X = 0.6444
Trigonometric Identities are equality statements that hold true for all values of the variables in the equation and that use trigonometry functions.
There are numerous distinctive trigonometric identities that relate a triangle's side length and angle. Only the right-angle triangle is consistent with the trigonometric identities.
The six trigonometric ratios serve as the foundation for all trigonometric identities. Sine, cosine, tangent, cosecant, secant, and cotangent are some of their names. The adjacent side, opposite side, and hypotenuse side of the right triangle are used to define each of these trigonometric ratios. The six trigonometric ratios are the source of all fundamental trigonometric identities.
tan x +sec x =2
⇒sin x /cosx + 1/ cos x = 2
⇒1+sin x / cos x =2
⇒ (sin² x/2 +cos ² x/2 +2 sin x/2 cos x/2 )/( cos ² x/2 - sin²x/2 ) = 2
⇒(cos x/2 +sin x/2)² / ( cos ² x/2 - sin²x/2 ) = 2
⇒( cos x/2+sin x/2)² / (cos x/2 + sin x/2)(cos x/2-sinx/2) = 2
⇒(cos x/2 +sin x/2)/ (cos x/2-sin x/2) = 2
Dividing by cos x/2 in both numerator and denominator,
⇒(1+tan x/2)/(1-tan x/2) =2
⇒ 1 + tan x/2 = 2 - 2tanx/2
⇒ tan x/2 = 1/3
⇒ x= 0.6444
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Use the following information to find x. Write the value of the variable.
B is between A and C;
AB=3x+6;
BC=15x – 2; and
AB≅BC .
Answer:
2/3
Step-by-step explanation:
[tex]AB \cong BC \implies AB=BC \\ \\ 3x+6=15x-2 \\ \\ 6=12x-2 \\ \\ 8=12x \\ \\ x=\frac{2}{3}[/tex]
A student club started a fundraising effort to support animal rescue organizations. The club sent an information flyer home to the n students in the school. It says, "We welcome donations of any amount, including any change you could spare!" Their goal is to raise T dollars, and to donate to a cat shelter and a dog shelter.
Match each quantity to an expression, an equation, or an inequality that describes it.
The dollar amount the club would have if every student at the school donated a quarter to the cause.
The dollar amount the school will raise is given by the expression 0.25n, where n is the number of students.
A combination of terms through addition, subtraction, multiplication, division, and other operations is known as an algebraic expression (or variable expression).
A connection that compares two numbers or other mathematical expressions inequitably is known as an inequality in mathematics.
The dollar amount the club would have if they reached one-fourth of their goal= [tex]\frac{1}{4} T[/tex]The dollar amount the club would have if every student at the school donated a quarter to the cause =[tex]\frac{1}{4} n[/tex]The dollar amount the club could donate to the cat shelter if they reached their goal and gave a quarter of the total donation to a dog shelter= [tex]\frac{3}{4} T[/tex]Therefore the dollar amount the school will raise is given by the expression 0.25n or [tex]\frac{1}{4} n[/tex] , where n is the number of students.
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Help please i do not understand................
Answer:
x = 5
Step-by-step explanation:
All the angles of a triangle add up to 180
83 + 61 + 4x + 16 = 180
160 + 4x = 180
180 - 160 = 4x
20 = 4x
20/4 = x
5 = x
I don’t understand help
The coordinates of the new triangle are P' = (5, 3), K' = (3, 1) and Y' = (1, 4)
How to determine the coordinates of the new triangle?The coordinates of the triangle in the figure are
P = (-5, -3)
K = (-3, -1)
Y = (-1, -4)
The transformation is given as 180 degrees rotation
The rule of this transformation is
(x, y) = (-x, -y)
When this is applied on the triangle, we have the coordinates of the new triangle to be
P' = (5, 3)
K' = (3, 1)
Y' = (1, 4)
Hence, the coordinates of the new triangle are P' = (5, 3), K' = (3, 1) and Y' = (1, 4)
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what is the unit rate for 1/4 kilometer in 1/3 hours
Answer: 0.75km
Step-by-step explanation:
CAN SOMEONE HELP ME ASAP PLEASE I WOULD REALLY APPRECIATE!!!
Answer:
See explanation
Step-by-step explanation:
a. f(x)=|x|
b. |x|==> -|x| ==> f(x) has been flipped over the y-axis.
-|x| ==> -2|x| ==> Then, f(x) doubled by 2, scale factor of 2
-2|x| ==> -2|x|-3 ==> Finally, f(x) became g(x) when it translated 3 units down
c. Use the transformations in part b to graph
Help
Please urgent please help please urgent quick mathematical question
The area occupied by the photograph in terms of x described by the quadratic equation A = x² - 20 · x + 100.
How to derive the expression for the area occupied by the photograph
Both the backing card and the photograph are represented by two concentric squares, the area of the square is equal to the square of the side length. The expression for the area occupied by the photograph is described by the following polynomial:
A = l²
A = (x - 10) · (x - 10)
A = (x - 10)²
A = x² - 20 · x + 100
The area occupied by the photograph in terms of x described by the quadratic equation A = x² - 20 · x + 100.
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Tres canastas tienen 575 manzanas. La primera canasta contiene 10 manzanas más que el segundo y 15 más que el tercero. ¿Cuántas manzanas hay en cada canasta? Jpancho
Step-by-step explanation:
what??? I don't understand what are you saying?????? please speak english :(
i wish you could help you but i don't know what you're saying
Rename the fraction as a decimal.
1/50 =
-
Answer:
0.02
Step-by-step explanation:
Need answers now...................
Answer:
[tex]\sqrt{17}[/tex]
( 3 x 5 + y 2 ) 2 (3x 5 +y 2 ) 2
The value of the expression (3x^5 + y^2)^2 is 9x^10 + 6x^5y^2 + y^4
How to evaluate the expression?The expression is given as:
(3x^5 + y^2)^2
Expand the expression
So, we have
(3x^5 + y^2)^2 = (3x^5 + y^2)(3x^5 + y^2)
Expand the bracket
(3x^5 + y^2)^2 = 9x^10 + 3x^5y^2 + 3x^5y^2 + y^4
Evaluate the sum
(3x^5 + y^2)^2 = 9x^10 + 6x^5y^2 + y^4
Hence, the value of the expression (3x^5 + y^2)^2 is 9x^10 + 6x^5y^2 + y^4
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4. Calculate the area of the triangle.
20 mm
11 mm
In a certain school, there were 180 students in year 7. 110 study french, 88 study german, 65 study indonesian, 40 study both french and german while 38 study german and german only. find the number of students who study all the three languages. also, find the number of students who study indonesian only
The number of students who study Indonesian only = 10
Total pupils= 110
Study French = 88
Study Indonesian = 65
Study French and German = 40
Study German and Indonesian = 38
Study French and Indonesian = 26
Study German only = 19
Students who study German only = G - F∩G - G∩I + F∩G∩I
19= 88-40-38 + F∩G∩I
F∩G∩I = 9
Students who study all three languages = 9
So the students who study only Indonesian = I - F∩I - G∩I + F∩G∩I
= 65- 38-26+ 9
= 10
Therefore the number of students studying Indonesian only = 10.
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The complete question is:
In a certain school, there are 180 pupils in Year 7. One hundred and
ten pupils study French, 88 study German and 65 study Indonesian.
Forty pupils study both French and German, 38 study German and
Indonesian, and 26 study both French and Indonesian, while 19 study
German only. Find the number of pupils who study Indonesian only.
Peyton needs to order some new supplies for the restaurant where she works. The restaurant needs at least 732 forks. There are currently 287 forks. If each sentence on sale contains 10 forks right and solve an inequality which can be used to determine X, The number of sets of forks Peyton could buy for the restaurant to have enough forks
Peyton needs to buy at least 45 sets for the restaurant to have enough forks.
Let the number of sets of forks be represented by 'x'. according to the question there are 10 forks in each set.
Since there are currently 287 forks available in the restaurant, and the restaurant needs at least 732 forks.
The inequality used to represent the given scenario is given by:
10x + 287 ≥ 732
10x ≥ 445
x ≥ 44.5
As Peyton cannot buy 44.5 sets of forks so we round it off to 45.
Therefore, he requires 45 sets in total.
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The function f(x) is given by the set of ordered pairs.
{(1,0), (–10,2), (0,6), (3,17), (–2,–1)}
Answer:
Question? where is a question...that is a statement
What is the value of cosine (startfraction 4 pi over 3 endfraction)? negative startfraction startroot 3 endroot over 2 endfraction negative one-half one-half startfraction startroot 3 endroot over 2 endfraction
The value of Cos(4π/3) is (-1/2) i.e., negative one half.
