Identify the domain and range of the function.

Answer:

The approximate value of [tex]f(\theta) = \frac{\sec \theta \cdot (\sec \theta+\tan \theta)}{1+\tan^{2}\theta}[/tex] is 1.366.

Step-by-step explanation:

Let [tex]f(\theta) = \frac{\sec \theta \cdot (\sec \theta+\tan \theta)}{1+\tan^{2}\theta}[/tex], we proceed to simplify the formula until a form based exclusively in sines and cosines is found. From Trigonometry, we shall use the following identities:

[tex]\sec \theta = \frac{1}{\cos \theta}[/tex] (1)

[tex]\tan\theta = \frac{\sin\theta}{\cos \theta}[/tex] (2)

[tex]\cos^{2}+\sin^{2} = 1[/tex] (3)

Then, we simplify the given formula:

[tex]f(\theta) = \frac{\left(\frac{1}{\cos \theta} \right)\cdot \left(\frac{1}{\cos \theta}+\frac{\sin \theta}{\cos \theta}\right) }{1+\frac{\sin^{2}\theta}{\cos^{2}\theta} }[/tex]

[tex]f(\theta) = \frac{\left(\frac{1}{\cos^{2} \theta} \right)\cdot (1+\sin \theta)}{\frac{\sin^{2}\theta + \cos^2{\theta}}{\cos^{2}\theta} }[/tex]

[tex]f(\theta) = \frac{\left(\frac{1}{\cos^{2}\theta}\right)\cdot (1+\sin \theta)}{\frac{1}{\cos^{2}\theta} }[/tex]

[tex]f(\theta) = 1+\sin \theta[/tex]

If we know that [tex]\sin \theta =\frac{\sqrt{3}-1}{2}[/tex], then the approximate value of the given function is:

[tex]f(\theta) = 1 +\frac{\sqrt{3}-1}{2}[/tex]

[tex]f(\theta) = \frac{\sqrt{3}+1}{2}[/tex]

[tex]f(\theta) \approx 1.366[/tex]

40% was the percentage change in price.

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.

Given, The original price of the shirt is $50 but you paid $30 for it on sale

From the general formula of percentage change:

Percentage change = change in value / original value * 100

In our case,

Original value = 50

Change in values = 50 - 30

Change in values = 20

Percentage change = 20/50 * 100

Percentage change = 40

Therefore,  the percentage change in price was 40%.

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Answer:

No picture?

Step-by-step explanation:

i need a picture to anwser

Answer:

what? it seems like you just spammed anything from the web O_o

Step-by-step explanation:

Hello!

[tex]\large\boxed{2x + y = 3}[/tex]

Begin by finding the slope that would be perpendicular to the given equation.

A perpendicular line has a slope that is the opposite reciprocal of the original. Therefore:

1/2 --> -2

Find the answer choice that contains a slope of -2 when rewritten in the form y = mx + b:

Choice 1:

x + 2y = 2

Move x to the other side:

2y = -x + 2

Divide both sides by 2:

y = -1/2x + 1. This choice is incorrect.

Choice 2:

x - 2y = -12

Move x to the other side:

-2y = -x - 12

Divide both sides by -2:

y = 1/2x + 6. This choice is incorrect.

Choice 3:

2x + y = 3

Move 2x to the other side:

y = -2x + 3. This contains a slope of -2, which is correct.

Choice 4:

y - 2x = -5

Move -2x to the opposite side:

y = 2x - 5. This contains a slope of positive 2, so it is incorrect.

The correct answer is 2x + y = 3.

Answer:

D. y-2x=-5

Step-by-step explanation:

Answer:

π/2

Step-by-step explanation:

Find the period of the graph shown below.

Total time to complete one oscillation is called the period.

The total number of oscillations in the graph is 7 oscillations:

Hence;

7 oscillations = 3π + π/2 = 7π/2

To get the period, we want to know thw angle it takes to complete just one oscillation that is;

1 oscillation = x

Divide both equations:

7/1 = (7π/2)/x

7x = 7π/2

14x = 7π

x = 7π/14

x = π/2

Hence the period of the wave is π/2

Answer:

49.8 calories were left!!!

Step-by-step explanation: Just subtract 91-41.2!

