we know that π/2 < θ < π, which is another way of saying that θ is in the II Quadrant, so half that angle will most likely be located on the I Quadrant, where cosine as well as sine are both positive.
Now, let's keep in mind that θ itself is in the II Quadrant, where the cosine is negative whilst the sine is positive.
[tex]\textit{Half-Angle Identities} \\\\ sin\left(\cfrac{\theta}{2}\right)=\pm \sqrt{\cfrac{1-cos(\theta)}{2}} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ sin(\theta )=\cfrac{\stackrel{opposite}{7}}{\underset{hypotenuse}{25}}\qquad \textit{let's now find the \underline{adjacent side}} \\\\\\ \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \pm\sqrt{c^2-b^2}=a \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases}[/tex]
[tex]\pm\sqrt{25^2-7^2}=a\implies \pm\sqrt{576}=a\implies \pm 24=a\implies \stackrel{II~Quadrant}{-24=a} \\\\[-0.35em] ~\dotfill\\\\ cos(\theta )=\cfrac{\stackrel{adjacent}{-24}}{\underset{hypotenuse}{25}} \\\\\\ sin\left(\cfrac{\theta}{2}\right)\implies \pm \sqrt{\cfrac{1-\left( -\frac{24}{25} \right)}{2}}\implies \pm \sqrt{\cfrac{1 +\frac{24}{25} }{2}}[/tex]
[tex]\pm\sqrt{\cfrac{~~\frac{49}{25} ~~}{2}}\implies \pm\sqrt{\cfrac{49}{50}}\implies \stackrel{I~Quadrant}{+\sqrt{\cfrac{49}{50}}}\implies \cfrac{\sqrt{49}}{\sqrt{50}}\implies \cfrac{7}{5\sqrt{2}} \\\\\\ \stackrel{\textit{rationalizing the denominator}}{\cfrac{7}{5\sqrt{2}}\cdot \cfrac{\sqrt{2}}{\sqrt{2}}\implies \cfrac{7\sqrt{2}}{5\sqrt{2^2}}}\implies \cfrac{7\sqrt{2}}{10}[/tex]
432 oranges are to be divided equally among a number of people. If there had been four people less, the share of each would have been 9 oranges more. Find the number of people.
Answer:
the number of people would have been 48
Convert ; (a) 125% to decimal (b) 0.75 to percentage
Answer:
125/100=0.125
(b) 7/10+5/100=75/100=75%
Answer:
a. 1.25
b. 75%
Step-by-step explanation:
Percentage to Decimal = Divide by 100
Decimal to Percentage = Multiply by 100
Express the inequality b≥−8 using interval notation
Answer:
[-8, infinity)
Step-by-step explanation:
Interval notation uses (, [, ], ) where the parentheses are exclusive and the brackets are inclusive. That means, we have:
[-8, infinity)
The reason we don't use the square bracket for infinity is because you can never include infinity in your set
Milo has 15 Dimes, 20 Nickels, 19 Pennies, 8 Quarters, and 1 Half Dollar. Which expression shows one way Milo can use some or all of these coins to get $5.00? A) 2(0.50) + 20(0.50) + 15(0.10) + 6(0.25) B) 3(0.50) + 20(0.05) + 15(0.10) + 6(0.25) C) 3(0.25) + 20(0.10) + 15(0.50) + 6(0.05) D) 6(0.25) + 20(0.05) + 15(0.01) + 1(0.50) E) 8(0.25) + 15(0.10) + 20(0.05)+ 1(0.50)
Answer:
E)
Step-by-step explanation:
in total milo has $5.19
A does not work because he does not have 22 half dollars, b does not work because he does not have 3 half dollars, c does not work because he does not have 20 dimes, D does not work work because it only adds up to $3.15.
E works
select one card at random from the deck let A be the event that the randomly select a card is a club and let B be the event that the card is a five
Answer:
1 and 52 chance
Step-by-step explanation:
PLEASE HELP ME WITH THIS QUESTION
The graph below shows the distances, in miles, that a dragonfly can travel in a certain number of hours:
A graph titled Motion of a Dragonfly shows Time in hours on the x axis and Distance in miles on the y axis. The scale on the x axis shows number from 0 to 10 at increments of 2, and on the y axis, the numbers are shown from 0 to 330 at increments of 66. A straight line joins the ordered pairs 0, 0 and 2, 66 and 4, 132 and 6, 198
Based on the graph, what is the dependent variable, what is the equation relating the two variables, and how far will the dragonfly travel in 24 hours if it continues to fly at the same speed?
The dependent variable is distance, the equation is y = 33x, and the dragonfly will travel 792 miles.
The dependent variable is distance, the equation is x = 33y, and the dragonfly will travel 1,056 miles.
