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Hi My name is Ella and I need help

The point −20, 21 is on the terminal arm of an angle = in standard position. Hence, sinФ = 21/29 and cos Ф = -20/29

Trigonometric identities are the functions that include trigonometric functions such as sine, cosine, tangents, secant, and, cot.

Given Data

A (-20 , 21)

We have to find sin = ? and cos = ?

The point is in the fourth quadrant

We have the Opposite side and the Adjacent side

Calculate the hypotenuse

     c² = (-20)² + (21)²

       c² = 400 + 441

       c² = 841

       c = 29

Hence,

sinФ = 21/29

cos Ф = -20/29

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The denominator is zero (0/0 is undefined), we cannot determine the exact value of f(-3) using this equation.

To solve the given equations, we need to find the value of the function f(x) for specific values of x.

"If f(x) / (x - 2) = x³ + 2x - 4 + 13/(x - 2), what is f(2)?"

To find f(2), we can substitute x = 2 into the equation and solve for f(2).

Plugging in x = 2, we get:

f(2) / (2 - 2) = 2³ + 2(2) - 4 + 13/(2 - 2)

Since the denominator is zero (2 - 2 = 0), the equation is undefined. Therefore, there is no solution for f(2) in this case.

"If f(x) / (x + 3) = 3x² - 4x + 2, what is f(-3)?"

To find f(-3), we can substitute x = -3 into the equation and solve for f(-3).

Plugging in x = -3, we get:

f(-3) / (-3 + 3) = 3(-3)² - 4(-3) + 2

Simplifying, we have:

f(-3) / 0 = 3(9) + 12 + 2

f(-3) / 0 = 27 + 12 + 2

f(-3) / 0 = 41

Additional information or context is needed to solve for f(-3).

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\(\\ \rm\hookrightarrow \sqrt{x-6}=x-12\)

\(\\ \rm\hookrightarrow x-6=(x-12)^2\)

\(\\ \rm\hookrightarrow x-6=x^2-24x+144\)

\(\\ \rm\hookrightarrow x^2-25x+150=0\)

\(\\ \rm\hookrightarrow x^2-10x-15x+150=0\)

\(\\ \rm\hookrightarrow (x-10)(x-15)=0\)

\(\\ \rm\hookrightarrow x=15\:or \:10\)

Answer:

\(x = 15,10\) || C and D is the correct choices.

Step-by-step explanation:

\(\sqrt{x-6}=x-12\)

\(x-6 =(x-12)^2\)

\(x-6 = x^2 -24x +144\)

\(x^2 -24x -x +144 +6 = 0\)

\(x^2 - 25x + 150= 0\)

\(x^2 -15x -10x +150=0\)

\(x(x-15)-10(x-15)=0\)

\((x-15)(x-10) = 0\)

\(x = 15,10\)

The solution to the system of given inequalities is (-7, 0).

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

The given system of inequalities are y> 2x-4 and y≤ -x-7.

The solution of the system of inequalities is the intersection region of all the solutions in the system.

x<y/2 +2 and x≤-y-7

The solution of the system of inequalities is (-7, 0)

Therefore, the solution to the system of given inequalities is (-7, 0).

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To find a particular solution of the non-homogeneous equation and the general solution of the equation, we can use the method of variation of parameters.

First, let's find the Wronskian of the homogeneous solutions y1(x) and y2(x):

W(y1, y2) = | y1 y2 |

| y1' y2' |

We have y1(x) = sin(x) / √x and y2(x) = cos(x) / √x. Differentiating these functions, we get:

y1'(x) = (cos(x) / √x - sin(x) / (2√x^3))

y2'(x) = (-sin(x) / √x - cos(x) / (2√x^3))

Substituting these values into the Wronskian:

W(y1, y2) = | sin(x) / √x cos(x) / √x |

| (cos(x) / √x - sin(x) / (2√x^3)) (-sin(x) / √x - cos(x) / (2√x^3)) |

Expanding the determinant:

W(y1, y2) = (sin(x) / √x) * (-sin(x) / √x - cos(x) / (2√x^3)) - (cos(x) / √x) * (cos(x) / √x - sin(x) / (2√x^3))

Simplifying:

W(y1, y2) = -1 / (2√x)

Now, we can find the particular solution using the variation of parameters formula:

y_p(x) = -y1(x) * ∫(y2(x) * g(x)) / W(y1, y2) dx + y2(x) * ∫(y1(x) * g(x)) / W(y1, y2) dx

Here, g(x) = 3x√xsin(x). Substituting the values:

y_p(x) = -((sin(x) / √x) * ∫((3x√xsin(x)) * (-1 / (2√x))) dx + (cos(x) / √x) * ∫((3x√xsin(x)) / (2√x)) dx

Simplifying the integrals:

y_p(x) = -(∫(-3sin^2(x)) dx) + (∫(3xcos(x)sin(x)) dx)

Integrating:

y_p(x) = 3/2 (xsin^2(x) - cos^2(x)) - 3/2 (xcos^2(x) + sin^2(x)) + C

Simplifying:

y_p(x) = 3x(sin^2(x) - cos^2(x)) + C

The general solution of the equation is given by the sum of the homogeneous solutions and the particular solution:

y(x) = C1 * (sin(x) / √x) + C2 * (cos(x) / √x) + 3x(sin^2(x) - cos^2(x)) + C

where C1, C2, and C are arbitrary constants.

Answer:

a=(-3,-6) and b=(12,4)

from -3 to 12 is 15 units

7/10 * 15=10.5

add 10.5 to -3 to get 7.5 for the x-coordinate

from -6 to 4 is 10 units

7/10 * 10=7

add 7 to -6 to get 1 for the y-coordinate

the point 7/10 of the way from a to b is (7.5,1) ANSWER

graph these points to check your answer (the point (7.5,1) is on the line segment AB))

also, the distance from a to b is 18.0277

7/10 of this is 12.62

the distance from (-3,-6) to (7.5,1) is also 12.62

Step-by-step explanation:

#33

LHS

\(\\ \rm\Rrightarrow \dfrac{sin\theta}{csc\theta}+\dfrac{cos\theta}{sec\theta}\)

\(\\ \rm\Rrightarrow \dfrac{sin\theta}{\dfrac{1}{sin\theta}}+\dfrac{cos\theta}{\dfrac{1}{cos\theta}}\)

\(\\ \rm\Rrightarrow sin^2\theta+cos^2\theta\)

\(\\ \rm\Rrightarrow 1\)

#34

LHS

\(\\ \rm\Rrightarrow tanAcsc^2A-tanA\)

\(\\ \rm\Rrightarrow \dfrac{sinA}{cosA}\times \dfrac{1}{sin^2A}-\dfrac{sinA}{cosA}\)

\(\\ \rm\Rrightarrow \dfrac{sinA}{sin^2AcosA}-\dfrac{sinA}{cosA}\)

\(\\ \rm\Rrightarrow \dfrac{1}{sinAcosA}-\dfrac{sinA}{cosA}\)

\(\\ \rm\Rrightarrow \dfrac{1-sin^2A}{sinAcosA}\)

\(\\ \rm\Rrightarrow \dfrac{cos^2A}{sinAcosA}\)

\(\\ \rm\Rrightarrow \dfrac{cosA}{sinA}\)

\(\\ \rm\Rrightarrow cotA\)

Proved

Answer:

Trigonometric Identities used:

\(\csc \theta=\dfrac{1}{\sin \theta}\)

\(\sec \theta=\dfrac{1}{\cos \theta}\)

\(\cot \theta=\dfrac{1}{\tan \theta}\)

\(\sin^2 \theta + \cos^2 \theta=1\)

\(\csc^2 \theta = 1 + \cot^2 \theta\)

Question 33

\(\large \begin{aligned}\dfrac{\sin \theta}{\csc \theta}+\dfrac{\cos \theta}{\sec \theta}& = \sin \theta \cdot \dfrac{1}{\csc \theta}+\cos \theta \cdot \dfrac{1}{\sec \theta}\\\\& = \sin \theta \cdot \dfrac{1}{\frac{1}{\sin \theta}}+\cos \theta \cdot \dfrac{1}{\frac{1}{\cos \theta}}\\\\& = \sin \theta \cdot \sin \theta+\cos \theta \cdot \cos \theta\\\\& = \sin^2 \theta + \cos^2 \theta\\\\& = 1\end{aligned}\)

Question 34

\(\large \begin{aligned}\tan \theta \csc^2 \theta - \tan \theta & = \tan \theta ( \csc^2 \theta - 1)\\\\& = \tan \theta (1 + \cot^2 \theta -1)\\\\& = \tan \theta \cot^2 \theta \\\\& = \dfrac{1}{\cot \theta} \cdot \cot^2 \theta \\\\& = \dfrac{\cot^2 \theta}{\cot \theta}\\\\& = \cot \theta\end{aligned}\)

200 pounds need to collect to earn the $50.00. Divide the cost per pound from the total amount needed, \(\frac{50.00}{0.25}\)= 200 pounds.

The official money of the U.k. and its regions is the GBP, or British pound sterling. The Pound is the earliest currency that is still accepted as legal tender in the entire world. The GBP, represented by pound sign (£), has one of the greatest trade volumes worldwide.

The development of the pounds sterling -The Latin word "libra," which means balance and weight, is where the name "pound sterling" comes from. During the years, the pound banknotes underwent various revisions before being initially printed by the Bank of England and over 300 years ago.

