cos² (x)(1+tan²(x)) = 1, establish the identity

Math instructor may provide feedback on Prudence's solution by advising her to check her solutions for extraneous solutions, showing more detailed work, and continuing to practice solving challenging problems to improve her skills for equation.

One possible comment the math instructor could make about Prudence's solution is that it is important to check the solutions she obtained to make sure they are valid. When solving rational equations, it is possible to obtain extraneous solutions, which are solutions that do not work in the original equation. Therefore, the instructor may advise Prudence to substitute her solutions back into the original equation and verify that they satisfy the equation.

Another comment the instructor could make is that Prudence should show her work and steps in more detail, especially if she is turning in her solution for a graded assignment. By showing more detailed work, Prudence can demonstrate a deeper understanding of the problem and how she arrived at her solution.

The instructor may also commend Prudence on her ability to solve a complex rational equation with multiple variables and parentheses. This shows that she has a strong grasp of algebraic concepts and can apply them effectively. However, the instructor may also suggest that Prudence continue to practice solving more challenging problems to further improve her skills.

Learn more about equation here:

https://brainly.com/question/14686792

#SPJ1

The area of one segment formed by a 6" square inscribed in a circle cxan be expressed as 5.13 square inches.

Two unique points on a line define the boundaries of a line segment. A line segment is sometimes referred to as a section of a line that links two places. The difference between a line and a line segment is that a line has no endpoints and can go on forever in either direction.

We can form a triangle from this and from trigonometry, let the hypotenus = diameter

C= √6^2 + 6^2 = 6√ 2

diameter = 6√ 2,

radius = 3√ 2

A rea of the segment can be calculated as

r^2/2 [π θ/180 -sin θ)

( 3√ 2)^2 [90π/180 - sinθ)

=9( π/2 - 1)

=5.13 square inches

Learn more about segment at:

https://brainly.com/question/17374569

#SPJ1

The value of angle B is 68 degrees and the length of the segments b is 27.81 and c is 11.28.

A triangle's sides and angles are related by the Law of Sines, a trigonometric formula. It specifically specifies that for all three sides and angles of the triangle, the ratio of the length of one side to the sine of the angle opposite that side is the same. This may be expressed as the following equation:

sin A/a = sin B/b = sin C/c

where a, b, and c are the lengths of the sides that are on each side of the triangle's three angles, A, B, and C.

For the give triangle we can use the Law of sines to find the missing values.

The law of sine is given as:

sin A/a = sin B/b = sin C/c

Given A = 90 degrees and C = 22 degrees,

sin 90 / 30 = sin 22 / c

c = 30 sin 22 / sin 90

c = 30 (0.37) / 1

c = 11.28

Now, Using the sum of triangles:

90 + 22 + B = 180

112 + b = 180

B = 68

Now,

sin A/a = sin B/b

Sin 90 / 30 = sin (68) / b

b = 30 sin (68)  sin 90

b = 27.81

Hence, the value of angle B is 68 degrees and the length of the segments b is 27.81 and c is 11.28.

Learn more about law of sines here:

https://brainly.com/question/17289163

#SPJ1

A. (1, 5), B. (4, 6), and C. (2, 4) is ordered pair is a solution to the system of inequalities where y > 2x y >  3

What is inequalities?

In mathematics, an inequality is a mathematical statement that indicates that two expressions are not equal. It is a statement that compares two values, usually using one of the following symbols: "<" (less than), ">" (greater than), "≤" (less than or equal to), or "≥" (greater than or equal to).

To check which ordered pair is a solution to the system of inequalities y > 2x and y > 3, we need to check if each pair satisfies both inequalities.

A. (1, 5)

Plugging in x=1 and y=5 into the inequalities, we get:

5 > 2(1) and 5 > 3

Both inequalities are true, so (1, 5) is a solution.

B. (4, 6)

Plugging in x=4 and y=6 into the inequalities, we get:

6 > 2(4) and 6 > 3

Both inequalities are true, so (4, 6) is a solution.

C. (2, 4)

Plugging in x=2 and y=4 into the inequalities, we get:

4 > 2(2) and 4 > 3

Both inequalities are true, so (2, 4) is a solution.