The dependent variable is time, the equation is y = 33x, and the dragonfly will travel 792 miles.
The dependent variable is time, the equation is x = 33y, and the dragonfly will travel 1,056 miles.
Answer:
The dependent variable is distance, the equation is y = 33x, and the dragonfly will travel 792 miles
Step-by-step explanation:
ordered pairs: (0, 0) (2, 66) (4, 132) (6, 198)
slope of linear equation = change in y ÷ change in x
⇒ slope = (132 - 66) ÷ (4 - 2) = 33
Therefore, equation of the line: y = 33x
When x = 24, y = 33 × 24 = 792 miles
Distance is dependent on time, therefore distance is the dependent variable and time is the independent variable.
What is the net decimal equivalent if 40%, 30% and 15% discounts were applied
Answer:
Well you can’t really stack these percentages discounts.
Assuming it’s in the same order as the problem then
We can find the decimal equivalent by just dividing.
So think of it like this way.
Your getting 40 percent off, the original price.
The original price of course is a 100 percent since its the one and only price.
When your taking 0.4 percent off then its taking off 0.4 from the 1.00
So you have 0.6.
Your now paying 60 percent of the price.
Now the 30 percent.
Same thing except this times its 0.6.
Now 30 percent of 60 is 18 percent and then subtract that by 0.6 which is 0.42
Now for the final 15 percent
Same thing except this time its 0.15
15 percent of 0.42 is 6.3 percent, subtract that by 0.42 is 0.357
After the discounts were applied you’d only have to pay 0.357 or 35.7%
In order to find the total amount of discounts just subtract the amount we have to pay by the original which was 100 %. 100 - 35.7 = 64.3
Final net percentage is equivalent 64.3%
If 2x = 14, find the value of 6 - 7x
Answer:
-43
Step-by-step explanation:
x=7
Answer:
The Answer Is 49.
Step-by-step explanation:
2x = 14. 2x means 2 x ??? = 14. but you can find what "X" is you can find it out by divideing, 2 divided by 14 is 7 so X = 7. To find 6 - 7x you know that is means 6 - (7 x 7). 7 x 7 is 49, 6 - 49 is -42. You answer is -43 and X means 7.
ANSWER CORRECTLY FOR 25 POINTS (Again smh)
Use this rule to fill in the table.
Rule: Divide the input by 4 to get the output.
Divide by 4
Input Output
12 |
16 |
20 |
Answer:
the answers are 3, 4, and 5
Suppose you obtain a $1300 T note with a 9% annual rate paid monthly with Matt Trinity in six years how much interest will be paid to you each month
Answer:
2
Step-by-step explanation:
2
https://brainly.com/question/5720183
From: rejkjavik
Ambitious
4.2K answers
10.3M people helped
Answer: simple interest = $9.75
Step-by-step explanation:
given data:
Principle = $1300
annual rate = 9%
time = 6 year =
we know that simple interest is given as
Simple interest
FOR ABOVE QUESTION
Time is 1 month
simple interest
simple interest = $9.75
I need help please ASAP !!
Step-by-step explanation:
5 An exterior angle of a triangle is equal to the sum of its two opposite non-adjacent interior angles. The sum of the exterior angle and the adjacent interior angle that is not opposite is equal to 180º.
Help!!!!!!!!!!!!!!!!
Answer:
13.8
Step-by-step explanation:
We know that 1 inch is 9.2 miles. The houses are 1.5 inches away. We need to divide 9.2 by 2. We get 4.6. 9.2+4.6=13.8!
13.8
give the value for b in terms of a and c from the following question -2(8a+10b)=6c
Answer:
b = (-4/5)a - (3/10)c
--------------
-2(8a + 10b) = 6c
8a + 10b = -3c
10b = -8a - 3c
b = (-8/10)a - (3/10)c
b = (-4/5)a - (3/10)c
The number line shows that x + 7 = 34.
What is the solution to the equation shown on the number line?
X+7
26 27 28 29 30 31 32 33 34 35 36
O A. x= 33
B. X= 24
O C. x = 19
D.
X = 27
Answer:
D=27
Step-by-step explanation:
34-7 to isolate x by itself
can a negative number be a real number
The real numbers include the positive and negative integers and fractions (or rational numbers) and also the irrational numbers.
1. 5(n-2) +9 =
2. n + 8n² - 17 =
Answer:
1. n = 0.2
2. n ≈ 1.396577191 or n ≈ -1.521577191
Step-by-step explanation:
Q1:
[tex]5(n-2)+9 = 0[/tex]
[tex]5n-10 = -9[/tex]
[tex]5n = 1[/tex]
[tex]n = 0.2[/tex]
Q2:
Use the quadratic formula on your calculator.
