16.81[tex]yards^{2}[/tex]

In conclusion, the perimeter and area of the given shapes are:

Figure 7; perimeter = 16.2mm, area = 12.64 square mm

Figure 8; perimeter = 15.2inches, area = 9.61 square inches

Figure 9; perimeter = 21.47yards,  area = 16.81 square yards

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Recently, bats have been disappearing from the wild due to a contagious fungus. To monitor the current population in a certain region, Troy collects 78 bats, marks them, and releases them. Later, Troy collects 600 bats, and finds that 39 of them are marked. To the nearest whole number, what is the best estimate for the bat population?

Answers

Answer:

1200 bats

Step-by-step explanation:

78 - 39 = 39

600 x 2 = 1200(bats).

Select ALL the correct answers. Observe the expression below and select the true statement(s). The "6" in the third term is a coefficient. The "7" in the third term is a coefficient. The "9" in the second term is a constant. The "y" in the third term is a factor. The "4" In the first term is a constant. The "x" in the first term is an exponent. 4r + 9 = y(6x + 7)​

Answers

An expression is defined as a set of numbers, variables, and mathematical operations. The statements that are true are 1, 3, and 5.

What is an Expression?

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

For the given expression 4x + 9 - y(6x + 7), the following things are can be written,

4 and 6 are coefficients.9 and 7 are constants.x and y are variables.

Thus, the statements that are true are:

The 6 in the third term is a coefficient.The 9 in the second term is a constant.The y in the third term is a factor.

Hence, the statements that are true are 1, 3, and 5.

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Which operation should be completed first to find the value of the expression below? 12 + 30/ (6 - 3) + 1


12 + 30

30 ÷ 6

3 + 1

6 - 3

Answers

The operation that should be completed first to find the value of the expression is 6 - 3

How to determine the first operation?

The expression is given as:

12 + 30/(6 - 3) + 1

When solving an expression;

All expressions in the bracket must be first evaluated

This means that the operation that should be completed first is 6 - 3

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What are the first three terms of a geometric sequence in which (picture below) and the common ratio is 5?

Answers

Answer:

5, 10, 15

Step-by-step explanation:

the increase in the sequence is 5 so since it starts from 0 which you can find out because 25 is the 5th sequence and that means that +2*5 =25 . x=0

0+ 5 = sequence 1

0+ 5+5 = seq 2

0+5+5+5= seq 3

Represent -5 / 4 and 5 / 4 on number line

Answers

Answer:

Image included:

Step-by-step explanation:

On a coordinate plane, solid circles appear at the following points: (negative 3, 2), (negative 3, 3), (1, 4), (1, negative 4), (2, negative 4), (2, negative 2).
How many points need to be removed from this graph so that it will be a function?

1 point
2 points
3 points
0 points

Answers

Three points must be removed from this graph so that it will be a function

How to determine the number of points?

The points are given as:

(-3, 2), (-3, 3), (1, 4), (1, -4), (2, -4), (2, -2).

For a set of point to represent a function;

Each x coordinate must point to only one y coordinate

From the given points, we have the following highlights:

The x value -3 has two y values (2 and 3)The x value 1 has two y values (4 and -4)The x value 2 has two y values (-4 and -2)

In the above highlights, one point each must be removed.

This means we have a total of 3 points

Hence, three points must be removed from this graph so that it will be a function

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Answer:

C. 3 points

Step-by-step explanation:

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