#18 please help me thank you

#18 Please Help Me Thank You

Answers

Answer 1

Answer:

The solutions of the equation is 0 , π , 2π

Step-by-step explanation:

* Lets revise some identities in the trigonometry

- tan²x + 1 = sec²x

- tan²x = sec²x - 1

* Now lets solve the equation

∵ tan²x sec²x + 2sec²x - tan²x = 2

* Lets replace tan²x by sec²x - 1

∴ (sec²x - 1) sec²x + 2sec²x - (sec²x - 1) = 2 ⇒ open the brackets

∴ sec^4 x - sec²x + 2sec²x - sec²x + 1 = 2 ⇒ add the like terms

∴ sec^4 x -2sec²x + 2sec²x + 1 = 2 ⇒ cancel -2sec²x with +2sec²x

∴ sec^4 x + 1 = 2 ⇒ subtract 1 from both sides

∴ sec^4 x = 1 ⇒ take root four to both sides

∴ sec x = ± 1 ⇒ x is on the axes

∵ sec x = 1/cos x

∵ sec x = 1 , then cos x = 1

∵ sec x = -1 , then cos x = -1

∵ 0 ≤ x ≤ 2π

∵ x = cos^-1 (1)

∴ x = 0 , 2π ⇒ x is on the positive part of x-axis

∵ x = cos^-1 (-1)

∴ x = π ⇒ x is on the negative part of x-axis

* The solutions of the equation is 0 , π , 2π


Related Questions

Rewrite the expression using the distributive property.

8(4x+6y-2z)

A. 12x + 14y - 6z
B. -4x + -2y - 10z
C. 32x + 48y - 16z
D. 0.5x + 0.75y - 0.25z

Answers

Answer:

32x + 48y - 16z

Step-by-step explanation:

WORTH 34 POINTS! PLEASE HELP ASAP!
Would you describe the association between the age of the car and its resale value as exhibiting a linear association, non-linear association, or no association? Explain your reasoning.

Answers

Answer:No assoication

Step-by-step explanation:

because they are not parellell with each other

Answer: No  association.

Step-by-step explanation: They aren't parallel with each other. So, it has to be no association.

Can someone please help me with these two

Answers

Answer:

For number 14, the answer should be 100 degrees. For number 15, the answer is 80 degrees. For number 16, the answer is 120 degrees.

Step-by-step explanation:

For number 14, if a minor arc is 80 degrees, then the major arc should be 100 degrees to add to make 180 degrees. For number 15, you can see the size of the 70 degrees angle, AB. Because DE is bigger than AB, we can conclude that it is probably 80 degrees. For number 16, if XY, YZ, and ZX are all the same, and a circle always adds up to 160 degrees, then 360 divided by the three arcs is 120.

given that ABCDEF = PQRSTU , solve for z

Answers

the answer is z=7 (as 3z-4=17)

Answer:

A. 5

Step-by-step explanation:

What is the solution of 4x 2 36?

Answers

Answer:

x= 8.5 or 9, or deciding if u adding or subtracting the problem, x= 9.5 or 10

Step-by-step explanation:

If you're meaning 4x+2=36 or 4x-2=36

                                  -2   -2          +2   +2

                              4x=34          4x=38

                              4     4            4     4

                               x= 8.5 or 9     x= 9.5 or 10

Hope i have helped you! :)

What is the volume of the following triangular prism?

A) 252 yd3
B) 126 yd3
C) 42 yd3
D) 84 yd3

Answers

Answer:

Option C. [tex]42\ yd^{3}[/tex]

Step-by-step explanation:

we know that

The volume of the triangular prism is equal to

[tex]V=BH[/tex]

where

B is the area of the triangular base

H is the height of the prism

Convert 9 ft to yd

Remember that

1 ft=1/3 yd

9 ft=9*(1/3)=3 yd

Find the area of the base B

[tex]B=\frac{1}{2}(3)(4)=6\ yd^{2}[/tex]

we have

[tex]H=7\ yd[/tex]

substitute the values in the formula

[tex]V=BH[/tex]

[tex]V=(6)(7)=42\ yd^{3}[/tex]

Answer:

The answer is 42 yards! Sry im late. :(

In a population of 300 pigeons, 55% are female. If 40% of the male pigeons are not white, how many male pigeons are white? 135 180 81

Answers

Answer:

81

Step-by-step explanation:

Assuming the pigeons are either male or female, the 45% of them that are not female are male. Of those, there are 40% that are not white, so 60% are white. Then the number of white male pigeons is ...

