Use the properties of 30-60-90 and 45-45-90 triangles to solve for x in each of the problems below. Then decode the secret message by matching the answer with the corresponding letter/symbol from the exercises.
Answers
With the help of trigonometric function, the above problems have been calculated. See explanation below.
What are Trigonometric functions?The term "trigonometric function" refers to functions that are periodic in nature and that shed light on how a right-angled triangle's angles and sides relate to one another.
The solutions to x in the respective problems is given as follows:
1) x = 5 /Sin(30°)
x = 10
!) Sin(45°) = 4/x
x = 4/sin(45°)
x = 4√2
I) Cos(45°) = √3 / x
x = √3 / Cos(45°)
x = √6
E) Tan(60°)
= (3√3) / x
x = (3√3) / 3
W) In trigonometry, every right-triangle that is isosceles in nature, the angle made by the legs and the hypotenuse will always equal 45°.
x = 45°
N) x² + x² = (7√2)²
x = 7
V) Tan(60°) = 7 / x
x = 7√3/3
K) x² + x² = (9)²
x = 9/√2
Y) Sin(60°) = 7√3/x
x = 14
M) Sin(30°) = x/11
x = 11/2
T) Sin(45°) = x/√10
x = √5
A) x + 2x + 90° = 180°
x = 30°
O) Sin(45°) = √2 / x
x = 2
R) Tan(30°) = x / 4
x = 4/√3
= 4√3 / 3
S) Sin(60°) = x / (10/3)
x = (5√3) / 3
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Related Questions
What is the turning point of the parabola with the equation?
y=27(x-64)squared+43
A: (-64,-43) B: (64,43) C: (64,-43) D: (1728,43) E: (-64,43)
Answers
The turning point of the parabola is (64, -43)
What is a turning point?Turning point is that point on a parabolic curve in which the gradient of the curve changes value.
It is also the point on the curve in which the curve starts rising or falling.
Analysis:
[tex]27(x-64)^{2}[/tex] + 43
27(x-64)(x-64) + 43
27([tex]x^{2}[/tex] -64x -64x +4096) + 43
27[tex]x^{2}[/tex] -3456x +110592 +43
27[tex]x^{2}[/tex] -3456x +110635
at turning point dy/dx = 0
dy/dx = 54x - 3456
54x - 3456 = 0
54x = 3456
x = 3456/54 = 64
To find the value of y at x = 64
27[tex](64)^{2}[/tex] -3456(64) +110635
110592 - 221184 +110635 = -43
Therefore the turning point of the parabola is (64, -43)
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The following graph describes function 1, and the equation below it describes function 2. Determine which function has a greater maximum value, and provide the ordered pair. (1 point)
Function 1
graph of function f of x equals negative x squared plus 8 multiplied by x minus 15
Function 2
f(x) = −x2 + 2x − 3
Function 1 has the larger maximum at (1, 4).
Function 1 has the larger maximum at (4, 1).
Function 2 has the larger maximum at (1, −2).
Function 2 has the larger maximum at (−2, 1).
Answers
Answer:
Function 1 has the larger maximum at (4, 1)
Explanation:
After observation, graph of function 1 has vertex at Maximum (4, 1)
In order to find vertex of function 2, complete square the equation.
f(x) = -x² + 2x - 3
f(x) = -(x² - 2x) - 3
f(x) = -(x - 1)² - 3 + (-1)²
f(x) = -(x - 1)² - 2
Vertex form: y = a(x - h)² + k where (h, k) is the vertex
So, here for function 2 vertex: Maximum (1, -2)
Conclusion:Function 1 = Maximum (4, 1), Function 2 = Maximum (1, -2)
Function 1 has greater maximum value of (4, 1) as "1 is greater than -2"
i honestly done know what to do (look at image)
Answers
Answer:
A is x - 4n / 3, B is 6k + 9n, C is 11k + 16n
Step-by-step explanation:
Pretty simple, you are adding the algebra grids, or substituting variables and making out an equation.
Solving for B: 4k + 6n + 2k + 3n = 6k + 9n
Solving for A: (2k + 3n) + x = 5k + 7n = x - 4n / 3
Solving for C: 6k + 9n + 5k + 7n = 11k + 16n
Please help me I’ll mark Brainly
Answers
state the domain and range of the following relation
x^2+y^2=16
Answers
The domain and range is [-4, 4] and [0, 4]
What is Domain and range?The domain of a function is the set of values that we are allowed to plug into our function.
The range of a function is the set of values that the function assumes.
x² + y² = 16
y = √16 - x²
For domain under root should not be negative quantity,
16 - x²≥0
16≥x²
So, x≤4 or x≥4
Thus, the domain is [-4, 4]
Range:
y is maximum at x=0, y=4
y is minimum at x=4, y=0
Thus, range = [0, 4]
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Write the equation in point-slope form of the line that passes
through the given point and has the given slope..
m= 5/3,(4, -2)
Answers
Answer:
y + 2 = 5/3(x - 4)
Step-by-step explanation:
Point-slope form of the equation of a line is a shortcut, fill-in-the-blank formula. You can write an equation just by filling in the slope and a point (hence the name, point-slope)
It looks like this:
y - Y = m(x - X)
The point given is (4,-2) fill in the -2 for the Y. Leave the first y just like it is, it stays a y. Fill in the 4 for X. Leave the first little x in the parenthesis alone Leave it an x.
y - -2 = m(x - 4)
Fill in the slope for the m.
y - -2 = 5/3(x - 4)
Simplify if possible.
y + 2 = 5/3 (x - 4)
The peak of Mount Everest is at 8,848 meters above sea level. The peak of Kanchenjunga is at 8,586 meters above sea level.
The elevation of Mount Everest's peak as a rational number is
meters. The elevation of Kanchenjunga's peak as a rational number is
meters.
Answers
Then, the elevation of Mount Everest's peak as a rational number is[tex]\frac{8,848}{1}[/tex] meters. The elevation of Kanchenjunga's peak as a rational number is [tex]\frac{8,586}{1}[/tex] meters.
1. The number 8,848 is an integer and the number 8,586 is also an integer.
2. Therefore, to solve this problem you must convert the integers shown above to fractions (Because a rational number is that one that can be written as a fraction), as you can see below:
Write each integer as the numerator of the fraction a write 1 as the denominator. This will not change the value.
What is the fraction?A fraction represents a part of a whole or, more generally, any number of equal parts. When spoken in everyday English, a fraction describes how many parts of a certain size there are, for example, one-half, eight-fifths, three-quarters.
Then you obtain the following fractions:
[tex]\frac{ 8,848}{1}[/tex]
[tex]\frac{8,586}{1}[/tex]
3. Then, the elevation of Mount Everest's peak as a rational number is[tex]\frac{8,848}{1}[/tex] meters. The elevation of Kanchenjunga's peak as a rational number is [tex]\frac{8,586}{1}[/tex] meters.
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for what values of the variables are the following expressions defined 1/x+y
Answers
The expression is defined for all the real values except x = -y , y = -x.
What is an Expression ?An expression is a mathematical statement consisting of constants , variables and mathematical operators.
The expression given in the question is 1/(x +y)
An expression f(x) is undefined when the denominator = 0
f(x) = 1/(x +y)
For the denominator to be zero,
x = -y
or y = -x
So the expression is defined for all the real values except x = -y , y = -x
It can be written as
E = {x ∈ R ∧ x ≠ -y} or
E = {y ∈ R ∧ y ≠ -x}
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use the distrubutive property to simply 2(-5-7j)
Answers
Answer:
2(-5 - 7j) = -10 - 14j
Step-by-step explanation:
Using the distributive property means that we have to multiply both -5 and -7j by 2:
2(-5 - 7j)
⇒ 2 × -5 + 2 × -7j
⇒ -10 - 14j
What is the quotient of (x cubed 3 x squared minus 4 x minus 12) divided by (x squared 5 x 6)?
Answers
The quotient of [tex]x^{3}+3x^{2} -4x-12[/tex] divided by [tex]x^{2} +5x+6[/tex] is (x-2_.
Given the polynomial [tex]x^{3}+3x^{2} -4x-12[/tex] and [tex]x^{2} +5x+6[/tex] and the first expression or polynomial is divided by second.
Quotient is a number that is obtained by dividing two numbers. It can be of two numbers or two expressions. Remainder is a number or an expression left after division of two numbers.
To find the quotient of [tex]x^{3}+3x^{2} -4x-12[/tex] divided by , we have to divide the expression first.
We know that ,
Divident=Divisor*Quotient+remainder
[tex]x^{3}+3x^{2} -4x-12[/tex]=[tex]x^{2} +5x-6[/tex]*(x-2)-12
If we carefully watch the above equation and compares with the above formula then we can easily find that the value of quotient is (x-2).
Hence the quotient of [tex]x^{3}+3x^{2} -4x-12[/tex] divided by [tex]x^{2} +5x-6[/tex] is (x-2).
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Question is incomplete as the given expressions are incomplete as they should be like this:
[tex]x^{3}+3x^{2} -4x-12[/tex] and [tex]x^{2} +5x-6[/tex].
which value of x is in the domain of f(x)= square root x-2
Answers
The domain of the function f(x)= [tex]\sqrt{x-2}[/tex]is all numbers greater than or up to 2.
Given Function f(x)=[tex]\sqrt{x-2}[/tex]
We have to search out the domain of the function f(x)=[tex]\sqrt{x-2}[/tex]
Domain is that the value of x which we put within the function to induce the various values and range is that the value which we get after putting the worth.
f(x)=[tex]\sqrt{x-2}[/tex]
put the function =0
squaring either side we get
x-2=0
x=2
So the domain of the function f(x)=[tex]\sqrt{x-2}[/tex] is [2,∞) because we are able to put all values greater than 2 within the function.
Hence the domain of the function is [2,∞).
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calculate AC to 1 decimal place ?
Answers
Step-by-step explanation:
first we need to find the length of CD, so that we can use Pythagoras to find AC.
to get CD we use again Pythagoras. there is a smaller right-angled triangle on top of the BCD rectangle.
so, AD = 11 = 4 + 7
7 = the vertical leg of the upper right-angled triangle.
the horizontal leg is congruent to CD and is
sqrt(16² - 7²) = sqrt(256 - 49) = sqrt(207).
AC² = sqrt(207)² + 11² = 207 + 121 = 328
AC = sqrt(328) = 18.11077028... cm ≈ 18.1 cm
Im taking precalc over edge 2022 right now. Cramming right before the deadline LOL. If i complete things after the deadline do they count for late credit?
Answers
Step-by-step explanation:
♦ Solution ♦ :-
Given Information :
The ratio of heights of the two girls = 5:7
Assumption
Consider their height be 5X cm and 7X cm
The height of the first girl = 5X cm
But According to the condition mentioned in given problem
The height of the first girl = 192 cm
=> 5X = 192
=> X = 192/5
=> X = 38.4
Therefore, X = 38.4 cm
Now the height of the second girl = 7X cm
=> 7 × 38.4 cm
=> 268.8 cm
♦ Alternative Method♦ :-
The ratio of the heights of the two girls = 5:7
The height of the first girl = 192 cm
Assume that the height of the second girl = X cm
Therefore, 5:7= 192:X
=> 5/7 = 192/X
=> 5X = 7×192
=> X = (7×192)/5
=> X = 7× 38.4
=> x = 268.8 cm
♦ Answer ♦ :-
The height of the second girl is 268.7 cm
Multiply 2x(x+28)
pls answer asap
Answers
Answer:
2x^2+56x
Step-by-step explanation:
convert 2.3 tn = _______ Ib show your work pls
Answers
Work: 2.3 * 2000
To prove that ΔAED ˜ ΔACB by SAS, Jose shows that StartFraction A E Over A C EndFraction = StartFraction A D Over A B EndFraction.
Triangle A E D is shown. Line segment B C is drawn from side A D to A E to form triangle A C B.
Jose also has to state that
Answers
The other equality which must be stated by Jose is that angles BAC and BAE are congruent and their measures are equal.
What other congruence statements must Jose state?It follows from the task content that Jose is trying to prove the congruence of both triangles by means of the Side-Angle-Side congruence theorem.
It therefore follows that since, Jose has identified that the ratio of corresponding sides are equal as indicated in the task content, the equality which Jose has to state is the angle congruence equality.
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Please help ill give whoever answers the best the brainliest answer ;0
Answers
Answer:
This could be described by the stock market. Suppose you had stock of tesla that went up then flat then down
Step-by-step explanation:
you went for a walk : you started at home, walked away, first slower, then a little bit faster, stayed a little bit first at one place, then started walking back home, stayed a really short time at a second place and finally walked back home.
how to get more brancells?
Answers
Answer:
Read books, watch documentaries, exercise, anything that benefits your body and mind
Step-by-step explanation:
What kind of compound inequality is
4x-5≥3
Or
5-x > 8
?
a. hole
b. intersection
c. conjunction
d. union
Answers
Answer: D) union
======================================================
Explanation:
Let's solve the first inequality for x.
4x-5 ≥ 3
4x ≥ 3+5
4x ≥ 8
x ≥ 8/4
x ≥ 2
Now solve the other inequality
5 - x > 8
5 > 8+x
8+x < 5
x < 5-8
x < -3
The two solutions we get are x < -3 or x ≥ 2
These two regions do not overlap. The key word "or" connecting the original inequalities also applies to the solutions.
Either x is smaller than -3, OR it is 2 or larger
I recommend drawing out a number line and shading the appropriate regions. The two disjoint regions do not connect which means we have a union of the two regions.
The total surface area of this cuboid is 112^2
Find the value of x
length = 10cm
width = 2cm
Hight = x
Answers
The value of x is 3
How to solve for x?The given parameters are:
Length = 10cm
width = 2cm
Height = x
The surface area is calculated as;
Area = 2 *(lw + lh + wh)
So, we have:
2 * (10 * 2 + 2x + 10x) = 112
Evaluate the like terms and divide by 2
20 + 12x = 56
Subtract 20 from both sides
12x = 36
Divide by 12
x = 3
hence, the value of x is 3
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Which expression is equivalent to the following complex fraction? StartFraction negative 2 Over x EndFraction + StartFraction 5 Over y EndFraction divided by StartFraction 3 Over y EndFraction minus StartFraction 2 Over x EndFraction StartFraction negative 2 y + 5 x Over 3 x minus 2 y EndFraction StartFraction 3 x minus 2 y Over negative 2 y + 5 x EndFraction StartFraction x squared y squared Over (negative 2 y + 5 x) (3 x minus 2 y) EndFraction StartFraction (negative 2 y + 5 x) (3 x minus 2 y) Over x squared y squared EndFraction
Answers
The expression that is equivalent to the given complex fraction is; (-2y+5x) / (3x - 2y)
How to simplify algebraic fractions?The given algebraic sentence can be rewritten as;
((-2/x) + (5/y))/((3/y) - (2/x))
The LCM is xy and as such when we put it in the denominators of each fraction, we have:
((-2y + 5x)/xy)/((3x - 2y)/xy)
Putting 'xy' in the numerator and denominator of the whole fraction:
(-2y + 5x)/(3x - 2y)
The final expression we have is (-2y + 5x)/(3x - 2y)
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Answer:
its A -2y+5x ÷ 3x-2y
Step-by-step explanation:
Edge 2022
There are 10 circles and 6 squares. What is the simplest ratio of squares to total
shapes?
Answers
Answer:
The simplest ratio would be 5:3
Step-by-step explanation:
Both 10 and 6 can be divided by 2.
They turn into 5 and 3.
Since you can't make 5 and 3 any smaller, this will be the answer.
5:3
Hope this helped! :D
Resolver y realizar la comprobacion del siguiente sistema de ecuacion aplicando el metodo grafico. [y=3-2x, y=8-7x
Answers
The solution for the system of equations: y = 3 - 2x and y = 8 - 7x, is x = 1, y = 1.
In the question, we are given a system of equations,
y = 3 -2x ... (i), and
y = 8 - 7x ... (ii).
We have been asked to solve the given system of equations.
To solve the system of equations, we do as follows:
Substitute the value of y = 3 - 2x, from (i) in (ii), to get:
y = 8 - 7x,
or, 3 - 2x = 8 - 7x, which is a linear equation in one variable.
To solve this, we follow these steps:
3 - 2x = 8 - 7x,
or, 3 - 2x + 7x = 8 - 7x + 7x {Adding 7x to both side of the equation},
or, 3 + 5x = 8 {Simplifying},
or, 3 + 5x - 3 = 8 - 3 {Subtracting 3 from both sides of the equation},
or, 5x = 5 {Simplifying},
or, 5x/5 = 5/5 {Dividing both sides of the equation by 5},
or, x = 1.
Substituting x = 1, in (i), we get:
y = 3 - 2x,
or, y = 3 - 2(1),
or, y = 3 - 2 = 1.
Thus, the solution for the system of equations: y = 3 - 2x and y = 8 - 7x, is x = 1, y = 1.
Note: The language seemed not gettable.
The question has been done assuming the question asking to solve the system of equations:
y = 3 - 2x, y = 8 - 7x.
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Slope BC and DE are both -0.4 what is their relationship
Answers
My example attached shows slope of 2 for both lines. It would be the same for -0.4 for both lines.
Which solution can be used to fill
in both blanks in the table? (1, 6)
(6, 1)
(7, 6)
(6, 7)
Answers
The solution which can be used to fill in both blanks in the table is; (6,7).
What is the solution for the system?It follows from the task content that the system given has been simplified to the point that;
3x = 18
x = 18/3 = 6.
Hence, the value of y can be evaluated as follows;
2y - x = 8. where (x=6.
2y = 8+6
y = 14/2 = 7.
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How many values of x will satisfy the equation |x-1| = | x+3|
Answers
The value of x that will satisfy the equation is x=-1.
We have given that,
[tex]\left|x-1\right|=\left|x+3\right|[/tex]
We have to solve the above inequality
What is inequality?
Inequality is a relation that makes a non-equal comparison between two numbers or other mathematical expressions.
Find the positive and negative intervals
[tex]x < -3,\:\:-3\le \:x < 1,\:\:x\ge \:1[/tex]
Solve the inequality for each interval
[tex]x < -3,\:\:-3\le \:x < 1,\:\:x\ge \:1[/tex]
[tex]\mathrm{No\:Solution}\quad \mathrm{or}\quad \:x=-1[/tex]
Therefore we get,
[tex]x=-1[/tex]
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What is the main benefit of building a connection with your community
Answers
Answer: Being connected means greater opportunities to learn from each other, mine each other's wisdom, and help each other thrive. Connecting. By being more closely interconnected, each member of the community is able to enjoy a wider, richer network of resources, wisdom, connections, and support.
A line passes through the two points (0, -2) and (9, 1). what is the y y -coordinate of the point on this line whose x x -coordinate is 12? a. -6 b. 0 c. 2 d. 4
Answers
Answer: 2
Step-by-step explanation:
The slope of the line is
[tex]\frac{-2-1}{0-9}=\frac{1}{3}[/tex]
So, the equation of the line is [tex]y=\frac{1}{3}x-2[/tex].
Substituting in x=12,
[tex]y=\frac{1}{3}(12)-2=2[/tex]
Gotta need answers fast like asap, it’s geometry, just fill the blanks pls
Answers
Two or more triangles are said to be congruent if and only if they have equal lengths of sides and equal measures of angles.
Thus, the required proof is as shown below:
STATEMENTS REASONS
1. ΔABC and ΔDEC with AB ≅ DE;
BC ≅ EC; <1 ≅ <2 Given
2. <1 and < ABC; < 2 and <DEC are sup Sum of angles on a straight line
3. <ABC ≅ <DEC Congruent angles of similar triangles
4. ∴ΔABC ≅ ΔDEC Side-Angle-Side (SAS) postulate
5. ∴<ACB ≅ <DCE CPCTC postulate
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Try It #2
Use function notation to express the weight of a pig in pounds as a function of its age in days d.
Answers
Based on the weight of the pig and the age in days, the function notation would be w = f (d).
What function expresses the pig's weight in days old?The function will take the form of:
y = f(x)
y will be the weight and x will be the age of the pig in days.
The function would therefore be:
w = f (d)
In conclusion, the function notation to express the pig's weight is w = f (d).
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