find the exact value of cos285 using the fact that 285=330-45

Answers

Answer 1
[tex]\bf \textit{Sum and Difference Identities} \\\\ cos(\alpha - \beta)= cos(\alpha)cos(\beta) + sin(\alpha)sin(\beta)\\\\ -------------------------------\\\\ cos(285^o) \\\\\\ cos(330^o-45^o)=cos(330^o)cos(45^o)+sin(330^o)sin(45^o) \\\\\\ cos(330^o-45^o)=\left( \frac{\sqrt{3}}{2} \right)\left( \frac{\sqrt{2}}{2} \right)~~+~~\left( \frac{1}{2} \right)\left( \frac{\sqrt{2}}{2} \right) \\\\\\ cos(330^o-45^o)=\cfrac{\sqrt{6}}{4}+\cfrac{\sqrt{2}}{4}\implies cos(330^o-45^o)=\cfrac{\sqrt{6}+\sqrt{2}}{4}[/tex]

Related Questions

Help why did I get this wrong? Corrections!!! Janie is analyzing a quadratic function f(x) and a linear function g(x). Will they intersect?

Answers

The quadratic function is f(x) = 2x^2 + 1.
The line is g(x) = 2x
Use www.cymath.com and enter the following line and press enter.
graph y = 2x^2 + 1; y = 2x

You will see that the line passes through the origin (0, 0), and goes up to the right and stays to the right of the parabola, so the two graphs do not intersect.

PLEASE HELP!
You work for a landscaper that has a customer needing to seed an area of land 80 feet by 40 feet in size. The garden center has 5-pound bags of grass seed. Each bag of seed can cover 25 square yards of land.

You calculate that the area you need to seed is 3200 square feet. You divide by 25 to find that you need 128 bags to seed the area. Is this correct?
A) Yes.
B) No, you need to convert the 3200 square feet to yards by dividing by 3. Then calculate the number of bags.
C) No, you need to convert the 3200 square feet to yards by dividing by 9. Then calculate the number of bags.
D) No, you need to convert the 3200 square feet to yards by multiplying by 9. Then calculate the number of bags.

Answers

1 yard = 3 feet
(1 yard)^2 = (3 feet)^2 ... square both sides
1 yard^2 = 9 feet^2
which means 1 square yard is equal to 9 square feet
think of a square yard as a 3x3 square where each smaller square is 1 square foot.

To convert from square feet to square yards, we multiply by the conversion factor (1 yard^2/9 feet^2). Or put simply we multiply by 1/9 which is the same as dividing by 9

This is why the answer is choice C.

Answer:

Since the mulch is measured in yards you need to either convert the area to be seeded to yards or the bag to feet. No, you need to convert the 3200 square feet to yards by dividing by 9. Then calculate the number of bags.

This is the term in a polynomial without a variable

Answers

It is a constant. hope this helps

Final answer:

A term in a polynomial without a variable is known as a constant. It is the term that does not change its value.

Explanation:

The term in a polynomial without a variable is often referred to as the constant term. In a polynomial expression, variables are raised to various powers and multiplied by coefficients. However, the constant term is a unique element within the polynomial because it does not involve any variables. It is a number on its own and typically represents the y-intercept of the polynomial graph when plotted on a Cartesian plane.

For example, in the polynomial expression "[tex]3x^2 + 5x - 7,"[/tex] the constant term is "-7." This term contributes a fixed value to the overall expression, regardless of the value of the variable "x." It's a crucial component in polynomial mathematics, as it affects the position of the polynomial graph on the vertical axis. Understanding the constant term is essential for polynomial evaluation, graphing, and solving equations involving these expressions. In essence, the constant term is the base value around which the polynomial varies as the variable changes.

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The gas tank I’ll be riding mower holds 5 L of gas how many 5 L gas tanks can you feel from a 20 L gas tank

Answers

(20 L)/(5 L) = 4

You can fill 4 gas tanks of 5 L capacity from a full 20 L gas tank.

Me. Adams divides 223 markers equally among the 26 students in his class. He puts the extra markers in a box. What is the least number of markers he puts in the box?