60% of 45% of 300 = 0.60 · 0.45 · 300 = 81

The president of a certain University receives a salary that is three times the salary of one of the department heads the total of the two salaries is 190000 what is the salary of the president of the University

Answers

Answer:

$142500

Step-by-step explanation:

We are given that the resident of a certain University receives a salary that is three times the salary of one of the department heads.

If the sum of the two salaries is $190000, we are to find the salary of the president of the University.

Let [tex]x[/tex] to be the department head's salary, we can write an equation:

[tex]3x+x=190000[/tex]

[tex]4x=190000[/tex]

[tex]x=47500[/tex]

Salary of the president of the University = [tex]3(47500)[/tex] = $142500

Answer:

$142,500

Step-by-step explanation:

Let's say x is the salary of the department head.... so the salary of the president of the university can be described as 3x.

Then, we know the total of the two salaries is 190,000.  We can express this as:

3x + x = 190,000

4x = 190,000

x = 47,500

x is for the department head.  To get the president's salary, we have to multiply that by 3:

p = 3 (47,500) = 142,500

The salary of the president is then of $142,500.

What is the function rule for the following situation? Rex paid $20 for a membership to the pool and pays $300 each time he goes to the pool.
y = 20x + 3
20 = 3x + y
y = x + 20
none of these

Answers

The function rule for the situation is none of the given options

What is the function rule for the situation

From the question, we have the following parameters that can be used in our computation:

Membership = $20

Payment each time = $300 per visit

using the above as a guide, we have the following:

f(x) = Membership + Payment each time * x

substitute the known values in the above equation, so, we have the following representation

f(x) = 20 + 300* x

Evaluate

f(x) = 20 + 300x

Hence, the expression is f(x) = 20 + 300x

Read more about linear relation at

https://brainly.com/question/30318449

#SPJ1

none of the given options

None of the provided options in the question are correct.

The function rule that correctly represents Rex's situation, given that he paid a $20 membership fee and pays $300 each time he goes to the pool, would be a linear equation that includes a one-time fee (membership) and a per-visit cost. Let's define x as the number of times Rex goes to the pool and y as the total cost. Therefore, the equation should include the initial membership fee and the per-visit cost multiplied by the number of visits.

The correct function rule is y = 20 + 300x, where 20 represents the one-time membership fee and 300 represents the cost per pool visit. None of the provided options are correct. The equation signifies that for every visit to the pool, the total cost increases by $300, and the initial membership cost is $20.

Ivan and Tanya share £150 in the ration 4 : 1
work out how much more Ivan gets compared to Tanya.

Answers

Add the ratio to get total shares: 4 +1 = 5

Divide the total amount to share by the total shares:

150 / 5 = 30

Now multiply each set of shares by that:

4 x 30 = 120

1 x 30 = 30

120-30 = 90 more

A triangular pyramid with a volume of 270 cubic centimeters, a base edge of 15 centimeters, and the height of the base as 4 centimeters has a height of____ centimeters.

Answers

Answer:

The height of the triangular pyramid is [tex]27\ cm[/tex]

Step-by-step explanation:

we know that

The volume of a triangular pyramid is equal to

[tex]V=\frac{1}{3}BH[/tex]

where

B is the area of the triangular base

H is the height of the pyramid

Find the area of the base B

[tex]B=\frac{1}{2}(15)(4)=30\ cm^{2}[/tex]

we have

[tex]V=270\ cm^{3}[/tex]

substitute and solve for H

[tex]270=\frac{1}{3}(30)H[/tex]

[tex]270=10H[/tex]

[tex]H=270/10=27\ cm[/tex]

Find a quadratic equ
{-2/5 7/5}​

Answers

{-2/5 7/5}={-2*7/5*5}={-14/25} or if you prefer :

Final answer:

The quadratic equation with roots -2/5 and 7/5 is 25x^2 - 25x - 14 = 0. This is derived by expressing the equation in the form a(x - α)(x - β) = 0 and substituting the given roots.