The given function is Cosine (Start fraction 4 pi over 3 end fraction) and this can be written simply as,
Cos(4π/3)
On splitting 4π/3 in two parts, this can also be written as
= Cos(π + (π/3))
(π + (π/3)) lies in the third quadrant and in the third quadrant the value of cosine function is negative. So, using quadrant sign for cosine function, this can be written as
= -Cos(π/3)
Now, Substitute the value of Cos(π/3) = 1/2.
= (-1/2)
Cos(4π/3) = (-1/2)
The value of Cos(4π/3) is (-1/2) i.e., negative one half.
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Answer:
It's B
Step-by-step explanation:
A middle school took all of its 6th grade students on a field trip to see a ballet at a theater that has 1700 seats. The students filled 442 of the seats in the theater. What percentage of the seats in the theater were filled by the 6th graders on the trip?
Answer:
26%
Step-by-step explanation:
Number of seats by 6th graders / Number of seats in total × 100% = Percentage of seats by 6th graders
442/1700 × 100% = 26%
Hope this helps! ^^
Please help!! Will mark brainliest
Answer:
100°
meron po bang D Wala namn ah
8 Simplify: 7x² + 4x-x²
[tex] \: \Large \mathbb{SOLUTION:}[/tex]
[tex] \: \: \rm{ {7x}^{2} + 4x - {x}^{2}}[/tex]
[tex] \: \: \text{Reorder and gather like terms}[/tex]
[tex] \: \: \rm{( {7x}^{2} - {x}^{2} ) + 4x}[/tex]
[tex] \: \: \text{Collect coeffiecients of like terms}[/tex]
[tex] \: \: \rm{(7 - 1) {x}^{2} + 4x}[/tex]
[tex] \: \: \text{Calculate the sum or difference}[/tex]
[tex] \: \: \rm{ \underline{ \underline{ {6x}^{2} + 4x}}}[/tex]
[tex] \rm{6x {}^{2} + 4x}[/tex]
Solution:Collect like terms
[tex] \red{7x {}^{2} } + 4x \red{ - x {}^{2} }[/tex]
[tex] \red{6x {}^{2} } + 4x [/tex]
Which of the following values is less than −|62|?
Answer:
-63, -90, -1924. -|63|, etc
Step-by-step explanation:
Point (w, z) is transformed by the rule (w 5, z) . what type of transformation occurred?
Scaling transformation onto the x co ordinate by a factor of 5.
What is a co-ordinate system ?A co-ordinate system represents two points one for x axis and another for y axis in a ordered pair (x,y)
According the given question Point (w, z) is transformed by the rule (w5, z).
Here w represents x co-ordinate points and z represents y co-ordinate points.
We can observe that the x co-ordinate point have been scaled by a factor of 5.We can think of that after this transformation the line has become less steeper from origin.
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11/20 in simplest form
Answer:
11/20
Step-by-step explanation:
this fraction is simplified as much as possible and no longer can be simplified. 11/20 is in its simplest form
hope this helps!
EASY PLEASE HELP I NEED ANSWER TO SEVEN
Answer: a, 9x10^9, largest number 900000000
Answer: greatest is A.
Step-by-step explanation:
Evaluate 40-15/t for t=5 step by step
Answer:
37
Step-by-step explanation:
Evaluate 40-15/t for t=5 step by step
first, remember PEMDAS
substitute in 5 for t
40-15/5
since division (D) comes before subtraction (S) in PEMDAS, we divide first
15/5 is 3
we are left with
40-3
if we subtract, we are left with
37
Answer:
37
Step-by-step explanation:
PEMDAS
Parenthesis
Exponents
Multiply
Divide
Add
Subtract
^
This is the order you should complete your problem in...
Two boats are traveling in a canal in opposite directions, where x represents the distance, in feet, between the boats. the equation 2(x 1) = 2x 2 models the paths of the boats. solve for x.
Answer: Hi The Answer is 3 (the third one)
Step-by-step explanation: Am not sure if this is correct am taking the test right now
Answer:
all real numbers
Step-by-step explanation:
Florida
someone please help me with this! i am very confused so explain too :) thank you
Answer: 14/15
Step-by-step explanation:
[tex]9x=10x-x[/tex]
Divide both parts of the equation by 9:
[tex]\displaystyle\\x=\frac{10x-x}{9}\\\\x=0,9333333...\\\\Hence,\\\\x=\frac{10*0,933333...-0,9333333...}{9} \\\\x=\frac{9,333333...-0,933333...}{9} \\\\x=\frac{8,4}{9} \\\\x=\frac{8,4*10}{9*10} \\\\ x=\frac{84}{90}\\\\x=\frac{14*6}{15*6} \\\\ x=\frac{14}{15}[/tex]
A line is perpendicular to y = -x-2
and intersects the point (-5, 10).
What is the equation of this
perpendicular line?
y = x + [?]
The equation of the perpendicular line is y = x + 15.
How to determine the equation of the perpendicular line
In this problem we need to determine the equation of the line perpendicular to another line, that intersects at the point (x, y) = (- 5, 10). The explicit form of the equation of the line is defined by the following first order polynomial:
y = m · x + b
Where:
m - Slopeb - y-Interceptx - Independent variabley - Dependent variableThe first line has a slope - 1 and the slope of the second line is:
m' = - 1 / m
m' = 1
Then, the intercept of the second line is:
b = y - m · x
b = 10 - (- 5)
b = 15
The equation of the perpendicular line is y = x + 15.
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what is an equation of the line shown on the graph in the point-slope form, using the point(1,-1)
The sum of three lengths of a fence ranges from 31 to 40 inches. two side lengths are 9 and 12 inches. if the length of the third side is x inches, write and solve a compound inequality to show the possible lengths of the third side. 31 ≤ x ≤ 40 22 ≤ x ≤ 28 10 ≤ x ≤ 19 9 ≤ x ≤ 12
If two side lengths of a fence are 9 and 12 inches and the sum of the three lengths ranges from 31 to 40 inches, then the length of the third side, x, can be presented by the compound inequality 10 < x < 19.
Inequality refers to the relationship between two non-equal expressions. It can be denoted by > for greater than, < for less than, >/= for greater than and equal to, and </= for less than and equal to.
Given that the sum of the three lengths of a fence ranges from 31 to 40 inches, the inequality can be written as:
31 < sum < 40
If two side lengths are 9 and 12 inches, and let x be the third length, the inequality becomes:
31 < 9 + 12 + x < 40
31 < 21 + x < 40
Subtracting 21 at all sides,
31 - 21 < 21 + x - 21 < 40 - 21
10 < x < 19
Hence, the compound inequality to show the length of the third side can be written as 10 < x < 19.
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a light is suspended at a height h above the floor. the illumination, i, at a point p is inversely proportional to the square of the distance, r, from the point p to the light and directly proportional to the cosine of the angle theta. assume k is the constant of proportionality. which of the following can be used to represent the illumination at point p? i
The light must be at a height of 7.07m from the floor for the maximum illumination at P.
How Distance is that?
Distance is the sum of an object's movements, regardless of direction. Distance can be defined as the amount of space an object has covered, regardless of its starting or ending position.Let I be the illumination at P then according to given conditions,
I = k cosθ/r²
Where k is constant of proportionality: since
r² = h² + 10²
cosθ = [tex]\frac{h}{\sqrt{h^{2} + 10^{2} } }[/tex]
then
I = k [tex]\frac{h}{( h^{2} + 100)^{3/2} }[/tex]
on differentiating
[tex]\frac{dI}{dh} = k \frac{h^{2} + 100)^{3/2} - 3h^{2 ( h^{2} + 100)^{1/2} } }{( h^{2} + 100)^{3} }[/tex]
[tex]= k \frac{( 100 - 2h^{2}) }{( h^{2} + 100)^{5/2} }[/tex]
[tex]\frac{dI}{dh} = 0[/tex]
gives
that is
h = √50 = 7.07
now
[tex]\frac{d^{2I} }{dh^{2} } = k \frac{( 6h^{3} - 900h }{( h^{2} +100)^{7/2} }[/tex]
for h = 7.07
[tex]\frac{d^{2}I }{dh^{2} } = - 10267.6[/tex]
then by second derivative test,I has a maximum ath=7.07
Hence the light must be at a height of 7.07m from the floor for the maximum illumination at P.
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