The polynomial equation x^(3)-x=0 has exactly one positive root and exactly one negative real root. Please select the best answer from the choices provided T F
Answer: T
Step-by-step explanation:
how much fabric will he need to create the tent
solve for x ( SHOW YOUR WORK )
Answer:
x+47+85+54=180°
x+186°=180
x=-6
Substitute the value of x in x+47
-6+47=41°
Your answer is 41°
pls Mark as brainliest
please help
solve the formula for r. suppose a merry-go-round is spinning once every 3 seconds. is the point on the outside edge has a speed of 12.56 ft per second, what is the radius of the merry-go-round? (use 3.14 for π)
Answer:
6 feet
Step-by-step explanation:
The circumference is given by ...
C = 2πr
Since we travel that distance in 3 seconds, our speed is ...
2πr/3 = 12.56 . . . . . . feet per second
6.28/3r = 12.56 . . . . using 3.14 for π
r = 12.56(3/6.28) = 6
The radius of the merry-go-round is 6 feet.
Solve 2/5=x/25 what is the c
Answer:
x=10
Step-by-step explanation:
By c, I am thinking x...
So, to solve this question, you do cross-multiplication
2/5=x/25
5*x=25*2
5x=50
x=10
This is the question I have on the picture that’s what it is
Refer to the figure. Find m SUV.
Help :(
Answer:122°
Since USM is 180° you take 180 and 58° and then subtract them and you get 122°.
what is the slope of the line that contains the points (13,-2) and (3,-2)? Be sure to simply result
Answer:
0
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(-2-(-2))/(3-13)
m=(-2+2)/-10
m=0/-10
m=0
Surya purchased 176 return gifts for his birthday party. He spent 52,624 for all the gifts. Find the cost of one gift.
Answer:
who the f who spend the much money anyways divide 176 52,624 and u get 0.003344 or 299
Step-by-step explanation:
Electric utility poles in the form of right cylinders are made out of wood that costs $11.07 per cubic foot. Calculate the cost of a utility pole with a diameter of 1.5 ft and a height of 40 ft. Round your answer to the nearest cent.
If the cylinders are made out of wood that costs $11.07 per cubic foot, the cost of the cylinder will be $782.10
How to calculate the volume of cylinderThe volume of a cylinder is expressed as:
V = πr²h
h is the height = 40ft
r is the radius = 1.5/2 = 0.75ft
Substitute:
V = π(0.75)²(40)
V = 3.14 * (0.75)²(40)
V = 70.65 cubic foot
If the cylinders are made out of wood that costs $11.07 per cubic foot, the cost of the cylinder will be 11.07 * 70.65 = $782.10
Learn more on volume of cylinder here: https://brainly.com/question/9554871
I need help pls pls
Answer:
number one: 814 x 42=34,188 number two: 814 x 47=38,258
Step-by-step explanation:
well, both are correct giving the fact that in the bottom they want you to fill in the blank, both answers i have given start with 3 and end with 8, hope this helped!!
The Ride for Health Bicycle Club has chosen a 33-mile course for this Saturday's ride. If the riders plan on averaging 11 mph while they are riding, and they have a 1-hour lunch break planned, how long will it take them to complete the trip?
Answer:
4 hours
Step-by-step explanation:
33/11 = 3 hours
Plus 1-hour lunch break
Total is 4 hours
Find the area of the figure. (Sides meet at right angles.)
2 ft
2 ft
5 ft
ft
8 ft
Bft
4 ft
8 ft
Answer:
44ft
Step-by-step explanation:
To find the answer, you need to first break down your shape. We can see that the 2 sides are identical so we can just multiply the area of on eof the sides by 2. The 2 sides equal 20 in all. Now lets look at the last section. To find an unknown side, we need to subract the 2 known sides. 8-5=3. 3x8=24
24+20=44
Hope this helps.
Answer:
44 ft²Step-by-step explanation:
A1 = 2(5 x 2) = 20
A2 = 8 x 3 = 24
total = 20 + 24
= 44 ft²
2.) Simplify:
10x + 6y +4x =
x(14) + 6y = 14x +6y
Answer:
{x,y} = {1,1}
Step-by-step explanation:
[2] 6y = -14x + 20
[2] y = -7x/3 + 10/3
// Plug this in for variable y in equation [1]
[1] -10x - 6•(-7x/3+10/3) = -16
[1] 4x = 4
// Solve equation [1] for the variable x
[1] 4x = 4
[1] x = 1
// By now we know this much :
x = 1
y = -7x/3+10/3
// Use the x value to solve for y
y = -(7/3)(1)+10/3 = 1
Solution :
{x,y} = {1,1}