unit 8 right triangle and trigonometry homework 5 trigonometry: finding sides and angles solve for x round to the nearest tenth.
plllls I will make brainlesst
Answers
Answer:
5. x = 25.6
6. x = 11.0
7. x = 41.8°
8. x = 64.2°
9. x = 12.8°
10. x = 51.3°
Step-by-step explanation:
Let's find the x value for each triangle.
For point 5
We have:
x: is the opposite cathetus to 52°
20: is the adjacent cathetus to 52°
52°: is the angle
We can find "x" with the following trigonometric function:
[tex] tan(52) = \frac{x}{20} [/tex]
[tex] x = tan(52)*20 = 25.6 [/tex]
For point 6
We have:
x: is the hypotenuse
5: is the opposite cathetus to the given angle
27°: is the angle
To find "x" we need to use the trigonometric function:
[tex] sin(27) = \frac{5}{x} [/tex]
[tex]x = \frac{5}{sin(27)} = 11.0[/tex]
For point 7
We know:
x°: is the angle
6: is the hypotenuse
4: is the opposite cathetus to x°
Hence, x is:
[tex] sin(x) = \frac{4}{6} [/tex]
[tex] x = sin^{-1}(\frac{4}{6}) = 41.8 [/tex]
For point 8
We have:
x°: is the angle
14: is the adjacent cathetus to x°
29: is the opposite cathetus to x°
To calculate "x" we need to use the trigonometric function tan(x):
[tex] tan(x) = \frac{29}{14} [/tex]
[tex] x = tan^{-1}(\frac{29}{14}) = 64.2 [/tex]
For point 9
We have:
x°: is the angle
54: is the hypotenuse
12: is the opposite cathetus to x°
We can use sin(x) to solve for x:
[tex] sin(x) = \frac{12}{54} [/tex]
[tex] x = sin^{-1}(\frac{12}{54}) = 12.8 [/tex]
For point 10
We have:
x°: is the angle
40: is the hypotenuse
25: is the adjacent cathetus to x°
We need to use cos(x) to solve for x:
[tex] cos(x) = \frac{25}{40} [/tex]
[tex] x = cos^{-1}(\frac{25}{40}) = 51.3 [/tex]
I hope it helps you!
To solve the given questions, either of the trigonometric functions; sine, cosine and tangent of an angle has to be applied appropriately to either of the questions. The answers to the questions are:
5. x = 25.60
6. x = 11.00
7. x = [tex]41.8^{o}[/tex]
8. x = [tex]64.2^{o}[/tex]
9. x = [tex]12.8^{o}[/tex]
10. x = [tex]51.3^{o}[/tex]
The questions given are right angled triangles which requires the application of trigonometric functions appropriately. A right angle triangle is one that has one of its angles to be [tex]90^{o}[/tex].
So, each of the questions can be solved as follows:
5. Tan θ = [tex]\frac{opposite}{adjacent}[/tex]
Tan 52 = [tex]\frac{x}{20}[/tex]
⇒ x = Tan 52 * 20
= 25.5988
x = 25.60
6. Sin θ = [tex]\frac{opposite}{hypotenuse}[/tex]
Sin 27 = [tex]\frac{5}{x}[/tex]
⇒ x = [tex]\frac{5}{Sin 27}[/tex]
= 11.0134
x = 11.00
7. Sin θ = [tex]\frac{opposite}{hypotenuse}[/tex]
Sin x = [tex]\frac{4}{6}[/tex]
= 0.66667
x = [tex]Sin^{-1}[/tex] 0.66667
= [tex]41.8^{o}[/tex]
x = [tex]41.8^{o}[/tex]
8. Tan θ = [tex]\frac{opposite}{adjacent}[/tex]
Tan x = [tex]\frac{29}{14}[/tex]
= 2.0714
x = [tex]Tan^{-1}[/tex] 2.0714
= [tex]64.2^{o}[/tex]
x = [tex]64.2^{o}[/tex]
9. Sin θ = [tex]\frac{opposite}{hypotenuse}[/tex]
Sin x = [tex]\frac{12}{54}[/tex]
= 0.22222
x = [tex]Sin^{-1}[/tex] 0.22222
= [tex]12.8^{o}[/tex]
x = [tex]12.8^{o}[/tex]
10. Cos θ = [tex]\frac{adjacent}{hypotenuse}[/tex]
Cos x = [tex]\frac{25}{40}[/tex]
= 0.625
x = [tex]Cos^{-1}[/tex] 0.625
= [tex]51.3^{o}[/tex]
x = [tex]51.3^{o}[/tex]
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Related Questions
Write an explicit formula for a_na
n
, the n^{\text{th}}n
th
term of the sequence 27, 9, 3, ...27,9,3,....
Answers
The equation which correctly represents the explicit formula for the nth term of the given sequence is; a (n) = a (n - 1) × ( 1 / 3 ) and a (1) = 27.
Which equation represents the nth term of the given sequence?As evident in the task content; the given sequence is a geometric sequence and the common ratio of the sequence can be determined as;
r = 3 / 9 = 9 / 27 = 1 / 3.
On this note, since the common ratio of the consecutive terms of the sequence is; 1/3 it follows that the required explicit formula which represents the nth term , a (n) is;
a (n) = a (n - 1) × ( 1 / 3 ) and a (1) = 27.
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Evaluate the expression 5(x – 6 + 3x)2 – 6 where x = 2.
Answers:
1: 974
2: 14
3: -16
4: 26
Answers
So the expression evaluates to 14 when x = 2.
To evaluate the expression, we first substitute x = 2 into the expression:
5(2 - 6 + 3*2)^2 - 6
There are two methods for solving simultaneous linear equations: graphical methods and algebraic methods. The algebraic technique includes the substitution method as one of its categories.
The value of one variable from one equation is substituted in the second equation using the substitution method. In this manner, a pair of linear equations is reduced into a single linear equation with only one variable, which can then be solved quickly.
Next, we simplify the expression inside the parentheses:
=5(2 - 6 + 6)^2 - 6
=5(2)^2 - 6
=5*4 - 6
=20 - 6
=14
So the expression evaluates to 14 when x = 2.
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If Marvin has 47 pencils and Mark has a total number of pencils is 4 tens
and 3 ones, who would have a greater total? Draw a math drawing to explain
how you know.
Answers
Number of pens x=10.
Number of pencils y=30.
How many pencils are there?The Five Principles are: freedom, efficiency, mutuality, responsibility, and quality. Victoria that she always incorporates The Five Principles into her conversations with other businesses, government officials, and other partners and leaders. The writing core is tougher and leaves a lighter trace on the paper as the number increases.
Let number of pens =x
And number of pencils =y
⇒ x+y=40
⇒(5+y)+(x−5)=4x
⇒3x=y
Substituting in above equations ;
⇒x+3x=40
⇒x=10
⇒y=30
∴number of pens =x=10
⇒number of pencils =y=30
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Alice, Bob, Charles and Darwin are sharing an orange. Bob got twice as many slices as Charles,
Charles got 5 times less slices than Darwin, and Darwin got 8 slices more than Charles. Find the
number of slices in the orange given that Alice got only the peel.
(A) 10 (B) 12 (C) 14 (D) 15 (E) 16
Answers
Answer:
E
Step-by-step explanation:
Let
A = # of slices Alice got
B = # of slices Bob got
C = # of slices Charles got
D = # of slices Darwin got
First, write equations based on given information:
A = 0
B = 2C
5C = D
D = C + 8
5C = D -> D = 5C
Now that we have two equations for D, we can set them equal to each other:
5C = C + 8
4C = 8
C = 2
Now just plug in the rest:
A = 0
B = 2(2) = 4
C = 2
D = 2 + 8 = 10
Add all solutions together to get (E) 16 slices
hi quick whats 18 x 1.25
step by step !!
Answers
Answer:
22.5
Step-by-step explanation:
125
x 18
---------
1. first set up your problem
2 4
125
x 18
------
1000
2. next multiply the 8 by 5 getting 40, drop the 0 anf move the 4 to the top above 2.
3. multiply 8 by 2 getting 16, then add the 4 you have ontop of the 2 to the 16 getting 20. Drop the 0 and bring the 2 over and place it above the one.
4. multiply 8 by 1 getting 8 then add the 2 above the 1 to 8 getting 10. Then put the ten infront of the tw zeros. 1000
125
x 18
--------
1000
0
Next add a 0 as a place filler under the 0 at the end.
125
x 18
-------
1000
1250
Then multiply the 1 by 5, then 1 by 2, then finnaly 1 by 1, getting you 1250.
1000
+1250
add together
getting 2250
then move 2 decimal places over to get 22.5
In its prime, Mr. Ford’s 2002 Focus would get 36
miles/gallon. Mr. Ford starts a road trip to San
Bernardino, Barstow, Kingman, Winona, and
Flagstaff, AZ. He starts with 13.2 gallons of gas in
his gas tank.
a) Write a slope-intercept equation that models how
much gas remains in his tank after each mile of of
travel(hint: g/mi)
Answers
Answer:
The fuel economy is 36 miles per gallon. For each mile 1/36 gallon will be used.
Initial volume is 13,2 gallons and x is the number of miles.
Our equation is:
y = 13.2 - 1/36xor
y = -1/36x + 13.2Let h(x)=[tex]\sqrt{x+3}[/tex] and k(x)=2x+7
Find the value of h(k(3))
Answers
Work out the length of x.
Give your answer rounded to 1 decimal place.
9 m
14.5 m
The diagram is not drawn accurately
Please help
Answers
Answer:
Calculate the value of x. Give your answer ... Hyp. 5.8 m. Opp. 1. Adi. Diagram NOT accurately drawn. POR is a triangle. Angle Q = 90° ... the value of x. Give your answer correct to 1 decimal place. ... a. Diagram NOT accumtely drawn. 9,6 cm. 6.4 cm. A. Hyp. To. Aaj. LMN is a right-angled triangle. MN = 9.6 cm. ... x = ton-14.5.
Step-by-step explanation:
please be right
Hello please evaluate the expression ( 2x - y)
Answers
Which exponential function has an initial value of 2?
Of(x) = 2(3)
Of(x) = 3(2)
X
-2
-1
f(x)
18
1
4
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On solving the provided question, we can say that - here in the equation, [tex]x^2- x = 4[/tex]
What is equation?An equation is a formula in mathematics that joins two statements with the equal symbol = to represent equality. The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions. In the equation 3x + 5 = 14, for instance, the terms 3x + 5 and 14 are separated by an equal sign. The link between two phrases on either side of a letter is expressed mathematically. There is often only one variable, which is also the symbol. instance: 2x - 4 Equals 2.
so, x = 2
therefore
[tex]x^2- x \\6-2\\4[/tex]
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Aiden is a spice trader.
The price he charges for an order of cumin (in dollars) as a function of the size of the order (in kilograms) is graphed.
What is the approximate average rate at which the total cost increases, as the order size increases from 100 to 600 kilograms?
Answers
Approximately $2.40 per kilogramme is the average rate that the total cost rises as the order size does, from 100 to 600 kg.
How much is the average rate?The average rate of change is the average change rate of one thing in respect to another. Simply explained, a computation that divides the amount of change in one thing by the comparable amount of change in another is known as an average rate of change function.
How are average rates calculated?Divide the y-value change by the x-value change to determine the average rate of change. When analyzing changes in observable parameters like average speed or average temperature, finding that average rate of change is especially helpful.
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Use the correct order of operations to solve the problem below.
14 - 8 + 6 - 10 ÷ 2
Answers
Answer: 7
Step-by-step explanation:
A line has a slope of – 1/7 and passes through the point (4,5). What is its equation in point-slope form?
Answers
Answer:
y-5=-1/7(x-4)
Step-by-step explanation:
The equation of the line in point-slope form is y-5=-1/7(x-4)
Answer:
y = -1/7 x + 39/7
Step-by-step explanation:
An equation in point slope form is
y = mx+b where m is the slope and b is the y intercept
We are given the slope
y = -1/7 x + b
Substitute in the point for x and y and solve for b
5 = -1/7(4) +b
5 = -4/7 +b
5 + 4/7 = b
5*7/7 + 4/7 = b
35/7 + 4/7 = b
39/7 = b
The equation is
y = -1/7 x + 39/7
2.
The table shows the number of absences at two middle schools over a period of two weeks.
Attendance Comparison
School Number of Absences by Date
2/12/2/2/3/2/4/2/5/2/8/2/9/2/10 2/11 2/12
Belmont 1612151018117 9 12 14
Tyler 13 10 12 10 20 13 8 6 6 11
Which statement best compares the means and medians of the data for the two schools?
Answers
Answer:
C.
Step-by-step explanation:
The mean at Belmont is 16.75, the median is 15.5, and the mode is 13.
The mean at Tyler is 10.9, the median is 10.5, and the mode is 13, 10, and 6.
Find the values of x and y
Answers
The values of x and y, given the angles in the diagram, can be found to be :
x = 11y = 17How to find the value of x and y ?The angles given above are called vertical angles and they are such that the two corresponding angles are equal to each other.
This means that ( 8 x + 7 ) ° is equal to ( 9 x - 4 )° and 5 y° is equal to ( 7y - 34 )°.
The value of x is :
8 x + 7 = 9 x - 4
9x - 8x = 7 + 4
x = 11
The value of y is :
5 y = 7y - 34
7y - 5y = 34
2 y = 34
y = 34 / 2
y = 17
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please help im giving 95 points
Answers
[tex]\\ \sf\longmapsto f(n)=2^n[/tex]
#a
[tex]\\ \sf\longmapsto f(1)=2(1)=2Amoebas[/tex]
#b
[tex]\\ \sf\longmapsto f(2)=2^2=4Amoebas[/tex]
#c
[tex]\\ \sf\longmapsto f(6)=2^6=64Amoebas[/tex]
#d
[tex]\\ \sf\longmapsto f(24)=2^24Amoebas[/tex]
what is the equation of the line that is perpendicular to the line y=3/5x+10 and passes through the point (15,-5)?
Answers
Answer:
y = -5/3x + 20
Step-by-step explanation:
y = -5/3x + b
-5 = -5/3(15) + b
-5 = -25 + b
20 = b
y = -5/3x + 20
Answer:
In other words.. The fourth option D.
Step-by-step explanation:
EDGE2022
i like your cut g
Janine and Laura both took a standardized math test. The test scores were normally distributed with a mean of 75 and a standard deviation of 11. Janine earned a score of 76, whereas Laura earned a score of 89.
About what percentage of people had a score between Janine's and Laura's scores?
a) 30%
b) 43%
c) 80%
d) 36%
Answers
About what percentage of people had a score between Janine's and Laura's scores?
Answer:
Its D) 36%
If m 2 = 23° and m3 = 68°, what is m 1?
O
A. 23°
B. 68°
C. 89°
D. 91°
Answers
Answer:
i think it is 68 degree i think
Answer:
D 91
Step-by-step explanation:
Add 3 +2 =68 +23=91
Sum of any angle in atringle is 180 (rule)
Then 180-91 =89 (the missing angle in the traingle)
Since the sum of any straight angle is 180 (Therom)
180 - 89 =91
Or
The some of 2 interior angle in a triangle equal to the opposite exterior angle (Therom)
So 68 +23 = 91
The graph of a function is line that passes through the points (1,4) (3,8) and (6,y) what is the value of y?
Answers
Step-by-step explanation:
First, find the slope from the first 2 points, then use the value of the slope and either one of the first 2 points to find y in the 3rd point.
m = (8 - 4)/(3 - 1) = 4/2 = 2
2 = (y - 4)/(6 - 1)
How Do You Solve 3 linear equations with 3 variables?
Answers
The standard way to solve 3 linear equations with 3 variables is to use elimination or substitution.
-Elimination: To solve the 3 equations using elimination, add or subtract equations together to eliminate one of the variables. Keep repeating this process until you are left with one equation with one variable. Solve the equation and then use the value of the variable to substitute back into the other equations to find the values of the other variables.
-Substitution: To solve the 3 equations using substitution, pick one of the equations and solve it for one of the variables. Then substitute the value of the variable into the other equations. Keep repeating this process with the other equations and variables until you have a system of equations with one variable that you can solve. Once you have the value of the variable, substitute it back into the other equations to find the value of the other variables.
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Please complete the square, show your work.
x^2 - 19x +c
Answers
Answer:
Step-by-step explanation:
We need to transform the given x^2 - 19x + c into the form
(x - a)^2 + d
by completing the square:
1. Take half of the coefficient (-19) of x, obtaining -19/2.
2. Square this result, obtaining 361/4.
3. Add this to x^2 - 19x, and then immediately subtract it:
x^2 - 19x + c becomes x^2 - 19x + 361/4 - 361/4+ c
4. Replace the first three terms with (x - 19/2)^2:
x^2 - 19x + 361/4 - 361/4+ c => (x - 19/2)^2 - 361/4 + c
5. Put this into final form: (x - 19/2)^2 - (361/4 - c)
What is the solution of 2x^2 3x 5 0?
Answers
Answer: The answer is 10x2
Step-by-step explanation:
Find the values of x and y 2x+2y=x+13
Answers
The rectangular floor of a classroom is 30 feet in length and 24 in width. A scale drawing of the floor has a length of 15 inches. What is the perimeter, in inches, of the floor in the scale drawing?
Answers
Answer: 54 inches squared
Step-by-step explanation:
Since it is a scale drawing, when we scale one variable up or down, we have to scale the other value the same amount because they are proportional. For example, if we divide one value by 3, we have to divide the other value by 3 also.
In this case, the real length is 30 feet, and the scale drawing length is 15 in. We divided by 2, so we have to divide the width by the same amount. 24/2 = 12 inches, so the width would be 12 inches or 1 foot.
need help on khan NOW! question is on picture. will report link and mark brainliest if right
Answers
Explanation: no matter how you do it you still get 1 bc its x divided by y which is 1
HELP!!!! Due to inflation, there were two price increases. After the second increase, the price of an item was twice its original price. By what percent did prices increase the first time if prices increased by 25% the second time?
Answers
The increase was 250% over the original price.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
let 'x' represent the original price, then 'x+0.25x' represents the first increase of 25%
six times greater, converted to a percentage:
(x+0.25x)×2×100 a second increase of six-fold
1.25x×2×100
250
The increase was 250% over the original price.
Hence, the increase was 250% over the original price.
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How do you find the slope of a line example?
Answers
The easiest way to find the slope of a line is converting the line equation into the slope-intercept form.
There are 3 forms of line equations:
- slope intercept form, the equation is given by:
y = mx + b
Where:
m = slope
- point slope form, the equation is given by:
y − y₁ = m (x - x₁)
Where:
m = slope
- standard form: Ax + By = C
The easiest way to find the slope of a line is to convert it into a slope-intercept form.
Example:
Line equation in standard form:
2x + 4y = 6
We will convert it into slope-intercept form.
4y = -2x + 6
y = (-2/4) x + 6
y = (-1/2) x + 6
Hence, the slope is (-1/2)
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What is the slope of the mine that passes Through the point (4.5, 2.5) and (2, -10)?
Answers
Answer:
slope = 5
Step-by-step explanation:
slope of a line = y2 -y1 / x2 - x1
where x1 =4.5 x2 =2 y1= 2.5 y2 = -10
slope = -10 - 2.5 / 2 - 4.5
slope = -12.5 / -2.5
slope = 5
How do you find the endpoint and midpoint?
Answers
To find the endpoint we have to calculate the distance between the known midpoint to the known endpoint. To calculate the midpoint we add two points and divide them by 2.
The formula for midpoint = (x1 + x2)/2, (y1 + y2)/2.
Substituting in the two x-coordinates and two y-coordinates from the endpoints.
Putting it together,
The endpoint formula is:
(x a ,ya)= ((2xm−xb),(2ym−yb))
( x a , y a ) = ( ( 2 x m − x b ) , ( 2 y m − y b ) ).
The end of a line at a point that is equally distant from both ends, a time interval between an event's beginning and end.
The point on a graph or figure where the figure stops might be referred to as the endpoint. It can be the point joining the sides of a polygon (the vertex), the common endpoint of two rays making an angle, the two extreme points of a line segment, the one end of a ray.
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