We are provided that [tex]{\sf \sin (64^{\circ})=p}[/tex] and we have to find the value of [tex]{\sf 8\sin (16^{\circ})\cdot \cos (16^{\circ})\cdot \cos (32^{\circ})}[/tex] . But let's recall a identity which is gonna be very helpful to do this question i.e
[tex]{\boxed{\sf 2\sin (\theta)\cos (\theta)=\sin (2\theta)}}[/tex]Now , coming back on the question ;
[tex]{:\implies \quad \sf 8\sin (16^{\circ})\cdot \cos (16^{\circ})\cdot \cos (32^{\circ})}[/tex]
[tex]{:\implies \quad \sf 4\{ 2\sin (16^{\circ})\cos (16^{\circ})\}\cos (32^{\circ})}[/tex]
Using the above identity ;
[tex]{:\implies \quad \sf 4\sin (32^{\circ})\cos (32^{\circ})}[/tex]
[tex]{:\implies \quad \sf 2\{2\sin (32^{\circ})\cos (32^{\circ})\}}[/tex]
Again using the same identity ;
[tex]{:\implies \quad \sf 2\sin (64^{\circ})}[/tex]
Putting the given value of [tex]{\sf \sin (64^{\circ})}[/tex]
[tex]{:\implies \quad \sf 2p}[/tex]
[tex]{:\implies \quad \bf \therefore \quad \underline{\underline{8\sin (16^{\circ})\cdot \cos (16^{\circ})\cdot \cos (32^{\circ})=2p}}}[/tex]
Proof of the above identity :-
We know that ;
[tex]{\quad \boxed{\sf \sin (A\pm B)=\sin (A)\cos (B)\pm \cos (A)\sin (B)}}[/tex]
So ;
[tex]{:\implies \quad \sf \sin (A+ B)=\sin (A)\cos (B)+\cos (A)\sin (B)}[/tex]
Putting [tex]{\sf A=B=\theta}[/tex] ,
[tex]{:\implies \quad \sf \sin (\theta+ \theta)=\sin (\theta)\cos (\theta)+\cos (\theta)\sin (\theta)}[/tex]
[tex]{:\implies \quad \bf \therefore \quad \underline{\underline{\sin (2\theta)=2\sin (\theta)\cos (\theta)}}}[/tex]
Hence , Proved :D
Find the area of a rectangle with base of 2 yd and a height of 5 ft.
Possible Answers:
30 Square feet ⭐⭐⭐⭐⭐
10 Square Yards ⭐⭐⭐⭐⭐
12960 square inches ⭐⭐
8.36127 square meters ⭐
Use a protractor to draw a pentagon so that the bottom side is horizontal and the left and right sides are perpendicular to the bottom side. The angles formed at the top left and right sides each measure 146°. What is the measure of the fifth angle?
A. 57°
B. 63°
C. 68°
D. 74°
Answer: 68
Step-by-step explanation:
Answer:
the answer is 68
Explanation:
PLS HELP ASAP THANKS ILL GIVE BRAINLKEST PLS THANKS PLS ASAP
Answer:
The answer is B.
Step-by-step explanation:
Point A is on (-6,7) is you move it two left and 2 up it changes to the point (-8,9)
Hope this helped.
A brainliest is always appreciated.
HELP DUE IN 5 mins The company ordered boxes of concrete nails weighing 3.35 kgs each and a box of 2.5 kgs of screws. The eight construction workers each received a box of nails and each worker used 1.23 kgs of concrete nails yesterday. What is the weight of the concrete nails left in each box? If the concrete nails were put together in a big toolbox, how much would the concrete nails weigh?
Answer: See below
Step-by-step explanation:
Weight of concrete nails - weight of concrete nails used = weight of concrete nails left
3.35 – 1.23 = 2.12
Weight of concrete nails left * number of workers = total weight of concrete nails
2.12 x 8 = 16.96
There are 2.12 kgs of concrete nails left in each of the boxes and there are 16.96 kgs of concrete nails altogether
change from typical notation to function notation
y = 5x - 2
Answer:
f(x) = 5x - 2
Step-by-step explanation:
To change from typical notation to function notation, simply replace y with f(x). Remember to ensure the variable you put in the brackets is the same as the variable in the equation.
So y = 5x - 2 becomes f(x) = 5x - 2 (since the variable is x)
And y = 5a - 2 becomes f(a) = 5a - 2 (since the variable is a)
The typical letter to use is f, but we can use other letters.
Other common function notations are g(x) and h(x).
Let's see
[tex]\\ \rm\rightarrowtail y=5x-2[/tex]
. Function notation.[tex]\\ \rm\rightarrowtail g(x)=5x-2[/tex]
Some test
g(2)=5(2)-2=8write the first four terms of the explict sequence f(n)=8n-2 (show all work)
Answer:
6, 14, 22, 30
Step-by-step explanation:
substitute n = 1, 2, 3, 4 into f(n)
f(1) = 8(1) - 2 = 8 - 2 = 6
f(2) = 8(2) - 2 = 16 - 2 = 14
f(3) = 8(3) - 2 = 24 - 2 = 22
f(4) = 8*4) - 2 = 32 - 2 = 30
6. You made cookies for a bake sale. You sold 24 cookies. This was 75% of the cookies you made. How many cookies did you make?
Answer: 32 cookies
Step-by-step explanation: Divide 24 by 3 to find 25% of the cookies you made. 24 divided by 3 is 8. Multiply 8 by 4, since 25% of your cookies times 4 would give you 100% of your cookies. 8 x 4 = 32 cookies.
Solve for x. Round your answer to the nearest tenth.
30
33
x
Step-by-step explanation:
it's an isosceles triangle
ht will intersect the base at 90°
so x^2 =33^2+15^2
x = 36.2
Find the circumference and area of the circle. Use 3.14 for π. Round to the nearest hundredth if necessary.
2 m
The circumference of the circle is about
m.
The area of the circle is about
m2.
Answer:
that's circumference is probably 11
If 50 witches drank a potion that makes 2 of them selfs how much withces will be there?
Answer:
100
Step-by-step explanation:
if you are doing this you need to do 50x2 which in this case equals = 100
You were playing fetch with your dog and accidentally
threw the toy and it got stuck on the roof of your house.
You leaned the ladder against your house at a 30° angle
of elevation. The foot of the ladder is 7 feet from the foot
of the house. How long is your ladder?
You leaned the ladder against your house at a 30 degrees angle -> This create a right triangle, with a 30 degree angle and your ladder is the hypotenuse.
The foot of the ladder is 7 feet from the foot of your house -> The opposite side = 7 feet
In a right triangle, the side that is opposite to a 30 degree angle = 1/2 of the hypotenuse
Since your ladder is the hypotenuse, and the opposite side is opposite to the 30 degree angle, your ladder is 7 x 2 = 14 ft long.
the radius pof a DVD is 60mm what is the DVDs circumfrance
Answer:
approx. 376.8mm
Formula = 2r×pi
Step-by-step explanation:
Hope this Helps!!!
What is the difference between the mean absolute deviation (MAD) for data set A and B?
Data set A 10, 9, 3, 8, 10
Data set B 5, 11, 2, 7, 16
Round your final answer to the nearest tenth.
2.2
0
14
10
Answer:
10
Step-by-step explanation:
100.11256 round to the nearest 10th
Answer:
100.10000
Step-by-step explanation:
Because tenth is 1rst number behind decimal so 1. and 1 is asking it's neighbor hundredths/1 for helps and since 1 is 4 and below it can't go up so it stays the same at 1.
Hope it helps have a great day:)
The measure of an angle is thirty-five times the measure of its complementary angle. What is the measure of each angle?
Answer:
35x + x = 180
36x = 180
x = 180/36
x = 5
the median of 17,2,4,1,7,10,11,16,12,18
Answer:
10.5
Step-by-step explanation:
Since 10 and 11 right there I split those in half so the middle of then is 5 so 10.5
Mean 9.8
Mode is all of them
Range is 17 since highest number 18 lowest number 1 18 - 1=17
Hope this helps have a great day:)
Who ever gets it I will give Brainly and 20 points
Answer:
15%
Step-by-step explanation:
You add up all the frequencies and divide by 9 (the amount 6 was rolled).
It adds up to 60. Divide 9 by 60 and you have 15%.
Complete the equation so that it has no solution 9(x-4)-5x=blank-30
96.1 i dont know if its right but try it
The complete equation so that is has no solution will be;
The number in blank ≠ 4x - 6
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The equation is,
⇒ 9 (x - 4) - 5x = blank - 30
Now,
Let the number in he blank = y
So, We get;
⇒ 9 (x - 4) - 5x = y - 30
⇒ 9x - 36 - 5x = y - 30
⇒ 4x - 36 = y - 30
⇒ 4x = y + 6
⇒ y = 4x - 6
Thus, The complete equation so that is has no solution will be;
The number in blank ≠ 4x - 6
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The top of a cube has an area of 25 square inches. What would be the length of one of its sides, s, be?
Please show work ty!
Check the picture below.
Describe two different ways you could change the values in the table so that the answer to problem 6 is different.
Answer:
6) brand B
Step-by-step explanation:
You need to find how much one-ounce costs so you do 18/2.5 = 7.2 and 24/3.5 = 6.9 so B is a better deal.
Junior bought a work truck for $13,000. The value of his truck will depreciate, or decrease, by 15% each year. Which recursive formula models the value of his truck after each year?
The correct recursive formula which models the value of his truck after each year is,
⇒ 13,000 (0.85)ⁿ
What is mean by Percentage?A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.
To Calculate the percent of a number , divide the number by whole number and multiply by 100.
Given that;
Junior bought a work truck for $13,000.
And, The value of his truck will depreciate, or decrease, by 15% each year.
Hence, We get;
The correct recursive formula which models the value of his truck after each year is,
⇒ 13,000 (1 - 15/100)ⁿ
⇒ 13,000 (1 - 0.15)ⁿ
⇒ 13,000 (0.85)ⁿ
Thus, The correct recursive formula which models the value of his truck after each year is,
⇒ 13,000 (0.85)ⁿ
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* I NEED THIS ASAP *
A box contains 4 bags of sugar. The total mass of all 4 bags is 6 kg. What is the mass of each bag in
grams
Answer:
1500 grams per bag of sugar.
Step-by-step explanation:
6kg is equivalent to 6000 grams. In order to find the mass of each bag, you divide the 6000 grams by the number of bags (4), which tells you there are 1500 grams per bag of sugar.
Two people (A and B) travel from X and Y along different routes. their journeys each take the same amount of time. a’s route is 90 km, B’s route is 60 km. B travels at an average speed of 40 km/h what is a’s average speed
Answer:
a’s average speed is 60km/h
Step-by-step explanation:
x = a’s average speed
60/40 = 90/x
Cross multiplication:
60x = 40x90
60x=3600
Divide both sides by 60
x= 60
Person A's average speed is 60 km/h.
What is speed?Speed is the ratio of the given distance and time.
It shows how fast an object is moving at a given time.
The formula is Distance / Time.
We can find the distance or time when the required values are given using this formula.
We have,
We can start by using the formula:
Distance = speed x time
Let's denote A's average speed as "S" and the time taken for both A and B as "T".
For person B, we have:
60 = 40 x T
Solving for T, we get:
T = 1.5 hours
Now we can use the same formula for person A:
90 = S x 1.5
Solving for S, we get:
S = 60 km/h
Therefore,
Person A's average speed is 60 km/h.
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a Martin took a tax from his home to the airport. The taxi driver charged an initial fee of $9.00 plus $2.75 per mile. The total fare was $50.25, not including the tip. How many miles did Martin travel by taxi on this ride?
Hollyville Elementary is having a pizza party. The school secretary plans on ordering 25 pizzas. There are 10 classes in the school. If each class is given pizzas, is 25 pizzas enough for the entire school? If so, how much pizza, if any, will be left over? If not, how many more pizzas will they need?
1, Yes, 25 pizzas are enough. There will be 2 pizzas left over.
2, No, 25 pizzas are not enough. They need 2 more pizzas.
3, No, 25 pizzas are not enough. They will need 1 more pizza.
4, Yes, 25 pizzas are exactly enough. There will not be any pizza left over.
If you flip a coin and get heads you win $8 but if you flip tails you get nothing. How
much money can you expect to win on average?
Answer:
$4 on average
Step-by-step explanation:
A fair coin has a 50/50 chance of being heads/tails.
You have a 50% chance to get heads and win $8.
If you flip the coin twice then it is likely you get heads once and tails once. So, on average, $8 divided by 2 flips = $4.
Álgebra 1 please help!!!
Answer:
a. geometric sequence
b. an = 5(2)^n-1
c. an+1 = an x 2
Step-by-step explanation:
The sequence: 5, 10, 20, 40,...
a. The sequence is geometric because the sequence has a common ratio of 2, each number is made by multiplying the previous number with the common ratio (2).
b. The explicit formula for this sequence is an = 5(2)^n-1
The explicit formula for a geometric sequence is
an = a1 (r)^n-1
Substituting that with the values we know, we will get
an = 5(2)^n-1
c. The recursive formula for this sequence is an+1 = an x 2
The recursive formula for a geometric sequence is
an+1 = an x r
Substituting for the values we know, we get
an+1 = an x 2
Let me know in the comments if you have any questions! If you could mark this answer as brainliest, I would very much appreciate it
1. Judy took $30 with her to spend on popcorn and drinks for herself and her friends at the movie theater. The price for each bag of popcorn was $5. The price of each drink was half the price of a bag of popcorn.
