Answers
Step-by-step explanation:
1 / (sin 10°) − √3 / (cos 10°)
Multiply top and bottom of the first fraction by ½ cos 10°.
½ cos 10° / (½ cos 10° sin 10°) − √3 / (cos 10°)
Multiply top and bottom of the second fraction by ½ sin 10°.
½ cos 10° / (½ cos 10° sin 10°) − ½√3 sin 10° / (½ sin 10° cos 10°)
Combine fractions.
(½ cos 10° − ½√3 sin 10°) / (½ sin 10° cos 10°)
Change ½ to sin 30°, and change ½√3 to cos 30°.
(sin 30° cos 10° − cos 30° sin 10°) / (½ sin 10° cos 10°)
Use angle sum formula.
sin(30° − 10°) / (½ sin 10° cos 10°)
sin 20° / (½ sin 10° cos 10°)
Multiply top and bottom by 4.
4 sin 20° / (2 sin 10° cos 10°)
Use double angle formula.
4 sin 20° / sin 20°
4
We are given the equation 1 / sin(10°) - √3 / cos(10°) = 4, and want to prove that 1 / sin(10°) - √3 / cos(10°) equals 4.
Let's start by combining the expressions '1 / sin(10°)' and '√3 / cos(10°)' in the expression '1 / sin(10°) - √3 / cos(10°).'
1 / sin(10°) - √3 / cos(10°)
= cos(10°) - √3sin(10°) / sin(10°) [tex]*[/tex] cos(10°)
Now let's multiply the numerator and denominator by a common value. In this case it's most suitable to multiply both by 2. We will receive the expression 2(cos(10°) - √3sin(10°)) / 2(sin(10°) [tex]*[/tex] cos(10°)). We can further simplify this expression knowing that 2(sin(10°) [tex]*[/tex] cos(10°)) = 2sin(20°).
2(cos(10°) - √3sin(10°)) / 2sin(20°)
We can now bring the two on the bottom to the numerator, becoming 1 / 2. Remember that the ' 1 / 2 ' will be distributed now. After the distribution we receive the expression 4( 1 / 2(cos(10°) - √3 / 2sin(10°)) / 2sin(20°). We can now use the trivial functions 1 / 2 = sin(30°), and √3 / 2 = cos(30°).
4(sin(30°)(cos(10°) - cos(30°)(sin(10°) ) / sin(20°))
= 4((sin(30 - 10°)) / sin(20°) = 4
Related Questions
The total distance in centimeters that a toy robot moves varies directly with the time in seconds the toy robot moves a total distance of 63 cm. In 9 seconds what is the time in seconds that the toy robot moves when the total distance is 49 cm
Answers
Answer:
Hey there!
The robot moves 63 cm in 9 seconds. Then in 1 second, it moves 7 cm.
If it goes 49 cm, it will take 7 seconds.
Let me know if this helps :)
A school bus uses 34 of a tank of gas to drive back and forth to school in a week with 5 school days. How much gas does the bus use to drive back and forth to school in a week with 4 school days? Write your answer in simplest form. The bus uses of a tank.
Answers
Answer:
27.2 of a tank
Step-by-step explanation:
[tex]\frac{34}{5}[/tex] = [tex]\frac{x}{4}[/tex]
136 = 5x
x = 27.2
Juanita and Lydia are each making lemonade. Juanita's recipe calls for 4 parts lemon juice to 2 parts sugar syrup. Lydia's recipe calls for 5 pets lemon juice to 3 parts sugar syrup. Which recipe has a stronger lemon flavor? WILL GIVE BRAINLIEST!!!
Answers
Juanita’s recipe will have a stronger lemon flavor.
Explanation:
Juanita has a ratio of 4:2,where as Lydia has a ratio of 5:3. If you divide 4 by 2 and 5 by 3, Juanita will have a value of 2, and Lydia will have a value of 1.67.
16) 65m
What is the prime factorization of 65m?
Answers
Answer:
Factors of 65: 1, 5, 13, 65. Prime factorization: 65 = 5 x 13.
Answer:
13*5*m
Step-by-step explanation:
65m
13 5 m
What is an opposite reciprocal?
Answers
Answer:
Opposite reciprocals are two numbers that are flipped fractions of eachother. For example, the reciprocal of 2/3 is 3/2.
Answer:
An Opposite reciprocal is like a number flipped
Step-by-step explanation:
4 = 1/4
2/3 = 3/2
In the classification of living organisms, which of the following is an example of a domain? Animalia Archaebateria Eubacteria Eukarya
PLEASE HELP
Answers
Answer:
I am 90% sure it is D
Step-by-step explanation:
M is the midpoint of AB, AM=2x+3, and AB= 8x-10. Find MB
Answers
Explanation:
In order to find this answer I simply tried getting x by it self
8x-10 = 2x+3
then subtracted 2 from both sides (F.Y.I choose to start from the the left since 2 is lower then 8) the 2x= -2x cancel then if subtracted 8x from -2x you should get 6x
From there it should be
6x-10=3
Add 10 from both sides
Then your left with 6x=13
Now for this answer I obviously got a decimal and I’m not sure how I would go about rounding so I just rounded it to the nearest tenth.
After rounding 2.166666666666667
I was left with 2.2
From there I plugged it into the the AM formula
in the question M is the midpoint of AB so AM is congruent to MB AM=MB
AM=2x+3 MB=?
if you plug 2.2 in replace of x
2(2.2)+3 it should equal 7.4.
I hope I’m right, truly sorry if I’m not! I’m a freshie on the job! Good luck wishes!
i need help #3 pleasee
Answers
x=4
subtract 8 instead of 2
I’m being timed!!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
y=mx+b
Step-by-step explanation:
y=mx+b
If you know the slope m , and y -intercept (0,b) of a line (the point where the line crosses the y -axis), you can write the equation of the line in slope-intercept form .
Answer:
y=mx+b
Step-by-step explanation:
m and b can be any two real numbers.
y=mx+b
No real work, one of those linear equations that should be memorized.
true or false 1+6=5+2 true or false ? ;-;
Answers
Answer: True
Step-by-step explanation: both equal 7
1 + 6 = 7
5 + 2 = 7
it has to be 20 characters long so i’m typing here
What is the inequality 4/5__1/2
Answers
Answer:
Step-by-step explanation:
Notice that:
● 1/2 = 0.5
● 4/5 = 0.8
0.8 is greater than 0.5.
So:
● 0.8 > 0.5
● 4/5 > 1/2
Answer:
4/5 > 1/2.
Step-by-step explanation:
4/5 is greater than 1/2.
What’s the constant 15-8y?
Answers
Answer:
15
Step-by-step explanation:
Does this picture represent the real number system correctly? True False
Answers
Answer:
No
Step-by-step explanation:
There are no real numbers that are both rational and irrational, and there are no real numbers that are neither rational nor irrational. The diagram is misleading.
___
A question is not true or false. A statement is true or false. If the statement is, "this picture represents real numbers correctly," then it is FALSE.
What is the degree for this
Answers
Answer:
4
Step-by-step explanation:
3 coins are tossed simultaneously. what is the probability of getting 3 heads or 3 tails?
Answers
Answer:
3/6
Step-by-step explanation:
A coin has 2 sides
3 coins = 6 sides
3 heads 3 tails
3 chances out of 6 to get heads
3 chances out of 6 to get tails
3/6 for both
Solve 2x + 3y = 11 and 2x - 4y = -24 and hence find the value of 'm' for which y=mx+3.
Answers
Answer:
m=-1
Step-by-step explanation:
2x+3y=11............. (eqn 1)
2x-4y=-24...........(eqn 2)
Subtract eqn 1 from eqn 2
7y=35
y=5
Substitute for y in eqn 1
2x+3(5)=11
2x+15=11
2x=11-15
2x=-4
x=-2
y=mx+3
5=-2m+3
5-3=-2m
2=-2m
m=-1
Answer:Here,
2x+3y=11..........(i)2x-4y= -24......... (ii)Subtracting (ii) from (i),we get
2x+3y=11
- 2x+4y=24
___________
7y =35
y=5
Substituting y = 5 in (i) we get
2x+3×5=11
or,2x +15 =11
or,2x = 11- 15
or,x= -2
Now,
We know,y=mx+c
5=m ×(-2) +3
or,2=m×(-2)
or,2/-2 =m
m= -1
Help idk the answer and it’s due tomorrow
Answers
Answer:
C. 14%
Step-by-step explanation:
We know that Dallas's wage increased from $9 to $10.25.
Let's say the percent increase is x. Then we write the expression:
9 + x * 9 = 10.25
Divide by 9 from both sides:
1 + x = 10.25 / 9 ≈ 1.14
Subtract 1 from both sides:
x = 1.14 - 1 = 0.14
Since x is a percent, that means x = k/100, where k is an integer. So we have:
x = k/100 = 0.14
Multiply both sides by 100:
k = 0.14 * 100 = 14%
The answer is thus C.
~ an aesthetics lover
Answer:
C.14%Step-by-step explanation:
[tex]Original\:price = \$9\\New\:price =\$10.25\\\\Increase = 10.25-9\\Increase = 1.25\\\\Increase \: \% = \frac{Increase}{Original \:price} \:\times 100\\\\= \frac{1.25}{9} \times 100\\\\= \frac{125}{9}\\ \\= 13.888\\= 14\%[/tex]
if EF bisects CD, CG =5x-1, GD = 7x-13, EF = 6x-4, and GF =13, find EG
Answers
Greetings from Brasil....
As stated in the statement of the question, EF is a bisector of CD, so point G is the median point of CD, so CG = GD
5X - 1 = 7X - 13
X = 6
EF = EG + GF
6X - 4 = EG + 13 x = 6, so
6·6 - 4 = EG + 13
EG = 19(see attachment)
A line segment is also a line but the line with finite length and having fixed endpoints. The length of the line segment EG is 19 unit.
What is a line?A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely.
Given that EF bisects CD at point G, therefore, the line segment CD will be divided into two equal parts, CG and GD. Therefore, we can write,
CG = GD
5x - 1 = 7x - 13
-1 + 13 = 7x - 5x
12 = 2x
x = 12/2
x = 6
Further, the length of segment EG will be,
EG = EF - GF
= 6x - 4 - (13)
= 6x - 4 - 13
= 6x - 17
= 6(6) - 17
= 36 - 17
= 19
Hence, the length of the line segment EG is 19 unit.
Learn more about Line here:
https://brainly.com/question/21511618
#SPJ2
The base of a triangle is 2 feet less than its height. Its area is 12 square feet. Find its base and height.
Answers
Answer:
Height of the triangle is 6 feet and base of the triangle is 4 feet.
Step-by-step explanation:
Area of a triangle is given by the formula,
Area = [tex]\frac{1}{2}(\text{Base})(\text{Height})[/tex]
Let the height of triangle = h feet
Since, base of the triangle is 2 feet less than its height then base of the triangle = (h - 2) feet
Area = [tex]\frac{1}{2}h(h-2)[/tex]
[tex]12=\frac{1}{2}h(h-2)[/tex]
h² - 2h - 24 = 0
h² - 6h + 4h - 24 = 0
h(h - 6) + 4(h - 6) = 0
(h + 4)(h - 6) = 0
h = -4, 6 feet
Since height of the triangle can not be negative, therefore, height of the triangle = 6 feet.
And base of the triangle = (h - 2) = 6 - 2
= 4 feet
Height of the triangle is 6 feet and base of the triangle is 4 feet.
Which side of the polygon is exactly 6 units long?
Answers
AB is the answer. :)
Which expression is equivalent to -36 - 8?
Answers
Answer:
-44
Step-by-step explanation:
What is the range of the relation shown in the graph?
Answers
Answer:
-2
Step-by-step explanation:
-10x-5=-125
find what x is
Answers
Answer: x=12
Step-by-step explanation:
Given
-10x-5=-125
Add 5 on both sides (addition property of equality)
-10x=-120
Divide -10 on both sides (division property of equality)
x=12
Hope this helps!! :)
Please let me know if you have any question
Answer: X=12
Step-by-step explanation:
Clear the X first to solve this problem
-10x - 5 = -125
125 - 5 = 10x
120/10 = x
12 = x
Find x when y=6 in the literal equation 5x+4y=39
A. 12.6
B. 15
C. 2.25
D. 3
Answers
Answer:
y=6
then,
5x+4y=39---> plug y in to the function
5x+4(6)=39
5x+ 24=39
5x= 39-24
5x= 15
x= 15/5
x= 3
So, the value of x when y=6 in that function is 3 (D)
-6x(-3x - 10) Distributive property! I’m so bad at it
Answers
If f(x) = x/2 -2 and g(x) = 2x^2 + x - 3, find (f+g) (x) A. 2x^2+3/2x +1 B. 2x^2+3/2x-5 C. x^2 - 6 D. 2X^2- x/2 + 1
Answers
Answer:
[tex]\bold{(f+g)(x)=2x^2+\frac32x-5}[/tex]
Step-by-step explanation:
[tex]f(x) =\frac x2-2\quad and\quad g(x) = 2x^2 + x - 3\\\\(f+g)(x)=f(x)+g(x)\\\\(f+g)(x)=\frac12x-2+2x^2+x-3\\\\(f+g)(x)=2x^2+\frac32x-5[/tex]
I don’t really get this.
Answers
Answer:
The answer is H. II and III only.
Step-by-step explanation:
A simple way to tell if a relation is a function is by taking a look at the X value, which is on the left. If the X value repeats again (ex: (0,1) (0,2) or (5,3 (5,7)) it is not a function. However, the Y value is allowed to repeat.
How long would it take for a car yo travel 200 km if it has the average speed of 55 km/HR
Answers
Answer:
3.64 hr, or 3 hr 38 min
Step-by-step explanation:
Recall that distance = (rate)(time). Thus,
time = (distance) / (rate)
Here we have:
time = (200 km) / (55 km/hr) = 3.64 hr, or 3 hr 38 min
PLSSS HELP ASAP & plsss SHOW WORK PLS AND TYY
if TV=14x-8, find TU
Answers
Answer:
[tex]x = 3[/tex]
Step-by-step explanation:
[tex]tu = tv - uv \\ tu = (14x - 8) - 5 \\ tu = 14x - 13 \: - - - (1) \\ \\ tu = 9x + 2 \: - - - (2) \\ \\ sub \: (1) \: into \: (2) \\ \\ 14x - 13 = 9x + 2 \\ 14x - 9x = 2 + 13 \\ 5x = 15 \\ x = \frac{15}{5} \\ x = 3[/tex]
HElp me please!!! IVE HAD TROUBLE W THIS SINCE 11
Answers
Answer:
Nocomplanar? Right because they’re not all in the same place?
Step-by-step explanation: