[tex]sin\left(\cfrac{\theta}{2}\right)=\pm \sqrt{\cfrac{1-cos(\theta)}{2}} \qquad cos\left(\cfrac{\theta}{2}\right)=\pm \sqrt{\cfrac{1+cos(\theta)}{2}} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ sin\left( \cfrac{30^o}{2} \right)\implies \sqrt{\cfrac{1-cos(30^o)}{2}}\implies \sqrt{\cfrac{1-\frac{\sqrt{3}}{2}}{2}}\implies \sqrt{\cfrac{~~\frac{2-\sqrt{3}}{2}~~}{2}}[/tex]
[tex]\sqrt{\cfrac{2-\sqrt{3}}{2}\cdot \cfrac{1}{2}}\implies \sqrt{\cfrac{2-\sqrt{3}}{4}}\implies \boxed{\cfrac{\sqrt{2-\sqrt{3}}}{2}} \\\\[-0.35em] ~\dotfill\\\\ cos\left( \cfrac{30^o}{2} \right)\implies \sqrt{\cfrac{1+cos(30^o)}{2}}\implies \sqrt{\cfrac{1+\frac{\sqrt{3}}{2}}{2}}\implies \sqrt{\cfrac{~~\frac{2+\sqrt{3}}{2}~~}{2}} \\\\\\ \sqrt{\cfrac{2+\sqrt{3}}{2}\cdot \cfrac{1}{2}}\implies \sqrt{\cfrac{2+\sqrt{3}}{4}}\implies \boxed{\cfrac{\sqrt{2+\sqrt{3}}}{2}} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\cfrac{~~ sin\left( \frac{30^o}{2} \right)~~}{cos\left( \frac{30^o}{2} \right)}\implies \cfrac{~~\frac{\sqrt{2-\sqrt{3}}}{2} ~~}{\frac{\sqrt{2+\sqrt{3}}}{2}}\implies \cfrac{\sqrt{2-\sqrt{3}}}{2}\cdot \cfrac{2}{\sqrt{2+\sqrt{3}}} \\\\\\ \cfrac{\sqrt{2-\sqrt{3}}}{\sqrt{2+\sqrt{3}}}\implies \blacktriangleright \sqrt{\cfrac{2-\sqrt{3}}{2+\sqrt{3}}} \blacktriangleleft[/tex]
Solve:........................
[tex] \frac{x}{3} + 4 = \frac{4x - 1}{5} [/tex]
Answer:
[tex] \frac{x}{3} + 4 = \frac{4x - 1}{5} \\ \\ \frac{x}{3} + \frac{12}{3} = \frac{4x - 1}{5} \\ \\ \frac{x + 12}{3} = \frac{4x - 1}{5} \\ \\ 3(4x - 1) = 5(x + 12) \\ \\ 12x - 3 = 5x + 60 \\ \\ 12x - 5x = 60 + 3 \\ \\ 7x = 63 \\ \\ x = \frac{63}{7} \\ \\ x = 9[/tex]
Reason Does the division 25/6 have a remainder?
How do you know?
Answer:
Yes
Step-by-step explanation:
If you divide 26 by six, you get s decimal smaller than 5. Remember, 5*5=25. 6*5=30, so that doesn't work. 6*4=24, so that does. Then you get four with a remainder of one.
A map of utah has scale 1cm :30 mi the southern border is about 285 mi long how long is the border on the map
Answer:
9 1/2 inches
Step-by-step explanation:
The scale of a map is the ratio of map distance to represented distance. This can be used to write a proportion.
__
map distance/represented distance = 1 in/(30 mi) = x/(285 mi)
where x represents the map length of the southern border.
Multiplying by 285 mi, we have ...
x = (285 mi)(1 in)/(30 mi) = 9.5 in
The border is 9.5 inches on the map.
PLEASE HELP ILL GIVE FIVE STARS AND GIVE BRAINLIEST
Ray is x years old. His brother Ron is y years older than Ray
What is the sum of their ages now?
Answer: The sum will be x+y because their ages are variables.
Step-by-step explanation:
Super easy 7th grade math worth a lot of points
Answer:
you can find the answer in the given attachment
Step-by-step explanation:
1-P
2-G
3-T
4-O
5-S
6-E
7-D
8-C
9-A
The value of a car decreases linearly with time. The car was bought new for $62,000 and had a value of $41,000 after 6 years.
find the slope of the line (3,5) (7,3)
.....................❣..........................
Use substitution to solve the system.
- 3x+y = 14
2x + 3y = -2
음
Х
5
?
y = 0
Answer:
x= -4 and y=2
Step-by-step explanation:
-3x+y=14 ...eqn 1
2x+3y= -2....eqn 2
from eqn 1
-3x+y=14
y=14+3x
substitute y=14+3x into eqn 2
2x+3(14+3x) = -2
2x+ 42+ 9x = -2
11x= -2-42
11x= -44
x = -4
substitute X = -4 into eqn 1 to get y
-3x+y=14
-3(-4) +y =14
12+y= 14
y= 14-12
y =2
how many faraday passes through a resistance in a circuit carrying a current of 1.68 A for 2 days (1F = 965000 (principal quantum number) is 3 A. FB. 2F C. 3F D. 4F
Answer:
b
Step-by-step explanation:
What is the median of the data set? -10, -5, -1, 0, 0, 3, 6, 8
A. 0
B. 0.125
C. 3
D. -1
Answer: A
Answer:
the anwer is a so 0
Step-by-step explanation:
the number that showed up the most is 0 so median is 0
PLEASE HELP ME 100 POINTS AND BRAINLY!!!
Answer:
1. 220 minutes
2. $45.6
Step-by-step explanation:
Linda counted different colored leaves on a tree. She counted 8 red leaves. She also counted 3 times as many yellow leaves as red leaves. How many yellow leaves did Linda count?
to find the number of yellow leaves you'll have to multiply number of red leaves she counted by 3.
8×3
=24
Linda counted 24 yellow leaves.
Linda counts 24 yellow leaves in total
How to determine the number of yellow leaves?The number of red leaves is given as:
Red = 8
The statement 3 times as many yellow leaves as red leaves means that:
Yellow = Red * 3
So, we have:
Yellow = 8 * 3
Evaluate the product
Yellow = 24
Hence, Linda counts 24 yellow leaves in total
Read more about products at:
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Use the quadratic formula to solve the equation 2k(k+5)= -25
So, we need to solve the quadratic equation from quadratic formula as per the question, but before starting, let's first recall that, for any quadratic equation of the form ax² + bc + c = 0, the discriminant is given by D = b² - 4ac, and the value of x is given by :
[tex]{\boxed{\bf{x=\dfrac{-b\pm \sqrt{D}}{2a}}}}[/tex]Also, their are no real solutions of x i.e their are only imaginary values of x iff D < 0, equal and real roots iff D = 0 and real and distinct roots iff D > 0. So, let's convert the given equation to the standard form ax² + bx + c = 0 and then we will find the discriminant and then we will be solving for k ;
[tex]{:\implies \quad \sf 2k(k+5)=-25}[/tex]
[tex]{:\implies \quad \sf 2k^{2}+10k=-25}[/tex]
[tex]{:\implies \quad \sf 2k^{2}+10k+25=0}[/tex]
Now, on comparing this with the standard equation, we will get a = 2, b = 10 and c = 25, and then D = (10)² - 4 × 2 × 25 = 100 - 200 = - 100, now as D < 0, so their will be imaginary values of k, so now solving for k will yield by using the Quadratic Formula ;
[tex]{:\implies \quad \sf k=\dfrac{-10\pm \sqrt{-100}}{2\times 2}}[/tex]
[tex]{:\implies \quad \sf k=\dfrac{-10\pm 10\iota}{2\times 2}}[/tex]
[tex]{:\implies \quad \sf k=\dfrac{2(-5\pm 5\iota)}{2\times 2}=\dfrac{-5\pm 5\iota}{2}}[/tex]
[tex]{:\implies \quad \boxed{\bf{k=\dfrac{-5+5\iota}{2}\:\:,\:\: \dfrac{-5-5\iota}{2}}}}[/tex]
This is the required answer
What is the median for the following set of data?
4, 4, 6, 10, 12, 13, 15, 16
a 12
b 10
c 11
d 16
Answer:
C
Step-by-step explanation:
The median is where we find the number that is in the middle of the data set. In this case, there cannot be a single number in the middle because the number of numbers in this data is even.
Knowing this, we need to add the two numbers that are in the middle (10 and 12). We add these two numbers and divide them by 2
[tex]\frac{10+12}{2} =\frac{22}{2} =11[/tex]
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2021-2022 T-Math-Alg1-Comprehensive-CBT: Section 2 - Calculator ...
Question 2-14
Andy and Brett are selling tickets to their high school baseball game
• A total of 234 tickets were sold to the game
• Student tickets cost $5 each
. General tickets cost $ each
. The total revenue from ticket sales was $1268
Which statements are true? Choose all that are correct
The total revenue from the student tickets was $925.
A total of 185 student tickets were sold.
Olfg is the number of general tickets sold and s is the number
11
student tickets sold, the total revenue generated by the student and general tickets can be represented by the oquation 58 + 79 = 1,268
O Atotal of 98 general tickets were sold.
The revenue from the general tickets was greater than the revenue from the student tickets.
Ifg is the number of general tickets sold and s is the number of student tickets sold, thens + g = 234
POUS
Type here to search
O
BI
Answer:
the 1st, 2nd and 6th statements are true.
and probably the 3rd statement is true.
I am not sure about the 3rd statement, as I cannot read the original in your screenshot, and your transcribed description is probably not correct and contains typos.
but all you need is in the explanation below to decide, if the actual 3rd statement is true or not.
if "58 + 79 = 1268" actually means "5s + 7g = 1268" then it is true. otherwise it is false.
Step-by-step explanation:
g = number of general tickets sold
s = number of student tickets sold
so, in total
g + s = 234
tickets were sold.
and the revenue was
7g + 5s = $1,268
out of these 2 basic equating we get
g = 234 - s
and then
7(234 - s) + 5s = 1,268
1,638 - 7s + 5s = 1,268
-2s = -370
s = 185
g = 234 - s = 234 - 185 = 49
so, we know
185 student tickets were sold for 5×185 = $925
49 general tickets were sold for 7×49 = $343
What is the value found using the linear approximation? ln(0.93) ≈
Answer:
I think its 0.9 I believe so
Justify the first step that David took in verifying that x = 5 is a solution for the equation
8x – 13 = 2x + 17.
8x – 13 = 2x + 17
8(5) – 13 = 2(5) + 17
A.
David multiplied 8 by 5.
B.
David subtracted 13 from both sides.
C.
David replaced x with 5.
D.
David added 17 to both sides.
Answer:
Step by step I don't see the correct first step.
Step-by-step explanation:
Solve for x:
8 x - 13 = 2 x + 17
Hint: | Move terms with x to the left hand side.
Subtract 2 x from both sides:
(8 x - 2 x) - 13 = (2 x - 2 x) + 17
Hint: | Combine like terms in 8 x - 2 x.
8 x - 2 x = 6 x:
6 x - 13 = (2 x - 2 x) + 17
Hint: | Look for the difference of two identical terms.
2 x - 2 x = 0:
6 x - 13 = 17
Hint: | Isolate terms with x to the left hand side.
Add 13 to both sides:
6 x + (13 - 13) = 13 + 17
Hint: | Look for the difference of two identical terms.
13 - 13 = 0:
6 x = 17 + 13
Hint: | Evaluate 17 + 13.
17 + 13 = 30:
6 x = 30
Hint: | Divide both sides by a constant to simplify the equation.
Divide both sides of 6 x = 30 by 6:
(6 x)/6 = 30/6
Hint: | Any nonzero number divided by itself is one.
6/6 = 1:
x = 30/6
Hint: | Reduce 30/6 to lowest terms. Start by finding the GCD of 30 and 6.
The gcd of 30 and 6 is 6, so 30/6 = (6×5)/(6×1) = 6/6×5 = 5:
Answer: x = 5
Emily wants to put trim around a square window and measures 3 ft on each side. How many feet of t r i m does she need?
Answer:
12ft trim
Step-by-step explanation:
assuming that she wants to use the same size on each side (3ft) of the window, we know that the window is a square
and a square has 4 sides
3 + 3 + 3 + 3 = 12ft
She needs 12 ft trim
Select the correct answer.
The parallelogram has an area of 20 square inches. What are the dimensions of the parallelogram, to the nearest hundredth of an inch?
40°
4 in
h
OA. I = 2.57 in, h = 7.78 in
OB. I = 6.22 in, h = 3.23 in
The dimensions of the parallelogram to the nearest hundredth of an inch are 6.54 in and 3.06 in.
What are the dimensions of the parallelogram?Trigonometry would be used to determine the base and the length of the parallelogram.
Base: cos 40 = adjacent /hypotenuse
0,7660 = adjacent / 4
adjacent = 4 x 0.7660 = 3.06 in
Length = area / base
20 / 3.06 = 6.54 in
To learn more about parallelograms, please check: https://brainly.com/question/15259486
The ratio of a basketball player's completed free throws to attempted free throws is 4 to 7. If she completed 12 free
throws, find how many free throws she attempted.
a 3 free throws
c. 21 free throws
b. 7 free throws
d. 4 free throws
B
С
D
Mark this and retum
Save and Exit
Next
Submit
Answer:
21
Step-by-step explanation:
I noticed that 4 times 3 equals 12, which is the number of free throws she completed. I multplied 3 by 7 and got 21
mhm so basically if you this about it the number of letters in the rainbow is also the color of your dog WAKE UP WAKEUP WAKEUP and if your dog's color matches the blue sky the answer is b
Please help me thank u!
Answer:
The odds of drawing a heart are 13:52
Explanation: A standard deck of card contains 52 card. There are 4 types of playing cards: clubs, diamonds, hearts and spades. Every type of them has 13 cards. How do u know that? Well just divide 52 by 4 and then you get 13.
Which of the following quadrilaterals is also a parallelogram?
Answer:
RECTANGLEA rectangle is a parallelogram with four right angles, so all rectangles are also parallelograms and quadrilaterals.
are these lines parallel or perpendicular? 2y=-3x=5 and y=3/2-6
Answer:
perpendicular because they have a positive and negative slope meaning on a graph they would be crossing each other.
Can someone tell me what I did wrong here
Answer:
no roots.
Step-by-step explanation:
1) [tex]\sqrt{8x+16}=2-8; \ - \ correct;[/tex]
2) [tex]\sqrt{8x+16}=-6; \ - \ correct;[/tex]
note, the value after operation 'square root' cannot be negative ('-6' is on the right side!), then
3) it means, the given equation has no real roots.
find the measure of angles 1, 2, 3, 4, 5 ,6 and 7
Answer:
angle1=70
angle2=65
angle4=115
angle7=45
angel6=45
angle5=45
Step-by-step explanation:
110+angle1 = 180
angle1 =180-70
angle1 = 70
115+angle2=180
angle2=180-115
angle2=65
angle4=115 because lines are parallel
angle1+angle2+angle7=180 because triangle
70+65+angle7=180
135+angle7=180
angle7=180-135
angle7=45
angel6=45
angle5=45
solve this system of equations 2x+4y=-48
Answer:
x=-24-2y
y=-12-x/2
Step-by-step explanation:
To solve for x move everything to one side, 2x=-48-4y, then you can divide by 2 to just get x, x=-24-2y.
To solve for y move everything to one side, 4y=-48-2x, then you can divide by 4 to just get y, y=-12-x/2.
Well has -55.00 in his account if he saves $2.50 his mom gives him lunch every day, how many days will it be until he has a balance of at least $0
Answer:
22 days
Step-by-step explanation:
55 divided by 2.5=22 days
Answer: 22 Days
Step-by-step explanation:
-55.00/2.50= -22
But since you can’t have a negative answer then you have to make it positive for your amount of days! So it would take that person 22 days to have 0 in his account!
- I hope this helped! I tried my best but definitely double check with your teacher for this answer!
Alyssa is enrolled in a public-speaking class. Each week she is required to give a speech of
greater length tharr the speech she gave the week before. The table below shows the
lengths of several of her speeches.
Alyssa's Speeches
Answer: this question search it up because i don't think and know if anyone knows this even i don't know so sorry
Step-by-step explanation:
if 2x2 is 4 then why is 2+2 5????
Answer:
Simple it's not
Step-by-step explanation:
Answer:
wait.... 2x2 is 4 2 + 2 = 4?
Step-by-step explanation:
Calculating the Surface Area of Prisms
4 yd
2 yd
5 yd.
3 yd
3 yd.
Find the surface area of the prism above.
I need help please someone!!
360 yd
Multiply all numbers to get 360 yd