Explanation:

To find a quadratic equation with roots -2/5 and 7/5, we use the fact that if α and β are the roots of the quadratic equation ax2 + bx + c = 0, then the equation can be written as a(x - α)(x - β) = 0. For roots -2/5 and 7/5, the quadratic equation becomes:

x2 - (sum of roots)x + (product of roots) = 0

x2 - ((-2/5) + (7/5))x + ((-2/5) × (7/5)) = 0

x2 - (5/5)x - (14/25) = 0

x2 - x - 14/25 = 0

Multiplying through by 25 to clear the fraction:

25x2 - 25x - 14 = 0

This is the quadratic equation with the given roots.

8 points! Please help me with this problem, what is sin(theta)?

Answers

sin=√17/7

or sin=sqrt(17)/7

Answer:

[tex]\frac{\sqrt{17} }{7}[/tex]

Step-by-step explanation:

Given

cosΘ = [tex]\frac{4\sqrt{2} }{7}[/tex] = [tex]\frac{adjacent}{hypotenuse}[/tex]

Then the hypotenuse of the right triangle is 7 and the adjacent side is 4[tex]\sqrt{2}[/tex]

To find the opposite side use Pythagoras' identity

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is

opp² + (4[tex]\sqrt{2}[/tex] )² = 7²

opp² + 32 = 49 ( subtract 32 from both sides )

opp² = 17 ( take the square root of both sides )

opp = [tex]\sqrt{17}[/tex]

Hence

sinΘ = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{\sqrt{17} }{7}[/tex]

calculate the slope of the line that contains the points (2,-3) and (6,-3)

Answers

Answer:

Step-by-step explanation:

y2-y1/x2-x1= -3-(-3)/6-2= 0/4

Find the probability that the next 1,000 cars purchased in your city will all be the color blue.

Answers

Assuming that the probability of a car being colored blue is not equal to 0 or 1, then the most logical answer would be the smallest probability.

P= 0.001

Answer:

0.001

Step-by-step explanation:

gradpoint

The box and whisker plot below represents students test scores of Mr. Ali’s history test.

C. Mr. Ali’s wanted more than half of the students to score 75 or greater on the test. Explain how you know that more than half of the students did NOT score greater than 75.

Answers

Answer:I know that more than half of the students did not score more than 75 because the median (the middle number) is 68.

Step-by-step explanation:

A shipping crate is packed with unit cubes. The length of the crate is 4 units, the width is 2 units and the height is 4 units. Find the volume If the shipping crate

Answers

Answer:

32 unit³

Step-by-step explanation:

Length of the crate has been given as 4 units

width of the crate = 2 units

Height of the crate = 4 units

Since the crate has been packed packed with the unit cubes.

Therefore, shape of the crate will be in the form of a rectangular prism.

Volume of the prism = Length × width × height

                     crate     = 4 × 2 × 4

                                   = 32 unit³

Volume of the shipping crate is 32 unit³.

Answer:

32 Units

Step-by-step explanation:

If u do 4x2x4=32 that is your answer all you got to do is x Lxwxh and U will find the volume

Which is the same distance from zero on the number line as 25? 1.) 50 2.) 0 3.) −25 4.) −50

Answers

Answer:

-25

Step-by-step explanation:

-25 is the same distance away from zero as is 25.

Answer:

-25

Step-by-step explanation:

this is a question about absolute value. with absolute value, if the number is negative, u simply take off the negative sign. so, ur looking 4 the opposit of 25, which is -25

a civil engineer has laid a graph down over the stretch of a new road system. a circular rotary has a diamater with endpoints (-3,5) and (5,11) what are the center and raduis of the rotary

Answers

[tex]\bf ~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ (\stackrel{x_1}{-3}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{11}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{5-3}{2}~~,~~\cfrac{11+5}{2} \right)\implies \left(\cfrac{2}{2}~,~ \cfrac{16}{2}\right)\implies \stackrel{center}{(1,8)} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ \stackrel{endpoint}{(\stackrel{x_1}{-3}~,~\stackrel{y_1}{5})}\qquad \stackrel{center}{(\stackrel{x_2}{1}~,~\stackrel{y_2}{8})}\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ \stackrel{radius}{r}=\sqrt{[1-(-3)]^2+[8-5]^2}\implies r=\sqrt{(1+3)^2+(8-5)^2} \\\\\\ r=\sqrt{16+9}\implies r=\sqrt{25}\implies r=5[/tex]

Do the midpoint formula. Which will give you (1,8)

Two and two fifths divided by one and a half

Answers

Answer:

8/5 or 1 3/5

Step-by-step explanation:

2 2/5 = 12/5

1 1/2 = 3/2

Now that we have fractions that are easier to divide, one must understand that the opposite of dividing is multiplying. So if you multiply 12/5 by the reciprocal* of 3/2, which would be 2/3, you would get your answer so...

12     3         12    2        24     8             3

—  ÷ —   =   — × —    =  —  = —   or  1  —

5       2         5     3        15      5             5

*the reciprocal is the opposite of the fraction you have. So the denominator would become the numerator, and vise versa.

John, Rick, and Molli can paint a room working together in 6 hours. Alone, John can paint the room in
12 hours. If Rick works alone, he can paint the room in 15 hours. Write an equation comparing the
group rate to the sum of the individual rates. Then find how long it will take Molli to paint the room if
working alone.

a. What is the equation?

b. What is the lowest common denominator for the equation in part a?

c. Show all work below in solving equation from part a.

Answers

Answer

a. [tex]\frac{1}{m}(6)+\frac{1}{12} (6)+\frac{1}{15} (6) =1[/tex]

b. 60hrs

Step-by-step explanation:

Let the time Molli will take to pint the room to be = t

Thus the amount of room that Molli can paint in 1 hour= 1/m

The amount of room John can paint is 1 hour= 1/12

The amount of room Rick can paint in 1 hour = 1/15

The equation for working together at a rate x time per work done will be;

[tex]\frac{1}{m} *6+\frac{1}{12} *6+\frac{1}{15} *6=1[/tex]

You multiply by 6 in the three terms of the equation because it takes 6 hours for John, Rick and Molli to complete painting.

[tex]\frac{6}{m} +\frac{1}{2} +\frac{2}{5} =1[/tex]

multiply by 10m in every part of the expression because 10m is the Least Common Multiple(LCM) is this case

Collect like terms and find value of m

[tex]60+5m+4m=10m\\\\60+9m=10m\\\\60=10m-9m\\\\60=m[/tex]

Molli will take 60 hours to paint the room if working alone

Given: x - 8 > -3.

Choose the solution set.

1.{x | x R, x > -9}
2.{x | x R, x > -5}
3.{x | x R, x > 5}
4.{x | x R, x > 14}

Answers

Answer:

x-8>-3 {x|R, x>5 is right answer

For this case we must find the solutions of the following inequality:

[tex]x-8> -3[/tex]

Adding 8 to both sides of the inequality we have:

[tex]x> -3 + 8\\x> 5[/tex]

Thus, the solutions of the variable "x" are given by all the real numbers greater than 5.

Answer:

Option C

What is the solution to the following system of equations?


2x + 3y = 3

-3x - 2y = 8​

Answers

The answer is (-6,5)

Answer:

Your answer will be (-6,5).  

Step-by-step explanation:

You multiply the first equation by 3 and the second equation by 2. You will then cancel out the x's and find your y which is 5. You plug y back into your first equation to find your x which is -6. You then have your solution set.

The price of a computer was decreased by 30% to £147. What was the price before the decrease?

Answers

A decrease by 30%, means that the price is now 70% of the original price ( 100% - 30% = 70%)

To find the original price divide the new price by the percent of the original price it is now.

147 / 0.70 = 210

The original price was £210

The price before the decrease is £210.

Given that,

The price of a computer was decreased by 30% to £147.

Based on the above information, the calculation is as follows:

[tex]= 147 \div 70\%[/tex]

=  £210

Therefore we can conclude that the price before the decrease is £210.

Learn more: brainly.com/question/6201432

5 pounds of birdseed cost $10.40. What is the price per ounce ?

Answers

$0.13 per ounce.  5 pounds of birdseed cost $10.40, then the price per ounce is $0.13.

The easiest way to solve this problem is using arithmetic operations and unit conversion.

We have to calculate the price per pound. Let's divide $10.40 by 5 pounds.

10.40/5 = 2.08

The price per pound is $2.08

To calculate the price per ounce, with 1 pound = 16 ounces. Let's divide $2.08 by 16 ounces.

2.08/16 = 0.13

The price per ounce is $0.13

Evaluate -3x3 - 4x for x = -1. 1 7 -1

Answers

Answer:

-5

Step-by-step explanation:

-3 x 3 - 4x

x=-1

-3 x 3 - 4(-1)

-3 x 3 + 4

-9 + 4

-5

Hope This Helps! :D

Answer:

-3-4x

=-3(-1

=-3*(-1)+4

=3+4

=7

Step-by-step explanation:

that should be all you need to know

15. The temperature C, in degrees, that is equivalent to a temperature of F degrees Fahrenheit is given by graph of this equation shows the temperature in Celsius for the corresponding temperatures in Fahrenheit.
a. Explain how linear equations can be used in temperature conversion.
b. Explain how could you could use the conversion graph to find the normal body temperature in degrees Celsius, which is 98.6°F.

Answers

Answer:

A. How can the equation be used in temperature conversion?

You take the conversion equation C = (5/9) (F - 32) and you replace the F by the value of Fahrenheit degrees...  then solve the calculations to get the degrees in Celsius.

For example, if you have 80°F to convert in °C:

C = (5/9) (80 - 32) = (5/9) (48) = 26.66 °C

B. How can you use the graph to find the body temp in C?

Using the graph will give a very imprecise measure due the scale of the graph.

But you would have to find 98.6 on the axis of X (it represents the °F), then go upwards until you find the line....

Then report that position on the line on the Y-axis (representing the °C) to get your measure.

Answer:

For A: The linear equation is [tex]C=\frac{5}{9}F-\frac{32}{9}[/tex]

For B: The temperature of normal body in degree Celsius is 37° C.

Explanation:

For A:

Linear equations are defined as the equations in which the highest power of a variable is '1'. The general equation for a linear equation is:

[tex]y=mx+c[/tex]

where,

y = Y-coordinate

m = slope of the line

x = X - coordinate

c = intercept on y-axis

For the given equation:

[tex]C=\frac{5}{9}(F-32)[/tex]

The linear equation representation for the given equation is:

[tex]C=\frac{5}{9}F-\frac{32}{9}[/tex]

For B:

We are given a value of temperature in degree Fahrenheit. To calculate its value in degree Celsius, we use the equation above.

Putting value of F = 98.6 in above equation, we get:

[tex]C=(\frac{5}{9}\times 98.6)-\frac{32}{9}\\\\C=37[/tex]

Hence, the temperature of normal body in degree Celsius is 37° C.

Solve the system of equations below.
x − y = 5
2x − 3y = 4

A (5, 0)
B (7, 2)
C (9, 4)
D (11, 6)

Answers

Final answer:

To solve the system of equations x − y = 5 and 2x − 3y = 4, we can use the method of substitution or elimination. By substituting the value of x from the first equation into the second equation, we can find the value of y. Then, substitute the value of y back into the first equation to find the value of x. The solution to the system of equations is (11, 6).

Explanation:

To solve the system of equations x − y = 5 and 2x − 3y = 4, we can use the method of substitution or elimination. Let's use the method of substitution:

From the first equation, we can rearrange it to x = y + 5. Now substitute this value of x into the second equation:

2(y + 5) − 3y = 4

Simplify and solve for y:

2y + 10 - 3y = 4

-y + 10 = 4

-y = -6

y = 6

Now substitute this value of y back into the first equation to find x:

x − 6 = 5

x = 11

Therefore, the solution to the system of equations is (11, 6). So, the correct answer is option D.

Information you may find on your paycheck stub may include _____.

pay period, taxable allowances, and dividends
deductions, dividends, and interest
employee benefits, date of hire, and number of dependents
employee ID, vacation time, pay period, and deductions

Answers

Answer:

Pay period, taxable allowances, and dividends

Step-by-step explanation:

Answer: Pay period, taxable allowances, and dividends

Explanation:

  Paycheck stub is the type of document which include the total paid amount to the employees. It is also known as pay slip and pay stub. The pay stub is basically received by the each pay slip and period.

This pay check stub document basically show the total earnings, deductions and the net pay after the all deductions.

We can also save the paycheck stub in our records so that we can easily access it in future. In case of the employees and employer, the paycheck stub prove that the payment and the income are both consistent.

Travis traveled a total distance of 3 1/2miles. He rode the bus 1 1/4mile.He walked 2/3 mile.He rode in a car the remainder of the 3 1/2 miles. How far in miles did he ride in a car?

Answers

Answer: 1  5/12

Step-by-step explanation: You need to find a common denominator 3 and 4 are the denominators you can do 3 times 4 is 12 and 4 times 3 is 12, but whatever you do to the denominator needs to be done to the numerator so 2 times 4 is 8 and 1 times 4 is 4 then you have the fractions 8/12 and 3/12 then you just subtract and you get 1  5/12.

*Hard to explain*

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