D. (0, 3)

Plugging in x=0 and y=3 into the inequalities, we get:

3 > 2(0) and 3 > 3

The first inequality is true, but the second inequality is false. Therefore, (0, 3) is not a solution.

Therefore, the solutions are A. (1, 5), B. (4, 6), and C. (2, 4).

To learn more about inequalities from the given link:

https://brainly.com/question/30231190

#SPJ1

Answer: 27 hours

Step-by-step explanation:

The E-cοli grοwth rate οf 26% per hοur. At the end οf the experiment there are 7693 E-cοli bacteria. The experiment was dοne last tο 27 hοurs.

Grοwth rates are the percentage changes in a given measure οver a given span οf time. Depending οn whether the size οf the variable is grοwing οr declining οver time, grοwth rates can be either pοsitive οr negative.

Grοwth rates have been used tο study ecοnοmic activity, business management, and financial yields since they were first used by biοlοgists tο study pοpulatiοn sizes.

Using the fοrmula mentiοned belοw-

[tex]A = P(1 + r) \wedge t[/tex]

Grοwth rate (r)= 26%= 26/100= 0.26

Initial vοlume (P)= 15

Final vοlume [tex](A)= 76937693= 15(1+0.26)^t[/tex]

Or, [tex](1.26)^t= 7693/15[/tex]

Or, t ln(1.26)= ln(7693/15)

Or, t≅27

Hence the experiment was dοne at 27 hοurs.

To learn more about growth rate from the given link

https://brainly.com/question/25849702

#SPJ1

Answer:

(7.51,-1.3)

Step-by-step explanation:

rewrite 5-0.7x=0.2y in terms of x,

divide both sides by 0.2 to get: 25-3.5x = y

substitute the y part in -y+0.4x=4.3 with the new equation that we made

(in bold)

so,

-(25-3.5x) +0.4x = 4.3

expand and simplify

so,

-25 +3.5x +0.4x = 4.3 -> -25 +3.9x = 4.3 -> 3.9x = 29.3 -> x ≈ 7.51

now, substitute  the new x (underlined) to the equation in bold

so,

25-3.5(7.51) = y -> y ≈ -1.3

graphing both equations on desmos can verify the answers (only if you rearrange the two equations to get y by itself)

Answer:

there are 120 different ways

Step-by-step explanation:

the factorial of 5

:)

The set of side lengths that can produce a triangle as required in the task content is; Choice E; 5, 7, 11.

It follows from the task content that the set of side lengths that could produce a triangle.

Recall from the triangle inequality theorem that the sum of any two side lengths is greater than the third side length. Also, the difference of any two side lengths is less than the third side length.

Hence, the correct answer choice is; Choice E; 5, 7, 11.

Read more on triangle inequality theorem;

https://brainly.com/question/309896

#SPJ1

Answer:

e. 22 years

Step-by-step explanation:

From the list of options, the expression that is correctly evaluated is: (a.) 6² = 36

The expression that is correctly evaluated is:

a.) 6² = 36

This is because 6² means 6 raised to the power of 2, which is the same as 6 multiplied by itself. So, 6² equals 6 times 6, which is 36.

For other expressions, we have

b.) 12¹ means 12 raised to the power of 1, which is simply 12. Therefore, 12¹ equals 12, not 0.

c.) 3^4 means 3 raised to the power of 4, which is 81, not 12.

d.) 10⁰ means 10 raised to the power of 0, which is always equal to 1, not 10.

Read more about expression at

https://brainly.com/question/1859113

#SPJ1

The solution of x using the graphing tool for the expression [tex]-3^{-x} -6 = -3^{x} + 10[/tex] is found as: x = 2.5.

A line represents the graph of a linear equation. The equation has a solution at each point along the line. We shall plot two lines for a set of two equations.

The given expression is-

[tex]-3^{-x} -6 = -3^{x} + 10[/tex]

The graph of the equation for this expression if plotted using graphing tool.

From the graph, the solution of x is found as: x = 2.5.

Know more about the graphing tool

https://brainly.com/question/3913093

#SPJ1

1. The length of the arc is 2π

2. The value of x is 22.95°

3. The measure of side m is (4√3)x

Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle.

sin(tetha) = opp/hyp

cos(tetha) = adj/hyp

tan(tetha) = opp/adj

1. The length of an arc = tetha/360 × 2πr

= π/3 × 1/360 × 2 × π × 6

= 2π

the length of the arc is 2π

2. Sin60 = y/23

√3/2 = y/23

23√3 = 2y

y = 11.5√3

sin x = 11.5√3/51

sinx = 0.39

x = sin^-1(0.39)

x= 22.95°

3. the measure of mis calculated from

cos 30 = 6x/m

√3/2 = 6x/m

12x = √3m

m = 12x/√3

= 12x√3/3

= 4x√3.

= (4√3)x.

learn more about trigonometric ratio from

https://brainly.com/question/24349828

#SPJ1

Therefore, 6:15 is less than 30:80.

Ratio is a mathematical term that describes the relationship between two or more quantities in terms of how many times one quantity contains another. It is usually expressed in the form of a fraction or a colon. For example, if there are 10 boys and 20 girls in a class, the ratio of boys to girls is 1:2, or 1/2. Ratios can be used to compare and analyze data in various fields, including finance, economics, and statistics.

To compare 3:5 and 30:80, we need to make sure they have the same denominator. We can find the equivalent ratio of 30:80 by dividing both terms by 10, which gives 3:8.

Now we can compare 3:5 and 3:8. The first term is the same in both ratios, so we can compare the second terms.

Since 5 is less than 8, we can say that:

6:15 ____ 30:80

Therefore, 6:15 is less than 30:80.

To learn know more about denominator, visit:

https://brainly.com/question/7067665

#SPJ1

The complete question is: The question is not clear. However, based on the given information, the task is to compare the two ratios "6:15" and "30:80" by entering either "K" (which means the first ratio is greater), "=" (which means the two ratios are equal), or "<" (which means the second ratio is greater) in the box.

Answer:

What is the question?

Step-by-step explanation:

N/A

The value of the functions are;

x = 1, f(x) = 1/2

x = 2, f(x) = -1

x = 3 , f(x) = -5/2

x = 3, f(x) = -4

Note that functions are expressions or equations that shows the relationship between variables.

The variables are;

From the information given, we have the function as;

f(x) = -3/2x + 2

Now, substitute the value of x as 1

f(1) = -3/2(1) + 2

f(1) = -3/2 + 2 = -3 + 4 /2 = 1/2

f(2) = -3/2(2) + 2

expand the bracket

f(2) = -6/2 + 2 =-6 + 4  /2 = -2/2 = -1

For the value of x = 3

f(3) = -3/2(3) + 2

expand the bracket'

f(3) = -9/2 + 2

f(3) = -5/2

For the value of x = 4

f(4) = -3/2(4) + 2

f(4) = -8/2

f(4) = -4

Learn about functions at: https://brainly.com/question/2328150

#SPJ1

A possible comment from Prudence math instructor would be Great job solving the rational equation! It's not an easy task, and you managed to find the solutions x = 1 and x = -4, which is correct.

Here are some other possible comments that Prudence's math instructor might make about her solution:

Make sure to check your solutions by plugging them back into the original equation. It's always a good practice to do so, as it helps you avoid mistakes and verify that your solutions are indeed valid.

When dealing with rational equations, you need to be careful about the restrictions on the domain. In this case, the denominator cannot be equal to zero, so x = -4 and x = 2 are not valid solutions. Make sure to mention this in your solution.

When simplifying the expression, make sure to distribute the negative sign (-) properly. In this case, you should have -7x - 20 instead of -7x + 20. Double-check your calculations to avoid such errors.

Make sure to show all the steps in your solution, including how you obtained the common denominator and how you simplified the expression. This helps the reader follow your thought process and understand your solution better.

Learn more about rational equation here: https://brainly.com/question/30035857

#SPJ1

Answer:

a. To find the perimeter of the first figure, we need to add up the lengths of all four sides. If the sides are equal, we can simply multiply the length of one side by 4. Therefore, the perimeter of a square with sides of 21 cm is:

Perimeter = 4 x side

Perimeter = 4 x 21 cm

Perimeter = 84 cm

b. To find the perimeter of the second figure, we need to add up the lengths of all three sides. Since all three sides are equal, we can simply multiply the length of one side by 3. Therefore, the perimeter of an equilateral triangle with sides of 35 cm is:

Perimeter = 3 x side

Perimeter = 3 x 35 cm

Perimeter = 105 cm

c. To find the perimeter of the third figure, we need to add up the lengths of all four sides. Therefore, the perimeter of a rectangle with sides of 6.75 cm and 2.25 cm is:

Perimeter = 2 x (length + width)

Perimeter = 2 x (6.75 cm + 2.25 cm)

Perimeter = 2 x 9 cm

Perimeter = 18 cm

Step-by-step explanation:

a. To find the perimeter of the first figure (a square with sides of 21 cm), we need to add up the lengths of all four sides. Since all four sides are equal, we can simply multiply the length of one side by 4. Therefore:

Perimeter = 4 x side

Perimeter = 4 x 21 cm

Perimeter = 84 cm

So the perimeter of the square is 84 cm.

b. To find the perimeter of the second figure (an equilateral triangle with sides of 35 cm), we need to add up the lengths of all three sides. Since all three sides are equal, we can simply multiply the length of one side by 3. Therefore:

Perimeter = 3 x side

Perimeter = 3 x 35 cm

Perimeter = 105 cm

So the perimeter of the equilateral triangle is 105 cm.

c. To find the perimeter of the third figure (a rectangle with sides of 6.75 cm and 2.25 cm), we need to add up the lengths of all four sides. Therefore:

Perimeter = 2 x (length + width)

Perimeter = 2 x (6.75 cm + 2.25 cm)

Perimeter = 2 x 9 cm

Perimeter = 18 cm

So the perimeter of the rectangle is 18 cm.

Lyla pays  $ 24.14 in total.

What is the total amount?

To add two or more numbers and determine the final total, use the sum. A series of any form of numbers, known as addends or summands, is added; the outcome is their sum or total.

Here, we have

Given: Lyla goes out to dinner with her friends where the subtotal is $23.89. A 7% tax and 18% tip are added to the subtotal.

we have to find out how much did she pay in total.

= $23.89 + 7% + 18%

= $23.89 + 7/100 + 18/100

= $23.89 + 0.07 + 0.18

= $ 24.14

Hence, Lyla pays  $ 24.14 in total.

To learn more about the total amount from the given link

https://brainly.com/question/25793394

#SPJ1

The derivative of the expression is: f'(x) = 9132(31x^30) + 6.

The derivative of this function can be obtained by applying the constant multiple rule in which the constant is multiplied by the derivative of the function. Next, we will apply the power rule of differentiation in which the power rule of differentiation. When these are applied, we will have the following:

First, the principle of linear differentiation is applied to all the values on the right as follows:

f'(x) = d/dx [9132x^31 + x + x + x + x + x + x]

     = d/dx [9132x^31] + d/dx [x] + d/dx [x] + d/dx [x] + d/dx [x] + d/dx [x]  

When we apply the constant multiple rule, this then equals:

     9132 d/dx [x^31] + d/dx [x] + d/dx [x] + d/dx [x] + d/dx [x] + d/dx [x]

Finally, we apply the power rule of differentiation to obtain:

     = 9132 (31x^30) + 1 + 1 + 1 + 1 + 1

     = 9132 (31x^30) + 6

So, the derivative of the function is f'(x) = 9132(31x^30) + 6.

Learn more about the derivatives of functions here:

https://brainly.com/question/12047216

#SPJ1

the answer is in the attachment below:

The difference  between the most expensive and the cheapest material is £1.78​

The term "difference" can also be used more generally to refer to the amount by which two quantities differ.

The concept of difference is closely related to the concept of distance, which refers to the numerical value of the separation between two points, or to prices as in the case we have here.

The difference  between the most expensive and the cheapest material is; £9.77 -  £7.99 =  £1.78​

Learn more about mathematical difference:https://brainly.com/question/11281810

#SPJ1

Answer:

Step-by-step explanation:

You want the solution in polar form of the system of equations ...

The usual solution methods for a system of equations apply. The attached calculator shows the currents to be ...

__

Additional comment

For systems of equations in which the coefficients don't lend themselves to elimination or substitution methods, we prefer matrix methods to find a solution. A suitable calculator makes this relatively easy.

Answer: A

Step-by-step explanation:

9 + 9 + 5 =23

CONSECUTIVE NUMBERS: 4,5,6,8

The largest number less than 1000 that is equal to sum of 4 natural consecutive numbers is 998.

The natural numbers include the positive integers (also known as non-negative integers) and a few examples include 1, 2, 3, 4, 5, 6, …∞. In other words, natural numbers are a set of all the whole numbers excluding 0. 23, 56, 78, 999, 100202, etc. are all examples of natural numbers.

We have to find the largest natural number less than 1000 that is equal to the sum of 4 natural consecutive.

First number is 999.

So, the sum is =  9 + 9 + 9 = 27

Now, the next number is

= 9 + 9 + 8

= 26

Also, 26 can be represented as sum of 4 Natural number as

= 5 + 6 + 7 + 8 = 26

Learn more about Natural Number here:

https://brainly.com/question/17429689

#SPJ2

Answer:

Seven Ones and two hundredths

One hundred thirty

Step-by-step explanation:

5.4 X 1.3= Seven Ones and two hundredths

13 X 10= One hundred thirty

Answer:1

Step-by-step explanation:

then, x should be smaller than 3

in this canse it is 1;

now, we could use the compound interest equation using a compounding period of 365 for a year with 365 days, so a daily compounding, OR we can just use the continuously compounding equation, which is equivalent.

[tex]~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 5000\\ P=\textit{original amount deposited}\dotfill & \$1000\\ r=rate\to 2\%\to \frac{2}{100}\dotfill &0.02\\ t=years \end{cases} \\\\\\ 5000 = 1000e^{0.02\cdot t} \implies \cfrac{5000}{1000}=e^{0.02t}\implies 5=e^{0.02t} \\\\\\ \log_e(5)=\log_e(e^{0.02t})\implies \log_e(5)=0.02t\implies \ln(5)=0.02t \\\\\\ \cfrac{\ln(5)}{0.02}=t\implies \boxed{80\approx t}[/tex]

The sum of the probabilities of choosing each weekday is:

0.12 + 0.07 + 0.05 + 0.28 + 0.15 + p(Friday) + p(Weekend) = 1

where p(Friday) is the probability of choosing Friday and p(Weekend) is the probability of choosing one of the weekend days (Saturday or Sunday).

We know that the probability of choosing one of the weekdays is:

p(Weekdays) = 0.12 + 0.07 + 0.05 + 0.28 = 0.52

So, the probability of not choosing one of the weekdays is:

p(Not Weekdays) = 1 - p(Weekdays) = 1 - 0.52 = 0.48

Therefore, the probability that it will not choose one of the weekdays is 0.48.

80 units  is the minimum unit cost.

What is cost and example?

Cost is the price paid, which is typically calculated based on the resources given up to accomplish a specific goal. It entails making a sacrifice in exchange for goods or services. Not all costs translate into expenses. Assets and expenses both have costs associated with them. Expiring costs are called expenses.

it means

the function C(x) = 0.9x² - 144x + 21,053

So, the derived of C(x) respect to "x" is

     C(x)' = 0.9 * 2x - 144

   Now, we make the previous expression equal to zero and clear "x":

       1.8x - 144 = 0

          1.8x = 144

            x = 144/1.8

            x = 80

Learn more about cost

brainly.com/question/30045916

#SPJ1

Answer:

20/81

Step-by-step explanation:

The total number of brownies is 2 + 2 + 5 = 9. The probability of Gavin taking a brownie with nuts on the first pick is 5/9. After putting it back, the total number of brownies is still 9, but the number of brownies with nuts is now 4. Therefore, the probability of Gavin taking a brownie without nuts on the second pick is 4/9. The probability of both events happening together is the product of the individual probabilities: (5/9) x (4/9) = 20/81. Therefore, the probability that Gavin will randomly take a brownie with nuts, put it back, and grab one without nuts is 20/81.

Answer:

if you add the whole amount, then 2+2+5 is 9. then divide by 4 (the number without nuts) 4/9 is 44 percent

Step-by-step explanation:

Answer:

1/6 x (21x^2 -82)    

Step-by-step explanation:

1.)  Multiply the numbers.  

2.) Combine Exponents.

3.) Combine like terms.

4.) Common factor.

5.) Find one factor.

this should be right