(a) Sketch the graph that represents the situation and label the intercepts. Use one axis to represent the number of bags of popcorn and the other axis to represent the number of drinks.
(b) Explain your graph.
Answer:
Step-by-step explanation:
The relationship between the number of popcorn and drinks is linear relationshipThe responses are;(a) Please find attached the required graph created with MS Excel(b) From the graph, we have that as the number of bags of popcorn Judy buys increases, the number of drinks decreases linearlyReasons:The given parameter are;Amount Judy took with her to spend on popcorn and drinks = $30Price of each bag of popcorn = $5Price of each drink = Half the price of a bag of popcorn∴ The price of each drink = (a) Let X represent the number of bags of popcorn Judy buys and let Y represent the number of drinks she buys, we have;5·X + 2.5·Y = 302.5·Y = 30 - 5·XWhich gives;Y = 12 - 2·XUsing the above equation, the graph of popcorn and drinks bought by Judy is plotted with MS Excel and attached here(b) The data in the graph are presented as followsThe point corresponding to the y-intercept is the point that gives the maximum number of drinks Judy can buy if she does not buy popcorn is 12 drinks. The number of drinks she can buy reduces by 2 for each bag of popcorn she buys, such that she can buy 6 bags of popcorn and no drinks which is the x-intercept.
Answer:
265
Step-by-step explanation:
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
The dot plot shows the number of books read by students in grades 7 and 8 as part of a summer reading program. Match each phrase to its correct value.
Answer: Im totally unsure but I think it is, 6,3,1/6,1.4.
Step-by-step explanation:
Again, I am completely unsure and it was a thoughtout guess.
hi guys can u help me with this
Hello.
The first fraction is
[tex]\displaystyle\frac{9}{15}[/tex]
Both the top and bottom can be divided by 3:
[tex]\displaystyle\frac{3}{5}[/tex] (Simplest Form)
Next fraction:
[tex]\displaystyle\frac{15}{40} =\frac{3}{8}[/tex]
We divided the top & bottom by 5.
Next:
[tex]\displaystyle\frac{20}{35}[/tex]
Divide the top & bottom by 5:
[tex]\displaystyle\frac{5}{7}[/tex]
Next:
[tex]\displaystyle\frac{12}{20} \\\text{Divide by 4:}\\\displaystyle\frac{3}{5}[/tex]
Next:
[tex]\displaystyle\frac{44}{48} =\frac{11}{12}[/tex]
Next:
[tex]\displaystyle\frac{5}{60} =\frac{1}{12}[/tex]
Next:
[tex]\displaystyle\frac{10}{24} =\frac{5}{12}[/tex]
next:
[tex]\displaystyle\frac{25}{30} =\frac{5}{6}[/tex]
next:
[tex]\displaystyle\frac{10}{18} =\frac{2}{9}[/tex]
next:
[tex]\displaystyle\frac{28}{40} =\frac{14}{20} =\frac{7}{10}[/tex]
[tex]\displaystyle\frac{8}{10} =\frac{4}{5}[/tex]
[tex]\displaystyle\frac{3}{9} =\frac{1}{3}[/tex]
[tex]\displaystyle\frac{15}{20} =\frac{3}{4}[/tex]
[tex]\displaystyle\frac{6}{9} =\frac{2}{3}[/tex]
[tex]\displaystyle\frac{20}{32} =\frac{5}{8}[/tex]
[tex]\displaystyle\frac{5}{35} =\frac{1}{7}[/tex]
[tex]\displaystyle\frac{2}{8} =\frac{1}{4}[/tex]
[tex]\displaystyle\frac{2}{20} =\frac{1}{10}[/tex]
[tex]\displaystyle\frac{33}{36} =\frac{11}{12}[/tex]
[tex]\displaystyle\frac{15}{40} =\frac{3}{8}[/tex]
[tex]\displaystyle\frac{32}{36}=\frac{8}{9}[/tex]
[tex]\displaystyle\frac{14}{20} =\frac{7}{10}[/tex]
I hope it helps.
Have a great day.
[tex]\boxed{imperturbability}[/tex]