Answers

He puts 15 markers in the box. Hope this helps.

PLEASE HELP ASAP! BRAINLIEST TO BEST/RIGHT ANSWER

Answers

A(n) =150 x (0.71) n-1; 27.06 cm

Tim’s bank requires its customers to have a 4-digit personal identification number (PIN) to access their accounts. If each digit can be a value from 0 to 9, and a 4-digit number is randomly generated, what is the probability that the number 1234 will be Tim’s PIN? A. 1 6,561 B. 1 5,040 C. 10,000 D.1 10,000

Answers

Answer:

1/10000

Step-by-step explanation:

There are 10 choices for each of the 4 digits.  This means the total number of choices for the PIN are

10(10)(10)(10) = 10000

The number 1234 will only appear 1 time in this list; this makes the probability it is Tim's PIN 1/10000.

Hence, the probability that the number [tex]1234[/tex] will be Tim’s PIN is

What are digits?

A numerical digit is a single symbol used alone or in combinations, to represent numbers in a positional numeral system.

The name "digit" comes from the fact that the ten digits of the hands correspond to the ten symbols of the common base [tex]10[/tex] numeral system, i.e. the decimal digits.

From the given information,

We have [tex]10[/tex] choices for each of the four digits.  

This means that the total number of choices for the PIN is:-

[tex]10(10)(10)(10) = 10000[/tex]

The number [tex]1234[/tex] will only appear one time in this list which makes the probability of the form Tim's PIN  [tex]\frac{1}{10000}[/tex].

Hence, the probability that the number [tex]1234[/tex] will be Tim’s PIN is [tex]\frac{1}{10000}[/tex].

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In need of some help please.

Answers

Asked and answered elsewhere.
https://brainly.com/question/9168336

In Emily's physics class, she had to solve the equation 9 = 12at2 + ut for u. Each step of her work is shown below.

Use the drop-down menus to explain each step.


Answers

Answer:

[tex]u=(9-\frac{1}{2}at^{2})/t[/tex]

Step-by-step explanation:

we have

[tex]9=\frac{1}{2}at^{2}+ut[/tex]

Solve for u

That means-------> isolate the variable u

step 1

Subtract  [tex]\frac{1}{2}at^{2}[/tex] both sides

[tex]9-\frac{1}{2}at^{2}=ut[/tex]

step 2

Divide by  [tex]t[/tex] both sides

[tex]u=(9-\frac{1}{2}at^{2})/t[/tex]

In Step 1, Emily subtracts (1/2)at² from both sides to isolate 'u.' In Step 2, she divides both sides by 't' to solve for 'u,' simplification of the equation further.

The equation is 9 = (1/2)at² + ut

Step 1 . 9 - (1/2)at² = ut

In this step, Emily subtracts (1/2)at² from both sides of the equation.

The purpose of this is to isolate the term containing 'u' on the right side of the equation.

Starting with the original equation, Emily recognizes that the term (1/2)at² is added to ut, and she wants to get rid of it from the right side.

To do that, she subtracts (1/2)at² from both sides to keep the equation balanced.

So, she ends up with 9 - (1/2)at² on the left side and ut on the right side.

This is a crucial step because it isolates the term ut, making it easier to solve for 'u' in the next step.

Step 2. [9 - (1/2)at²] / t = u

In this step, Emily divides both sides of the equation by 't' to solve for 'u.' The purpose is to isolate 'u' on the right side of the equation.

Starting with the equation from Step 1 (9 - (1/2)at² = ut), Emily recognizes that she wants to isolate 'u' by itself.

To do that, she divides both sides of the equation by 't.'

This division cancels out 't' on the right side, leaving 'u' alone.

Therefore, simplification of the equation ends up with [9 - (1/2)at²] / t on the left side and 'u' on the right side, this step allows her to find the value of 'u' using the given values of 'a,' 't,' and '9.'

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the yearly changes in the population of a town for four consecutive years were, respectively, 25% increase, 25% increase, 25% decrease, and 25% decrease. what is the net present decrease over the four years, rounded to the nearest percent?

Answers

Answer: The net change is a 12.11% decrease.

