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The values of s in the interval [0, 2π) such that tan s = -(√3)/3 are 5π/6 and 11π/6.

What is trigonometry and how is it assessed?
Simply put, trigonometric functions—also referred to as circular functions: are the functions of a triangle's angle. This means that these trig functions provide the relationship between the angles and sides of a triangle. Sine, cosine, tangent, cotangent, secant, and cosecant are the fundamental trigonometric functions. Numerous trigonometric identities and formulas indicate the relationship between the functions and aid in determining the triangle's angles.
The quadrants determine the values of the trigonometric functions.


Given, tan s = -(√3)/3 ⇒ tan s = -(√3)/(√3)² ⇒ tan s = (-1)/(√3)
Therefore, the simplified value of tangent of s is tan s = (-1)/(√3)
Again the interval of the function is [0, 2π), so only the second and fourth quadrants can contain the given value of tangent being negative.
For the value of s in second quadrant, we have:
tan s = (-1)/(√3) ⇒ tan s = tan (π - (π/6)) ⇒ tan s = tan (5π/6) ⇒ s = 5π/6
For the value of s in the fourth quadrant, we have:
tan s = (-1)/(√3) ⇒ tan s = tan (2π - (π/6)) ⇒ tan s = tan (11π/6) ⇒ s = 11π/6
Thus, the values of s in the interval [0, 2π) such that tan s = -(√3)/3 are 5π/6 and 11π/6.

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Given:

Amount of chocolate chips needed = 30 ounces

Amount of chocolate you have already = 8 ounces

Let's find the inequality that can be used to find the ounces of chocolate chips you need to buy.

To write the inequality, we have:

8 + x ≥ 30

Where x represents the ounces of chocolate chips you need to buy.

Therefore, the inequality that could be used to fid how many ounces of chocolate chips needed is:

8 + x ≥ 30

ANSWER:

8 + x ≥ 30

The temperature of the object is -456.97 degrees

To determine the exact value of sin A we get -2/√13

What is determinant?

the determinant is a scalar of value that is a function of to the  entries of a square matrix. It is  allows characterizing of  some  properties of to the  matrix and the linear map of represented by the matrix.

It is a scalar value which is associated with the square matrix.

Sol-Cos A =3/√13

angle A is not in quadrant I

So angle A is in quadrant IV

Thus,

Sin A =-√(√13)^2-3^2/√13

           =-√13-9/√13

           =-√4/√13

           =-2/√13

Thus the answer is -2/√13.

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Hello there. To solve this question, we'll have to remember some properties about triangles.

Given the triangle:

Notice in this case we have two consecutive angles and a side between them. This is a case of ASA (angle-side-angle).

With respect to the side with measure x, we have two consecutive angles then the side, hence AAS.

To find x, we'll have to apply the law of sines:

In this case, the angle opposite to x measures 73º and the angle opposite to 4 measures 85º, hence:

Multiply both sides by a factor of sin(73º)

Using a calculator, we get the following approximation (rounding to the nearest tenth):

This is the measure of x we're looking for.

The average rate of change of the function is the average rate at which one quantity is changing with respect to another.

Average rate of change = (y2 - y1)/(x2 - x1)

y represents the output values and it is also called f(x)

x represents the input values

For the given interval,

for f(- 1), x = -1 and f(x) = 8

For f(1), x = 1, f(x) = 4

Average rate of change = (4 - 8)/1 - - 1) = - 4/(1 + 1) = - 4/2

Average rate of change = - 2

The quadrants on the coordinate plane are the following:

then, we have that the upper left quadrant is quadrant II

Answer:

x=13

Step-by-step explanation:

50+3x=89

89-50=3x

39=3x

13=x

We have to solve this inequality:

We now use the properties of the absolute value. We will have two boundaries: one corresponding to when 4x+5 is negative and the other is when 4x+5 is positive.

When 4x+5 is negative, the absolute value function will change the sign of the expression, so we will have:

The other interval will be defined when 4x+5 is positive. In this case, the absolute function does not change the sign and we get:

Then, the solution set is the union of the intervals x < -3.25 and x > 0.75.

We can express the interval as (-∞, -3.25) ∪ (0.75, ∞).

Answer: (-∞, -3.25) ∪ (0.75, ∞)

Any number raised to the power of zero equals 1, then

then, we need to substitute the value 10 in the variable s. It yields,

Then, the answer is

that is, 1 / 100.

Unknown, the correct equation is:

- 4,863 + 81.1m = - 3,645 + 76.9m

And to solve for m, you use the standard form:

Like terms:

81.1m - 76.9m = -3,645 + 4,863

4.2m = 1,218

Answer:Nuts

Step-by-step explanation:

green on green

Recalling the laws of exponents:

So, for the number 3^5 times 3^4, we have:

Therefore, the answer is the option b) 3^9.

Car B was 5 miles east of car A, Option A

Answer

Option C is correct.

The roots of the given function include

2, -3i, (4 + i), (4 - i)

Explanation

To solve this, we would put the given roots of the solution into the place of x. The ones that give 0 are the roots of the expression

The expression is

f(x) = x⁵ - 10x⁴ + 42x³ - 124x² + 297x - 306

Starting with 2

f(x) = x⁵ - 10x⁴ + 42x³ - 124x² + 297x - 306

f(2) = 2⁵ - 10(2)⁴ + 42(2)³ - 124(2)² + 297(2) - 306

= 32 - 160 + 336 - 496 + 594 - 306

= 0

So, 2 is a root

-3i

f(x) = x⁵ - 10x⁴ + 42x³ - 124x² + 297x - 306

f(-3i) = (-3i)⁵ - 10(-3i)⁴ + 42(-3i)³ - 124(-3i)² + 297(-3i) - 306

= -243i - 810 + 1134i - 1116 - 891i - 306

= 0

So, -3i is also a root

4 + i

f(x) = x⁵ - 10x⁴ + 42x³ - 124x² + 297x - 306

f(4 + i) = (4 + i)⁵ - 10(4 + i)⁴ + 42(4 + i)³ - 124(4 + i)² + 297(4 + i) - 306

= 0

So, we know that the right root, when inserted and expanded will reduce the expression to 0.

4 - i

f(x) = x⁵ - 10x⁴ + 42x³ - 124x² + 297x - 306

f(4 - i) = (4 - i)⁵ - 10(4 - i)⁴ + 42(4 - i)³ - 124(4 - i)² + 297(4 - i) - 306

= 0

Inserting any of the other answers will result in answers other than 0 and show that they aren't roots/zeros for this expression.

Hope this Helps!!!

Answer:

2

Step-by-step explanation:

The distance on the x-coordinate from N to M is:

distance = 2 - (-3) = 2 + 3 = 5

Because 2 is the x-coordinate of M and -3 is the x-coordinate of N

Then, 1/4 of the distance is:

1/4*distance = (1/4)*5 = 5/4 = 1.25

So, the x-coordinate of R is:

(x-coordinate of N) + (1/4*distance) = -3 + 1.25 = -7/4 = -1.75

At the same way, the distance on the y-coordinae from N to M is:

distance = 3 - (-3) = 3 + 3 = 6

Then, 1/4 of the distance is:

1/4*distance = (1/4)*6 = 6/4 = 1.5

So, the y-coordinate of R is:

(y-coordinate of N) + (1/4*distance) = -3 + 1.5 = -1.5

Answer: R(x, y) = (-1.75, -1.5)

Answer:

Option 2

Step-by-step explanation:

hope this helps

EXPLANATION

Since 150% represents a percentage bigger than 156, the appropiate relationship would be as follows:

Where the whole number is 156 and the percentage is 150%:

In conclusion, the solution is 234

Solution

- The solution steps are given below:

Final Answer

111 ft

In general, a quadratic equation can be written in terms of its solutions:

Now, notice that:

when x= -1/2, and it is equivalent to:

Therefore, you can write the quadratic equation as:

Computing the above multiplication, you get:

Simplifying the above equation you get:

The exponential expression as required to be chosen is; 10⁴.

The expanded form of the expression is; 10 × 10 × 10 × 10.

The standard form of the expression is; 10,000.

It follows from the task content that the exponential expression is to be written in expanded and standard form.

Since the exponential expression must have 10 as the base and an even number between 1 and 10 as the exponent.

An example of such exponential expression is therefore;

10⁴.

Hence, to write the expression in expanded form; it is written as a product of factors as follows;

10 × 10 × 10 × 10

Also, the expression can be written in standard form as the result of the multiplication above;

= 10,000.

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By theorem, we will have that m

m

=> m

=>2m

Then, we replace values and solve:

2m m

So, we have that m

It is said that the dressmaker bought 5 yards of cotton and silk. Let's see the first equation of the system:

And that he spent $46 on those 5 yards. Also, it is said that silk costs $17 per yard and cotton $4 per yard. Let's see the second equation of the system:

If 46 is how much the dressmaker spent, and 17 and 4 represent how much silk and cotton cost PER YARD then we know that x and y represent how much of each fabric did the dressmaker bought. Also, in the first equation you see that the total is 5 yards. So, if you solve this system you will find that 'x' is how many yards of silk the dressmaker bought and 'y' is how many yards of cotton he bought.

In summary, the solution of this system represents how may yards of silk (x) and cotton (y) the dressmaker bought.

The equation of the word is,

Using the z-distribution, it is found that:

a. The 90% confidence interval to estimate of the percentage of yellow peas is: (34.04%, 41.58%).

b. The correct option is: Yes, the confidence interval does not include 0.25, so the true percentage could not equal 25%.

The bounds of a confidence interval of proportions is given according to the equation presented as follows:

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which the parameters are described as follows:

The confidence level is of 90%, hence the critical value is z = 1.645, using a z-distribution calculator.

The values of the sample size and of the estimate are given as follows:

[tex]n = 447, \pi = \frac{169}{447} = 0.3781[/tex]

Hence the lower bound of the interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.3781 - 1.645\sqrt{\frac{0.3781(0.6219)}{447}} = 0.3404[/tex]

The upper bound is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.3781 + 1.645\sqrt{\frac{0.3781(0.6219)}{447}} = 0.4158[/tex]

As a percentage, the interval is given as follows: (34.04%, 41.58%).

The confidence interval does not contain 0.25, hence the true percentage would not be equal to 25%, contradicting the expectation.

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Explanation

The first step is to draw a representation of the given parameters.

Since this is a right-angle triangle, the Pythagorean theorem applies. This can be seen below;

We can then apply it to the sides of the triangle.

DF is the longest side. Therefore,

Answer

Given:

Solve :

The function g(x) convert then x is equal to h(x) then:

7 out of every 500 Americans are aged 13-17 years generation are vegetarian

Thus the ratio of the vegetarian is 7 : 500

In a group of 350,

Let x be the number of people who are vegetarian

So, the ratio out of 350 who are vegetarian are : x : 350

SInce the ratio is same so:

So, the number of people who are vegetarian out of 350 people is 4 people

From the given circle, the measure of the arc or the central angle indicated is as shown at the center of the circle is subtended by the arc

Hence, the measure of the arc or central angle indicated is 65° ,Option B