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Answer:

i think A=20

A=pq/2 =4·10/2 =20

Hope i helped

-lvr

Answer:

the area is 20

Step-by-step explanation:

Answer:

The answer is B

Step-by-step explanation:

1B, 2D, 3C, 4A

on Edge this is the correct answer

Brainliest would be awesome

Answer:

yes just multiply it once more by -1

Step-by-step explanation:

Answer:

66

Step-by-step explanation:

the difference of 54 and 32 is 54 - 32 = 22

the difference of 8 and 5 is 8 - 5 = 3

then

22 × 3 = 66

What is the question?

Computing the total number of counters in the class as 1,108, the mean number of counters that the 46 children have is 24.

The mean refers to the average value.

The average is the quotient of the total value divided by the number of items in the data set.

The number of boys in the class = 26

The number of girls in the class = 20

The total number of boys and girls in the class = 46

The mean number of counters that the boys have = 28

The total number of counters that the boys have = 728 (28 x 26)

The mean number of counters that the girls have =19

The total number of counters that the girls have = 380 (19 x 20)

The total number of counters that the class has = 1,108 (728 + 380)

The average or mean number of counters in the class = 24 (1,108 ÷ 46)

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Answer:

33x−27

Step-by-step explanation:

Answer:

5/16

Step-by-step explanation:

10/32

Find common factor: 2

Divide by common factor

10/32 ÷ 2/2

=5/16

Answer:

5/16

Step-by-step explanation:

Find lowest common factor of both 10 and 32, which is 2. Divide both 10 in numerator and 32 in denominator by 2 to get \(\frac{5}{16}\)

The equation that  matches this problem is 15 + 3p = 117

Let the cost of one pair of pants be represented by the variable p.

Then, the cost of three pairs of pants is 3p.

We are also given that the cost of a t-shirt is $15.

The total cost of Amelia's purchase is $117.

Therefore, the equation that matches this problem is:

15 + 3p = 117

This equation represents the total cost of Amelia's purchase, which includes the cost of one t-shirt and three pairs of pants.

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The question provides the following parameters for the sector under consideration:

PART A: Arc Length

The formula to calculate the Arc Length is given as

Therefore, we can substitute the values for the parameters and solve as

The arc length is 14.7 inches.

PART B: Sector Area

The formula to calculate the Arc Length is given as

Therefore, we can substitute the values and solve as

The sector area is 102.6 square inches.

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The centre coordinates would be the opposite value of what is in the brackets

For example, the x value in the brackets is -3, the centre coordinate x value would be positive 3

The same would apply to the y value

The radius would be the square root of 36

Thus, your answer would be option A

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The image you described features a number line that goes from 0 to 6.5 in increments of 0.5.

On this number line, there is an arrow that starts at 0 and extends to 2.5, and then continues from 2.5 to 5.

This image can be visualized as follows:

0        1        2        3        4        5        6        6.5

|--------|--------|--------|--------|--------|--------|--------|

        |------------------------|------------------------|

             0 to 2.5                 2.5 to 5

The vertical lines represent the increments of 0.5 on the number line, and the arrow indicates the segments from 0 to 2.5 and from 2.5 to 5.

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Answer:

Step-by-step explanation:

The first part is already solved.

We got the scale factor

Use this to find the missing side:

Answer:

a. EXPLAINED IN THE PIC

b. 20

Step-by-step explanation:

*in the line 4, the number which I wrote, was 4*

Answer:

4 hours. 1 3/4 is about 2, and 2 1/4 rounds to 2. 1/4 would round to 0, but it would not affect the estimate's accuracy much because we rounded up by 1/4 on 1 3/4 already. Philipe spent about 4 hours on activities.  

Step-by-step explanation:

Answer:

Numbers that can be expressed as a ratio of two number (p/q form) are termed as a rational number. Numbers that cannot be expressed as a ratio of two numbers are termed as an irrational number.

Step-by-step explanation:

Answer:

Step-by-step explanation:

C and E

The value of x that makes the line containing (1,2) and (5,3) perpendicular to the line containing (x,4) and (3,0) is x = 2.

To determine the value of x such that the line containing (1,2) and (5,3) is perpendicular to the line containing (x,4) and (3,0), we need to find the slope of both lines and apply the concept of perpendicular lines.

The slope of a line can be found using the formula:

slope = (change in y) / (change in x)

For the line containing (1,2) and (5,3), the slope is:

slope1 = (3 - 2) / (5 - 1) = 1 / 4

To find the slope of the line containing (x,4) and (3,0), we use the same formula:

slope2 = (0 - 4) / (3 - x) = -4 / (3 - x)

Perpendicular lines have slopes that are negative reciprocals of each other. In other words, if the slope of one line is m, then the slope of a line perpendicular to it is -1/m.

So, we can set up the equation:

-1 / (1/4) = -4 / (3 - x)

Simplifying this equation:

-4 = -4 / (3 - x)

To remove the fraction, we can multiply both sides by (3 - x):

-4(3 - x) = -4

Expanding and simplifying:

-12 + 4x = -4

Adding 12 to both sides:

4x = 8

Dividing both sides by 4:

x = 2

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