Answers
Answer:
[tex]x = 18[/tex]
[tex]y = 6\sqrt{3}[/tex]
Step-by-step explanation:
Trigonometric Ratios
The ratios of the sides of a right triangle are called trigonometric ratios. The longest side of a right triangle is called the hypotenuse and the other two sides are called the legs.
Selecting any of the acute angles as a reference, it has an adjacent side and an opposite side. The trigonometric ratios are defined upon those sides as follows:
Cosine Ratio
[tex]\displaystyle \cos\theta=\frac{\text{adjacent leg}}{\text{hypotenuse}}[/tex]
Sine Ratio
[tex]\displaystyle \sin\theta=\frac{\text{opposite leg}}{\text{hypotenuse}}[/tex]
Consider the angle of θ=30°, then we can write:
[tex]\displaystyle \cos 30^\circ=\frac{x}{12\sqrt{3}}[/tex]
Solving for x:
[tex]x=12\sqrt{3}\cos 30^\circ[/tex]
Since:
[tex]\cos 30^\circ=\frac{\sqrt{3}}{2}[/tex]
Then:
[tex]x=12\sqrt{3}\cdot \frac{\sqrt{3}}{2}[/tex]
[tex]x = 18[/tex]
Now apply the sine:
[tex]\displaystyle \sin 30^\circ=\frac{y}{12\sqrt{3}}[/tex]
Solving for y:
[tex]y=12\sqrt{3}\sin 30^\circ[/tex]
Since:
[tex]\sin 30^\circ=\frac{1}{2}[/tex]
Then:
[tex]y=12\sqrt{3}\cdot \frac{1}{2}[/tex]
[tex]y = 6\sqrt{3}[/tex]
Answer:
[tex]x = 18[/tex]
[tex]y = 6\sqrt{3}[/tex]
Related Questions
-20 > -2x + 4 inequality
Answers
Step-by-step explanation:
-20 > -2x + 4
2x > 4 + 20
2x > 24
x > 12
or
x ∈ 《12 , + ∞》
-20 > -2x + 4
-20 -4 > -2x
-24 > -2x
-24/-2 < x <inequality changes when you divide by a -ve no. >
12 < x
What is 4.35 divided by 2.5?
Answers
it’s 1.74
explanation
Answer:
1.74
Step-by-step explanation:
Amy and Ben share £21 between them in the ratio 5 : 2. How much does Amy get?
(Im really sorry I just don't understand ratio.)
Answers
Answer:
✑ [tex] \underline{ \underline{ \sf{First ,\: Let's \: learn \: about \: the \: ratio}}} : [/tex]
Let us consider , there are 30 boys and 40 girls in a school. So, the ratio of number of boys to number of girls = [tex] \sf{ \frac{30}{40} = \frac{3}{4} = 3:4}[/tex] and read as 3 is to 4. We can say , the ratio compares two of more quantities of same unit. Until two quantities have same units , it is meaningless to compare by ratio. So, to find the ratio of two quantities , it is necessary to express them in same unit or of same kind. Since , they are in division form. So ,ratio is unit less quantity. Thus , the ratio is a comparison of two quantities of the same kind in division which doesn't have any units. For example : [tex] \sf{ \frac{a}{b}} [/tex] is a ratio and is read as ' a is to b ' in which ' a : is antecedent and ' b ' is called consequent.
✎ [tex] \underline{ \underline{ \sf{Now \: let's \: solve : }}}[/tex]
☪ [tex] \underline{ \sf{Solution}} : [/tex]
£ 21 is to be divided between Amy and Ben in the ratio 5 : 2. So, let Amy get £ 5x and Ben get £ 2x.
Then , According to the question , [tex] \text{5x +2x = 21}[/tex]
Solve for x :
⇝ [tex] \sf{7x = 21}[/tex]
⇝ [tex] \sf{ \frac{7x}{7} = \frac{21}{7} }[/tex]
⇝ [tex] \sf{x = 3}[/tex]
The value of x is 3. Now , substitute the value of x in 5x :
Amy received £ 5x = 5 × 3 = £ 15 .
☥ [tex] \boxed{ \boxed{ \tt{Our \: final \: answer \: is \bold{£ \: 15}}}}[/tex]
Hope I helped ! ツ
Have a wonderful day / night ♡
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The volume of the world's oceans is nearly 1.5⋅10^9 cubic kilometers. Write this number in scientific notation.
Answers
Answer:
"The World Ocean." The Columbia Encyclopedia. CD-ROM. 2007, 6th Ed. New York: Columbia University Press. "The World ocean has an area of about 361 million sq km (139,400,000 sq mi), an average depth of about 3,730 m (12,230)
Viau, Elizabeth Anne. World Builders: Water on Earth. California State University Los Angeles. 2003.
There are two origins of water: comets (extraterrestrial bombardment) and out gassing (condensation of steam from early volcanism). These processes are continuing today.
Step-by-step explanation:
Hey ! I’m trying to find the slope. If you could help me that’ll be great thank you !!
Answers that might be:
A. 2/3
B. 1
C. 0
D. -1
Answers
Answer:
The answer is B. 1
Step-by-step explanation:
rise over run
1/1=1
Answer:
I'm pretty sure it's B. 1
Step-by-step explanation:
Because I got 2 points where the line crosses and I made a triangle joining the points
Then I did the change in y/change in x
and so I did 2/2 and got 1
hopefully that's right :)
What is the sum of all prime numbers beetween 70 to 80?
What is the product of prime numbers immediately before and after 50?
Answer both plz thx....
Answers
Answer:
Prime numbers between 70 and 80 are 71,73,79
71+73+79=223
50 =2x5x5=2x5^2
Simplify: 5d?(3d - 2)
A
8d8 + 3d2
B.
15d3 + 3d
C 15d3 - 10d2
D 8d3-10d?
Answers
4 +14 x 17 x 4 + 3
Orders of operations
Answers
You do 14 times 17 then times that by 4 that add 4 and 3
Isaac walks 6/10 of a mile of a mile in 1/5 of an hour. If Isaac’s walking rate remains constant, what is Isaacs walking rate in miles per hour?
Answers
Answer:
3 miles per hour.
Step-by-step explanation:
To get his walking rate in miles per hour, we multiply 1/5 by its reciprocal, 5/1. We also multiply 6/10 by 5/1. This gets us 30/10 of a mile in an hour. We can simplify 30/10 to 3. This means he walks at 3 miles per hour.
A delivery truck drove 52 miles per hour. It took 4 hours to travel between two towns. What is the distance between the two towns? Use the equation dert, where d is distance, r is rate, and t is time. The distance between the two towns is miles.
Answers
Answer:
104?
Step-by-step explanation:
52*4 = 208 ÷ 2 = 104
Which of the following correctly uses absolute value to show the distance between -80 and 15? (5 points)
a
|-80 - 15| = |-95| = -95 units
b
|-80 + 15| = |-65| = 65 units
c
|-80 - 15| = |-95| = 95 units
d
|-80 + 15| = |-65| = -65 units
Answers
Answer:
it's answer is b
|-80+15| = |-65| = 65 units
Hope this helps :)
This question is about displacement. Displacement is a set of vectors. So the answer is - can't be + can't be.
so,answer-b
Which expression is equivalent to 12(4m−2n+4)?
1.2m−n+2
2.2m−2n+4
3.8m−4n+4
4.8m−4n+8
Answers
Answer:
1. 2m - n + 2
Step-by-step explanation:
12×4m - 12×2n + 12×4. ( because 12 is multipled by whole bracket)
48m - 24n + 48.
2m - n + 2. (by finding common factor 24)
which graph could represent a function ? ?
Answers
Answer:
The third Graph
Step-by-step explanation:
Using the vertical line test to determine whether or not a graph represents a function. If a vertical line is moved across the graph and, at any time, touches the graph at only one point, then the graph is a function. If the vertical line touches the graph at more than one point, then the graph is not a function.
Answer:
The third Graph
Step-by-step explanation:
37.
An express train travelled at a certain average speed from Town X to Town Y which was
150 km away. It then continued its journey to Town Z at an average speed 20 km/h faster than
its initial average speed. Town Ywas 200 km from Town Z. If it took the same time to travel for
both parts of the journey, what was the train's average speed for the first part of the journey?
Answers
Answer:
60 km/hr
Step-by-step explanation:
Let the speed at the initial average speed from Town X to Town Y be a.
We are told that it journeyed to Town Z at an average speed 20 km/h faster than its initial average speed. Thus, its average speed here is (a + 20) km/hr.
Town Y was 200 km from Town Z.
Thus, time spent here is;
t_2 = 200/(a + 20)
Time from X to Y is; t_1 = 150/a
We are told that it took the same time to travel for both parts of the journey.
Thus; t_1 = t_2
150/a = 200/(a + 20)
Cross multiply to get;
150(a + 20) = 200a
150a + 3000 = 200a
200a - 150a = 3000
50a = 3000
a = 3000/50
a = 60 km/hr
Brian has reduced his cholesterol level by 13% after his last check up. If his original level was 240, what is his approximate cholesterol level now?
Answers
Answer:
208.8
Step-by-step explanation:
240 times 0.87 is 208.8
Find the total amount given the original price and tax rate. Round to the nearest cent if necessary.
$15.25,7%
Answers
Given:
Original price = $15.25
Tax rate = 7%
To find:
The total amount.
Solution:
We know that,
Total amount = Original price + Tax
According to the question,
Total amount = 15.25 + 7% of 15.25
[tex]\text{Total amount}=15.25+\dfrac{7}{100}\times 15.25[/tex]
[tex]\text{Total amount}=15.25+1.0675[/tex]
[tex]\text{Total amount}=16.3175[/tex]
Round to the nearest cent (two decimal places).
[tex]\text{Total amount}\approx 16.32[/tex]
Therefore, the total value is $16.32.
Help In math pls this a slope problem
Answers
Answer:
D
Step-by-step explanation:
they finish
There are 4 athletes at a track meet. How many different ways can
first, second, and third?
Answers
Answer:
4 ways i think
Step-by-step explanation:
Hope this helps!
Answer:
its 20
Step-by-step explanation:
hope this helps
A piece of timber is x cm long. 9 cm is cut off how much is left
Answers
Answer:
x-9cm
Step-by-step explanation:
compute
Tell whether the ordered pair (-4,-2) is a solution of the system of linear equations.
Y= 2x+6
Y= -3x-14
Answers
Can someone tell just the answer
Answers
Answer:
Option D is correct .
Step by step explanation:
A function is given to us and we need to find its inverse . The function is g(x) = -2x⁵ - 2.
So for finding its inverse , exachange x with y .
⇒ g(x) = -2x⁵ - 2 .
Let g(x) = y ,
⇒ y = -2x⁵ - 2 .
Replace x with y ,
⇒ x = -2y⁵ - 2
⇒ x + 2 = -2y⁵
⇒ y⁵ = x+2 / -2
⇒ y⁵ = (-1) ( x + 2) / (-1)(-2)
⇒ y⁵ = -x - 2/ 2
⇒ y = ⁵√ [ ( -x -2)/2 ]
Hence the inverse of the function is ,
[tex]\boxed{\red{\bf f^{-1}(x)=\sqrt[5]{\dfrac{-x-2}{2}}}}[/tex]
Hence the correct option is (D) .What is the value of x? B 75° Enter your answer in the box. X=
Answers
Answer:
55
Step-by-step explanation:
75+50=125
180-125=55
the _________ is a number that is multiplied. the number that indicates how many times this number is used as a factor is the ___________
Answers
The base is a number that is multiplied. The number that indicates how many times this number is used as a factor is the exponent
For example, the number 2^3 expands out to 2*2*2. We have three copies of the base '2' being multiplied.
Another example: 5^2 = 5*5.
Answer:
The "Factor" is a number that is multiplied. The number that indicates how many times this number is used as a factor is the "Exponent".
Step-by-step explanation:
Example: 7 • 7 can be written as 72, 7 is the base and 2 is the exponent. The exponent 2 means there are two factors.
Hope it helped : )
Not every straight line will pass the vertical line test. What is the only type of straight line that would fail the vertical line test?
Answers
Answer:
Gfdyuihgff hibhhiuuuuyyygfxf. Hugfti. Hffty9
Answer:
vertical line
Step-by-step explanation:
PLEASE HELP!!
Graph the line with the equation
Answers
Answer:
Step-by-step explanation:
Write as a power of 10. How did you do it? a) 100 b) 10 000 c) 100 000 d) 10 e) 1000 f) 1 000 000
Answers
Answer: ↓↓↓
Step-by-step explanation:
a.) 100 - 10^2
b.) 10,000 - 10^4
c.) 100,000 - 10^5
d.) 10 - 10^1
e.) 1000 - 10^3
f.) 1,000,000 - 10^6
What I do personally is that I count the number of zeros in the number and that is how many powers the ten powers to. Like a, there are two zeros in 100 so its 10 to the power of 2.
pls help i’ll give you brainliest
Answers
Step-by-step explanation:
5x and -7x are like terms
5x-7x+9=-2x+9 and there's your equivalent expression
Answer:
i want to say 7x is the answer
Step-by-step explanation:
because if you add 5x to 9 = to 14 the -7 = to 7x
3 + 7 Is what
A) 10
B) 18
C) 37
Answers
Answer:
A)10
Step-by-step explanation:
hope it helps u
Which of the following is not a function?
a. (1,1),(2,2), (3,3), (4,4)
b. (2,3), (2,4), (3,3), (3,4)
c (2,4),(4,8).(10,12). (4,10)
d. (2,4), (3,4), (5,4), (6,4)
Answers
Number on the left: x-value
Number on the right: y-value
If there are 2 y-values for one x-value it is NOT considered a function.
For instance in the answer:
(2,3), (2,4), (3,3), (3,4)
You can clearly see that the x-values (2 & 3) repeat more than once; therefore, it is NOT a function.
On the other hand if you have 2 DIFFERENT x-values for the same y-value it IS A FUNCTION.
For ex D: (2,4), (3,4), (5,4), (6,4)
As you can see there are 4 DIFFERENT x-values with same y-value; therefore it is A FUNCTION
To make it easier:
If x-values appear more than once = NOT A FUNCTION
If x-values appear only ONCE = FUNCTION
Remember: y-values are ALLOWED to repeat
I hope this helps. If you have any questions please let me know in the comments.
5 12 14 will form a acute?
True or false
Answers
No it won't. it's false
cuz proofs here.
(5²)+(12²)= (169)
√(169) = 13
.. so if 13 was the number at 14
it would have been true.
currently the answer is false