To see what is going on in this problem, we should write an equation. Let's start by using P to represent the total population.

P x 1.25 x 12.5 x 0.75 x 0.75 = 0.8789

For the increases, we multiplied by 1.25. For the decreases, we multiplied by 0.75.

The final result is the P gets multiplied by 0.8789. In other words it is made smaller by 12.11%.  100% - 87.89% = 12.11%

_____a function is the same as moving a function ... im not totally sure

Answers

shifting a function is the same as moving it

A party size bag of tortilla normally coast 3.80. the supermarket has them on sale today for 2.25. what is the percentage of the discount

Answers

% discount = ((sale price)/(regular price) -1)*100%
.. = (2.25/3.80 -1)*100%
.. = (0.5921 -1)*100%
.. = -0.4079*100%
.. = -40.79%

The discount is about 41% from the regular price.

HELLPPPP ASAP

Identify the type of function represented by f(x)=(1/2) x (3)^x

A. Decreasing linear
B. Exponential decay
C. Exponential growth
D. Increasing linear

Answers

Answer:

The correct option is (C) Exponential growth.

Step-by-step explanation:

The simplest exponential function is: f(x) = [tex]a^{x}[/tex], a>0, a≠1

If the x is positive then graph of exponential is increasing and if the x is negative then graph of exponential is decreasing.

In given function [tex]f(x)=\frac{1}{2}\times(3)^x[/tex]

x is positive so, it is graph of exponential growth.

Hence, the correct option is (C) Exponential growth.

Answer:C

Step-by-step explanation:

BIG BRAIN

The vertex form of a function is g(x) = (x – 3)2 + 9. How does the graph of g(x) compare to the graph of the function
f(x) = x2?

A.g(x) is shifted 3 units left and 9 units up.
B.g(x) is shifted 3 units right and 9 units up.
C.g(x) is shifted 9 units left and 3 units down.
D.g(x) is shifted 9 units right and 3 units down.

Answers

the  -3 shifts the graph 3 units to the right
and The + 9 moves the graph upwards 9 units

Its B

For this case we have that the main function is given by:

[tex]f (x) = x ^ 2[/tex]

First, we apply the horizontal transformation. To do this, we evaluate the function for x-3, that is, we move the graph 3 units to the right.

[tex]f (x-3) = (x-3) ^ 2[/tex]

We apply the vertical transformation. To do this, add to the function 9 units, that is, we move the graph 9 units up.

[tex]f (x-3) +9 = (x-3) ^ 2 + 9[/tex]

We have then:

[tex]g (x) = (x-3) ^ 2 + 9[/tex]

Answer:

B.g (x) is shifted 3 units right and 9 units up.

Marvin and some of his classmates are painting their classroom at school. They only have gallon of paint left. How much of the paint will each person get if Marvin and 4 of his classmates share the paint equally?

Answers

1/4 of a gallon or 1 quart each

WILL GIVE BRAINLIEST-Let ​ f(x)=x2−3x−4​ .

What is the average rate of change from x = 7 to x = 10?



Enter your answer in the box.

Answers

The graph doesn't even show the points of interest.

The average rate of change on that interval is 14.

Answer:

14

Step-by-step explanation:

14

A recipe for lemon cranberry pound cake calls for 80 milliliters of lemon juice and 240 milliliters of plain yogurt. How many liters of lemon juice and yogurt are needed to make 11 cakes?

Answers

we know that
1 liter------------> is equal to 1000 ml

if for one cake--------------> are required 80 milliliters of lemon juice
 for 11 cakes--------------> X
X=11*80---------> 880 ml

if for one cake--------------> are required 240 milliliters of plain yogurt
 for 11 cakes--------------> X
X=11*240---------> 2640 ml

liters of lemon juice needed to make 11 cakes
880 ml/1000------> 0.88 lt

liters of yogurt needed to make 11 cakes
2640 ml/1000--------> 2.64 lt

the answer is
are needed 0.88 lt of lemon juice and 2.64 lt of yogurt to make 11 cakes

Answer: 3 liters 520 milliliters

Step-by-step explanation:

Total liquid amount:

80 ml + 240 ml = 320 milliliters

Total amount for 11 cakes:

320 milliliters × 11 = 3,520 milliliters

Total amount for 11 cakes conversion:

3,520 milliliters ÷ 1,000 = 3 remainder 520 = 3 liters 520 milliliters

A triangle has an area of 1102 m², and two of the sides of the triangle have lengths 60 m and 56 m. find the angle included by these two sides.