Answer: Greater than

Step-by-step explanation:

36/0.6 = 60

60 is more than 36

Answer:

x = 3130/3

Step-by-step explanation:

3125 -5 +10 = 3X

3130 = 3x

x = 3130/3   or 1043 1/3

Answer:

The expected growth is 17.2%

Step-by-step explanation:

Let us have a present initial value of 500

we then proceed to get the value after 4 years

We use the compound interest formula to get the amount

That will be;

A = P( 1 + r/n)^nt

P = 500

r = 4% = 4/100 = 0.04

n is 2: semi annually means twice per year

t is 4

So

using the formula, we have that;

P = 500(1 + 0.04/2)^(2 * 4)

= 500(1.02)^8

= 586 approximately

So the percentage growth rate is as follows

(586-500)/500 * 100

= 86/500 * 100 = 17.2%

Answer:

35.09hours

Step-by-step explanation:

Since we are not told what to find, we can as well look for the time it took to ascend

Given

Distance below surface of water = 2000m

Speed = 57m/hr

Required

Time

Using the formula;

Speed = Distance/Time

Time = Distance/Speed

Time = 2000/57

Time = 35.09hours

Hence it took 35.09hours to ascend

Answer:

since it takes 1 additional stick to bake a cake,then it takes 84 additional sticks to bake 42 cakes

Answer:

slope is 3

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

Answer:

y=3.7+0.15(1)

Step-by-step explanation:

Note we are not given the options to choose from in this question, let us solve for the answer directly

Step one:

given data

The puppy's weight increases by 15% each week for the first 6 months

=0.15

The puppy currently weighs 3.7 pounds

Step two:

let the number of weeks be x

and the weight after x weeks be y

so

y= 3.7+0.15x

after 1 week the expression to calculate the weight is

y=3.7+0.15(1)

Answer:

c. -2x+10

Step-by-step explanation:

distributive property

(-2)x-(-2)5= -2x-(-10)

keep change change

-2x+10

where the answer is -2x+10

Answer:

-2x-10

Step-by-step explanation: so WE CAN SLOVE THIS EQUATION BY distrubutive property, -2 times x = -2x, we got 1 part of the equation. Now we distrubute -2 and -5.

-2 x -5 = -10.

So we get = -2x-10

Answer:

p=11/4

Step-by-step explanation:

Solve the rational equation by combining expressions and isolating the variable  p .

Answer: w = -9/4

Step-by-step explanation:

Answer:

43.407 years

Step-by-step explanation:

Zoe invest $600 in college savings account. The account earns 5.7% interest compounded quarterly. How many years will it take for Zoe's account to reach $7,000?

We are asked to find time t in a compound interest formula

The formula is given as:

t = log(A/P) / n[log(1 + r/n)]

A = Total amount = $7000

P = Principal = $600

n = number of times interest is compounded = Quarterly =4

r = Interest rate = 5.7% = 0.057

Hence,

t = log(7000/600) /4[log (1 + 0.057/4)]

t = 43.407 years

Answer:

Idkasd

Step-by-step explanation:

Keep trying

Answer:

the x-intercept is (-4,0)

the y-intercept is (0,-7)

Answer:

8

Step-by-step explanation:

Answer:

8 cups of water

Step-by-step explanation:

2 cups of water = 3 cups of flour

x cups of water = 12 cups of flour

12/3=4

2x4= 8

Answer:

-2x + 3y + z + 1

Step-by-step explanation:

Answer: D) 504

Step-by-step explanation:

9! = 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1

6! = 6 x 5 x 4 x 3 x 2 x 1

Using this, we can rewrite the initial expression as:

9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 / 6 x 5 x 4 x 3 x 2 x 1

We can see that 6 x 5 x 4 x 3 x 2 x 1 is in both the numerator and the denominator, so we can cancel it out, leaving us with 9 x 8 x 7 which equals 504.

Answer:

A

Step-by-step explanation:

Getting closer together means that both are becoming more accurate.

A valid model is such model whose calculated value approximates to the actual value. If it doesn't approximate to the actual value, it must be close to the actual value.

The model is valid if the results from the survey are close enough, together.

Given that:

[tex]p_1 = 75\%[/tex] -- the actual estimation of satisfied students

[tex]p_2 = 70\%[/tex] -- the second estimation of satisfied students

For a model to be valid, the calculated value must be close to the actual value.

If after Mateo's survey of more students, the result of satisfied or very satisfied students is still close to 75%, then Mateo's model is valid.

If otherwise, then the model is invalid.

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Answer:

None

Step-by-step explanation:

If i'm being honest i don't remember why it was none when I took the quiz but I had a reason for choosing none and its correct. I promise

Answer:

none

Step-by-step explanation:

sorry I know everyone already knows but I could use the 20 points

Answer:

The answer is below

Step-by-step explanation:

Two polygons are said to be congruent if they have the same size and shape that is their corresponding angles and sides are equal.

Hence since Quadrilaterals ABCD is congruent to EFGH, then their corresponding angles and sides are equal.

In quadrilateral ABCD:

∠A + ∠B + ∠C + ∠D = 360° (sum of angles in a quadrilateral)

Substituting:

47 + 39 + 112 + ∠D = 360

∠D + 198 = 360

∠D = 360 - 198

∠D = 162°

The image of Quadrilaterals ABCD and EFGH is not given but let us assume that they have the same orientation, hence:

∠A = ∠E = 47°

∠B = ∠F = 39°

∠C = ∠G = 112°

∠D = ∠H = 162°

Answer: The answer is C

Step-by-step explanation: