Answers
The values of the trigonometric functions are
7. [tex]sin\theta = \frac{12}{13}[/tex]
[tex]cos\theta = \frac{5}{13}[/tex]
[tex]tan\theta = \frac{12}{5}[/tex]
[tex]csc\theta =\frac{13}{12}[/tex]
[tex]sec\theta =\frac{13}{5}[/tex]
[tex]cot\theta =\frac{5}{12}[/tex]
8. [tex]sin\theta = \frac{\sqrt{7} }{4}[/tex]
[tex]cos\theta = \frac{12}{16}[/tex]
[tex]tan\theta =\frac{\sqrt{7} }{3}[/tex]
[tex]csc\theta = \frac{4}{\sqrt{7} } \ OR \ \frac{4\sqrt{7}}{7}[/tex]
[tex]sec\theta =\frac{16}{12}[/tex]
[tex]cot\theta = \frac{3}{\sqrt{7}} \ OR \ \frac{3\sqrt{7}}{7}[/tex]
Trigonometric functionsFrom the question, we are to determine the values of the given trigonometric functions
7.
In the given triangle,
Opposite = 12
Adjacent = 5
Hypotenuse = ?
Hyp² = Opp² + Adj² (Pythagorean theorem)
∴ Hyp² = 12² + 5²
Hyp² = 144 + 25
Hyp² = 169
Hyp =√169
Hyp = 13
Using SOH CAH TOA
[tex]sin\theta = \frac{12}{13}[/tex]
[tex]cos\theta = \frac{5}{13}[/tex]
[tex]tan\theta = \frac{12}{5}[/tex]
[tex]csc\theta =\frac{1}{sin\theta} =\frac{13}{12}[/tex]
[tex]sec\theta =\frac{1}{cos\theta} =\frac{13}{5}[/tex]
[tex]cot\theta =\frac{1}{tan\theta} =\frac{5}{12}[/tex]
8.
Hypotenuse = 16
Adjacent = 12
Opposite = ?
Hyp² = Opp² + Adj² (Pythagorean theorem)
Opp² = Hyp² - Adj²
∴ Opp² = 16² - 12²
Opp² = 256 - 144
Opp² = 112
Opp =√112
Opp = 4√7
Using SOH CAH TOA
[tex]sin\theta = \frac{4\sqrt{7} }{16} = \frac{\sqrt{7} }{4}[/tex]
[tex]cos\theta = \frac{12}{16}[/tex]
[tex]tan\theta = \frac{4\sqrt{7} }{12}= \frac{\sqrt{7} }{3}[/tex]
[tex]csc\theta =\frac{1}{sin\theta} =\frac{16}{4\sqrt{7} } = \frac{4}{\sqrt{7} } \ OR \ \frac{4\sqrt{7}}{7}[/tex]
[tex]sec\theta =\frac{1}{cos\theta} =\frac{16}{12}[/tex]
[tex]cot\theta =\frac{1}{tan\theta} =\frac{12}{4\sqrt{7}} = \frac{3}{\sqrt{7}} \ OR \ \frac{3\sqrt{7}}{7}[/tex]
Hence, the values of the trigonometric functions are
7. [tex]sin\theta = \frac{12}{13}[/tex]
[tex]cos\theta = \frac{5}{13}[/tex]
[tex]tan\theta = \frac{12}{5}[/tex]
[tex]csc\theta =\frac{13}{12}[/tex]
[tex]sec\theta =\frac{13}{5}[/tex]
[tex]cot\theta =\frac{5}{12}[/tex]
8. [tex]sin\theta = \frac{\sqrt{7} }{4}[/tex]
[tex]cos\theta = \frac{12}{16}[/tex]
[tex]tan\theta =\frac{\sqrt{7} }{3}[/tex]
[tex]csc\theta = \frac{4}{\sqrt{7} } \ OR \ \frac{4\sqrt{7}}{7}[/tex]
[tex]sec\theta =\frac{16}{12}[/tex]
[tex]cot\theta = \frac{3}{\sqrt{7}} \ OR \ \frac{3\sqrt{7}}{7}[/tex]
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Related Questions
[tex]\huge\fbox\purple{Question}[/tex]
1)Find the H.C.F of the following set of numbers by finding all the possible factors.
a)6 and 15
b)12 and 18
c)15 and 24
d)24 and 36
e)30 and 48
f)36 and 54
g)32,40 and 56
h)28,42 and 70
I)30,75 and 90
Note=
Answer with proper explanation required and all steps to be mentioned .
Answers
The HCF are
3631261881415What is HCF?This is the common factor that is the highest that a group of numbers can have in common.
1. 6 and 15
factors of 6 = 1, 2, 3, 6
factors of 15: 1, 3, 5, 15
The HCF is the number they have in common = 3
2. 12 and 18
The factors of 12: 1, 2, 3, 4, 6, 12
The factors of 18: 1, 2, 3, 6, 9, 18
The HCF = 6
3. 15 and 24
Factors of 15: 1, 3, 5, 15
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
The HCF = 3
4. 24 and 36
The factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
The factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
The HCF : 12
5. 30 and 48
The factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
The factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
The HCF = 6
6. 36 and 54
The factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
The factors of 54: 1, 2, 3, 6, 9, 18, 27, 54
The hcf = 18
7. 32,40 and 56
The factors of 32: 1, 2, 4, 8, 16, 32
The factors of 40: 1, 2, 4, 5, 8, 10, 20, 40
The factors of 56: 1, 2, 4, 7, 8, 14, 28, 56
The HCF is 8
8. 28,42 and 70
The factors of 28: 1, 2, 4, 7, 14, 28
The factors of 42: 1, 2, 3, 6, 7, 14, 21, 42
The factors of 70: 1, 2, 5, 7, 10, 14, 35, 70
The HCF = 14
9. 30,75 and 90
The factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
The factors of 75: 1, 3, 5, 15, 25, 75
The factors of 90: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90
The HCF is 15
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help me quik please!! 20 points
Answers
Because 6 times six is 36
Minus 2 times 4 is 8
36-8 is
28
There are 135 people in a sport centre. 77 people use the gym. 62 people use the swimming pool. 65 people use the track. 27 people use the gym and the pool. 23 people use the pool and the track. 31 people use the gym and the track. 4 people use all three facilities. Given that a randomly selected person uses the gym and the track, what is the probability they do not use the swimming pool
Answers
The probability that the person uses the gym and track but not the pool is; 1/5.
What is the probability that a person uses the gym and track but not the pool?According to.the task content, it follows that 31 people use the gym and track while 4 people use all three facilities.
Hence, it follows that; 31-4 = 27 people use the gym and track but not the pool. On this note, the required probability is; 27/135 = 1/5.
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19. For the following exercises, use the descriptions of each pair of lines given below to find the slopes of Line 1 and Line 2. Is each pair of lines parallel, perpendicular, or neither?
19. Line 1: Passes through (-8, -55) and (10, 89)
Line 2: Passes through (9, -44) and (4, -14)
Answers
Answer:
The given lines are un-related.
Step-by-step explanation:
In the question, two lines are given as line 1 passes through (-8,-55) and (10,89). Whereas, line 2 passes through (9,-44) and (4,-14).
It is required to find the slope of given lines and figure out whether they are perpendicular, parallel or neither.
To solve this question, first find the slope of both lines. Check if their product is equal to -1, then they are perpendicular. If the slopes are equal the lines are parallel.
Step 1 of 2
Find the slope of first line.
[tex]$$\begin{aligned}&m_{1}=\frac{89-(-55)}{10-(-8)} \\&m_{1}=\frac{144}{18} \\&m_{1}=8\end{aligned}$$[/tex]
Step 2 of 2
Find the slope of first line.
[tex]$$\begin{aligned}&m_{2}=\frac{-14-(-44)}{4-9} \\&m_{2}=\frac{30}{-5} \\&m_{2}=-6\end{aligned}$$[/tex]
Since, both slopes are neither equal nor reciprocal of each other.
Therefore, the lines are un-related.
The given diagram shows the steps for constructing a line parallel to line AB and passing through point P, but an error has occurred in the construction. What needs to be corrected in the diagram to fix the error? A. The third arc should be drawn centered at point F. B. A fourth arc needs drawn so that it passes through point P. C. The second arc should be drawn centered at point D. D. The first arc should pass through point B.
Answers
Construction is a process in which required steps are considered to draw a given shape by the use of construction instruments and materials. Thus to correct the error in the given question, the third arc should be drawn centered at point F. Answer is option A.
Majorly, the use of a straight edge and a pair of compasses to draw the image of a given object is referred to as construction. Which required adhering to some steps.
The construction of a parallel line through a given point to a given line involves following the appropriate procedure. If not, an error would be committed which would result in an inappropriate shape or figure.
Therefore, to fix the error in the given question, it is important that the third arc should be drawn centered at point F. Thus, the correct answer is option A.
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Given the equation startfraction 2 x 2 over y endfraction = 4 w 2 what is the value of x?
Answers
The value of x is 2wy + y - 1.
Given: (2x + 2)/y = 4w + 2
To find: the value of x
the following steps will be used.
First, Multiply both sides by y
y * (2x + 2)/y = (4w + 2) * y
2x + 2 = 4wy + 2y
Subtract 2 from both sides
2x + 2 - 2 = 4wy + 2y - 2
2x = 4wy + 2y - 2
Multiply both sides by ½
½ * 2x = ½(4wy + 2y - 2)
x = ½(4wy + 2y - 2)
Open bracket
x = ½ * 4wy + ½ * 2y - ½ * 2
x = 2wy + y - 1
Hence, the value of x is 2wy + y - 1.
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use the geometric model to factor 3x^2+4x+1
Answers
The geometric model to factor 3x²+4x+1 can be shown as given below in the form of geometric tiles.
\What is a quadratic equation?A quadratic equation is an equation whose leading coefficient is of second degree also the equation has only one unknown while it has 3 unknown numbers. It is written in the form of ax²+bx+c.
The geometric model to factor 3x²+4x+1 can be shown as given below in the form of geometric tiles.
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Marissa is painting her rectangular patio, with the exception of a bench that does not need to be painted: rectangle with a length of x plus 15 and width of x plus 10 with a rectangle in the bottom right corner labeled bench that has a length of 5 and width of 1 write an equation to determine the area, a, of the patio that will be painted. a = (x 20)(x 11) a = (x 15)(x 10) 5 a = (x 15)(x 10) − 5 a = (x 9)(x 10)
Answers
The equation which determines the painted area is (x+15)(x+10)-5.
Given that there is a rectangle with a length of x plus 15 and width of x plus 10 with a rectangle in the bottom right corner labeled bench that has a given length of 5 and width of 1.
A rectangle is a two-dimensional (2D) form in which the four angles are all right angles and the opposite sides are parallel and equal to one another. The region that the rectangle's perimeter encloses is known as its area, which is equal to the product of its length and width.
Let the length of the patio be L=x+15.
The width of the patio be W=x+10.
So, the Area of the patio will be painted is, A₁=L×W
A₁=(x+15)(x+10)
Let the Length of the bench be L₁=5
The width of the bench be W₁=1
So, the Area of the bench will be painted is, A=L₁×W₁
A₂=5×1
A₂=5
The net area of the patio that will be painted is
A=A₁-A₂
A=(x+15)(x+10)-5
Hence, the equation which is used determines the area, A, of the patio that will be painted is (x+15)(x+10)-5.
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4 12-sided dice are rolled. What is the probability that the number of dice showing a two digit number is equal to the number of dice showing a one digit number
Answers
Probability means Possibility. It states how likely an event is about to happen. The probability of an event can exist only between 0 and 1 where 0 indicates that event is not going to happen i.e. Impossibility and 1 indicates that it is going to happen for sure i.e. Certainty.
I'll take a stab at this one. if the number of dice showing a two-digit number = the number of dice showing a one-digit number, then 2 must show a two-digit number and 2 must show a one-digit number
There are 3 two-digit numbers and 9 one-digit numbers on each die
So....the probability is
C(4,2) (3/12)^2 (9/12)^2 =
C(4,2) (1/4)^2 (3/4)^2 =
27/128.
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A company invests $32000. after 4 years of growth at the same rate each year, the investment is worth $42692. find the annual growth rate as a percentage.
Answers
Answer:
R = 33.35%
Step-by-step explanation:
that is the solution above
Four teachers offer an after-school chess club the table shows the number of students who joined
Answers
Because you make a "half circle" when you bisect an angle, neither a ruler nor a compasses are needed. Because a bisected angle wouldn't be straight, you wouldn't need either of the two.
Teams of no more than six pupils will be formed from the total group of participating students by the teachers.
What is the smallest number of teams that may be formed with every student?Four teachers offer an after-school chess club the table shows the number of students who joined In the box, type your response. teams Part B With 18 chess sets at its beginning, the chess club. Three cases of 15 chess sets were ordered by the professors. To provide each teacher an equal number of chess sets, they will divide the total number of chess sets. Any extra sets will then be donated to the school library.
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If the zeros of a quadratic equation are -3
and 5, what would be the x-intercepts?
Answers
Answer:
To find the x-intercepts of a quadratic equation, let y = 0. Write down the new equation ax squared + bx + c = 0 and the quadratic formula that gives the solution as x = -b plus or minus the square root of (b squared - 4ac), all divided by 2a.
Step-by-step explanation:
Hope this helps.
Answer:
-3, 5
Step-by-step explanation:
The x-intercepts are the same as the zeros.
A single card is drawn from each of two decks of 52 cards. What is the probability of getting a heart from the first deck and then a diamond on the second deck?
A. 0.09%
B. 6.25%
C. 13%
D. 52%
Answers
Probability helps us to know the chances of an event occurring. The correct option is A.
What is Probability?Probability helps us to know the chances of an event occurring.
[tex]\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]
The probability of getting a heart from the first deck is 13/52. And the probability of getting a diamond from the second deck is 13/52. The probability of getting a heart from the first deck and then a diamond on the second deck is,
Probability = (13/52) × (13/52) = 0.0625 = 6.25%
Hence, the correct option is A.
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you have two exponential functions. one has the formula h(x)=2^x +3. the other function, g(x), has the graph shown below. which equation or inequality below is true
g(2)>h(2)
g(2)>h(2)=7
g(7)=h(7)=2
g(2)
please i rlly need helpppppp!!!!
Answers
The true equation about the functions is (d) g(2) = h(2) = 7
How to determine the true statement?The graph that completes the question is added as an attachment
The function is given as:
h(x) = 2^x + 3
Calculate h(2) and h(7)
h(2) = 2^2 + 3 = 7
h(7) = 2^7 + 3 = 131
From the graph, we have:
g(2) = 7
g(7) = 610
By comparison, we have:
g(2) = h(2) = 7
Hence, the true equation is (d) g(2) = h(2) = 7
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can you please help with these two gradient questions I'm giving brainliest :)
Answers
The line with a gradient of 6 is line A, and the gradient of line A is 4
The line with a gradient of 6The gradients are given as:
-0.5, 0, 2 and 6
A line with a negative gradient (i.e. -0.5) would decrease as the x values increase.
This is represented by line D
A line with a 0 gradient is a horizontal line
This is represented by line C
The line closer to the y-axis have a higher gradient.
This means that line A has a higher gradient than line B, because of its proximity to the y-axis
Hence, the line with a gradient of 6 is line A
The gradient of line AThe gradient of line B is given as:
Gradient = 4
Line A and line B are parallel lines
Parallel lines have the same gradient
Hence, the gradient of line A is 4
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What is the formula for the sum of the first n terms in the following sequence in terms of n:
1, 1+2, 1+2+2^2, 1+2+2^2+2^3, ...
Answers
Let [tex]S_n[/tex] be the [tex]n[/tex]-th term in this sequence, so
[tex]S_1 = 1[/tex]
[tex]S_2 = 1 + 2[/tex]
[tex]S_3 = 1 + 2 + 2^2[/tex]
and so on, with general [tex]n[/tex]-th term
[tex]S_n = 1 + 2 + 2^2 + \cdots + 2^{n-1} = \displaystyle \sum_{i=1}^n 2^{i-1}[/tex]
Observe that
[tex]2 S_n = 2 + 2^2 + 2^3 + \cdots + 2^n[/tex]
and by subtracting this from [tex]S_n[/tex], we eliminate all but the outermost terms, namely
[tex]S_n - 2S_n = 1 - 2^n[/tex]
so that
[tex]-S_n = 1 - 2^n[/tex]
[tex]S_n = 2^n - 1[/tex]
Now, the sum of the first [tex]n[/tex] terms of the sequence [tex]\{S_1,S_2,S_3,\ldots,S_n\}[/tex] is
[tex]S = S_1 + S_2 + S_3 + \cdots + S_n[/tex]
[tex]S = \displaystyle \sum_{i=1}^n S_i[/tex]
[tex]S = \displaystyle \sum_{i=1}^n (2^i - 1)[/tex]
[tex]S = \displaystyle \sum_{i=1}^n 2^i - \sum_{i=1}^n 1[/tex]
[tex]S = \displaystyle 2 \underbrace{\sum_{i=1}^n 2^{i-1}}_{S_n} - n[/tex]
[tex]S = 2(2^n - 1) - n[/tex]
[tex]S = \boxed{2^{n+1} - n - 2}[/tex]
What is the opposite of –(–24)
And, what is the opposite of +(+15)
Answers
Answer:
Step-by-step explanation:
hello :
the opposite of +(+15) is : +(-15)
the opposite of -(-24) is : +(-24)
I need some help please
What is the equation of the function shown in the graph?
Answers
Answer:
y = -2x+2
Step-by-step explanation:
See attached image
Consider the following system of linear inequalities and corresponding graph:
Answers
The solution to the graph is the yellow area highlighted in the graph. The point (2, 0) is a solution since it lies on the yellow area.
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
The compound inequality represented by the graph is y ≥ 2x - 4, x > -3 and y < 5.
The solution to the graph is the yellow area highlighted in the graph. The point (2, 0) is a solution since it lies on the yellow area.
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Which descriptions from the list below accurately describe the relationship
between AABC and ADEF? Check all that apply.
E
5/37
53
A 3 C D
10
53
6
37
A. Same area
B. Same size
8
C. Congruent
D. Congruent after a dilation
Answers
Triangle ABC was dilated to form triangle DEF, hence both triangles have the same shape and are similar.
What is transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformations are reflection, translation, rotation and dilation.
Rigid transformation preserves the shape and size of the figure. Reflection, translation, rotation are rigid transformations.
Dilation preserves the shape but not the size.
Triangle ABC was dilated to form triangle DEF, hence both triangles have the same shape and are similar.
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Which pair of complex numbers has a real-number product? (1 3i)(6i) (1 3i)(2 – 3i) (1 3i)(1 – 3i) (1 3i)(3i)
Answers
Answer:
(1+3i)(1-3i)
Step-by-step explanation:
When these terms have the same pair of numbers in them, but one set has a PLUS and one set has a MINUS, these are called CONJUGATES.
When you multiply CONJUGATES, you will eliminate the imaginary number, i.
Remember i^2=-1
see image.
Choose the most convenient method to graph the line 3x−2y=−12.
Select the correct answer below:
Recognize the equation as that of a vertical line passing through the x-axis at −12.
Recognize the equation as that of a horizontal line passing through the y-axis at −12.
Identify the slope and y-intercept, and then graph.
Find the x- and y-intercepts and then graph.
Answers
Further explanation
3x-2y= -12
Change to y intercept form
2y = 3x + 12
Solve by dividing both sides by 2
y = 3/2x +6
PLEASE HELP
Which linear equation can be derived from this proportion?
12/( x + 8 ) = 7/( x + 1 )
A.
12x + 8 = 7x + 1
B.
12x + 12 = 7x + 56
C.
12x + 1 = 7x + 8
D.
12x + 96 = 7x + 7
Answers
7(x+8)=12(x+1)
7x+56=12x+12
Therefore your answer is B
Hope this helped :)
Answer:
B. 12x + 12 = 7x + 56
Explanation:
[tex]Given : \ \sf \dfrac{12}{ x +8} = \dfrac{7}{x + 1}[/tex]
cross multiply formula: if [tex]\sf \dfrac{a}{b} = \dfrac{c}{d}[/tex] then [tex]\sf ad = cb[/tex]
[tex]\sf 12(x +1) = 7(x + 8)[/tex]
distribute inside parenthesis
[tex]\sf 12x + 12= 7x + 56[/tex]
collect like terms
[tex]\sf 12x -7x = 56 - 12[/tex]
simplify the following
[tex]\sf 5x = 44[/tex]
dividing both sides by 5
[tex]\sf x = 8.8[/tex]
Solve for x in terms of b: 2x + b = 3
Answers
2x + b - b = 3 - b
2x = 3 - b
x = (3 - b)/2
HELP!! What is the equation of the graphed line?
(y=mx+b)
Answers
rise/run
So use a graphed point, 0, -5 and you rise or count up quadrants up to a point and then horizontally move to when you find that point.
So from 0,-5 go up 9 vertically, and you would be on the 4
Go horizontal 3 spots and your on a designated point.
So the rise is four and the run is 3
So 4/3 is the slope
In the y= Mx + b equation you would set the equation like this:
y= 4/3 + -5
The m in this formula stands for the slop and the b stands for the y-intercept
The y-intercept is the point that is on the y-axis and where it starts.
Can someone solve this?
Answers
Answer:
n(AnB)= {4, 29}
n(BnC)= {9,29}
n(AnC)= {29}
Determine the quadrant ( I, II, III, and IV ) or axis (x and y ) where each of the following point is located.
1. ( 0,-6 )
2. ( 15,4 )
3. ( 100, -5 )
4. ( 0.004, .05 )
5. ( -4,0 )
8. ( -7.5, -6.3 )
9. ( 0.1000)
Answers
Answer:
1. ( 0,-6 ) is y-axis
2. ( 15,4 ) is l quadrant
3. ( 100, -5 ) is lV quadrant
4. ( 0.004, .05 ) is l quadrant
5. ( -4,0 ) is x-axis
8. ( -7.5, -6.3 ) is lll quadrant
9. ( 0.1000) is y-axis.
There is a reflection at the boundary between two materials if there is a change of __________ at the boundary.
Answers
There is a reflection at the boundary between two materials if there is a change of the speed of light in the material at the boundary.
This bending is referred to as refraction. whilst a wave traveling at an angle adjusts its velocity upon crossing a boundary among materials,. This bending is known as refraction. As a wave crosses a boundary into a new medium, its pace, and wavelength exchange simultaneously as its frequency stays equal.
While light from air hits a smooth piece of glass (n = 1. five) with the ray perpendicular to the glass floor, of the subsequent will occur while light from air hits a clean piece of glass with the ray perpendicular to the glass surface, the part of the light passing into the glass: will now not exchange its frequency.
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B = 54°, b=15, c=
c = ? (Round answers to
the nearest hundredth.)
Answers
Answer:
18.54
Step-by-step explanation:
sine is opposite/hypotenuse, and you have opposite (b=15), so use that
sin(54) = 15/c
c = 15/sin54
then use calculator
c = 18.54
Draw a ratio box for this problem. Then solve the
problem using a proportion.
her piano students and that 40% of the
Ms. Smith noted that there were 12 girls among
students were boys. How many piano students
did Ms. Smith teach?
Answers
There are total 30 students in the piano class.
What is Ratio and Proportion ?When a number can be divided by another number then they can be written as p : q , when two ratios can be equated using an equal sign then they are said to be in proportion.
It is given that the total number of girls is 40% of the total students
The ratio of total students to girls is 100 :40
= 10 :4
= 5 : 2
It is also given that in the total number of students 12 were girls
Let total students be x
Then the ratio is x : 12
As both the ratio are same and so can be equated and the proportion will be
5 : 2 = x : 12
5/2 = x /12
x = 30
Therefore there are total 30 students in the piano class.
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