(Trigonometry) Find the values of x and y. Round your answers to the nearest tenth.
Answers
Answer:
[tex]x = 38.1[/tex]
[tex]y = 23.4[/tex]
Step-by-step explanation:
The given triangle is a right triangle. This is indicated by the box around one of the angles, signifying that the angle measure is (9) degrees. By its definition, a right triangle is a triangle with a (90) degree angle, thus the given triangle is a right triangle. In this situation, one can use right-angle trigonometry to find the value of the unknown side. In essence, right triangle trigonometry provides one with a series of ratios to describe the relationship between the sides and angles of the right trinagle. These ratios are the following,
[tex]sin(\theta)=\frac{opposite}{hypotenuse}\\\\cos(\theta)=\frac{adjacent}{hypotenuse}\\\\tan(\theta)=\frac{opposite}{adjacent}[/tex]
Keep in mind that the way a side is named is relative to the angle it is being described from. Thus, the (opposite) and (adjacent) sides acquire different names based on the angle relative to them. However, the (hypotenuse) is the hypotenuse no matter the angle, as the hypotenuse is the side opposite the right angle.
Solve for (y) first. One is given the angle measure and the measure of the side opposite the angle measure. One is asked to find the measure of the side adjacent to the angle. Use the ratio of tangent (tan) to achieve this.
[tex]tan(\theta)=\frac{opposite}{adajcent}\\[/tex]
Substitute,
[tex]tan(52)=\frac{30}{y}[/tex]
Inverse operations,
[tex]y=\frac{30}{tan(52)}[/tex]
Simplify,
[tex]y = 23.4386[/tex]
Now solve for the hypotenuse (x). One could use the Pythagorean theorem to do this, but since this is trigonometry, one might as well use the trigonometric ratios. One is given an angle, as well as the side opposite the angle, one is asked to find the hypotenuse. To do this, one can use the trigonometric ratio of sine (sin).
[tex]sin(\theta)=\frac{opposite}{hypotenuse}[/tex]
Substitute,
[tex]sin(52)=\frac{30}{x}[/tex]
Inverse operations,
[tex]x=\frac{30}{sin(52)}[/tex]
Simplify,
[tex]x = 38.0705[/tex]
Related Questions
Please help ASAP!!
I'll mark brainliest!
Answers
Answer:
729 x [tex]\frac{1}{3}[/tex]^x
Step-by-step explanation:
the third option
- trial and error
11. What is the perimeter of the garden?
Answers
Answer:
19[tex]\frac{1}{4}[/tex] or 18[tex]\frac{5}{4}[/tex]
Step-by-step explanation:
First, add the whole numbers
3, 7, and 8
18
Add the fractions
[tex]\frac{1}{2}[/tex]+[tex]\frac{3}{4}[/tex]=[tex]\frac{5}{4}[/tex]
IF YOU WANT SIMPLIFIED NUMBER DO THIS
[tex]\frac{5}{4}[/tex]=1[tex]\frac{1}{4}[/tex]
18+1[tex]\frac{1}{4}[/tex]=19[tex]\frac{1}{4}[/tex]
Which is the best description for the graph below?
A graph decreases from (0, 3) to (9, 0).
Answers
Answer:
Step-by-step explanation:
As we move from (0, 3) to (9, 0), we see x increasing by 9. This is the 'run.'
At the same time, we see y decreasing by 3. This is the 'rise.'
The slope of this line (graph) is m = rise / run = -3/9, or m = -1/3
Since we witness a decrease in y as we move from the first point to the second, we immediately suspect that the slope is negative.
Find the sum of the arithmetic series...........
3 + 5 + 7 + 9 + 11 + for 100 terms.
Answers
Answer:
Step-by-step explanation:
3 + 5 +7 +9 + 11 + ....
n = 100
a = 3
d = 5 - 3 = 2
[tex]S_{n}=\frac{n}{2}(2a + (n-1)d)\\\\S_{100}=\frac{100}{2}(2*3+99*2)\\\\=50*(6+198)\\\\= 50 * 204\\= 10200\\[/tex]
PLZZZZ ANSWERrrrrrrrrrrr
Answers
The vertex form of the equation of a parabola is y = 2(x + 4)2 - 7.
What is the standard form of the equation?
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y = 2[x^2 + 8x + 16 - 7], or
y = 2[x^2 + 8x + 9],
or y = 2x^2 + 16x + 18
None of the given possible answers match. The fourth one, D, is closest to the above result, differing only in the constant term (25 versus 18).
PLEASE HELP WILL NAME BRAINLIEST NO LINKS PLEASE
Use the drawing tool(s) to form the correct answer on the provided graph.
Plot the axis of symmetry and the vertex for this function:
h(x) = (x - 5)2 - 7.
Answers
Answer:
Step-by-step explanation:
First, you should put the axis of symetry as 5, -7 because f(x)= (x-h)^2+k and h is 5 and k is -7. the axis of symetry is x=5 because that is the "folding point" of the graph. Next, you would have to plug In 4 and 6 as your helping points to tell you where the other points of the function are going to be.
Plug 4 in and you get -6. plug 6 in and you get -6. plot the points (4, -6) and (6,-6).
Hope this helps!
:)
50 POINTS
Find the approximate values of the five-number summary for the data set represented by this box plot.
Answers
Answer:
From the box plot we get:
Minimum - 14Maximum - 88Quartile 1 - 34Quartile 3 - 65Median - 48Answer:
the other person is correct!
Step-by-step explanation:
Show them some love <3!
what is 20/100 in it's simplest form?
ik this i just wanna give someone my points lol
Answers
Answer:
1/5
Step-by-step explanation:
20/100
Divide the top and bottom by 20
20/20 =1
100/20 =5
20/100 = 1/5
20/100
Divide the top and bottom by 20
20/20 =1
100/20 =5
20/100 = 1/5
[tex] \tt \: \verified \: \: \: \red{ \checkmark}[/tex]
point e is the midpoint of ca and bd. which statements about the diagram are true?
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Answer:
Step-by-step explanation: i don’t know to be honest
Find the range of the given data set. 5/8,3/4,1 1/8,1 1/4
Answers
3/4 and 1/8
3 x 8 - 1 x 4 = 24 - 4
4 x 8 = 32
24/32
8 goes into each to simplify the fraction
24/8 = 3 & 32/8 = 4
Answer 3/4
HELP FAST LOL HAHAHAH
Answers
Answer:
184
Step-by-step explanation:
First, note that the sides that are opposite to each other are congruent (this will come into play in a second). We can find the area of each triangle by doing 0.5(b)(h) (aka half * base* height). Since we've established tha opposite sides are congruent and the triangles are opposite to each other, they must be congruent. That means that the area is going to be the exact same for both triangles. So, we get the expression (0.5)(6)(4)(2), which comes out to 6*4 = 24. Then, to find the area of the 2 rectangles that are the sides, just do 5*10*2 = 100 square meters for both rectangles combines. Lastly, we need to find the area of the floor. The dimensions of the floor are 6 and 10, so we just do 6*10 = 60. Now, add all those numbers together. We get 100+60+24 = 184. Hope this helps! Let me know if anything is still confusing.
All of the following numbers are rational except _____.
Answers
Answer:
What are the numbers?
Step-by-step explanation:
I can help if you give the numbers :)
which following algebraic statements are true
Answers
Answer:
All of them are true.
Step-by-step explanation:
x^2 y - z / x^2 is true. x^2, when divided by itself, cancels itself out, so the equation that is left is y - z.
For the second one, a/c + b/c is true because when you add a + b = it will change; it will be added together. the remaining c will stay the same, as it is the denominator/the same, so you keep it as it is.
For the final one, you distribute ^2 to (a+b), so they become a^2 + b^2.
This means that all of the statements are true.
Describe the transformation of f(x) to g(x).
(answers and graph in picture) PLSSSS HELP
Answers
Answer: b
Step-by-step explanation:
becuz now brainliest
The transformation of a function may involve any change. The correct option is A.
How does the transformation of a function happen?The transformation of a function may involve any change.
Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs) etc.
If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:
Horizontal shift (also called phase shift):
Left shift by c units, y=f(x+c) (same output, but c units earlier)Right shift by c units, y=f(x-c)(same output, but c units late)Vertical shift
Up by d units: y = f(x) + dDown by d units: y = f(x) - dStretching:
Vertical stretch by a factor k: y = k × f(x)Horizontal stretch by a factor k: y = f(x/k)Given the function of f(x) as sin(x), Now it can be seen the graph of the two functions is parallel, but the function f(x) has a y-intercept of 0, while h(x) has a y-intercept of 1. Therefore, we can write,
h(x) = f(x) + 1
The function is shifted up by 1 unit.
Hence, the transformation of the function is correctly described in the first option.
Learn more about Transforming functions:
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Which of the following graphs is the solution set of -10 < 3x - 4 < 8?
Answers
Answer:
3rd option
Step-by-step explanation:
Solving the inequality
- 10 < 3x - 4 < 8 ( add 4 to each interval )
- 6 < 3x < 12 ( divide each interval by 3 )
- 2 < x < 4
Since -2 less than x and x less than 4
This is indicated by an open circle at - 2 and 4 on the number line and the line between them is shown in black.
The solution is represented on the 3rd graph
Answer:
its the 3rd graph
Step-by-step explanation:
i need help please. and explanation will help for tomorrow in a test:)
Answers
When you’re multiplying variables like the one in the problem above, instead of actually multiplying, you add. You only multiply in cases where there are coefficients.
Example : z^4 * z^2
Instead of multiplying, you would add the exponents together like so, z^6.
A rectangle has a length of 2x+7 and a width of 3x+8.
Write and simplify an expression for the perimeter of that rectangle
Answers
Answer:
2(2x+7)=4x+14
2(3x+8)=6x+16
4x+14+6x+16
4x+6x+14+16
The answer is:
10x+30
[tex] \frac{12}{20} - \frac{30}{20} [/tex]
Answers
Answer:
-9/10
Step-by-step explanation:
12/20 - 30/20
Since the denominators are the same, we can subtract the numerators
12-30 = -18
Put this over the denominator
-18/20
Simplify by dividing the top and bottom by 2
-9/10
A school survey asked students which candidate they supported for class president. the survey data are shown in the relative frequency table.
Answers
Answer:
C. 24%
Step-by-step explanation:
hope it works
Answer:
39%
Step-by-step explanation:
A watch that originally cost $110 has been marked down to $88. What is the percent of the markdown?
12%
10%
25%
20%
Answers
Answer:
20%
Step-by-step explanation:
110-88=22
22/110=20
Solve the following for y: 4x + 2y = −2 (5 points)
y = −2x + 1
y = 2x + 1
y = −2x − 1
y = 2x − 1
Answers
Answer:
Step-by-step explanation:
4x + 2y = −2
Divide by two on both sides
2x+y = -1
subtract 2x from both sides
y = -1 -2x = -2x -1
Answer:
y = -2x - 1
Step-by-step explanation:
4x + 2y = -2
→ Minus 4x from both sides
2y = -4x - 2
→ Divide both sides by 2
y = -2x - 1
Use the function below to find F(3).
F(x) = 4•C**
O A.
H im
O B.
O c.
4
27
O D.
81
Answers
Answer:
4-3
Step-by-step explanation:
solve for x
Value of function f(x) = 4(1/3)ˣ when x = 3, f(3) = 4/27
Correct option is C.
What is exponential function?As the name suggests, the exponential function contains an exponent. Note, however, that the exponential function has a constant as its base and a variable as its exponent, not vice versa (if a function has a variable as its base and a constant as its exponent, it is a power function). The exponential function can be in one of the following forms:
Definition of exponential function
In mathematics, an exponential function is a function of the form f(x) = aˣ. where "x" is a variable and "a" is a constant called the base of the function, which must be greater than 0.
Given, exponential function
f(x) = 4(1/3)ˣ
exponential function is defined for x∈R
Putting x = 3
f(3) = 4(1/3)³
f(3) = 4/27
Hence, 4/27 is value of function f(x) = 4(1/3)ˣ when x = 3
Learn more about exponential function here:
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What is the measure of Rsl?
Answers
Answer:
x = 13
Step-by-step explanation:
[tex](9x + 27) = (6x + 66) \\ 9x - 6x = 66 - 27 \\ 3x = 39 \\ x = \frac{39}{3} \\ x= 13 [/tex]
plzz help everything is due tonight! 29 pointssss
Answers
Answer:
Step-by-step explanation:
given= -3(2n-3)=25-8n
distributive property=-6n+9=25-8n
subtraction property= 2n+9=25
division property =2n=16
n=8
The temperature in Anchorage, Alaska one morning was -8 degrees Fahrenheit. It rose slightly, increasing only 10 degrees by lunchtime. By dinnertime, the temperature had fallen 8 degrees. What was the ending temperature?
Answers
Answer:
The ending temperature was -6 degrees Fahrenheit.
Step-by-step explanation:
First, it was -8 degrees
Then, it was -8+10=2 degrees
Lastly, it was 2-8=-6 degrees
ZABC and ZQRS are complementary angles. If the measure of ZABC= 41º, what is the measure of ZQRS?
Answers
Answer:
m∠QRS = 139°
Step-by-step explanation:
yes
Quadrilateral R S T Q is shown. Angle R is 132 degrees, angle Q is 56 degrees, and angle T is 79 degrees.
What is the measure of angle S?
48o
56o
93o
101o
Answers
Answer:
C) 93o
Step-by-step explanation:
Trust the process
edge 2021
Answer:
Got a 100% on the Unit Test on Edge and 93 is the correct answer like the person above added! :D
Find the area of an equilateral triangle (regular 3 Gon) with the given measurement 9 in perimeter a=SQ.in
Answers
Answer:
3.897 [tex]in^{2}[/tex]
Step-by-step explanation:
equilateral triangles are also equiangular, meaning the have equal angles.
Triangle sum theory says that angles of a triangle add up to 180.
That means each angle is 60.
A = bh/2
You need the (h). The base of is 3. Perimeter = 9, so each side is 3
Draw a perpendicular line for the height. The line cuts the base in half (1.5)
Using trigonometry you can find the height.
tan 60° = h/1.5
h = height, 1.5 is half of 3, 60° is the base angle.
multiply each side by 1.5
1.5(tan 60°) = h
h=2.598
then substitute h into formula
A= (2.598)(3)
2
A = 3.897 rounded
What is the image of (-8,-8) after dilation by a scale factor of {1/4} centered at the origin?
Answers
Answer:
(-2, -2)
Step-by-step explanation:
To scale a factor by 1/4, you just need to divide the numbers by 4, or multiply them by 1/4.
-8/4=-2
Answer:
It would be (-2, -2)
