According to the trignonmentry of half angles, the value of sin(x/2) is √(1-5/6)/2, cos(x/2) is √(1+5/6)/2 and the value of tan(x/2) is √11/6/(√(1 + 5/6)
Trigonometry of half angles
Trigonometry of half-angle formula is used to determine the exact values of the trigonometric ratios of angles such as 15° that is half of the standard angle 30° and 22.5° that is the half of the standard angle 45 and so on. So if θ is an angle, then the half angle is represented by θ/2.
Given,
Here we need to find if cos(x)=5/6 , and x is in quadrant I, determine the exact value of each of the following.
sin(x/2), cos(x/2), tan(x/2).
According to the concepts in trigonometry,
We know that the following formulas.
=> sin(x/2) = √(1-cosx)/2
=> cos(x/2) = √(1+cosx)/2
=> tan( x/2)=sin x/1+cosx
Here we know that cos (x) = 5/6
Thus implies that 5 is the opposite and 6 is the hypotenuse, then the adjacent is
Therefore, we can calculate the value of the adjacent a as,
=> a = √(6²-5²)
=> a = √36-25
=> a= √11
Therefore the value of sin x= √11/6
So, the value of sin(x/2)= √(1 - 5/6)/2
And the value of cos(x/2)= √(1 + 5/6)/2
Finally, the value of tan(x/2)=√11/6/(√(1 + 5/6)
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Find a point-slope form for the line with slope 1/2 and passing through the point (-1,-4)
The linear equation with the given slope in the slope-point form is:
y = (1/2)*(x + 1) + 4
How to find the equation for the slope?
We know that for a line with a slope m and a point (a, b), the point-slope form of the line is written as:
y = m*(x - a) + b
In this case, we know that our line has a slope of 1/2 and it passes through the point (-1, 4), so we can replace this on the above formula to get:
y = (1/2)*(x + 1) + 4
This is the linear equation in the point-slope form.
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Write the phrase as an expression. Then evaluate when y=20.
3 less than the quotient of a number y and 4
write the Expression:
The value of 3 less than the quotient of a number y and 4 when y is 20 is 2.
What is an expression?Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.
The expression less than the quotient of a number y and 4 will be:
y/4 - 3
When y is 20, the value will be:
y/4 - 3
20/4 - 3
5 - 3
= 2
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Consider the equation and the following ordered pairs: (3,y) and (x,1).
y=−2x+1
Compute the missing x and y values so that each ordered pair will satisfy the given equation.
The missing x and y values so that each ordered pair will satisfy the given equation y= −2x +1 is computed to bee
How to compute the missing valuesThe equation is a linear function representing a straight line
for ordered pair (3, y)
y = −2x + 1
substitute the value of x
y = -2 * 3 + 1
y = -6 + 1
y = -5
hence the ordered pair is (3, -5)
for ordered pair (x, 1)
y = −2x + 1
2x = 1 - y
x = (1 - y) / 2
substitute the value of y
x = (1 - 1) / 2
x = 0
hence the ordered pair is (0, 1)
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students were asked which night they planned on attending the book fair. the results of the survey are shown in the table.
monday= 55 students
tuesday= 80 students
wednesday= 70 students
thursday= 112 students
friday= 65 students
20% of the students who planned to attend on Wednesday attended on Thursday instead. 25% of the students who planned to attend on Thursday attended on Wednesday instead. which day, Wednesday or Thursday, had a greater actual attendance? by how many students?
The day with greater actual attendance is Thursday with 98 students
How to determine the day that had a greater actual attendance?
A percentage is defined as the ratio that can be expressed as a fraction of 100
Given:
Expected numbers: Wednesday= 70 students andThursday= 112 students
20% of Wednesday = 20/100 x 70 = 14 students. That is 14 students are absent on Wednesday but attended on Thursday instead. This means 56 (70 -14) students scheduled for Wednesday attended.
25% of the students who planned to attend on Thursday attended on Wednesday instead:
25% of Thursday = 25/100 x 112 = 28 students. This means 84 students scheduled for Thursday attended
Actual Wednesday attendance = 56 + 28 = 84 students
Actual Thursday attendance = 14 + 84 = 98 students
Therefore, Thursday had a greater actual attendance with 98 students
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sorry this is hard haha :(
Answer: 192.07 mm
Step-by-step explanation:
I don't feel like it rn, so here's an image with the hexagonal prism volume equation.
Brainliest if correct 5 points
(a²-8a26) ÷ (a + 2) synthetic division
Value of the expression (a²- 8a - 26) ÷ (a + 2) using synthetic division is given by quotient is a - 10 and remainder is -6.
As given in the question,
Given expression is equal to,
(a²- 8a - 26) ÷ (a + 2)
Simplify the given expression using synthetic division is shown in the attached file,
Another way of division,
(a²- 8a - 26)
= a² -10a + 2a -20 -6
= a (a -10) + 2( a - 10) -6
= ( a + 2 )( a - 10 ) - 6
Quotient of the given division is equal to ( a - 10 )
Remainder of the given division is equal to -6
Therefore, value of the expression (a²- 8a - 26) ÷ (a + 2) using synthetic division is given by quotient is a - 10 and remainder is -6.
The complete question is :
Evaluate the given expression using synthetic division :
(a²- 8a - 26) ÷ (a + 2)
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Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true? Select three options. The radius of the circle is 3 units. The center of the circle lies on the x-axis. The center of the circle lies on the y-axis. The standard form of the equation is (x – 1)² + y² = 3. The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
The true statements about the circle are the radius of the circle is 3 units, the center of the circle lies on the x-axis and the radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9
How to determine true statements about the circle?Given: the equation is x²+y²–2x–8 = 0
In order to determine true statements about the circle, we have to rewrite the given equation and compare it with the standard form of the equation of a circle.
The standard form of the equation of a circle is
(x-a)² + (y-b)² = r²
where (a, b) is the center and r is the radius
using the completing square method on the given equation:
x²+y²–2x–8 = 0
x²-2x + (-1)² + y² + (0)²= 8 + (-1)²
(x-1)² + (y-0)² = 9
(x-1)² + (y-0)² = 3²
Thus, the center is (0, 1) and the radius is 3
Therefore, the options are the radius of the circle is 3 units, the center of the circle lies on the x-axis and the radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9
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If 125 kg of food is sufficient for 30 soldiers for 6 days, how long will the food last for 45 soldiers?
Answer:
30 = 6
45 = x
cross multiply
30x = 45*6
30x = 270
divide both sides by
30x/30 = 270/30
X = 9
9-6 = 3 days
what is the slope of the line that passes thru (7,-6) and (6,-6)
The slope of the straight line passing through the two given points is undefined which means the line is parallel to the y-axis.
Let us consider the two points A(x₁,y₁) and B(x₂,y₂) be the two points (7,-6) and (6,-6) on the cartesian coordinates.
Let the slope of the line joining A (7,-6) and B(6,-6) be m.
We know that the slope of a line is given by:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Slope of the line
= (6-7) / (-6+6)
= -1 / 0
= undefined
Since the slope is undefined we can say that the straight line is parallel to the y axis.
we know that tan 90° = ∞
So any line parallel to this line will have the same slope as the y axis.
Hence the slope of the given line is undefined or infinity.
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Please help I was sick and missed out on class.Thank you
What was the question? or was this only meant for your classmates?
Factor -4 out of -8+20 factored expression
Factoring -4 out of -8+20 factored expression is -4(2 + 5).
What is a factor?Factor expressions, also known as factoring, refer to the process of rewriting an expression as the product of factors. 3x + 12y, for example, can be factored into a simple expression of 3 (x + 4y). Calculations become easier in this manner. The terms 3 and (x + 4y) are referred to as factors.
To factor a given expression goes thus:
Each term should be written as the prime factorization.
Determine the factors that all of the terms share.
Multiply those common variables.
In this case, factoring 4 out of -8+20 factored expression is -4(2 + 5).
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Which point is the midpoint of AB
Which graph shows the solution to this system of linear inequalities?
y> -2x+2
y<2x-1
The portion of the graph which does not contain (0, 0) is shaded.
What are Linear Inequalities?
When two mathematical statements or two numbers are compared in an unequal way, it is known as an inequality in mathematics. Inequalities can generally be classified as either algebraic or numerical or as a combination of the two. When a polynomial of degree 1 is compared to another algebraic expression of a degree less than or equal to 1, this is an example of a linear inequality, which is an inequality involving at least one linear algebraic expression.
Given the inequalities :
y ≥>2x + 1
y ≤<2x - 2
From y > 2x + 1 ;
Since the inequality sign is ≥, a solid line is used to draw the straight line graph of y > 2x + 1
From :
y = mx + c
Where, m = slope ; c = intercept
Hence, a straight line graph with ;
Intercept, c = 1 (where the line crosses the y-intercept)
Slope, m = 2
Consider a point, which isn't on the line ;
Take point (0,0) and use it to test the inequality :
0 > 2(0) + 1
0 >0 + 1
0 >1
This is false, hence, the portion of the graph which does not contain (0, 0) is shaded.
From : y < 2x - 2
Since the inequality sign is ≤, a solid line is used to draw the straight line graph of y < 2x - 2
Graph the line y < 2x - 2, with ;
Intercept, c = - 2
Slope = 2
Consider a point, which isn't on the line ;
Take point (0,0) and use it to test the inequality y < 2x - 2:
0 < 2(0) - 2
0 < 0 - 2
0 < - 2
This is false, hence, the portion of the graph which does not contain (0, 0) is shaded.
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what is 15 times 2 divided by 3
(((20 POINTS)))
△ABC has a right angle at C, BC=9.2 centimeters, and m∠A=63∘.
What is CA ?
Enter your answer rounded to the nearest tenth in the box
Answer:
4.7 cm
Step-by-step explanation:
Solve the following linear equation and simplify your answer.
8z−6=−2(−4z+3)
Answer:
Step-by-step explanation:
8z-6=-2(-4+3)
8z-6=8z-6
on transposing,
8z-8z-6+6=0
Has slope of 2 and passes through (-2, 1) write equation in point slope form of the line that passes through the given point and has the given slope. write the equation in slope intercept form.
Slope = m = 2
y = mx + b
y = 2x + b
Plug in (-2, 1) to find b
1 = 2(-2) + b
b = 5
y = 2x + 5
Studies show that the minimum half-life of
Diazepam is 20 hours.
Use the following to construct a function
that will model the minimum amount of
Diazepam left in the body after an initial
dose of 35 mg.
Q(t) = Pert
Where Q(t) describes the amount of
Diazepam left in the body after t hours
following an initial dose of P mg.
1. Q(t) =
2. How long (in hours) will it take for the
amount of Diazepam left in the body to
reach 7 mg?
1. After constructing the function according to the question, Q(t) = [tex]35e^{\frac{-ln2}{20}t}[/tex].
2. It will take 50 hours for the amount of Diazepam left in the body to reach 7 mg.
What is a function?
Exactly one element of Y is assigned to each element of X in a mathematical function from a set X to a set Y. Both the set X and the set Y are referred to as the function of the domain and codomain, respectively. Examples include f(x) = x/2 ("f of x equals x split by 2") ("f of x equals x divided by 2") Every input "x" has a single output "x/2," which makes it a function: • f(2) = 1.
Solution explained:
According to the question,
Q(t) = [tex]Pe^{rt}[/tex]
The half-life of Diazepam is 20 hours = t
Q(0) = p = 35 { the initial value}
Q(20) = [tex]35e^{20r} = \frac{1}{2} X 35[/tex]
= [tex]e^{20r} = \frac{1}{2}[/tex]
= [tex]20r = -ln2[/tex]
= [tex]r = \frac{-ln2}{20}[/tex]
Therefore, Q(t) = [tex]35e^{\frac{-ln2}{20}t}[/tex]
Now, Let
Q(t) = 7
[tex]35e^{\frac{-ln2}{20}t}[/tex] = 7
[tex]e^{\frac{-ln2}{20}t} = \frac{1}{5}[/tex]
[tex]{\frac{-ln2}{20}t} = -ln5[/tex]
After calculating,
t = 50 (hours)
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The telephone company offers two types of service. With plan A, you can make an unlimited number of local calls for $50 per month plus a $25 plan activation fee. With plan B you pay $25 monthly plus $50 activation fee
Y=mx+b form please
Forming the two telephone charge plans in a slope intercept equation form, like Y=mx + b, is as follows:
Plan A: Y = 50x + 25Plan B: Y = 25x + 50.What is the slope intercept equation?The slope intercept equation is an equation of a straight-line with its slope (constant unit rate) combining the x and y intercepts.
Generally, the formula y = mx + b depicts the slope intercept equation with the following values:
y = y coordinate
m = slope
x = x coordinate
b = y intercept
Plan A Plan B
Fixed cost (b) $25 $50
Variable cost (m) 50 25
x = monthly 12 12
y = the total cost for the period
Thus, Plan A will have a total cost of 50x + 25 and Plan B will have a total cost of 25x + 50.
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please help me solve this question !
The solution of the function is x = 12
What are trigonometric ratios?Trigonometric ratios are the ratios of sides of a right-angle triangle. The most common trigonometric ratios are sine, cosine, and tangent.
Consider a right-angle triangle ABC, right-angled at C. In that case, side AB will be the hypotenuse. Also, if we chose AC as the base and BC as the perpendicular. Then, for ∠BAC, value of sinθ = Perpendicular/ hypotenuse = BC/AB
6cos(5x) = 3
divide both sides by 6, we have
cos(5x) = 3/6
cos(5x) = 0.5
taking the anti cosine of both sides
5x = Arc cos 0.5
5x = 60
x = 60/5
x = 12°
In conclusion, the value of x = 12°
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A system contains two or more linear equations that can be solved or graphed together at once.
True
False
The statement "A system contains two or more linear equations that can be solved or graphed together at once" is true.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
We have,
A system contains two or more linear equations that can be solved or graphed together at once.
This statement is true.
For example,
The two linear equations can be:
ax + by = c ____(1)
dx + ey = F _____(2)
We can solve this equation using the substitution method or elimination method.
We can find the point of intersection.
And we can solve and graph together at once.
Thus,
The statement "A system contains two or more linear equations that can be solved or graphed together at once" is true.
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The following is a list of movie tickets sold each day for 10 days.
8, 15, 47, 12, 52, 27, 29, 32, 83, 77
Which of the following intervals are appropriate to use when creating a histogram of the data?
0 – 14, 15 – 29, 30 – 44, 45 – 59, 60 – 75
0 – 25, 25 – 50, 50 – 75, 75 – 100
0 – 19, 20 – 39, 40 – 59, 60 – 79, 80 – 99
0 – 20, 20 – 35, 35 – 50, 55 – 70, 75 – 90
Answer:
(c) 0 – 19, 20 – 39, 40 – 59, 60 – 79, 80 – 99
Step-by-step explanation:
You want to know the intervals suitable for creating a histogram of the given set of 10 data points.
HistogramThe intervals used to categorize data for a histogram must meet two requirements:
they must cover the range of the datathe binning must be unambiguousRangeThe range of the given data is 8 to 83. All the suggested answer choices include a bin that will contain 8. Choice A does not have a bin that contains 88.
ClassificationWhen bins are defined like 0–25, 25–50, the location of the data value 25 is unclear. No data value can fall on a bin boundary, so bins need to be defined to prevent that possibility. For integer data values, bin ranges like 0–14, 15–29, or 0–19, 20–39 are appropriate. This eliminates answer choices B and D, which have ambiguous bin boundaries.
The only reasonable answer choice is C:
0–19, 20–39, 40–59, 60–79, 80–99
__
Additional comment
Histograms tend to be most useful if they have between 5 and 20 bins. The idea is to produce a picture of the data distribution in a general way, without so much detail that the big picture is obscured.
Here, the selected bin set will have numbers of 3, 3, 2, 1, 1 in the bins. This gives the impression of a data set skewed to the right, as it should.
<95141404393>
Are M, N, and O collinear? If so, name the line on which they lie.
Answer: MO
Step-by-step explanation:
Estimate the difference of 25.92 - 5 4/10
Answer: 20 [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
First of all, 5 [tex]\frac{4}{10}[/tex] = 5.4
Remember, 1/10 = 0.1, 2/10 = 0.2, and so on.
This means we can change the equation to 25.92 - 5.4, which gives us 20.52.
This is close to 20.50, which is equivalent to 20 [tex]\frac{5}{10}[/tex], which is equivalent to 20 [tex]\frac{1}{2}[/tex].
PLEASE HELP I WILL GIVE BRAINLIEST IF ANSWERED QUICKLY
The compound expression (a⁵ · a ÷ a⁻³)⁻¹ is equivalent to the power a⁻⁹.
How to simplify a power expression by algebraic properties
In this problem we find a compound expression formed by several powers of equal base that must be simplified in a single power with the same base. This can be done by using algebra properties related to powers. First, write the given expression:
(a⁵ · a ÷ a⁻³)⁻¹
Second, multiply the powers of equal base:
(a⁵⁺¹ ÷ a⁻³)⁻¹
(a⁶ ÷ a⁻³)⁻¹
Third, by definition of division and the power of a power:
[a⁶ · (a⁻³)⁻¹]⁻¹
(a⁶ · a³)⁻¹
Fourth, use the multiplication of power of same base:
(a⁶⁺³)⁻¹
(a⁹)⁻¹
Fifth, use the property of a power of a power once again:
a⁻⁹
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help pls, i’ll mark brainliest!!
Answer: x = 9.; B=4
Step-by-step explanation:
AABC = AKLM
AB=LK
8=28 — b= 4
LC=LM
27=3x — x=9
Congruent triangles correspond to equal angles and sides
Answer:
x=11
t=6
Step-by-step explanation:
angle M=angle C
3x=33
/3. /3
x=11
Side AB= Side KL
18=3t
/3. /3
6=t
Hopes this helps please mark brainliest
i need help haha and i got the wrong answer
Answer:
76.5
Step-by-step explanation:
Volume for prisms is "V = bH", where b = base and H = height.
b = 3 * 3 * 0.5
b = 4.5
H = 17
bH = 4.5 * 17 = 76.5
Express cot 2x in terms of cot x
Answer:
cot x = 2cot(2x) + tan x
Step-by-step explanation:
[tex] \rm \implies cot \: 2x = \dfrac{cos \: 2x}{sin \: 2x} \\ \\ \rm \implies cot \: 2x = \dfrac{ {cos}^{2}(x) - {sin}^{2}(x) }{2(sin \: x)(cos \: x)} \\ \\ \rm \implies cot \: 2x = \frac{1}{2} \bigg( \frac{cos \: x}{sin \: x} - \frac{sin \: x}{cos \: x} \bigg) \\ \\ \rm \implies cot \: 2x = \frac{1}{2} (cot \: x - tan \: x) \\ \\ \rm \implies 2cot ( 2x )= cot \: x - tan \: x \\ \\ \rm \implies cot \: x = 2cot (2x) + tan \: x[/tex]
An awning that covers a sliding glass door that is 88 inches tall forms an angle of with the wall. The purpose of the awning is to prevent sunlight from entering the house when the angle of elevation of the sun is more than See the figure. Find the length L of the awning.
If the purpose of the awning is to prevent sunlight from entering the house when the angle of elevation of the sun is more than the length L of the awning is 38.50 in.
How to find the length?Let L represent the length
Hence,
sin 105° / 88 = sin 25° /L
88 × sin 25° / sin 105°
88 × 0.4226 / 0.9659
L= 37.1888/ 0.9659
L = 38.50 in
Therefore the length is 38.50 in.
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The complete question is :
An awning that covers a sliding glass door that is 88 inches tall forms an
angle of 50° with the wall. The purpose of the awning is to prevent sunlight
from entering the hours when the angle of elevation of the sun is more than 65°. Find the length L of the awning