Answers

A = (1/2)*a*b*sin(C)
1102 m^2 = (1/2)*(60 m)*(56 m)*sin(C)
2*1102/(60*56) = 551/840 = sin(C)
C = arcsin(551/840) ≈ 41°

Cory has a square piece of wood that is 4.5 feet by 4.5 feet. He wants to make a circular tabletop out of it. What is the area of the largest circle that he can cut out of the wood? Round to the nearest tenth.

Answers

In this circle, the diameter is the same as the length of the side of the square.  The diameter is 4.5 ft; so, the radius is 2.25 ft., so. A πr²= π(2.25)²=15.90 ft²

The area of the largest circle is  15.9 feet^2

what is area ?

The area is the amount of space within the perimeter of a 2 D shape. It is    measured in square units, such as cm², m², etc.

formula used to find the area is :

A = π r^2

Given : diameter = 4.5 feet

r = d/2

⇒ 4.5 / 2

⇒ 2.25

r = 2.25

A = π × (2.25)^2

A = 3.14 × 5.0625

A  =  15.89625  feet^2

round to nearest tenth is :

A = 15.9 feet ^2

Hence , the area of the largest circle is 15.9 feet ^2

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Kiki works in a furniture store. Her base salary is $150 per day, plus 8 percent commission on her sales. She sells several high-priced items. table What is the total amount she earned over these three days?

Answers

Answer:

614

Step-by-step explanation:

614 can also look like this ^!$ if you hold down caps.

Kiki works in a furniture store. Her base salary is $150 per day, plus 8 percent commission on her sales. She sells several high-priced items.

 

What is the total amount she earned over these three days?

$ 614

 

                 Got it correct.

                       Hope it helps

George Orwell based his novel, 1984, on the idea of

capitalism


totalitarianism


fascism


constitutional monarchy

Answers

The correct answer is


totalitarianism

Given the lengths of two sides of a triangle, find the range for the length of the third side (between what two numbers should the length of the third side be). Write the inequalities for each case. 11.5 and 23.6

Answers

The shortest the third side can be is the difference of the other two sides:
.. 23.6 -11.5 = 12.1
The longest the third side can be is the sum of the other two sides:
.. 23.6 +11.5 = 35.1

12.1 < third side < 35.1

Final answer:

To determine the range for the length of the third side of a triangle with side lengths 11.5 and 23.6, we apply the triangle inequality theorem which tells us that the third side must be greater than 12.1 and less than 35.1.

Explanation:

To find the range for the length of the third side of a triangle when given the lengths of two sides, one must use the triangle inequality theorem. This theorem states that the length of any side of a triangle is less than the sum of the lengths of the other two sides but greater than the absolute difference between these lengths. Given the side lengths of 11.5 and 23.6, the inequalities would be:

The length of the third side must be greater than the absolute difference between 23.6 and 11.5, which is 12.1. Therefore, the third side > 12.1.The length of the third side must also be less than the sum of 23.6 and 11.5, which is 35.1. Therefore, third side < 35.1.

Combining these inequalities gives us the range: 12.1 < third side < 35.1.

Please SOMEONE help me on this asap!!!
BRAinliEST AVAILABLE TO CORRECT ANSWER
Options from the 1st blank:
Less than, greater than, or the same as

Options for 2nd blank:
Greater than, the same as, less than

Answers

As x increases, the value of p(x) approaches a number that is y-int value of q(x)
y- int of the function p is -2 (one more) the y-int of the function q

What choices there are, then I can answer more exactly

you need to draw the graph for
[tex] { \frac{2}{5} }^{x} - 3[/tex]
it doesn't need to be perfect but there are two
things to keep in mind
first: -3 lowers our graph by three points in the y axis
second: in:
[tex] { \frac{a}{b} }^{x} [/tex]
the bigger a/b is the wider the graph is thereful our graph isn't that big. if you want a better mental picture think of it as the miniature version of q(x). now that we know how p(x) looks like lets answer the questions

1st blank:
greater than

2nd blank:
greater than

How to solve 6+5c=-29

Answers

6 + 5c = -29
•You are trying to find C
Therefore you make C your subject by subtracting 6 on both sides then divide by 5.
Like this ;
6 - 6 + 5c = -29 - 6
5c/5 = -35/5
c = -7
hence
C = -7.

To check or prove that your answer is correct, simply sustitute (-7) into the equation in place of C and if the result is -29 than its the correct answer.
•Check;
6 + 5 (-7) = ?
6 + (-35) = ?

6 - 35 = -29
Your answer is proved so C = -7

The value of equation 6+5c=-29 is c= -7.

What is Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

Equation: 6+5c=-29

Solving the equation for c

6+5c=-29

Subtract 6 from both side

6 + 5c - 6 = -29 - 6

5c = -35

Divide both side by (5) we get

5c / 5 = -35 /5

c= -7

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What is the first step in solving the problem 3/4 + 1/8?

Answers

The first thing you should know is that there are many ways to solve this problem.
 One of the ways, for example, is a simple addition of fractions.
 We have then:
 Step 1:
 Cross product
 3/4 + 1/8 = ((3 * 8) + (1 * 4)) / (4 * 8)
 Step 2:
 Rewrite
 ((3 * 8) + (1 * 4)) / (4 * 8) = (24 + 4) / (32) = 28/32
 Step 3:
 simplify
 28/32 = 14/16 = 7/8
 Answer: 
 Step 1: 
 Cross product
 3/4 + 1/8 = ((3 * 8) + (1 * 4)) / (4 * 8)

A board is leaning against a vertical wall, The board makes a 62 degree angle with the ground and touches the wall at a point that is 45 in, above the ground. What is the length of the board, rounded to the nearest inch?

Answers

Angle A = 62°
Angle B = 90°
Side a = 45
The length of the board is side b

Use the Law of Sines to find side b. 
b / sin(B) = a / sin(A) 
b / sin(90°) = 45 / sin(62°) 
b = (sin(90°) x 45) / sin(62°) 
b = 50.966

Rounded to the nearest inch is 51 inches.

Hope this helps!

Answer:

Option C. 51 in.

Step-by-step explanation:

In the given right angle triangle height is given as 45 in. above the ground.

Length of the board is making an angle of 62°with the ground.

Therefore by sine rule

sin 62° = height / hypotenuse

sin 62° = 45/h

0.8829 = 45/h

h = 45/0.8829 = 50.96 ≈ 51 in.

Therefore option C. 51 in. is the answer.

Which statements are always true regarding the diagram? Check all that apply.
CAN SOMEONE PLEASE ANSWEERRRRRR

m∠3 + m∠4 = 180°
m∠2 + m∠4 + m∠6 = 180°
m∠2 + m∠4 = m∠5
m∠1 + m∠2 = 90°
m∠4 + m∠6 = m∠2
m∠2 + m∠6 = m∠5

Answers

m∠3 + m∠4 = 180°
As these 2 angles make up a straight line, the sum of the magnitude of angles is 180° so this is true 

m∠2 + m∠4 + m∠6 = 180°
these 3 angles are the interior angles of a triangle. the sum of all the interior angles of a triangle sum up to 180° so this is true.

m∠2 + m∠4 = m∠5
for this statement, use the previously stated concepts 
m∠2 + m∠4 + m∠6 = 180°
m∠5 + m∠6 = 180°
since both equations are equal lets put them into one equation
m∠2 + m∠4 + m∠6 =m∠5 + m∠6
since m∠6 is common for both sides lets cancel it out which leaves us with 
m∠2 + m∠4 = m∠5
therefore this statement is true 

m∠1 + m∠2 = 90°
sum of the angles making up a straight line is 180 °, therefore this is incorrect

m∠4 + m∠6 = m∠2
lets use the following equation
m∠2 + m∠4 + m∠6 = 180° 
if m∠6 + m∠4 = m∠2
then using this we substitute in the previous equation
m∠2 + ∠m∠2 = 180°
m∠2 = 90°
so this angle should be a right angle, but in the diagram its not a right angle therefore this is incorrect 

m∠2 + m∠6 = m∠5
since 
m∠5 + m∠6 = 180°
m∠2 + m∠4 + m∠6 = 180° 
then putting both the equations in one as they are both equal
m∠2 + m∠4 + m∠6 = m∠5 + m∠6
this shows that 
m∠2 + m∠4 = m∠5 
then m∠4 should be equal to m∠6
but judging from the sides opposite to the angles m∠4 and m∠6 the sides aren't equal so these angles too cannot be equal so this statement is wrong.
m∠3 + m∠4 = 180°
m∠2 + m∠4 + m∠6 = 180°m∠2 + m∠4 = m∠5

What is the angle of 135 degrees equal to in radian measure? Show all work.

Answers

180= pi(sorry I dont have pi sign)
135= x
than cross multiply this to find the value of x
U'll get 3/4pi

25 points need help ASAP!!!

Answers

What is the question

I’m sorry there is no attachment. I am not able to help you.

A video game system that normally sells for $249 is on sale for 15% off

Answers

15% = 0.15

249 x 0.15 = $37.35 ( amount of discount)

249 - 37.35 = $211.65 ( sale price )


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Parker is single and paying off his graduate student loan. The monthly payment is $679.34. He is hoping to receive an income tax refund that is large enough to make at least one monthly payment. His taxable income is $77,911 and his employer withheld $19,458 in federal taxes. a. How much of a refund will Tony receive? b. How many loan payments will Parker be able to make with this refund? 1. The _______ button automatically displays next to the data when you select a range of numeric data, which is an available option for creating a chart. A. Recommended Charts B. Chart Elements C. Chart Styles D. Quick Analysis How did khrushchev respond to kennedy's refusal to remove western powers from berlin? Think of this painting as propaganda. Which main idea is it trying to spread?Poor farmers have little skill as soldiers.The Communist Party gives farmers power.Mao Zedong is not holding a weapon.Guns are much more effective than spears. choose the answer that best completes the sentence. if you know a root of a function is -2 + sqrt3 , then __A. 2 + sqrt3 is a possible rootB. 2 + sqrt3 is a known root.C. -2 - sqrt3 is a possible root.D. -2 - sqrt3 is a known root. The Ferris wheel at the Comal County Fair is a three minute ride that takes its riders on a thrilling ride up to a maximum height of 105 feet and a low point of 5 feet. Assuming that the Ferris wheel rotates at 6 revolutions per minute and a rider starts his stopwatch immediately as his ride starts at its low point, The dominant form of government in eastern europe in the 1920s and 1930s was An ethnic group is any group whose members share a common culture different from other groups.true or false In humans, the process of meiosis and the fertilization of the egg and the sperm ensures that the same offspring will never be created twice. Explain the three events during meiosis/fertilization that make this possible Can someone check these? Yo ______ la cama ayer. hicistehacehizohice (my choice) Ellos me ______ un collar.didistedieron (my choice)disteis _______ usted el trabajo?Hizo Hiciste (my choice)HiceHicieron What was the message of the French Revolution? what is the first step in a scientific poll? A car travels 31.2 miles in 36.0 minutes. What is the average speed of the car during this trip, in miles per hour (mph)? how are members of congress influenced by outside forces Which of the following represents the number of subsets of five elements can be formed from a set of six elements?5!C(6, 5)P(6, 5) which macromolecule makes up the majority of the cell membrane?A.) nucleotide B.) lipidC.) proteinD.) carbohydrate why is baking soda an ionic bond What country does not share a border with Spain? a. Portugal b. ItalyC. France The figure shows the letter M and four of its transformed imagesA, B, C, and D:Which of the four images was formed by a reflection of the letter M? How did industrialization impact US foreign policy in the late 19th century