Please Help Me. Use an identity to find the exact value of each expression: Note: You are not allowed to use decimals in your answer. sin(96∘)cos(264∘)+cos(96∘)sin(264∘)= and sin⁡(258∘)cos⁡(33∘)−cos⁡(258∘)sin⁡(33∘)=

Answers

Answer 1
[tex]\bf \textit{Sum and Difference Identities} \\ \quad \\ sin({{ \alpha}} + {{ \beta}})=sin({{ \alpha}})cos({{ \beta}}) + cos({{ \alpha}})sin({{ \beta}}) \\ \quad \\ sin({{ \alpha}} - {{ \beta}})=sin({{ \alpha}})cos({{ \beta}})- cos({{ \alpha}})sin({{ \beta}}) \\ \quad \\ cos({{ \alpha}} + {{ \beta}})= cos({{ \alpha}})cos({{ \beta}})- sin({{ \alpha}})sin({{ \beta}}) \\ \quad \\ cos({{ \alpha}} - {{ \beta}})= cos({{ \alpha}})cos({{ \beta}}) + sin({{ \alpha}})sin({{ \beta}})\\\\ -------------------------------[/tex]

[tex]\bf sin(96^o)cos(264^o)+cos(96^o)sin(264^o)\implies sin(96^o+264^o) \\\\\\ sin(360^o)\implies 0\\\\ -------------------------------\\\\ sin(258^o)cos(33^o)-cos(258^o)sin(33^o)\implies sin(258^o-33^o) \\\\\\ sin(225^o)\implies -\cfrac{\sqrt{2}}{2}[/tex]
Answer 2

Utilize trigonometric identities to find exact values without decimals:

To find the exact values of the given trigonometric expressions, we can use the trigonometric identity sine of the sum of angles: sin(A + B) = sinA x cosB + cosA  x sinB.

1. For the first expression, sin(96°)cos(264°) + cos(96°)sin(264°), using the identity, it simplifies to sin(96° + 264°), which equals sin(360°), and sin(360°) equals 0.

2. For the second expression, sin(258°)cos(33°) - cos(258°)sin(33°), applying the identity yields sin(258° - 33°), which is sin(225°), and sin(225°) simplifies to -√2/2.


Related Questions

pick any number and add 1 to it. find the sum of the new number and the original number. Add 9 to the sum. Divide the new sum by 2 and subtract the original number from the quotient

Answers

The correct answer is x+1 

Help me asap! I will mark you brainly and a heart tysm!


:D

Answers

The answer is A) -4/25 because when you multiply 8/15 and -3/10, you can simplify the expression to 4/5 times -1/5, which equals -4/25.  
8 /15 * -3/10 =  -24/150  =  -4/25

Geometry.

The circle described by the equation (x - 3)² + (y + 4)² = 9 is translated 5 units to the left and one unit up.
At what point is the center of the image circle located?

A) (-8,5)
B) (8, -5)
C) (2, -3)
D) (-2, -3)

Answers

Greetings!

Answer:

New coordinates are (-2, -3)

Step-by-step explanation:

First we need the centre coordiates. In (x - a)² + ( y - b)² = r² , a is the x coordinate for the circle centre and b is the y coordinate for the circle centre, so this means the coordinate of the circle centre is:

(3 , -4)

If moving to the left 5 spaces, then 5 has to be subtracted from the x coordinate:

3 - 5 = -2

Now moving one up you add one to the y coordinate:

-4 + 1 = -3

So the new coordinates are (-2, -3)


Hope this helps!

Use the variable t for the number of teeth in one row. Write an expression to determine the number of teeth in a sharks mouth.

Answers

if t represents the number of teeth in one row...and a shark has 3 rows of teeth...then the expression to find out how many teeth he has in his entire mouth is : 3t
Final answer:

The total number of teeth in a shark's mouth can theoretically be determined by multiplying the number of teeth in a single row by the total number of rows of teeth. The multiplication will be defined by the particular shark species.

Explanation:

Assuming that we want to find out the total number of teeth in a shark's mouth and we know the number of teeth in one row (coded as t), we would need to multiply this number by the number of rows of teeth in the shark's mouth. For instance, if a shark has two rows of teeth, the total number of teeth would be 2t.

It is important to recognize that each species of shark might have a different number of rows of teeth, so without specifying the particular species, the exact total of teeth can't be computed but it would still be 't' times the number of rows. But in general, a Sand Tiger Sharks like Carcharias Taurus for example, can have around 3 to 7 rows of teeth.

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Solve: 2(4x - 6) = 6x - 4

A) 4
B) 8
C) -4
D) no solution

Answers

it's A .positive 4 ¡!!!!!!!!!

A company wants to decrease their energy use by 15%. If their electric bill is currently $1300 a month, what will their bill be if they are successful?

Answers

Since 15%=0.15 by moving the decimal 2 places to the right, 15% of 1300 can be found by multiplying 1300 by 0.15, resulting in 195 as 15%. Since we have to subtract 15% from our answer (15% is not our final answer), 1300-195=1105 as our answer

I need help with #6 plzzzz

Answers

First, find the unit rate.
Since the car travels 476 miles with 14 gallons of gas, then 476/14 = 34, so the car can travel 34 miles per gallon.

The distance is 34 times the number of gallons

d = 34g

Now you are given 578 miles, and you need to find the gallons.

578 = 34g

Solve for g by dividing both sides by 34.

g = 17

He needs 17 gallons.

how do you graph y=-6x+3 ?

Answers

start on 3 as your y-intercept

then do down 6 points and over one

write the number in expanded form 259,341

Answers

the answer is 200,00 + 50,000 + 9,000 + 300 + 40 + 1 hope that helps!

The formula for kinetic energy is shown. In the formula, m represents mass and v represents velocity. If mass is measured in grams and velocity is measured in centimeters per minute, what is the unit for kinetic energy
A) grams-centimeters per minute

B) grams-centimeters squared per minute
C) grams-centimeters per minute squared

D) grams-centimeters squared per minute squared

Answers

Hello,

Answer D

E=mv²/2 ==> gram*cm²/min²
BUT it should be JOULES!!!

The unit for kinetic energy, when mass is in grams and velocity is in centimeters per minute, is D) grams-centimeters squared per minute squared.

The formula for kinetic energy is given by KE = 1/2 mv², where m represents mass and v represents velocity. To find the units of kinetic energy, we need to plug in the units of mass and velocity into the formula.

If m is measured in grams (g) and v is measured in centimeters per minute (cm/min), the units for velocity squared will be (cm/min)². Therefore:

KE = 1/2 (grams) (centimeters/minute)²

When we square velocity (cm/min), we get cm²/min². Thus, the units for kinetic energy become:

D) grams-centimeters squared per minute squared (g∙cm²/min²)

One-third cup of black beans provides 20% of the potassium you need daily. You must get the remaining 1,360 milligrams from other sources. How many milligrams of potassium should you consume daily?

Answers

5×20%=100% so 1360mg is 80% of the daily requirement. The total requirement is 1360/0.8=13600/8=1700 mg.

80 percent of needed milligrams is 1360

so

1360/.80 = x/1  

1700 milligrams or 1,700 milligrams of potassium

Simplify (−3.5)(−3)(−6.4).
−672
−67.2
67.2
672

Answers

 (−3.5)(−3)(−6.4) = -67.2

answer
−67.2 

Answer:

-67.2

Step-by-step explanation:

Simplify the given expression (−3.5)(−3)(−6.4)

WE apply PEMDAS rule to simplify it

Lets start with parenthesis part

We multiply first two parenthesis

(−3.5)(−3)

Negative and negative becomes positive

(−3.5)(−3) is 10.5

Now we multiply it with -6.4. Positive times negative is negative.

[tex]10.5 \cdot (-6.4)= -67.2[/tex]

[tex](-3.5)(-3)(-6.4)=-67.2[/tex]

If mP = 85°, which is a possible measure for Y?
mY = 80°mY = 85°mY = 100°mY = 180

Answers

Answer:c is the answer

Step-by-step explanation:

Answer:

C. m∠Y = 100°

Step-by-step explanation:

Which fraction is equivalent to 0.16? A. 1/16 B. 16/100 C. 1/6 D. 1/3

Answers

B 16/100 is equivalent to 0.16
I'm assuming that this decimal terminates and none of the digits repeat forever. 

The 1 is in the tenths decimal place
The 6 is in the hundredths decimal place

So put together 0.16 is spoken out as "16 hundredths" meaning we have the fraction 16/100

We simply write the numbers after the decimal "16" over the value 100

Another example is 0.37 = 37/100

-------------------------------------------------------------------

Answer: Choice B) 16/100

If a line of one billion people standing shoulder to shoulder stretches 346,439 miles long, what is the average shoulder width, in feet, of the people in the line?

Answers

Final answer:

Given a line of one billion people extending for 346,439 miles, the average shoulder width of a person in the line is approximately 1.83 feet.

Explanation:

To find the average shoulder width of the people in the line, we need to convert the total miles into feet, since the result wanted is in feet. There are 5,280 feet in one mile. So the total length in feet would be 346,439 miles * 5,280 feet/mile = 1,829,029,920 feet. Now, if there are 1 billion people in this line, then the average width of a person's shoulders would be the total length divided by the total number of people. Hence, the average shoulder width = 1,829,029,920 feet / 1,000,000,000 people = approximately 1.83 feet.

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Write the contrapositive of the conditional statement. If a polygon is regular, then it has congruent angles and congruent sides.

Answers

The contra positive of the conditional statement is this: IF A POLYGON DOES NOT HAVE CONGRUENT ANGLES AND CONGRUENT SIDES THEN IT IS NOT A REGULAR POLYGON.
forming a contra positive statement involves switching the hypothesis and the conclusion portions of conditional statement  and negating both. 

Hector made a batch of pancakes for his guests. He used 6 cups of milk, 3 eggs, and 9 cups of pancake mix. What is the constant of proportionality for the ratio of pancake mix to milk?

Answers

9:6
is the ratio of pancake to milk

Answer:

I just got it right the answer is 9:6

Step-by-step explanation:

Assume you have such a watch. if a minimum of 18.0% of the original tritium is needed to read the dial in dark places, for how many years could you read the time at night? assume first-order kinetics.

Answers

Given that the half life of 3H is 12.3 years.

The amount of substance left of a radioactive substance with half life of [tex]t_{ \frac{1}{2} }[/tex] after t years is given by

[tex]N(t)=N_0\left(\frac{1}{2} \right)^{ \frac{t}{t_{\frac{1}{2}} }[/tex]

Therefore, the number of years it will take for 18% of the original tritinum to remain is given by

[tex]18 \% = 100 \% \left(\frac{1}{2} \right)^{ \frac{t}{12.3}} \\ \\ \Rightarrow\left(\frac{1}{2} \right)^{ \frac{t}{12.3}} =0.18 \\ \\ \Rightarrow\frac{t}{12.3}\ln\left(\frac{1}{2} \right)=\ln0.18 \\ \\ \Rightarrow\frac{t}{12.3}= \frac{\ln0.18}{\ln\left(\frac{1}{2} \right)} = \frac{-1.715}{-0.6931} =2.474\\ \\ \Rightarrow t=2.474(12.3)=30.4[/tex]

Therefore, the number of years that the time could be read at night is 30.4 years.

Final answer:

You could read the time on a tritium-based watch in dark places for approximately 34.87 years before the tritium decays below 18% of its original amount, necessitating this calculation using first-order kinetics and the half-life of tritium (12.32 years).

Explanation:

To calculate how many years you could read the time at night with a watch containing tritium, we need to understand first-order kinetics and the half-life of tritium.

Tritium has a half-life of 12.32 years, meaning after 12.32 years, half of the original tritium remains.

The question specifies that a minimum of 18% of the original tritium is needed for readability in dark places.

To find the number of years you could read the time, we use the formula for first-order decay:

[tex]N = N_0(1/2)^{(t/T)[/tex],

where N is the final amount of substance left, N_0 is the initial amount of substance, t is the time in years, and T is the half-life (12.32 years in this case).

We rearrange the formula to solve for t:

t = T*log(N/N_0)/log(1/2).

Plugging in the values, assuming N/N_0 = 0.18 (18%), and T = 12.32 years, we get:

t = 12.32*log(0.18)/log(1/2) ≈ 34.87 years.

Therefore, you could read the time on a tritium-based watch in dark places for approximately 34.87 years before the tritium decays below the level necessary for visibility.

Jordan has 260 basketball cards. He divides them into 4 equal groups. How many cards are in each group?

Answers

Jordan has 260 basketball cards and divides them evenly into 4 groups, resulting in 65 cards per group.

Jordan has 260 basketball cards and wants to divide them into 4 equal groups. To find the number of cards in each group, we need to perform a simple division. By dividing 260 by 4, we get:

Divide 260 by 4.

260 \/ 4 = 65.

Each group will have 65 cards.

Therefore, Jordan will have 65 basketball cards in each of the four groups.

Rewrite the following statement using a number in scientific notation.

The diameter of a certain bacterium is about
0.00000002
0.00000002 meters.

Answers

[tex]\bf 0.\stackrel{\textit{8 decimals}}{00000002}\implies 2.0\times 10^{-8}~meters[/tex]

since 2 is the first significant digit, a nonzero, then we move the dot that way, it just so happen it's 8 spots to the right.

If 9/10 yard of material is needed to make a blanket, how many blankets can be made from 27 yards of material

Answers

27 / (9/10) =
27 * 10/9 =
270/9 =
30 <=== 30 blankets can be made with 27 yds of material

Jordan is chopping wood for the winter. For 10 days in a row, he follows the same process: In the morning, he chops 20 pieces of wood, and in the evening, he chops an additional 30 pieces of wood. On the 11 day, Jordan chops only 5 pieces of wood. Write a numerical expression with parentheses for the total number of pieces of wood Jordan chopped. Do not simplify your expression.

Answers

i would write this:

total = 10(20+30) +5

10 x (20 + 30) + 5
10 x 50 + 5
500 + 5

Dane is 10 times Brian's age. The difference in their age is 27, how old is Brian

Answers

Brian is 3 years old.
Hope this helps!

Answer:

Brain is 3 years old.

Step-by-step explanation:

Let B represent Brain's age and D represent Dane's age.

We have been given that Dane is 10 times Brian's age. We can represent this information in an equation as:

[tex]D=10B...(1)[/tex]

We are also told that the difference in their age is 27. We can represent this information in an equation as:

[tex]D-B=27...(2)[/tex]

Upon substituting equation (1) i equation (2), we will get:

[tex]10B-B=27[/tex]

[tex]9B=27[/tex]

[tex]\frac{9B}{9}=\frac{27}{9}[/tex]

[tex]B=3[/tex]

Therefore, Brain is 3 years old.

If the probability of Stephan Curry missing a free throw is 6%, what are the odds of him hitting the next free throw?

Answers

Answer:

  47 : 3

Step-by-step explanation:

Odds of hitting are the ratio of hits to misses:

  94 : 6, or 47 : 3.

Of the students at Milton Middle School, 99 are girls. If 45% of the students are girls, how many total students are there at Milton Middle school?

Answers

that is how i found the answer
220-45%=121
220-99=121
 220

Grass can grow up to 6 inches in a week depending on temperature humidity and time of year at this rate how tall grass grow in 24 days

Answers

keeping in mind there are 7 days in a week.

[tex]\bf \begin{array}{ccll} inches&days\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 6&7\\ x&24 \end{array}\implies \cfrac{6}{x}=\cfrac{7}{24}\implies \cfrac{6\cdot 24}{7}=x[/tex]

PLEASE ANSWER IVE BEEN WAITING FOR AN HOUR

Rachel earned 34 in 4 hours at her job today she wants to know how much she could earn (e) tommorow if she works 10 hours at the same hourly rate

A. E/34 = 4/10
B. 34/4 = E/10
Solve the proportion to determine how much Rachel will earn in 10 hours.

Answers

So she earned $34 in 4 hours, meaning she was earning at the rate of 34/4 or $8.5/hour.  Is she works for 10 hours at the same rate, it would be 8.5 x 10 = $85.  B is the correct proportion.
The correct equation of proportions would be $34                             x
                                                                         ------- .  Set this = to --------
                                                                          4 hr                          10 hr

$34           x
_____  = ---------    Cross multiply:  ($34)(10 hr) = 4(hr)x
 4 hr         10 hr                                                                

Cancel "hr" on both sides.  Then $340 = 4x, and x = $85.

She could earn $85 working 10 hours.

What is a equivalent fraction for 4/21

Answers

One equivalent fraction for 4/21 could be 8/42.

Final answer:

An equivalent fraction for 4/21 can be found by multiplying the numerator and denominator by the same non-zero number, such as 2 to get 8/42.

Explanation:

An equivalent fraction for 4/21 is a fraction that has the same value but is expressed with different numerator and denominator. To find an equivalent fraction, you can multiply or divide both the numerator and denominator by the same non-zero number. For example, if we multiply the numerator and denominator by 2, we will get 8/42, which is an equivalent fraction to 4/21. It's important to note that this new fraction can be simplified further, just like 4/21 can be simplified to its lowest terms if there were any common factors.

what is the answer to 2(6b + 8) = 4 + 6b

Answers

2(6b + 8)=4 +6b
or, 12b+16=4+6b
or,12b-6b=4-16
or,6b= -12
or,b= -12/6
or, b= -2
Step 1. Distribute the 2 into the parenthesis ( we do this because the whole parenthesis and the 2 are multiplying)
Step 2. Get “b” by itself. ( to solve for a letter like b, we need to have it on one side of the equal sign)
Step3. Divide by 6 because we are undoing the multiplication of 6timesB. ( what you do on one side you do to the other side) divide the 6 into the -12.
There you go the answer is B= -2

Simplify the expression
–5.6 + 8.2
Answers:

–2.6


–13.8


2.6


13.8

Answers

This can be rewritten as 8.2 - 5.6 so it is easier to solve.

8.2 - 5.6 = 2.6

Hope this helps!

–5.6 + 8.2

The answer is 2.6 because with a - and + you subtract the two number and whichever is the highest number that is the sign that you put. In this case, the highest number is a +8.2 so your answer will be POSITIVE.

If the highest number was a negative for example, 5.6+ -8.2 then your answer will be -2.6


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