Step-by-step explanation:
If the log82x, log4x and log2x, in that order, form a geometric progression with a positive common ratio.
Let a = log82x, b = log4x and c = log2x
If a = log8 2x; 8^a = 2x... (1)
If b = log4 x; 4^b = x ... (2)
If c = log2 x; 2^c = x...(3)
Since a, b c are in GP, then b/a = c/b
Cross multiplying:
b² = ac ...(4)
From eqn 1, x = 8^a/2
x = 2^3a/2
x = 2^(3a-1)
From eqn 2; x = 4^b
x = 2^2b
From eqn 3: x = 2^c
Equating all the values of x, we have;
2^(3a-1) = 2^2b = 2^c
3a-1 = 2b = c
3a-1 = c and 2b = c
a = c+1/3 and b = c/2
Substituting the value of a = c+1/3 and b = c/2 into equation 4 we have;
(c/2)² = c+1/3×c
c²/4 = c(c+1)/3
c/4 = c+1/3
Cross multiplying;
3c = 4(c+1)
3c = 4c+4
3c-4c = 4
-c = 4
c = -4
Substituting c = -4 into equation 3 to get the value of x we have;
2^c = x
2^-4 = x
x = 1/2^4
x = 1/16
Since the number x can be written as m/n, then x = 1/16 = m/n
This shows that m = 1, n = 16
m+n = 1+16
m+n = 17
The required answer is 17.
The value of m+n in which m and n are relatively prime positive integers is 17.
What is geometric sequence?Geometric sequence is the sequence in which the next term is obtained by multiplying the previous term with the same number for the whole series.
There is a unique positive real number x such that the three numbers log82x, log4x and log2x, in that order, form a geometric progression with a positive common ratio. The progression is,
[tex]\log_82 x,\log_4x, \log_2x[/tex]
The above numbers are in geometric progression. Thus, the ratio of first two terms will be equal to the ratio of next two terms as,
[tex]\dfrac{\log_4x}{\log_82x}=\dfrac{\log_2x}{\log_4x}\\(\log_4x)^2={\log_2x}\times{\log_82x}\\[/tex]
Using the base rule of logarithmic function,
[tex]\left(\dfrac{\log x}{\log 4}\right)^2=\dfrac{\log x}{\log2}\times\dfrac{\log2x}{\log8}\\\left(\dfrac{\log x}{\log 2^2}\right)^2=\dfrac{\log x}{\log2}\times\dfrac{\log2x}{\log2^3}[/tex]
Using the Power rule of logarithmic function,
[tex]\left(\dfrac{\log x}{2\log 2}\right)^2=\dfrac{\log x}{\log2}\times\dfrac{\log2x}{3\log2}\\\dfrac{\log x}{4}=\dfrac{\log 2+\log x}{3}\\3\log x=4(\log2x)\\\log x^3=\log(2x)^4\\x^3=16x^4\\x=\dfrac{1}{16}[/tex]
The number x can be written as
[tex]\dfrac{m}{n}[/tex]
Here, m and n are relatively prime positive integers. Thus, the value of m+n is,
[tex]m+n=1+16=17[/tex]
Hence, the value of m+n in which m and n are relatively prime positive integers is 17.
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But The aquarium charges $12 per ticket for adults and $5per ticket for children. A group of 90 children and adult chaperones visited the aquartum on a held trip. If the total cost of their tickets was $548, how mamy chaperones were there?
Answer:
There were 76 childrens and 14 adults.
Step-by-step explanation:
Since the group has a total of 90 children and adults, then the sum of the number of adults with the number of children must be equal to 90 as shown below:
children + adults = 90
Since the total cost for their tickets was 548 then the number of children multiplied by the price of their ticket summed by the number of adults multiplied by the price of their ticket must be equal to that. We have:
5*children + 12*adults = 548
With these two equations we have a system of equations shown below:
children + adults = 90
5*children + 12*adults = 548
In order to solve this we will multiply the first equation by -5, and sum both equations we have:
-5*children - 5*adults = -450
5*children + 12*adults = 548
7*adults = 98
adults = 98/7 = 14
children + 14 = 90
children = 90 - 14 = 76
There were 76 childrens and 14 adults.
Enunciado: Traza la gráfica de la función. Traza también la gráfica de la asíntota, si es distinta al eje de x o al eje y. Define el Rango y el Dominio. h(x)=log(1/3) x
Answer:
The given function is
[tex]h(x)=log_{\frac{1}{3} } (x)[/tex]
It's important to know that logarithms are the opposite function to exponentials, which means their domains and ranges are defined the opposite way.
The domain of logarithms is restricted, because negative numbers or the zero is not allowed in their domains. So, the domain of this function is: [tex]D:(0, infinite][/tex]
On the other hand, its range is not restricted, so it's defined: [tex]R: (infinite, -infinite)[/tex]
The image shows the graph of this function, there you can observe its domain and range set definitions.
the graph of the invertible function ggg is shown on the grid below.
What is the value of g^-1(7)
Answer:
[tex]g^{-1} (7)=5[/tex]
Step-by-step explanation:
We are asked to find [tex]g^{-1} (7)[/tex].
One thing to remember about the inverse of a function is what exactly an inverse means.
If we have the ordered pair [tex](a,b)[/tex] of function [tex]g[/tex], then the corresponding ordered pair of [tex]g^{-1}[/tex] would be [tex](b,a)[/tex].
As we are asked to find [tex](7,b)[/tex] of [tex]g^{-1}[/tex], we can instead find [tex](b,7)[/tex] of [tex]g[/tex].
This means that we are looking for where [tex]g(b)=7[/tex].
From the graph, we can see that for this to be true, [tex]b=5[/tex]
This means that [tex]g^{-1} (7)=5[/tex]
The value of g^-1(7) is 5.
What is the value of g^-1(7)?
What is invertible function?A function f from a set X to a set Y is said to be invertible if for every y in Y and x in X, there exists a function g from Y to X such that f(g(y)) = y and g(f(x)) = x. function is invertible only if each input has a unique output. That is, each output is paired with exactly one input. That way, when the mapping is reversed, it will still be a function.
Given that:
One thing to remember about the inverse of a function is what exactly an inverse means.
If we have the ordered pair (a, b) of function g , then the corresponding ordered pair of g^-1 would be (b, a).
As we are asked to find (7,b) of g^-1, we can instead find (b, 7) of g .
This means that we are looking for where g(b)=7.
From the graph, we can see that for this to be true, b=5.
So, the value of g^-1(7) is 5.
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How to use Cosine to calculate the side of a right triangle?
Answer:
Cosine is Adj/Hyp
a simple trick i use when doing these kind of problems is first finding the sides. If you only know the Hypotenuse then you multiply that with the cos(x) or whatever angle it is. If you only know Adjacent then you divide the adjacent with the Cos(x) and you get the answer
Step-by-step explanation:
1. If 5tanA=4, Find the value of (5sinA-3cosA)/(4cosA+5sinA)
2. Solve for θ, sinθ/(1+cosθ) + (1+cosθ)/sinθ =4, 0°<θ<90°
3. Prove that tan〖θ-cotθ 〗 = (〖2sin〗^2 θ-1)/sinθcosθ
4. Without using trigonometric tables ,show that
tan 10°tan15°tan75°tan80°=1
5. If x=acosθ-bsinθ and y=asinθ + bcosθ prove that x^2+y^2=a^2+b^2
Answer:
1. (5·sin(A) - 3·cos(A)/(4·cos(A) + 5·sin(A)) = 1/8
2. θ = 30°
3. tan(θ) - cot(θ) = (2·sin²(θ) -1)/((cos(θ)×sin(θ))
from tan(θ) - 1/tan(θ) = sin(θ)/cos(θ) - cos(θ)/sin(θ) and sin²(θ) + cos²(θ) = 1
4. tan10°·tan15°·tan75°·tan80°= 1 from;
sin(α)·sin(β) = 1/2[cos(α - β) - cos(α + β)]
cos(α)·cos(β) = 1/2[cos(α - β) + cos(α + β)]
5. x² + y² = a² + b² where x = a·cosθ - b·sinθ and y = a·sinθ + b·cosθ from;
cos²θ + sin²θ = 1
Step-by-step explanation:
1. Here we have 5·tan(A) = 5·sin(A)/cos(A) = 4
∴ 5·sin(A) = 4·cos(A)
Hence to find the value of (5·sin(A) - 3·cos(A)/(4·cos(A) + 5·sin(A)) we have;
Substituting the value for 5·sin(A) = 4·cos(A) into the above equation in both the numerator and denominator we have;
(4·cos(A) - 3·cos(A)/(4·cos(A) + 4·cos(A)) = cos(A)/(8·cos(A)) = 1/8
Therefore, (5·sin(A) - 3·cos(A)/(4·cos(A) + 5·sin(A)) = 1/8
2. For the equation as follows, we have
[tex]\frac{sin \theta}{1 + cos \theta} + \frac{1 + cos \theta}{sin \theta} = 4[/tex] this gives
[tex]\frac{2sin (\theta/2) cos (\theta/2) }{2 cos^2 (\theta/2)} + \frac{2 cos^2 (\theta/2)}{2sin (\theta/2) cos (\theta/2) } = 4[/tex]
[tex]tan\frac{\theta}{2} + \frac{1}{tan\frac{\theta}{2} } = 4[/tex]
[tex]tan^2\frac{\theta}{2} + 1 = 4\times tan\frac{\theta}{2}[/tex]
[tex]tan^2\frac{\theta}{2} - 4\cdot tan\frac{\theta}{2} + 1 = 0[/tex]
We place;
[tex]tan\frac{\theta}{2} = x[/tex]
∴ x² - 4·x + 1 = 0
Factorizing we have
(x - (2 - √3))·(x - (2 + √3))
Therefore, tan(θ/2) = (2 - √3) or (2 + √3)
Solving, we have;
θ/2 = tan⁻¹(2 - √3) or tan⁻¹(2 + √3)
Which gives, θ/2 = 15° or 75°
Hence, θ = 30° or 150°
Since 0° < θ < 90°, therefore, θ = 30°
3. We have tan(θ) - cot(θ) = tan(θ) - 1/tan(θ)
Hence, tan(θ) - 1/tan(θ) = sin(θ)/cos(θ) - cos(θ)/sin(θ)
∴ tan(θ) - 1/tan(θ) = (sin²(θ) - cos²(θ))/(cos(θ)×sin(θ))...........(1)
From sin²(θ) + cos²(θ) = 1, we have;
cos²(θ) = 1 - sin²(θ), substituting the value of sin²(θ) in the equation (1) above, we have;
(sin²(θ) - (1 - sin²(θ)))/(cos(θ)×sin(θ)) = (2·sin²(θ) -1)/((cos(θ)×sin(θ))
Therefore;
tan(θ) - cot(θ) = (2·sin²(θ) -1)/((cos(θ)×sin(θ))
4. tan10°·tan15°·tan75°·tan80°= 1
Here we have since;
sin(α)·sin(β) = 1/2[cos(α - β) - cos(α + β)]
cos(α)·cos(β) = 1/2[cos(α - β) + cos(α + β)]
Then;
tan 10°·tan15°·tan75°·tan80° = tan 10°·tan80°·tan15°·tan75°
tan 10°·tan80°·tan15°·tan75° = [tex]\frac{sin(10^{\circ})}{cos(10^{\circ})} \times \frac{sin(80^{\circ})}{cos(80^{\circ})} \times \frac{sin(15^{\circ})}{cos(15^{\circ})} \times \frac{sin(75^{\circ})}{cos(75^{\circ})}[/tex]
Which gives;
[tex]\frac{sin(10^{\circ}) \cdot sin(80^{\circ})}{cos(10^{\circ})\cdot cos(80^{\circ})} \times \frac{sin(15^{\circ}) \cdot sin(75^{\circ})}{cos(15^{\circ})\cdot cos(75^{\circ})}[/tex]
[tex]=\frac{1/2[cos(80 - 10) - cos(80 + 10)]}{1/2[cos(80 - 10) + cos(80 + 10)]} \times \frac{1/2[cos(75 - 15) - cos(75 + 15)]}{1/2[cos(75 - 15) + cos(75 + 15)]}[/tex]
[tex]=\frac{1/2[cos(70) - cos(90)]}{1/2[cos(70) + cos(90)]} \times \frac{1/2[cos(60) - cos(90)]}{1/2[cos(60) + cos(90)]}[/tex]
[tex]=\frac{[cos(70)]}{[cos(70) ]} \times \frac{[cos(60)]}{[cos(60) ]} =1[/tex]
5. If x = a·cosθ - b·sinθ and y = a·sinθ + b·cosθ
∴ x² + y² = (a·cosθ - b·sinθ)² + (a·sinθ + b·cosθ)²
= a²·cos²θ - 2·a·cosθ·b·sinθ +b²·sin²θ + a²·sin²θ + 2·a·sinθ·b·cosθ + b²·cos²θ
= a²·cos²θ + b²·sin²θ + a²·sin²θ + b²·cos²θ
= a²·cos²θ + b²·cos²θ + b²·sin²θ + a²·sin²θ
= (a² + b²)·cos²θ + (a² + b²)·sin²θ
= (a² + b²)·(cos²θ + sin²θ) since cos²θ + sin²θ = 1, we have
= (a² + b²)×1 = a² + b²
Find the volume of the square pyramid shown. Round to the nearest whole number. The diagrams are not drawn to scale.
12.
9 cm
(1 point)
13 cm
13 cm
507 cm3
351 cm3
39 cm3
O 761 cm
The volume of the square pyramid having base edge and height as [tex]13[/tex] [tex]cm[/tex] and [tex]9[/tex] [tex]cm[/tex] respectively is [tex]507[/tex] [tex]cm^{3}[/tex].
Volume of a square pyramidVolume [tex]=\frac{1}{3}[/tex] × (base area) × (height)
How to find the volume of a square pyramid?First, find the area of the square base
Given, the edge of the square base [tex]=13 cm[/tex]
Then, the area of the square base [tex]=13^{2}=169cm^{2}[/tex]
Given, the height of the square pyramid [tex]=9cm[/tex]
Now, apply the volume formulae
Volume [tex]=\frac{1}{3}[/tex] × [tex]169[/tex] × [tex]9=507cm^{3}[/tex]
Hence, the volume of the square pyramid is [tex]507cm^{3}[/tex].
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Which equation is true for x = –6 and x = 2?
2x2 – 16x + 12 = 0
2x2 + 8x – 24 = 0
3x2 – 4x – 12 = 0
3x2 + 12x + 36 = 0
Answer:
2x2 + 8x – 24 = 0
Step-by-step explanation:
[tex]2 {x}^{2} + 8x - 24 = 0 \\ lhs \\ =2 {x}^{2} + 8x - 24 ..(plug \: x = - 6) \\ 2 {( - 6)}^{2} + 8( - 6) - 24 \\ = 72 - 48 - 24 \\ 72 - 72 \\ = 0 \\ = rhs \\ \\ lhs \\ =2 {x}^{2} + 8x - 24 ..(plug \: x = 2) \\ 2 {( 2)}^{2} + 8( 2) - 24 \\ = 8 + 16 - 24 \\ 24 - 24 \\ = 0 \\ = rhs \\ [/tex]
why is tesla stock increasing/decreasing in value
Answer:
elon musk
Step-by-step explanation:
elon sends out random, uncalled for tweets, which mess with the stock value.
For example, when the stock was very high, he tweeted,"Tesla stock too high"
What is the volume of a sphere with a radius of 41 in, rounded to the nearest tenth of a cubic inch?
Step-by-step explanation:
Volume of a sphere is given by
[tex]V = \frac{4}{3} \pi {r}^{3} [/tex]
Where r is the radius of the sphere
From the question
radius = 41 in
Substitute the value into the above formula
We have
[tex]V = \frac{4}{3} \times {41}^{3} \pi[/tex]
[tex] = \frac{275684}{3} \pi[/tex]
= 288695.6097
We have the final answer as
Volume = 288695.6 in³ to the nearest tenthHope this helps you
The answer on deltamath is
288695.6 in³
The angle of depression from a roof of a building to a car is 75°. If the roof is 12 m above
the level of the car, then the distance of the car from the building is closest to:
(A) 3.11 m
(B) 3.22 m
(C) 11.59 m
(D) 12.42 m
Which equation could Sameer use to solve for the value of n if n + 13 = 17?
Answer:
n = 17-13
Step-by-step explanation:
n+13=17
Subtract 13 from each side
n+13-13 = 17-13
n = 17-13
A square unit that is 1 unit wide and 1 unit long is a?
Answer:
A square with side length 1 unit, called 'a unit square,' is said to have 'one square unit' of area, and can be used to measure area.
kadeem and quinn both drive 25 miles. Kadeem drives at a constant speed of 50 miles an hour. Quinn drives at a constant speed of 75 miles an hour. Who takes longer to drive the 25 miles? How much loner?
Answer:
I believe it is Kadeem who takes longer by 10 minutes.
Step-by-step explanation:
A person whose speed is slow will take longer to reach so Kadeem takes longer by 0.5 hours.
Given that,
Kadeem and Quinn both drive 25 miles.
Kadeem drives at a constant speed of 50 miles an hour.
Quinn drives at a constant speed of 75 miles an hour.
To determine who takes longer to drive the 25 miles.
Distance is defined as the object traveling at a particular speed in time from one point to another.
Here,
Time is taken by Kadeem to reach 25 miles with a speed of 25 miles per hour
= 25 / 50 = 0.5 hour
Time is taken by Quinn to reach 25 miles with a speed of 75 miles per hour,
= 25 / 75 = 0.34 hour
Thus, a person whose speed is slow will take longer to reach so Kadeem takes longer by 0.5 hours.
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Jackson and Xavier are both solving the multiplication 0.8 x 5. Jackson gets 4 as a solution, and Xavier gets 0.4. Xavier said to Jackson, "Your answer of 4 can't be right for 0.8 x 5. You need a decimal point because a product always has the same number
Answer:
Jackson
0.8×5=4
Xavier
0.8×5=0.4
If Xavier said to Jackson that his answer of 4 can't be right.
Jackson needs a decimal point because a product always have the same answer.
Then,
Xavier is right with his sayings but wrong with the answer of 0.4
The correct answer is 4.0
The decimal point should be counted from the back not from the front as Xavier did
A cylinder and it’s dimensions are diameter 8.4cm and height 10.9cm. Which measurement is closest to the lateral surface area of the cylinder in square centimeters
Answer:
287.64
Step-by-step explanation:
2πrh is the formula you use for the lateral surface area.
to get radius, we know its half of the diameter so 4.2.
plug them in and you get your answer :)
the company shows that its median listing is $150,000. if the range of the listings is $50,000, is it possible for the company to have a house listed for $200,000?
Answer:
no
Step-by-step explanation:
HELP MATH ASAP PLEASE
I WILL GIVE BRAINLEST
Answer:
The answer is D
Step-by-step explanation:
HEEEEELP I IS TTTTTTIIIIIMMMMMEEEEEDDDD
What is the shape of the cross section of the figure that is perpendicular to the triangular bases and passes through a vertex of the triangular bases?
A triangular prism.
a parallelogram that is not a rectangle
a rectangle
a triangle that must have the same dimensions as the bases
a triangle that may not have the same dimensions as the bases
Answer:
b
Step-by-step explanation:
Answer:
I dink Bs
Step-by-step explanation:
You arrive in my class 45 seconds after leaving math which is 90 meters away. How fast did you travel?
Answer:
2 m/s=90 meters/45 seconds
Find the value of k ,if x=2 and y=3.Find the equation of 2x+3y=k
Answer:
k=13
Step-by-step explanation:
substitute x and y
4+9=k
k=13
Answer:
13
Step-by-step explanation:
Plug in the given x and y values: 2(2) + 3 (3) = k
Then multiply 4 + 9 = k
Then add 13 = k
Select all of the following expressions that require use of the distributive property to simplify.
√5(-√2)
√5(√7-√2)
(√5+√2)(-√7)
(3√5)(-7√2)
Answer:
√5(√7-√2)
(√5+√2)(-√7)
Step-by-step explanation:
The Distributive Property:
a ( b + c ) = ab + ac
Where a, b and c are any real numbers.
The given options the correct expressions that require the use of the distributive property to simplify are √5(√7-√2) and
(√5+√2)(-√7)
Distributive propertyGiven the integers A, B, and C. According to the distributive property;
A(B + C) = AB + ACFrom the expression, you can see that A is distributed over B and C
So for distributive property, there must be a factor and the sum of terms in parenthesis. Based on the given options the correct expressions that require the use of the distributive property to simplify are √5(√7-√2) and
(√5+√2)(-√7)
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A survey showed that 7/15 of a class liked soccer and 2/5 liked baseball. Which sport was liked less?
Answer:
baseball my guy
Step-by-step explanation:QUICK MATHS
Answer: baseball is liked less
Step-by-step explanation: its liked less because the common denominator is 15 and whatever you times the bottom by you times the top by. so 2/5 x 3= 6/15<7/15 hope that helped!:)
Which expression is equivalent to 2(5 − 3x)?
Answer:
10-6x
Step-by-step explanation:
Hope this helped, have a great day! (mark brainliest if you want to help XD)
Answer:
10 - 6x
as 2 x 5= 10
and 2 x 3 = 6
10 - 6x
Step-by-step explanation:
It takes my father 3 hours to plow our cornfield with his new tractor. Using the old tractor it takes me 5 hours. If we both plow for one hour before I go to school, how long will it take him to finish the plowing?
It takes my Father 3 hours to plow the our cornfield with his new tractor.
Using the old tractor it takes me 5 hours.
If we both plow for 1 hour before I go to school,how long will it take him to finish
:
let t = time Dad plows after he goes to school
:
Let the completed job = 1; (a plowed field)
:
A shared work equation
%28%28t%2B1%29%29%2F3 + 1%2F5 = 1
Multiply by 15, results
5(t+1) + 3 = 15
5t + 5 + 3 = 15
5t = 15 - 8
t = 7%2F5
ANSWER
t = 1.4 hrs or 1 + .4(60) = 1 hr 24 more minutes to finish
hope this helps :)
not good with these someone should help me:( picture included
Answer:
Volume=2/6cu.ft
Step-by-step explanation:
.........................
option B
Which of the following equations have exactly one solution?
Choose all answers that apply:
Choose all answers that apply:
(Choice A)
A
-19x-18=-19x+18−19x−18=−19x+18minus, 19, x, minus, 18, equals, minus, 19, x, plus, 18
(Choice B)
B
-19x+18=-19x+18−19x+18=−19x+18minus, 19, x, plus, 18, equals, minus, 19, x, plus, 18
(Choice C)
C
19x-18=-19x+1819x−18=−19x+1819, x, minus, 18, equals, minus, 19, x, plus, 18
(Choice D)
D
19x+18=-19x+1819x+18=−19x+18
Answer:
Options C and D.
Step-by-step explanation:
Choice (A).
-19x - 18 = -19x + 18
Here we are equating two equations,
y = -19x - 18
y = -19x + 18
Since slopes of these equations are same as (-19), both are parallel.
Therefore, there is no solution for the given system of equations.
Choice (B)
-19x + 18 = -19x + 18
Equations are,
y = -19x + 18
y = -19x + 18
Since both the equations represent the same line, so the system of equations will have infinite solutions.
Choice (C)
19x - 18 = -19x + 18
System of equations is,
y = 19x - 18
y = -19x + 18
Slopes of both the lines are different (19 and -19)
Therefore, the system of equations will have exactly one solution.
Choice (D)
19x + 18 = -19x + 18
System of equations is,
y = 19x + 18
y = -19x + 18
This system of equations have the different slopes.
Therefore, the system of equations will have exactly one solution.
Answer:
It got B and D
Step-by-step explanation:
....
......
sorry if it’s wrong
actauloy edit there is two of them and one of them is this answer and one of them is another one so take your luck and make sure to match up the numbers
2p^2+p-4=0
Can someone please help and show how you did it I am not understanding this thank you so much
See the attached picture:
Unit 6. 2) Please help. What is the probability that a student is absent given that today is Monday?
Enter your answer as a fraction in simplest form, formatted like this: 3/14
Answer:
Let's denote:
The probability that today is Monday: P(A)
The probability that a student is absent: P(B)
The probability that a student is absent given that day is Monday: P(B|A)
As given,
P(A intersect B) = 3/100
P(A) = 1/5
=> P(B|A) x P(A) = P(A intersect B)
=> P(B|A) = P(A intersect B)/P(A) = (3/100)/(1/5) = 15/100 = 3/20
Hope this helps!
:)
never mind LOL i got it
Answer:
C.
Step-by-step explanation:
Adjacent / Hypotenuse = 24 / 25
How many servings of
cups are in 5 cups of ice cream?
Answer:
5
Step-by-step explanation:
