By applying the definitions of trigonometric functions, the exact values of the sine, secant and tangent of the point on the terminal side are [tex]\sin \theta = \frac{2}{\sqrt{53}}[/tex], [tex]\sec \theta = -\frac{\sqrt{53}}{7}[/tex] and [tex]\tan \theta = -\frac{2}{7}[/tex].
How to determine the exact values
In this question we need to find the exact values of three trigonometric functions associated with the terminal side of an angle. The following definitions are used:
Sine
[tex]\sin \theta = \frac{y}{\sqrt{x^{2}+y^{2}}}[/tex] (1)
Secant
[tex]\sec \theta = \frac{\sqrt{x^{2}+y^{2}}}{x}[/tex] (2)
Tangent
[tex]\tan \theta = \frac{y}{x}[/tex] (3)
If we know that x = - 7 and y = 2, then the exact values of the three trigonometric functions:
Sine
[tex]\sin \theta = \frac{2}{\sqrt{53}}[/tex]
Secant
[tex]\sec \theta = -\frac{\sqrt{53}}{7}[/tex]
Tangent
[tex]\tan \theta = -\frac{2}{7}[/tex]
By applying the definitions of trigonometric functions, the exact values of the sine, secant and tangent of the point on the terminal side are [tex]\sin \theta = \frac{2}{\sqrt{53}}[/tex], [tex]\sec \theta = -\frac{\sqrt{53}}{7}[/tex] and [tex]\tan \theta = -\frac{2}{7}[/tex].
Remark
The statement reports typing errors, correct form is shown below:
Let (x, y) = (- 7, 2) be a point on the terminal side of θ. Find the exact value of sin θ, sec θ and tan θ.
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Name the types of angles shown?
Answer: B and C
Step-by-step explanation:
Let's start off with some definitions.
Supplementary Angles: Two angles that add up to 180°.
Right Angle: One angle equal to 90°. Also identified with a square on the angle.
Complementary Angles: Two angles that add up to 90°.
Straight Angle: A straight line, which equals to 180°.
Right off the bad, we can knock off A and D because there is no proof of those being seen.
The angle <EFH is a right angle because it is equal to 90°. If you pay close attention, the angles <EFG and <GFH both add up to 90°, making them complementary angles.
Therefore, the correct answers are B and C.
I hope this helps! Pls mark brainliest!! :)
The circumference of a circle is 237 cm.
What is the area, in square centimeters?
Express your answer in terms of T.
Answer:
Circumference of a circle = 2 pie r
237 = 2 * pie * r
237 / 2 * Pie
118.5/ pie = r
118.5 = Pie*r
Area of circle = Pie *r²
= Pie r * r
= 118.5 * 118.5/ Pie
= 118.5 * 118.5 / pie
= 14042.25/ pie
taking value of pie = 3.14
= 4472.05 sq. cm
A box in the shape of a rectangular prism has a width that is 5 inches greater than the height and a length that is 2 inches greater than the width. Write a polynomial expression in standard form for the volume of the box. Explain the meaning of any variables used.
The volume of the rectangular prism can be express in standard polynomial as follows:
x³ + 12x² + 35x
How to find the volume of a rectangular prism?volume of a rectangular prism = lwh
where
l = lengthw = widthh = heightTherefore,
let
height = x
width = x + 5
length = x + 5 + 2 = x + 7
Therefore,
volume = x(x + 5)(x + 7)
volume = x(x² + 7x + 5x + 35)
volume = x(x² + 12x + 35)
volume = x³ + 12x² + 35x
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Solve the equation.
3/4x+3-2= -1/4+1/2x+5
Answer:
15
Step-by-step explanation:
3x/4+1=19/4+1x/2
3x/4-x/2=19/4-1
x/4=15/4
collect like terms
x=15
Which function represents the inverse of function f?
Answer: Choice [B]
Step-by-step explanation:
Hii, I'd love to help you out! (:
This particular problem is all about finding inverse functions.
This can be done in 3 easy steps, which are shown below.
Replace f(x) with ySwitch x and y placesSolve for yThe process is shown below.
[tex]\multimap\quad \tt f(x)=3x+5 \\ y=3x+5\\ x=3y+5\\Solve\;for\;y[/tex]
[tex]\multimap\quad \tt x=3y+5\\x-5=3y\\\cfrac{x-5}{3}=y[/tex]
Why doesn't our answer show up among the answer choices? Has all of our hardwork been in vain?
Ofc not! There's just one more thing that can be done to simplify our answer.
[tex]\tt \cfrac{x}{5}-\cfrac{5}{3}[/tex]
We're getting closer!
[tex]\tt \cfrac{1}{3}x-\cfrac{5}{3}[/tex]
Voila! There's our answer, cheers! (;
________________
Hope I helped!
Best wishes.
Reach far.
Aim high.
Dream big.
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The sin (0) = - and lies in Quadrant III. Find the exact values of the sine
6'
and cosine of 20.
Answer:
Can you give exanation
I don't understand
If a gas filled balloons rises 40 feet in the 1 minutes, 60 feet in the 2 minute, and 80 feet in the 3 minute, how many feet will the balloon rise during the 15 minute
Answer:
600
Step-by-step explanation:
15*40=600
Dixie lives in a $67,000 wood house in the country whose contents are valued at $12,000. She wants to know her monthly property insurance premium. Use the table above to calculate her monthly property insurance premium.
Without the table indicating the stated premium rates and applicable discounts, the monthly property insurance cannot be computed. Hence, on the assumption that the rate is 2.5% and the discount applicable is 7.5% the premium per month will come to $152.24
What is Property Insurance?
The simple definition of Property Insurance is, it is an insurance policy that covers a policyholder for the structure of a building and its contents against stated or agreed perils.
What is the calculation for the above?Given (based on assumption) that the applicable annual rate is 2.5%
and that:
Value of Wooden House = $67,000Value of the contents of the House = $12,000Applicable discount = 7.5% of premium/annumHence annual premium will be:
= (67,000 + 12000) * (2.5/100) * 0.925
Annual Premium Payable = $1,826.89.............A
Recall that we are asked to derive the monthly Insurance premium.
This is thus given as: Answer in A/12
→ 1,826.89/12
= $152.24
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Write the ratio using fraction notation and reduce.
HINT: Be sure to compare like units.
$5 to $35
A. 7
B. 15
C. 5
D. 17
The ratio using fraction notation of $5 to $35 would be 7.
What is a fraction?A fraction represents a part of a number or any number of equal parts.
To convert a ratio into a fraction,
We will simply use the first number as the numerator and the second number as the denominator.
So the fraction = 35/5.
= 7
Since there are no more common factors, the fraction is in its lowest form which is 7.
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PLEASE HELP! SO CONFUSED! 25 POINTS!!
Answer:
D
Step-by-step explanation:
(f • g)(x)
= f(x) × g(x)
= (x + 4)(3x² - 7)
each term in the second factor is multiplied by each term in the first factor , that is
x(3x² - 7) + 4(3x² - 7) ← distribute both parenthesis
= 3x³ - 7x + 12x² - 28
= 3x³ + 12x² - 7x - 28 ← in standard form
Here is a rectangle.
A (-3,0)
D(-2,-3)
B (3,2)
C (4,-1) What is CD unit number?
Step-by-step explanation:
Let the area of rectangle with given points are as follows :
A(-3,3)
B(3,2)
C(4,-1) = C( x1,y1)
D(-2,-3) = D( x2, y2)
Now,
The distance of CD = root under(x2-x)^2 +( y2 - y1)^2
= root under (-2-4)^2 + ( -3+1)^2
= root under (-6)^2 + (-2)^2
= root under 36 + 4
= root under 40
= 2root 10
Therefore; the unit number if CD is 2 root 10.
Box y, box y, and box z each contain a pencil and a highlighter. An item is drawn randomly from each box. A) Draw a tree diagram to represent the possible outcomes.
B) Determine the probability that the items drawn are two pencils and one highlighter.
The probability that the items drawn are two pencils and one highlighter is 0.25
How to draw the tree diagramTo do this, we make use of the following representations:
P represents PencilsT represents HighlightersSince there are three boxes, the number of possible outcomes is:
Outcomes = 2³
Outcomes = 8
See attachment for the tree diagram.
How to determine the probability?From the tree diagram, we have:
Outcomes = 8Two pencils and one highlighter (PPT) = 2So, the probability is:
P = 2/8
Evaluate
P = 0.25
Hence, the probability that the items drawn are two pencils and one highlighter is 0.25
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1. Kelsey spent 55 hours over 2 weeks working on a ELA project. She worked 32 hours the
Answer:
23
Step-by-step explanation:
If Kelsey spent 32 hours in the first week. We subtract 32 from 55. 55-32=23. That means she worked 23 hours in the second week.
Please help me answer question 8/11 asap
The value of a₄₁ mean the expression in 4th row and 1st column will be 2. Then the correct option is B.
The complete question is attached below.
What is the matrix?A matrix is a specific arrangement of items, particularly numbers. A matrix is a row-and-column mathematical structure. The [tex]\rm a_{ij}[/tex] element in a matrix, such as M, refers to the i-th row and j-th column element.
The matrix is given below.
[tex]\begin{bmatrix} 1&3&8&5&\\ 5&4&6&2\\6&7&1&8\\2&9&3&7&\\\end{bmatrix}[/tex]
Then the value of a₄₁ mean the expression in 4th row and 1st column will be 2.
Then the correct option is B.
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Select the correct answer.
In the given figure, m AD = 79° and m
Answer:
2 or 3
Step-by-step explanation:
write it down dummy
Expand and simplify x(x + 2)(x + 4)
Answer:
Step-by-step explanation:
Comment
Expand the second and 3rd factors first. Then worry about the x.
Solution
x(x + 2)(x + 4)
first: x * x = x^2
Outside: 4*x = 4x
Inside: 2*x = 2x
Last: 2*4 = 8
Combine
x^2 + 4x + 2x + 8
x^2 + 6x + 8
Now is the time to worry about the extra x
x(x^2 + 6x + 8)
remove the brackets.
x*x^2 + x*6x + 8*x
Combine
Answer: x^3 + 6x^2 + 8x
The graph of a line goes up and to the right when:
When the coefficient of x is positive, the graph of a line rises and moves to the right. Option C is correct.
What is a graph?A diagram depicting the relationship between two or more variables, each measured along with one of a pair of axes at right angles.
The complete question is
"The graph of a line goes up and to the right when:
a) the coefficient of x is 0
b) the coefficient of x is negative
c) the coefficient of x is positive
d) there is no coefficient of x"
When the coefficient of x is positive, we know that the graph of a line will move upward and to the right.
Since we are aware that a line's upward and rightward movement indicates that the line is advancing, we will obtain a positive slope for the line, and we are also aware that the slope-intercept of a line is provided as:
y= mx+c
If m is a positive number, then positive is the coefficient of x.
The graph of a line goes up and to the right when the coefficient of x is positive.
Hence option C is correct.
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Let f(x)=6/-2+2e^-0.3x. what is f(4)? enter your answer rounded to the nearest tenth
The value of the function f(x)=6/-2+2[tex]e^{-0.3x}[/tex] at x=4 after rounded to the nearest tenth is -2.4.
Given Function of x : f(x)=6/-2+2[tex]e^{-0.3x}[/tex]
The given function showing the relationship between x and f(x) is f(x)=6/-2+2[tex]e^{-0.3x}[/tex] where e is exponential and we have to find the value of f(4) by just putting the value of x=4 in the given function and round to the nearest tenth means replacing a number with an approximate value.
f(4)=6/-2+2[tex]e^{-0.3*4}[/tex] ( The value of e is 2.7812)
f(4)=-3+2[tex]e^{-1.2}[/tex]
f(4)=-3+2*0.30119 (The value of [tex]e^{-1.2}[/tex] is 0.30119)
f(4)=-3+0.60238
f(4)=-2.3972
Round -2.3972 to tenth is -2.4.
Hence the value of function of at x=4 is -2.4.
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The value of f(4) is -4.3.
The function is a relation between two different sets X and set Y which are in one-one or many-one relation. Here set X is called as the domain and set Y is called as the codomain.
For example: f(x)=3x+9
To get the value of the function at any point of x, we have to put the number in the function to get its function value.
For example the value of f(x) in above function at x=a will be f(a)=3a+9
Similarly given function in the question
[tex]f(x)=\frac{6}{-2+2e^{-0.3x}}[/tex]
to get the value of f(x) at x=4 put the value of x in the function,
[tex]f(x)=\frac{6}{-2+2e^{-0.3*4}}[/tex]
⇒[tex]f(x)=\frac{6}{-2+2e^{-1.2}}[/tex]
⇒f(x)=-4.3
Therefore the value of f(4) is -4.3.
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An airplane can seat up to 175 passengers. The airline has already sold 87 tickets for a flight on the airplane. Which graph represents the solution to the inequality that finds the number of tickets the airline can still sell?
The inequality x ≤ 88 represents the situation, and the line graph first represents the solution to the inequality option first is correct.
What is inequality?
It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.
The missing options are in the picture, please refer to the picture.
We have:
An airplane can seat up to 175 passengers. The airline has already sold 87 tickets for a flight on the airplane.
Let's suppose the number of tickets is represented by x
Total number of passengers = 175
The inequality can be framed:
x + 87 ≤ 175
x ≤ 88
Thus, the inequality x ≤ 88 represents the situation, and the line graph first represents the solution to the inequality option first is correct.
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Given the function f(x) = −5x2 − x + 20, find f(3).
which of the sentence is true?
Answer:
The graph of the circle is not a function
What is the measure of the unknown angle?
straight angle divided into a one hundred thirty two degree angle and an unknown angle
48°
49°
51°
53°
Determine f(4) for A piecewise function f of x in three pieces. The function is defined by part 1, which is x cubed for x less than negative 3, part 2, which is 2 times x squared minus 9 for negative 3 is less than or equal to x which is less than or equal to 4, and part 3 which is 5 times x plus 4, for x greater than 4..
23
24
41
64
Answer:
23
Step-by-step explanation:
seen it before
On a coordinate plane, a right triangle has points A (negative 5, negative 6), B (negative 5, negative 2), C (negative 2, negative 2). Examine the right triangle ABC. Which rise and run would create a similar right triangle on the same line? a rise of 6 and a run of 8 a rise of 8 and a run of 6 a rise of 6 and a run of 5 a rise of 5 and a run of 6
A rise of 8 and a run of 6. Then the correct option is B.
What is a coordinate geometry?Coordinate geometry is the study of geometry using the points in space.
On a coordinate plane, a right triangle has points A (-5, -6), B (-5, -2), and C (-2, -2).
The distance between AB will be
AB² = (-5 + 5)² + (-2 + 4)²
AB² = 4²
AB = 4
The distance between BC will be
BC² = (-2 + 5)² + (-2 + 2)²
BC² = 3²
BC = 3
Then the rise and run will be
rise / run = 4 / 3
Then this can be written as
rise / run = 8 / 6
Then the correct option is B.
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Solve the simultaneous equations
2
x
+
3
y
=
5
5
x
−
2
y
=
−
16
Answer:
x = -2, y = 3
Step-by-step explanation:
2x + 3y = 5
5x - 2y = -16
In order to find the value of a variable, we must eliminate the other variable by multiplying the equations to get the same coefficient.
We can multiply the first equation by 5 and the second one by 2 to get the same coefficient for x, the equations then become:
10x + 15y = 25
10x - 4y = -32
Now we can subtract:
19y = 57
y = 3
Since we know the value of y, we can substitute it into one of the original equations:
2x + 3(3) = 5
2x + 9 = 5
2x = -4
x = -2
tony invest 2000 at a 4.5 percent rate.
Answer:
$2,999
Step-by-step explanation:
A = P(1 + r) ^ tA = 2000(1 + .045) ^ 9A ≈ 2999FACTOR THE EXPRESSION GIVEN BELOW. WRITE EACH FACTOR AS A POLYNOMIAL IN DESCENDING ORDER. ENTER EXPONENTS USING THE CARET (^). FOR EXAMPLE, YOU WOULD ENTER x TO THE POWER OF 2 AS x^2.
343x^3 + 216y^3
Each given factor written as a polynomial in descending order is; (7x + 6y)(49x² - 42xy + 36y²)
How to factorize Polynomials?We are given the polynomial;
343x³ + 216y³
343x³ + 216y³ is a sum of cubes and factors in general as;
a³ + b³ = (a + b)(a² - ab + b²)
Thus;
343x³ + 216y³ = (7x)³ + (6y)³
= (7x + 6y)((7x)² - 7x(6y) + (6y)² )
= (7x + 6y)(49x² - 42xy + 36y²)
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Kitchen chairs are purchased wholesale for $36 each by a discount furniture store. Then, the store marks up the chairs by 60 percent. The store has a special sale where all items are marked down by 20 percent. How much would two chairs cost during the sale?
$46.08
$57.60
$92.16
$115.20
Drag the boxes to order the decimals from least to greatest from left to right.
316.011
306.324
306.359
Answer:
306.324
306.359
316.011
Step-by-step explanation:
Hope it helped!
What are the solutions to the following system of equations?
y = x² + 7x-5
2x - y = -9
Answer:
Step-by-step explanation:
y = x² + 7x - 5 ............ (1)
2x - y = - 9 ................ (2)
(1) ------> (2)
2x - ( x² + 7x - 5 ) = - 9
- x² - 5x + 14 = 0 ........ (3)
- 1 × (3)
x² + 5x - 14 = 0
( x + 7 )( x - 2 ) = 0
[tex]x_{1}[/tex] = - 7 and [tex]x_{2}[/tex] = 2
2( - 7) - [tex]y_{1}[/tex] = - 9 ⇒ [tex]y_{1}[/tex] = - 5
2(2) - [tex]y_{2}[/tex] = - 9 ⇒ [tex]y_{2}[/tex] = 13
The solutions of system are
( - 7, - 5 ) and ( 2, 13 )
