If three numbers 36,54 and another number have a G.C.D of 6 and L.C.M of 216, find the other number
Answers
Answer:
24
Step-by-step explanation:
The GCD of a set of numbers is the product of the prime factors, each to the lowest of the powers it has as a factor of any of the numbers.
The LCM of a set of numbers is the product of the prime factors, each to the highest of the powers it has as a factor of any of the numbers.
__
The factorizations of the given numbers are ...
36 = 2^2 × 3^2
54 = 2 × 3^3
__
6 = 2 × 3 . . . . . . . . . . . GCD
216 = 2^3 × 3^3 . . . . . LCM
This tells us the lowest powers of 2 and 3 are 2^1 and 3^1, and the highest powers of 2 and 3 are 2^3 and 3^3. Already, the lowest power of 2 matches the GCD, and the highest power of 3 matches the LCM. What we need is a number with a power of 2 that is 3, and a power of 3 that is 1:
2^3 × 3^1 = 24
The other number is 24.
Related Questions
Solve for x
12
(x + 2)/
B
O 14
O 10
12
06
Answers
Answer:
opposite sides of ||gram are equal and parallel therefore
12=x+2
12-2=x
10=x
pls mark as brainliest
(HELP!!!)
Identify the variable expression that is “not” a polynomial.
A. x+2
B. XA+7
C. 24
D. y + x
Answers
Identify the variable expression that is “not” a polynomial.
Try looking for the one that breaks the rules of it being a polynomial.
If n'(x) = 2sin(2x) and n(0) = 0 what is the absolute maximum of n(x) on (0,2-}?
Answers
The absolute maximum of n(x) = 1 - 2 · cos 2x, whose first derivative is n(0) = 0, exists at x = 0.5π on (0, 2π]. The value of the absolute maximum is 3.
How to find the absolute maximum of a differentiable function
A function is differentiable in a given interval if and only if its derivative exists for every value of the interval. To determine the absolute maximum of n(x), we need to integrate the given function, apply first derivative and second derivative test and finally evaluate n(x).
First, we integrate n'(x) in terms of x:
n(x) = 2 ∫ sin 2x dx = 2 · (- 0.5 · cos 2x) + C = - cos 2x + C
- cos 0 + C = 0
C = 1
Then, n(x) = 1 - 2 · cos 2x.
Now we proceed to apply first and second derivative tests:
First derivative test2 · sin 2x = 0
sin 2x = 0
2 · x = sin⁻¹ 0
2 · x = π ∨ 2π
x = 0.5π ∨ π
Second derivative testn''(x) = 4 · cos 2x
n''(π) = 4 · cos 2π
n''(π) = 4
There is an absolute minimum for x = π. [tex]\blacksquare[/tex]
n''(0.5π) = 4 · cos π
n''(0.5π) = - 4
There is an absolute maximum for x = 0.5π. [tex]\blacksquare[/tex]
Finally, we evaluate n(x) for x = 0.5π to determine the absolute maximum:
n(0.5π) = 1 - 2 · cos π
n(0.5π) = 3
The absolute maximum of n(x) = 1 - 2 · cos 2x, whose first derivative is n(0) = 0, exists at x = 0.5π on (0, 2π]. The value of the absolute maximum is 3. [tex]\blacksquare[/tex]
RemarkThe statement of the question is poorly formatted and reports several mistakes, correct form is introduced below:
If n'(x) = 2 · sin 2x and n(0) = 0. What is the absolute maximum of n(x) on (0, 2π]?
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What is the domain of the function on the graph? 5 01 4. 3 O all real numbers all real numbers greater than or equal to 0 all real numbers greater than or equal to -2 all real numbers greater than or equal to -3 2 1 + 5 4 3 2 1 1 2 3 4 5 X -21 -3+ -4 J
Answers
Option (4) all real numbers greater than or equal to -3
Step-by-step explanation:
Domain: Domain of function is defined by the x-values (Input values) on the graph.
Range: Range of a function is defined by the y-values (output values) on the graph.
x-values are starting from (-3) to infinity.
Therefore, domain of the function will be all real numbers greater than equal to (-3). Option (4) will be the answer.
The domain of the function are all real numbers greater than or equal to -3.
What is function?A function is a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.
Given is a graph, we need to find domain of the function on the graph,
Domain is the set of all possible inputs or x-values, for which the given function is defined.
The given graph is defined form -3 to positive infinity. The point -3 included in the set of input because there is a closed circle at x=-3.
So, domain of the function are all real numbers greater than or equal to –3.
Hence, the domain of the function are all real numbers greater than or equal to -3.
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P=1/2
q=-1/3
r=1/5
30pqr(p+q+r)/(p+q)(p+r)
Answer -22/7
Answers
Answer:
Given:
[tex]p=\dfrac12[/tex][tex]q=-\dfrac13[/tex][tex]r=\dfrac15[/tex]Given expression:
[tex]\dfrac{30pqr(p+q+r)}{(p+q)(p+r)}[/tex]
Substitute given values into given expression:
[tex]\implies \dfrac{30\cdot\dfrac12\cdot-\dfrac13\cdot\dfrac15\left(\dfrac12-\dfrac13+\dfrac15\right)}{\left(\dfrac12-\dfrac13\right)\left(\dfrac12+\dfrac15\right)}[/tex]
[tex]\implies \dfrac{-\dfrac{30}{30}\left(\dfrac{15}{30}-\dfrac{10}{30}+\dfrac{6}{30}\right)}{\left(\dfrac36-\dfrac26\right)\left(\dfrac{5}{10}+\dfrac{2}{10}\right)}[/tex]
[tex]\implies \dfrac{-1\left(\dfrac{11}{30}\right)}{\left(\dfrac16\right)\left(\dfrac{7}{10}\right)}[/tex]
[tex]\implies \dfrac{-\dfrac{11}{30}}{\dfrac{7}{60}}[/tex]
[tex]\implies -\dfrac{11}{30}\times \dfrac{60}{7}[/tex]
[tex]\implies -\dfrac{660}{210}[/tex]
[tex]\implies -\dfrac{22}{7}[/tex]
Anthony is 3 years older than his brother. write an equation you can use to find their ages. do not solve
Answers
equation: 3+x=
anthony= 3 years older
x= age of his brother
You must add 3 more years to the brother's age.
please help urgent math photo attached
Answers
Answer:
K = (-5, 14)
Step-by-step explanation:
For writing equations of parallel and perpendicular lines, it is convenient to start with equations in general form:
ax +by +c = 0
Rewriting the given equations, we have ...
y = 1/2x -1
x -2y -2 = 0 . . . . . line d
y = -3x +2
3x +y -2 = 0 . . . . . line d'
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A parallel line will have the same coefficients, but a constant appropriate to the required point on the line.
Parallel to d' through A(-1, 2):
3(x -(-1)) +(y -2) = 0
3x +y +1 = 0 . . . . . . . . simplify
__
A perpendicular line will have the coefficients swapped and one of them negated. Again, the constant is appropriate to the required point.
Perpendicular to d through B(3, -2):
2(x -3) +(y -(-2)) = 0
2x +y -4 = 0 . . . . . . . . simplify
__
The solution to this system of equations can be found by subtracting the second equation from the first:
(3x +y +1) -(2x +y -4) = (0) -(0)
x +5 = 0
x = -5
Substituting into the second equation gives ...
2(-5) +y -4 = 0
y -14 = 0
y = 14
The coordinates of point K are ...
K = (-5, 14)
_____
Additional comment
The general line through the origin ...
ax +by = 0
can be translated to go through point (h, k) by the usual method for translating functions. The variable x is replaced by (x -h), and the variable y is replaced by (y -k). Using the general form equation means we can keep the variables and constants all on the same side of the equal sign, saving a bit of work and confusion.
a(x -h) +b(y -k) = 0 . . . . . . line through point (h, k)
__
The graph is drawn by a geometry program capable of drawing parallel and perpendicular lines through given points. It confirms the equations and th solution.
Solve the inequality below: (Remember to use x < or >or< or > ) and then choose the solution set on the number line below.-4x-5<-25 Part A SOlve the inequality
Answers
Answer:
{x : x > 5}
Step-by-step explanation:
-4x - 5 < -25
-4x < -20
When dividing/multiplying both sides with a negative number, change the inequality symbol to the opposite direction. e.g. < to > or > to <.
x > -20/-4
x > 5
Hence, the solution set is {x : x > 5}.
What does 48906478×78955680 equal to
Answers
Answer:
3861444226895040
Step-by-step explanation:
You do not want to know.
help its for calculus
Answers
Answer:
the first one
Step-by-step explanation:
Answer:
its 1/sqrt{5}+2
Find the missing length. Round to the nearest tenth, if necessary. A right triangle has legs measuring 8 units and x units and a hypotenuse measuring 21 units.
Answers
Answer:
168
Step-by-step explanation:
y = -7⁄2 x + 86
y = -7⁄2 (10) + 86
y = 51 points
Answers
Answer:
I think you are incorrect
Step-by-step explanation:
this was the answer i got 121
Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).
For which intervals is the function increasing?
Select each correct answer.
(2, ∞)
(1, 2)
(−∞, 0)
(0, 1)
Answers
Answer:
That would be (2, infinite)
Step-by-step explanation:
hope this helps
helpppp!! i’m willing to give all my points and brainliest, especially w explanation!
Answers
One angle is always 90° or right angle.
The side opposite angle 90° is the hypotenuse.
The hypotenuse is always the longest side.
The sum of the other two interior angles is equal to 90°.
The other two sides adjacent to the right angle are called base and perpendicular.
a quick way to find angle 1, is just to look at the figure. there seems to be bisecting angles, so angle FCE and angle 1 are congruent. (meaning angle 1 is also 34 degrees)
hope this helps! lmk.
How can you determine which part of the triangle is the base and which is the height?
Answers
URGENTTTTT
Describe the graph of f(x)=-3(x+1)^2 (x-3) (x-5)^3. Include as much information in your description as possible.
(i will not click on links so dont even try-)
Answers
The graph is not symmetric, and it has no vertical or horizontal asymptotes.
What is coordinate geometry ?Coordinate geometry is a branch of mathematics that combines algebraic and geometric concepts to study the properties of geometric figures using a coordinate system. It involves representing geometric figures such as points, lines, curves, and shapes in a plane or space using numerical values called coordinates.
According to given information :The graph of the function [tex]f(x)=-3(x+1)^2 (x-3) (x-5)^3[/tex] is a cubic polynomial function with several important characteristics:
Degree: The degree of the function is 7, which means that the graph has 7 x-intercepts.
Symmetry: The function is not symmetric with respect to the y-axis or the origin.
End Behavior: As x approaches negative infinity, the function approaches negative infinity, and as x approaches positive infinity, the function approaches negative infinity.
Zeros: The function has x-intercepts at x = -1, x = 3, and x = 5. The intercept at x = -1 has a multiplicity of 2, while the intercepts at x = 3 and x = 5 have a multiplicity of 3. This means that the graph touches the x-axis at x = -1 and bounces off at x = 3 and x = 5.
Turning Points: The function has two turning points, one at x = -1 and one at x = 3. The turning point at x = -1 is a local maximum, while the turning point at x = 3 is a local minimum.
Behavior near Zeros: Near each of the x-intercepts, the function changes direction. At x = -1, the function changes from decreasing to increasing. At x = 3 and x = 5, the function changes from increasing to decreasing.
Vertical Asymptotes: The function has no vertical asymptotes.
Horizontal Asymptotes: The function has no horizontal asymptotes.
Intercepts: The y-intercept of the function is at y = 0.
Overall, the graph of the function [tex]f(x)=-3(x+1)^2 (x-3) (x-5)^3[/tex] is a complicated cubic polynomial with multiple x-intercepts, turning points, and changing directions near the intercepts.
Therefore, the graph is not symmetric, and it has no vertical or horizontal asymptotes.
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This graph plots the number of wins last year and this year for a sample of professional football teams.
Based on the line of best fit, which is the BEST prediction for wins this year for a team that won 4 games last year?
2
4
5
7
Answers
Answer:
5 won 4 games last year . This is the best prediction based on the lime fit
Bob is selling raffle tickets. For every 3 tickets, he charges $27 complete the table below showing the number of tickets and the amount Bob charges. (Number of tickets 3 ? 6 ? 9) (charge ($) 27 36 ? 72 ?)
Answers
Those are the number and their corresponding charges. Hope that helps!
Remove the largest possible common factor. Check your answer by multiplication. 9x^(4)+15x^(3)-12x
Factor out the greatest common factor.
Answers
Check x^4 , x^3 , x we can see the largest possible common factor is x
Therefore : the answer is
3x( 3x^3+ 5x^2 - 4)
Answer:
[tex]\bold{3x\left(3x^3+5x^2-4\right)}[/tex]Factor the following
[tex]\hookrightarrow \sf 9x^4+15x^3-12x[/tex]
rewrite the following
[tex]\hookrightarrow \sf 3\cdot \:3x^3x+3\cdot \:5x^2x-3\cdot \:4x[/tex]
factor out the common term 3(x)
[tex]\hookrightarrow \sf 3x\left(3x^3+5x^2-4\right)[/tex]
check for answer through multiplication
[tex]\dashrightarrow \sf 3x\left(3x^3+5x^2-4\right)[/tex]
[tex]\dashrightarrow \sf 3x\left(3x^3)+3x(5x^2)+3x(-4)[/tex]
[tex]\sf \dashrightarrow 9x^4+15x^3-12x[/tex]
Carter says that 0.08 is equivalent to 8/10. Describe and correct Carter's error
Answers
Answer:
Step-by-step explanation:
If we divide 8 by 10, we get 8/10, which reduces to 4/5 or 0.8. Carter misplaced his decimal point.
According to a survey of workers 6/50 of them walk to break 3/50 bike 10/50 carpool and 31/50 Drive alone what percent of workers walk or bike to work
Answers
Answer:
Step-by-step explanation:
6+3=9/50
9/50 x 100=18 percent
If I gallon = 4 quarts, how many gallons are equal to 108 quarts? Explain Your Answer.
Answers
Answer:
27
Step-by-step explanation:
108 ÷ 4 = 27
proportion
if 1/x = 4/108
4x = 108
x = 108/4
x = 27
Will give 30 points to who answers!
Answers
sqrt(5x15)/(3x15)=sqrt75/45
sqrt75=sqrt25 x sqrt3= 5sqrt3
5sqrt3/45
=sqrt3/9
You are considering the two different car loans.
Using the payment table, which loan has the lowest monthly payment?
Answers
Loan A has the lower monthly payment
=========================================================
Explanation:
Loan A is at a rate of 6.9% over 5 years. The table says that if you borrowed $100 at this interest rate and time period, then the monthly payment would be $1.98 per month.
However, you are borrowing $17,601 which is 176.01 times greater than 100 since (17601)/(100) = 176.01
So 1.98*176.01 = 348.4998 = 348.50 is the monthly payment of loan A.
------------------
Meanwhile, loan B has an interest rate of 8.9% and lasts for 3 years. Use the table to see that borrowing $100 at this rate and time means the monthly payment is $3.18
The multiplier this time is 162.90 because (16290)/(100) = 162.90
Therefore, 162.90*3.18 = 518.022 = 518.02 is the monthly payment of loan B.
--------------------
To summarize, we have these monthly payments
loan A monthly payment = $348.50loan B monthly payment = $518.02Loan A has the lower monthly payment
Determine the volume of a rectangular prism if
length = 5 inches
width = 4 inches
height = 4 inches
Answers
Answer:
80 inches cubed
Step-by-step explanation:
V=bh
b= 5 x4 h=4
5 x 4 x 4 = 80
Writing Expressions and Equations the product of 6 and 11
Answers
Answer:
The product of 6 and 11 is 66
But what is the reason for this?The product of two or more numbers is the same as multiplying those numbers together. The product will always be the result.
[tex]6 * 11 = 66~or~66 / 11 = 6[/tex]
Notice how the division problem is just the multiplication problem backwards, for the purpose of better understanding.
Hence, the correct answer is 66
Translate this phrase into an algebraic expression.
7 increased by twice Gail's height
Use the variable g to represent Gail's height.
Answers
Answer:
7+2g
Step-by-step explanation:
7 increased by means 7 +
twice Gali's height =2g
everything now becomes 7+2g
How many cubes with side lengths of 1/2 cm does it take to fill the prism?
Answers
Check the picture below.
so, let's get the volume of the prism.
then let's get the volume of the smaller cube.
then let's see how many times the volume of the cube goes into the prism's volume, so in short a division.
[tex]\stackrel{\textit{prism's volume}}{\left( \frac{5}{2} \right)(2)(1)\implies 5~cm^3}~\hfill \stackrel{\textit{cube's volume}}{\left( \frac{1}{2} \right)\left( \frac{1}{2} \right)\left( \frac{1}{2} \right)\implies \frac{1}{8}~cm^3} \\\\[-0.35em] ~\dotfill\\\\ 5\div \cfrac{1}{8}\implies \cfrac{5}{1}\div \cfrac{1}{8}\implies \cfrac{5}{1}\cdot \cfrac{8}{1}\implies 40~~cubes[/tex]
What do we do to both sides of this equation to solve?
5x=20
Question 3 options:
Add 5 to both sides
Subtract 5 from both sides
Multiply both sides by 5
Divide both sides by 5
Answers
Hello there! :)
Answer:
Divide both sides by 5
Step-by-step explanation:
we are given an equation 5x=20.
First, Add 20 to both sides
[tex]\boxed{x=\frac{20}{5} }[/tex]
Then, Divide both sides by 5.
[tex]\boxed{x=4}[/tex]
Divide 20 by 5 to get 4.
And there you go Our answer is Divide by sides by 5.
-Hope this helps
-Have an awesome weekend :)
[tex]-Yuri-[/tex]
what is 1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18+19+20+21+22+23+24+25+26+27+28+29+30*0.0
Answers
Answer:
435
Step-by-step explanation:
1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18+19+20+21+22+23+24+25+26+27+28+29+30*0.0= 435
Answer:
the answer is: 435
Step-by-step explanation:
