12 more than m machines
Answer:
m+12
Step-by-step explanation:
m+12
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 number x can be written as m/n, where m and n are relatively prime positive integers.
Find m+n.
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.
Learn more about the geometric sequence here;
https://brainly.com/question/1509142
how many solutions to x^2 =-16
Answer:
no real solutions
Step-by-step explanation:
I cant fail please help
Question is on picture
Answer:
the answer is A
Step-by-step explanation:
Given the fractions 8/15 and 18/35, find the largest number that these fractions can be divided by, so that the quotient will be a whole number.
Answer:
Therefore the largest number that these fractions can be divided by to give them a whole number is
a) 8/15 = The largest number is 8/15
b) 18/35 = The largest number is 18/35
Step-by-step explanation:
A quotient is the result obtained by dividing two numbers.
So that the quotient obtained is a whole number we have to find out, what number they can be divided by to give them that.
Let's assume the whole number is 1
a. 8/15
8/15 ÷ x = 1
8/15 × 1/x = 1
8/15x = 1
We would cross multiply
8 = 15x
We would divide both sides by 15
8/ 15 = x
Hence the largest number that would divide 8/15 and give it a whole number = 8/15
b) 18/35
18/35÷ x = 1
18/35 × 1/x = 1
18/35x = 1
We would cross multiply
18 = 35x
We would divide both sides by 35
18/ 315 = x
Hence the largest number that would divide 18/35 and give it a whole number = 18/35
Answer:
The answer is 2/105
Step-by-step explanation:
first we have to find the LCM of both denominators. IN this case, the LCM of 15 and 35 is 105. Then we have to find the GCF of these numerators. IN this case, the GCF of 8 and 18 is 2.
Now, put the GCF you found over the LCM.
ANSWER: 2/105
This fraction is the largest number you can divide both numbers by to get a whole number.
Which best describes the transformation that occurs from
the graph of f(x) = x2 to g(x) = (x - 2)²+ 3?
Answer:
The graph changes from the original position to right 3 units and down 1 unit.
I hope this helps. If you have any more questions, please feel free to post them and someone will be able to help you, whether it's myself or others. Please leave a like, rating, and if possible, Brainliest. Have a great day!
Natalie is out for a run. She decides to run a park in town. The length of sides of the park are 15 feet, 1o feet, 12 feet and 14 feet. How many feet will natalie run?
Answer:
51 feet
Step-by-step explanation:
To find how many feet will Natalie run, we just need to sum the four sides of the park that she will run:
Total distance = 15 + 10 + 12 + 14 = 51 feet
So if Natalie runs the sides of the park, she will run a total of 51 feet.
This value is also the perimeter of the park, that is, the sum of all 4 sides of the park.
x^2+y=3
x^2-y=5
solve by using substitution
show work please
Answer:
x = 2
y = -1
Step-by-step explanation:
x² + y = 3 --------------------(i)
x² = 3 - y
x² - y = 5 ---------------------(ii)
substitute x² = 3 - y in equation (ii)
x² - y = 5
3 - y -y = 5 {Add like terms}
3 - 2y = 5 {Subtract 3 from both sides}
3 - 2y -3 = 5 - 3
-2y = 2 {divide both sides by -2}
-2y/-2 = 2/-2
y = -1
Substitute the value of y in equation (i)
x² + y = 3
x² - 1= 3 {Add 1 to both sides}
x² - 1 + 1 = 3+ 1
x² = 4
x = √4
x = 2
Emma Punch with 3/4 gallons of pineapple juice 1 1/2 gallons of orange juice and 7/8 gallons of apple juice how much gallons of Ginger ale does she need to add to make the total of 4 gallons of punch
Answer:
7/8 gallons of Ginger aleStep-by-step explanation:
Total gallons of punch mixture = gallons of pineapple juice + orange juice + gallons of apple juice + gallons of Ginger ale
Given gallons of pineapple juice = 3/4 gallons
Orange juice = 1 1/2 gallons
Gallons of apple juice = 7/8
Total gallons of punch = 4 gallons
On substituting into the formula above:
4 = [tex]\frac{3}{4} +\frac{3}{2}+\frac{7}{8}+Gallons\ of\ ginger\ ale[/tex]
[tex]4=\frac{6+12+7}{8} + Gallons\ of\ ginger\ ale[/tex]]
gallons of ginger ale = [tex]4-\frac{25}{8}[/tex]
gallons ginger ale = [tex]\frac{7}{8}[/tex]
She needs 7/8 gallons of Ginger ale to make the total of 4 gallons of punch
Answer:
Emma would need 7/8 gallons of Ginger Ale to make the total of 4 gallons of punch.
Step-by-step explanation:
In the question, Emma used different quantities of juice to make a punch. To find the remainder, needed to make 4 gallons, we sum up the given quantities, and subtract it from the expected amount.
The summation of the given quantities of juice is as follows;
3/4 + 1 1/2 +7/8 = 25/8
We no subtract the quantity we already have from the expected amount, which is 4 gallons, thus;
4 - 25/8 = 7/8 gallons of Ginger Ale.
To confirm the answer, we sum up all the given quantities. Therefore;
3/4 + 1 1/2 + 7/8 + 7/8 = 4 gallons of punch.
hi!! <3 i attached a picture of a easy trigonometry question can you please help if you don’t mind <33
Answer:
Side AB has a length of 4, and side BC has a length of 11.7
5(2k-3)+17 helppppppppp i need it simplified
Answer:
2(5k + 1)
Step-by-step explanation:
5(2k - 3) + 17 =
10k - 15 + 17
10k + 17 - 15
10k + 2
2(5k + 1)
Describe the process for calculating the volume of a cylinder.
Answer:
the formulae for the volume of a cylinder= πr²h
so we then put the figures at their respective positions. and for the pie we put either 22/7 or 3.143 or 3.14
What is the equation of the following line? Be sure to scroll down first to see all answer options.
A. y = 3x
B. y = x
C. y = 2x
D. y = -1/3x
E. y = -3x
F. y = 1/3x
1. The speed of a motorcycle increases from 10 km/hr to 50 km/hr in 9
seconds. What is its acceleration?*
Answer:
The acceleration is 4.4 km/sec/sec
Step-by-step explanation:
Acceleration of motorcycle is 4.44 km/sec²
Given that;Starting velocity = 10 km/hr
Final velocity = 50 km/hr
Time taken = 9 second
Find:Acceleration of motorcycle
Computation:Acceleration of motorcycle = [Final velocity - Initial velocity] / Time taken
Acceleration of motorcycle = [50 - 10] / 9
Acceleration of motorcycle = [40] / 9
Acceleration of motorcycle = 4.44 km/sec²
Learn more:https://brainly.com/question/12550364?referrer=searchResults
how many days are in a year. ALSO ANSWER MY OTHER MATH QUESTION PLEASE!
Answer:
365 1/4 days
Also I haven't seen your other question
Answer:
365, 366 every 4 years. 366 on 2020, 2024, 2028, 2032, 2036, 2040 and so on
1.-En una estación de autobuses de la Ciudad de México hay dos líneas que llevan a Cuautla, Morelos. Ambas tienen salidas desde las 6:00 am, la primera, tiene salidas cada 15 minutos y la segunda cada 20. Si los primeros camiones de ambas líneas salen a las 6:00, ¿a qué hora coincidirán nuevamente en la salida?
2.-Tita está haciendo unos recuerdos y está colocando dulces en ellos. Tiene 48 paletas de malvavisco y 32 bolsitas de lunetas. Quiere repartirlos en partes iguales y que a cada familiar le toque el número mayor de dulces y de manera exacta. Calcula el número máximo que le puede tocar a cada persona, cuánto le toca a cada uno y hasta cuántos recuerdos puede hacer.
Answer:
1) 7 : 00 am, 2) 3 paletas de malvavisco, 2 bolsitas de lunetas, 16 recuerdos.
Step-by-step explanation:
(Both exercises are written in Spanish. Hence, explanations will be held in that language)
1) Las ecuaciones que describen el tiempo transcurrido en función del número de salidas de cada línea son, respectivamente:
Primera Línea
[tex]t_{1} = 15\cdot n_{1}[/tex]
Segunda Línea
[tex]t_{2} = 20\cdot n_{2}[/tex]
Donde t se mide en minutos. La siguiente relación se obtiene a partir de de igualar y sustituir el tiempo de ambas ecuaciones.
[tex]15\cdot n_{1} = 20\cdot n_{2}[/tex]
La siguiente relación es construida:
[tex]n_{1} = \frac{20}{15}\cdot n_{2}[/tex]
[tex]n_{1} = \frac{4}{3}\cdot n_{2}[/tex]
Tanto [tex]n_{1}[/tex] como [tex]n_{2}[/tex] son números naturales, si [tex]n_{2} = 3[/tex], entonces:
[tex]n_{1} = 4[/tex]
Finalmente, el tiempo transcurrido es:
[tex]t_{1} = 15\cdot (4)[/tex]
[tex]t_{1} = 60\,min[/tex]
En consecuencia, las salidas coincidirán a las 7 : 00 am.
2) El máximo número de recuerdos es determinado por el menor número de determinados dulces. Las bolsitas de lunetas representan el limitante, la razón de paletas de malvavisco a bolsitas de lunetas es:
[tex]x = \frac{48\,m}{32\,l}[/tex]
[tex]x = \frac{3\,m}{2\,l}[/tex]
La proporción óptima es de 3 paletas de malvavisco por cada 2 bolsitas de lunetas. Entonces, el máximo número de recuerdos es:
[tex]y = \frac{32}{2}[/tex]
[tex]y = 16[/tex]
El máximo número de recuerdos es 16.
plzzzzzzzzzzzzzaaaaaa
Answer:
C
Step-by-step explanation:
[tex]y^2+4y-32=0\\(y+8)(y-4)=0\\y=4,-8[/tex]
Therefore, the answer is C. Hope this helps!
Let m=x^2-5m=x 2 −5m, equals, x, squared, minus, 5. Which equation is equivalent to (x^2-5)^2-3x^2+15=-2(x 2 −5) 2 −3x 2 +15=−2left parenthesis, x, squared, minus, 5, right parenthesis, squared, minus, 3, x, squared, plus, 15, equals, minus, 2 in terms of m ?
Answer:
[tex]m^2-3m=-2[/tex][tex]m^2-3m+2=0[/tex]Step-by-step explanation:
Let [tex]m=x^2-5[/tex]
We want to express the equation [tex](x^2-5)^2-3x^2+15=-2[/tex] in terms of m.
Given: [tex](x^2-5)^2-3x^2+15=-2[/tex]
Factorizing the third and fourth term, we obtain:
[tex](x^2-5)^2-3(x^2-5)=-2[/tex]
Substituting [tex]m=x^2-5[/tex], the above equation becomes:
[tex]m^2-3m=-2[/tex]
Since the options are not given, the equivalent equation is:
[tex]m^2-3m=-2[/tex]
It could also be written in a rearranged form as:
[tex]m^2-3m+2=0[/tex]
Sadie uses 9.8 pints of blue paint and white paint to paint her bedroom walls. 1 4 of this amount is blue paint, and the rest is white paint. How many pints of white paint did she use to paint her bedroom walls?
Answer:
7.35 pints
Step-by-step explanation:
If we use 1/4 of the 9.8 pints for blue, then the remaining white paint takes up 3/4 of the 9.8 pints of paint. To find how many pints of paint is equal to 3/4 of it, you must multiply that fraction by the amount (9.8).
[tex]\frac{3}{4}[/tex] * 9.8 (or 0.75 * 9.8) = 7.35
Therefore, 7.35 pints of the total paint used is white.
Hope I helped! Please give me brainliest!
3a/4+2a/3-a/12
a. a/3
b. 4/3
c. (4a)/3
Answer: C
Step-by-step explanation:
[tex]\frac{3a}{4}+\frac{2a}{3}-\frac{a}{12}[/tex]
Find the least common denominator of 4, 3, and 12.
4-3-12 | 3
4-1-4 | 4
1-1-1 |-------- 12
The first fractions needs to be multiplied by 3, and the second fraction, by 4
[tex](\frac{(3a)*3}{(4)*3})+(\frac{(2a)*4}{(3)*4})-\frac{a}{12}[/tex]
Solve;
[tex]\frac{9a}{12}+\frac{8a}{12}-\frac{a}{12}[/tex]
Add the fractions with positive signs and subtract the one with negative sign.
[tex]\frac{(9a+8a)-a}{12}[/tex]
Solve;
[tex]\frac{17a-a}{12}=\frac{16a}{12}[/tex]
Simplify by 4;
16/4=4
12/4=3
[tex]\frac{4a}{3}[/tex]
Answer:
(4a)/3
Step-by-step explanation:
3a/4+2a/3-a/12
find L.C.M
9a+8a-1a/12=16a/12
16a/12=(4a)/3
The areas of the squares adjacent to two sides of a right triangle are 32 units^2 and 32 units^2
Answer:
64 square units.Step-by-step explanation:
In this problem, we have to find the area of an square adjacent to the third side of the right triangle.
To solve this problem, we need to use Pythagorean's Theorem, beacuse it's about a right triangle. Also, this theorem is about square areas, that's the geomtrical meaning of it.
[tex]h^{2} =32 \ u^{2} + 32 \ u^{2} = 64\ u^{2} \\h=\sqrt{64 \ u^{2} } =8u[/tex]
Therefore, the area of a square adjacent to the third side is 64 square units.
Answer:the answer is 8
Step-by-step explanation:
An economy package of cups has 250 green cups if the green cups are 10% of the total package, how many cups are in the package?
Answer:
There are a total of 2500 cups
Step-by-step explanation:
10% of the cups are green
you can set up a equation for this
x = total cups
.10x = 250
multiply both sides by 10 to make x a whole number
x = 2500
Solve the equation for x, and enter your answer below.
10x - 15x + 5= -45 + 40
Answer: x = 2
Step-by-step explanation:
[tex]10x - 15x + 5= -45 + 40[/tex]
subtract 5
[tex]10x - 15x= -45 + 40-5[/tex]
Combine like terms;
[tex]-5x=-10[/tex]
Divide by -5
[tex]x=\frac{-10}{-5}\\ x=2[/tex]
Answer:
[tex]x = 2[/tex]
Step-by-step explanation:
[tex]10x - 15x + 5 = - 45 + 40 \\ 10x - 15x = - 5 - 45 + 40 \\ - 5x = - 10 \\ \frac{ - 5x}{ - 5} = \frac{ - 10}{ - 5} \\ x = 2[/tex]
I'll give Brainliest!!!
What is 5 1/2 divided by 5 1/3 equal?
A hockey team has a 75% chance of winning against the opposing team in each game of a playoff series. To win the series, the team must be the first to win 4 games.
A) Design a simulation for this event,
B) what counts as a successful outcome?
C) Estimate the probability using your simulation.
Can anyone help me? I’m kind of confused on this problem
Answer:
C. Estimate the probability using your simulation.
Step-by-step explanation:
7. How many Cones will it take to fill a Cylinder with the same height and radius?
O 6 cones
O 3 cones
O 1 cone
O 2 cones
Answer:
3 cones
Step-by-step explanation:
This is why the formula for the volume of a cone is 1/3 (π×r^2)× h, while the volume for a cylinder is (π× r^2)× h, respectively.
Answer:
C) 3 Cones.
Explanation:
Hope this helps! :)
volume of cone with radius of 6 and heights of 8
Hey there! I'm happy to help!
To find the volume of a cone, you multiply the base by the height and then divide by three.
The base of a cone is a circle. To find the area of a circle, we square the radius and then multiply it by pi (we will use 3.14). Let's find the base below.
6²=36
36×3.14=113.04
Now, we multiply by the height.
113.04×8=904.32
Finally, we divide by three.
904.32÷3=301.44
Therefore, the volume of this cone is about 301.44 units cubed.
Now you can find the area of cones! I hope that this helps! Have a wonderful day!
Answer:
301.44
Step-by-step explanation:
The price of a shirt was marked up from $24 to $30What is the percent of increase?
Answer:
25% increase
Step-by-step explanation:
First take the new price and subtract the original price
30-24 = 6
Divide by the original price
6/24 = 1/4 = .25
Change to percent form
25%
The price went up so it is an increase
25% increase
Answ believe 25%er:
Step-by-step explanation:
In the past twenty years, scientists have seen the sea level rise at a rate of approximately 0.13 inches per year. If this rate continues, which best represents the change in sea level over the next 27 months (2.25 years)?
Answer:
The change in the sea level will be by 0.2925 inches
Step-by-step explanation:
First of all , we will need to write out the rate at which the sea level is rising. This is 0.13 inches, per year. This means that every year, the sea level increases by 0.13 inches.
Since the sea level increases by 0.13 inches every year, in 2.25 years, to get the sea level, we will have to multiply the current rate at which it is rising by that duration of time.
This will be 2.25 years X 0.13 inches/ year = 0.2925 inches
Therefore, the change in the sea level will be by 0.2925 inches
Answer:
0.2925 inches
Step-by-step explanation:
