Compare the equations represented in the table, equation, and graph over
the interval
[-5, 3]. Which function is increasing the fastest?

This is not an identity.

[tex]\dfrac{2(\cos(x)\sin(x) - \sin(x)\cos(2x))}{\sin(2x)} \neq \sec(x)[/tex]

Check x = π/4, for which we have cos(π/4) = sin(π/4) = 1/√2. Together with sin(2•π/4) = sin(π/2) = 1 and cos(2•π/4) = cos(π/2) = 0, the left side becomes 1, while sec(π/4) = 1/cos(π/4) = √2.

Keeping the left side unchanged, the correct identity would be

[tex]\dfrac{2(\cos(x)\sin(x) - \sin(x)\cos(2x))}{\sin(2x)} = -2\cos(x) + 1 + \sec(x)[/tex]

To show this, recall

• sin(2x) = 2 sin(x) cos(x)

• cos(2x) = cos²(x) - sin²(x)

• cos²(x) + sin²(x) = 1

Then we have

[tex]\dfrac{2(\cos(x)\sin(x) - \sin(x)\cos(2x))}{\sin(2x)} = \dfrac{2\cos(x)\sin(x) - 2\sin(x)\cos(2x)}{\sin(2x)} \\\\ = \dfrac{\sin(2x) - 2\sin(x)\cos(2x)}{\sin(2x)} \\\\ = 1 - \dfrac{2\sin(x)\cos(2x)}{\sin(2x)} \\\\ = 1 - \dfrac{2\sin(x)(\cos^2(x) - \sin^2(x))}{2 \sin(x)\cos(x)} \\\\ = 1 - \dfrac{\cos^2(x) - \sin^2(x)}{\cos(x)} \\\\ = 1 - \cos(x) + \dfrac{\sin^2(x)}{\cos(x)} \\\\ = 1 - \cos(x) + \dfrac{1 - \cos^2(x)}{\cos(x)} \\\\ = 1 - \cos(x) + \sec(x) - \cos(x) \\\\ = -2\cos(x) + 1 + \sec(x)[/tex]

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Work Shown:

(160 with blue eyes)/(500 total) = (x with blue eyes)/(2500 total)

160/500 = x/2500

x = 2500*(160/500)

x = 800

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

Another approach:

160/500 = 0.32 = 32% of the first group has blue eyes

Assuming this percentage is the same for any group, then,

32% of 2500 = 0.32*2500 = 800 people of the second group are estimated to have blue eyes, of the 2500 total.

Answer:

2, 10, 50, 250

Step-by-step explanation:

For geometric sequences, multiply the previous term by the common ratio.

Using the formula for geometric sequences [tex]a_{n} =ar^{n-1}[/tex] , with [tex]a_{n}[/tex] being the nth term (so n=4 for the fourth term), a being the first term, and r being the common ratio.

Our starting term is 2. So that is automatically the first term of the four.

Second term:

[tex]a_{2} =2*5^{2-1}=2*5^1=2*5=10[/tex]

Third term:

[tex]a_{3} =2*5^{3-1}=2*5^2=2*25=50[/tex]

Fourth term:

[tex]a_{4} =2*5^{4-1}=2*5^3=2*5*5*5=10*25=250[/tex]

The value of x in all case is

1. The value of x is 2

2. The value of x is 1

3.The value of x is 57

4.The value of x is 93

If the sum of two angles is 180 degrees then they are said to be b angles, which form a linear angle together. Whereas if the sum of two angles is 90 degrees, then they are said to be complementary angles, and they form a right angle together.

1. As the given angle is 90 degree i.e., complementary angle.

So,

54+10x+16=90

20=10x

x=2

2. 65x-12=43x+10  (Vertically opposite angle)

 22x= 22

x=1

3. 72= x+15  (Vertically opposite angle)

x= 57

4.x+244+23=360  (Complete angle)

 x=93

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Step-by-step explanation:

the picture is not representing the real angle sizes. so, don't let yourself get confused by that.

the right neighbor angle of 90° at E is also 90°.

it has to be, because it is the supplementary angle to the left 90° (that means together they are 180°).

remember, all angles around a single point on one side of a line have to sum up to 180° (because the line can be seen as the diameter of a circle, with the point being the center of the circle, and so one side of the line is representing a half-circle and therefore 180°).

for the same reason angle 1 (the lower neighbor of the 90° angle at A) is also 90°.

for the same reason the lower neighbor angle of the 60° angle at E is 180 - 60 = 120°.

for the same reason the angle ABC is 180 - 40 = 140°.

for the angle BCD we need to remember :

the sum of interior angles of a polygon with n sides is

(n − 2) × 180°.

in our case ABCDE has 5 sides, so the sum of all interior angles is

(5 - 2) × 180 = 3×180 = 540°

we know 4 of the interior angles already, so

angle BCD = 540 - 90 - 90 - 120 - 140 = 100°

x is now the supplementary angle to the angle BCD.

so,

x = 180 - 100 = 80°

Answer:

-16.

Step-by-step explanation:

2/3 * (-3) * (4*5 + 6 - 2(-3)^2)

= -2(20 + 6 - 18)

= -2 * 8

= -16.

Answer:

Angle AED: 40
Angle BEC: 105

Explanation:
1) To find Angle AED, you have to do arc BC minus arc AD then divide by 2.
120 - 40 = 80.
80 / 2 = 40

2) To find Angle BEC, you have to do arc BA + CD then divide by 2. But that's only angle CED. You'll have to double the number because BEA is vertical; then minus 360.

62 + 88 = 150
150 / 2 = 75
75 times 2 = 150
360 - 150 = 210
210 / 2 = 105
- You'll divide 210 by 2 because of the vertical angles of AED and BEC.

Answer: 18 kilograms

Step-by-step explanation:

If each pumpkin weighs 3 kilograms and the farmer has 6 pumpkins the equation would be 6x3=18 in order to find the mass of the farmer's pumpkins.

Answer:

There are infinitely many solutions to the system because the equations represent the same line

Step-by-step explanation:

please mark me as brainlest

Answer: x = 4/3

Step-by-step explanation: I just answered the answer

Answer:

C. 91.46

Step-by-step explanation:

Use BODMAS!

Answer:

C. 91.46

Step-by-step explanation:

Using Pemdas to solve:

5.9 (9 - 5) + 4^3 + 3.86

First you have to solve in the parenthesis

5.9 (9 - 5) + 4^3 + 3.86

= 4

New equation:

5.9 x 4 + 4^3 + 3.86

Now solve the exponent:

5.9 x 4 + 4^3 + 3.86

= 64

New equation:

5.9 x 4 + 64 + 3.86

Now we have to do multiplication:

5.9 x 4 + 64 + 3.86

= 23.6

New equation:

23.6 + 64 + 3.86

Now all you have to do is add all that together and you have your answer:

23.6 + 64 + 3.86

= 91.46

Hope this helps.

The number of rows in the arena is 26

The hockey arena illustrates an arithmetic sequence, and it has the following parameters:

The number of rows (i.e. the number of terms) is calculated using:

[tex]S_n = \frac{n}{2}(2a + (n -1) * d)[/tex]

So,we have:

[tex]10920 = \frac{n}{2}(2 * 220 + (n -1) * 16)[/tex]

Evaluate the terms and factors

[tex]21840 = n(440 + 16n -16)[/tex]

Evaluate the like terms

21840 = n(424+ 16n)

Expand

21840 = 424n + 16n^2

Rewrite as:

16n^2 + 424n - 21840 = 0

Using a graphical tool, we have:

n = 26

Hence, the number of rows in the arena is 26

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Answer: SAS similarity theorem

Proportional relationship:

[tex]\sf \dfrac{AB}{AC} = \dfrac{AM}{AN}[/tex]

insert values

[tex]\rightarrow \sf \dfrac{21+9}{14+6} = \dfrac{21}{14}[/tex]

simplify

[tex]\rightarrow \sf 1 = 1[/tex]

L.H.S = R.H.S

The triangles are congruent and follows the rule SAS similarity theorem.

The triangles has/starts from the same angle, corner (A).

Using proportions, it is found that he can be expected to hit 36 home runs during the 162 game season.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

In this problem, the player hits 10 home runs in 45 games, hence the proportion is:

p = 10/45.

Then, in 162 games, the amount is:

HR = 10/45 x 162 = 36.

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The quadrants is tan⁻¹x restricted is A. Quadrants I and IV

To answer the question, we need to know what tan⁻¹x is.

tan⁻¹x is the inverse trigonometric function of tanx, which is the value of the angle for tanx.

To find the quadrants in which tan⁻¹x is restricted, we know that tanx lies in the range

-∞ ≤ tanx ≤ +∞ for -90° ≤ x ≤ 90°.

tan⁻¹x lies between quadrant I and IV

So, the quadrants is tan⁻¹x restricted is A. Quadrants I and IV

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Answer: A = π r2

r=8 and 8 squared is 64 and 64×3.14=200.96 or rounded to the nearest whole number it would be 201

Step-by-step explanation: brainliest please?

The value of the cos P + cos Q is 7/5 if sin Q = 4/5 after applying the identities of trigonometric.

Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.

We know that:

P + Q are complementary, which means that

P+Q = 90°

Then R is a right angle, i.e. it measures 90°.

sin(90-x) = cos (x)

cos(90-x) = sin (x)

Then sinQ = 4/5  

cos(90-Q) = cosP = 4/5

Now sin²(P) + cos²(P) = 1

sin²(P) = 1 - cos²(P)

sin²(P) = 1 -[4/5]² =9/25

sin(P) = 3/5

cos(Q) = sin(P) = 3/5

cos(P) + cos(Q) = 4/5 + 3/5 = 7/5

Thus, the value of the cos P + cos Q is 7/5 if sin Q = 4/5 after applying the identities of trigonometric.

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The probability that she will NOT take out an orange, then an apple, and finally a grapefruit in that order is 0.2917.

Probability helps us to know the chances of an event occurring.

[tex]\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]

A.) The probability that she will NOT randomly take out two oranges in a row,

Probability = 1 - (5/12)² = 0.8264

B.) The probability that she will NOT randomly take out two grapefruits in a row,

Probability = 1 - (4/12)² = 0.8264 = 0.8889

C.) The probability that she will NOT randomly take out two apples in a row,

Probability = 1 - (3/12)² = 0.8264 = 0.9375

D.) The probability that she will NOT take out an orange, then an apple, and finally a grapefruit in that order,

Probability = (7/12) × (9/12) × (8/12) = 0.2917

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Answer:

C

Step-by-step explanation:

M is less than n because it comes before it in the number line

Answer:

x=5 and y=7

Step-by-step explanation:

Just substitute in y=x+2 into the equation 5x-4y=-3 to get 5x-4(x+2)=-3 which simplifies to x=5. Substitute x into y=x+2 to find y=7

Answer:

=4x³-4x²+4x-3

Step-by-step explanation:

(f+g)(x)=4x³+2x²-6x²+4x-6+3

=4x³-4x²+4x-3

Answer:

Can't see the problem. Send a picture of it.

Answer:

Step-by-step explanation:

Formula

The sin(A) =  opposite / hypotenuse

Givens

Opposite = CB = 11

Hypotenuse = AB = 61

Solution

Sin(A) = 11/61

Sin(A) = 0.1803

Answer

Sin(A) = 11/61

Sin(A) = 0.1803

The pair of angles that share a ray as a common side in the given diagram is: ∠FAB and ∠FAD.

Adjacent angles are angles that lie adjacent or next to each other sharing a common vertex and have the same ray as a common side.

In the diagram attached below, ∠FAB and ∠FAD share a common vertex, A, and a ray FA as a common side.

Therefore, the pair of angles is: ∠FAB and ∠FAD.

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Since the paper representing her desk is 1 1/4 inches by 2 1/4 inches, the actual dimensions of her desk are D: 2 ¹/₂ ft by 4 ¹/₂ ft

To answer the question, we need to know what scale is

A scale is the ratio of two dimension and it is given on a scale drawing.

Given that Chelsea makes a scale drawing of the room and cuts out pieces of paper to represent her furniture, and the paper representing her desk is 1 1/4 inches by 2 1/4 inches.

Since on the scale, we have 1/2 in = 1 foot ⇒ 1 in = 2 ft

So, the actual dimensions of her desk are

1 ¹/₄ in by 2 ¹/₄ in = 5/4 in by 9/4 in

= 5/4 × 1 in by 9/4 × 1 in

= 5/4 × 2 ft by 9/4 × 2 ft

= 5/2 ft by 9/2 ft

= 2 ¹/₂ ft by 4 ¹/₂ ft

So, the actual dimensions of her desk are D: 2 ¹/₂ ft by 4 ¹/₂ ft

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Step-by-step explanation:

it is very simple :

the midpoint coordinates are created as the midpoint of the x coordinates, and the midpoint of the y coordinates.

the x coordinate of the midpoint is

(0 + 10)/2 = 10/2 = 5

the y coordinate of the midpoint is

(-2 + -6)/2 = -8/2 = -4

Answer:

w = 10

Step-by-step explanation:

First we take the two values for the breadth of the rectangle

So:

5x - 9 = 3x + 7

now we solve this equation as follows:

5x - 3x = 9 + 7

2x = 16

x = 8

now that we have found the value for x, we can substitute it in the equation, 5x - 9,or in the equation, 3x + 7.

when we substitute x in any of these equations, we get

5(8) - 9 = 31

3(8) + 7 = 31

now that we have the value for the breadth we can form the following equation:

31 × w = 310

31w = 310

w = 310/31 = 10

Answer:

10

Step-by-step explanation:

Firstly, we find the value of X

since 5X-9 and 3X+7 are lenghts

5X-9= 3X+7

5X-3X= 7+9

2X = 16

dividing bothsides by 2

2X/2= 16/2

X = 8

Hence,

5X-9= 5(8)-9= 40-9 = 31

3X+7=3(8)+7= 24+7= 31

To find the width

Area= lenght×width

310= 31×w

31w= 310

w= 310/31

W= 10

Answer:

30

Step-by-step explanation:

[tex]\frac{5\cdot\frac{6}{6} }{2\cdot\frac{6}{6} } = \frac{25}{30}, \frac{12}{30}[/tex]

Answer:

25.5

Step-by-step explanation:

I did the same assignment