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We have#f=X^35X^2+a,ainRR#.How to prove that #f# has at most a root in #ZZ#?

We have#f=X^32X^2+2X+m,m inRR#.How to prove that #f# does not have
all roots in #RR#?

We have#f=X^32X^2+2X+m,m inRR#.How to prove that #f# does not have
all roots in #RR#?

We have #A(0,0) B(21,0), C(0,21)#.How to find number of points that have both coordinates integer numbers inside triangle #ABC#?

How do you rationalize the denominator and simplify #(3sqrt9)/sqrt27#?

How do you solve #2abs(4x  6)  8 = 12#?

A committee of three is to be selected at random from five married couples.What is the probability that no two members of the committee are married to each other?

How do you find the fourth partial sum of #Sigma 5(1/2)^i# from i=1 to #oo#?

How do you prove this equality #sqrt(3+sqrt(3)+(10+6sqrt(3))^(2/3))=sqrt(3)+1# ?

We have#f:{1,2,3}>{1,2}# and #g:{1,2,3}>{1,2,3,4}#.How many injective #f# and #g# funtions exist?

How I resolve this limit?

Are the given infinite geometric series below has a sum? If they do, how to find it?
(1) 100 + 110 + 121 + .....
(2) 100 + 10 + 1 + .....
(3) 0.3 + 0.6 + 1.2 + .....

How do you find the compositions given #f(x) = x  2#, #g(x) = sqrtx#?

How to write a formula for the nth term of the geometric sequence below and how to use that formula for #a_n# to find #a_8#, which is the 8th term of the sequence?
(1) 4, 4, 4, 4, .....
(2) 16, 8, 4, .....

Find the range of values of k for which #" "x^2 + (k+3)x +4k >3# for all real values of #x#?

Cos (x+π/2)=sinx...but if this whole function is powered by even number what will be the answer?

How do you solve #7x  15<20#?

Who's interested in a new Socratic on a different website?

How do you find three consecutive even integers such that the sum of twice the first and third is 40?

How do I find the limits of piecewise functions?

Thoughts on the recent announcement made about the future of the Socratic website? Share them here!

How do I use one sided derivatives to show that the function #f(x)=x^3 , x<=1#
#f(x)=3x , x>1# is not differentiable at x=1?

How do you solve #x+2+x2=4#?

What is the X intercept of
Y + 12=3(x9)?
Substitute 0 for X or y? And solve for ??? X or y?

A cylinder has a height of 7 cm and a diameter of 5 cm. What is the volume of the cylinder?

How do you find #int(e^x)/(1+e^x)dx#?

Does the series converge or diverge?

Two fair dice are thrown,what is the probability of getting two odd numbers?

40% of the boys, 70% of the girls in a class attend a picnic and ratio of boys to girls in the class is 3:2 if the number on the picnic was 27. How many are there in the whole class?

How do you solve the system using the elimination method for 9x  6y = 12 and 3x  2y = 20?

A sequence is defined by the recursive formula f (n + 1) = f(n) – 2. If f(1) = 18, what is f(5)?

The value of 'x' for which f(x)=x  x+1 is discontinuos is ?

How do you write a rule for the nth term 7,5,3,1,1?

Given the nth term for each arithmetic sequence, how to find the common difference and write out the first four terms here?
(1) #a_n=2n+7#
(2) #a_n=3n2#

How can I solve this limit?
(1) lim x>infinity (sin x) / x
(2) lim x>infinity ( cos x)/x

In a certain isosceles right triangle, the altitude to the hypotenuse has length 4#sqrt(2)# . What is the area of the triangle?

Please explain, this is a Linear transformation or not ?

How do you graph and solve #8n+4 > 4#?

Find the value of k if f(x) has three distinct real roots ?

The sum of two numbers is 72, and twice their difference is 24. What is the smaller of the two numbers?

How do you solve #3( x  3)  7x =  5#?

How do you find domain and range for #y= x^22#?

Show that the equation x^4 + 2x^2 − 2 = 0 has exactly one solution on
[0, 1]?

Find the equation of straight line having a gradient of #1/t# and passing through the point(#t^2#,2t).(pls see details below). ?

Find range of a function given the domain??

What is the difference between set notation and interval notation?

What is the domain and range of y=the square root of 2x7? Thanks

What is the scientific notation for 8 million?

How do you find the domain of #f(x) = 3x + 1#?

#m2+14m+33=#?

Show that the set is a vector space in the field of real numbers?

How do you simplify #52!#?

The numbers x, y, and z are the first three terms of an arithmetic sequence. How do you express z in terms of x and y?

In the sequence 1,2,2,4,4,4,4,8,8,8,8,8,8,8,8 where n consective terms have the value n, then 1025th term is?

How do you graph # ln(x2)#?

How do you write the equation of the circle with diameter that has endpoints at (–4, –1) and (–8, –9)?

How do I find the lower bound of a function?

How do you write the standard form of the equation of the circle with center (0,0) R=6?

How do you find the number of distinguishable permutations of the group of letters: A, L, G, E, B, R, A?

Proving Trigonometric Identities?

How do you solve #12<8+x#?

Can a triangle have more than one obtuse angle?

Draw the graphof leniar equation
x+y=4?

Lilly let her friend borrow 1/10 of the money in her purse to buy a snack. How do you write the fraction as a decimal?

How do you solve #sqrtv = 2# and find any extraneous solutions?

Any tips about the solution ??? using the Mathematical induction and thanks :)

If x28x1=0 then prove that x2+1/x2 ?

If #A= <5 ,4 ,7 ># and #B= <2 ,9 ,8 >#, what is #A*B A B#?

Prove that if G is not equal to {e} and G has no proper nontrivial subgroup,then G is finite and o(G) is a prime number.?

What is 20% of 46.60?

Help plz !
we say that 1) #x\inuuu_(n\inN)A_n# if #x\inA_n# for some #n\inN# and
2)#x\innnn_(n\inN)A_n# if #x\inA_n# for all #n\inN#
prove or dispprove #nnn_(n\inN)A_n\sube uuu_(n\inN)A_n# for any index set #N# ?

What is Six more than half of a number x ?

What is four times a number b which is 3 more than h ?

Find the equation of the circle centered at (3,4) and radius =5?

How to show that #S_oo S_n= (1/3)^n# ,given, #S_oo=9/4# and #S_n=9/4(1(1/3)^n)#?

How do you solve #y=2/7x+2, 6x21y=42#?

How do you solve #(x+1)/3 = (2x1)/4#?

Jack usually mows his lawn in 5 hours. Marilyn can mow the same yard in 7 hours. How much time would it take for them to mow the lawn together?

How do you solve and graph #5h+ 4>=6# and #7h+11<32#?

Six times the sum of a number and 3 is 12 less than 12 times the number. How do you find the number?

If f(x)=2x^3/5+7 ,find f^1(x)?

What is the distance between points( 6 , 9 ) and( 6 , − 9 ) on a coordinate plane?

What is the simplified expression of ³(the square root of)64⁶ ?

How do you solve #8e^(p)=49#?

How to prove this ?
#2k^2# then #2k# for some #k\inZZ#

What is the equation of the line with slope # m= 3/7 # that passes through # (17/13,14/7) #?

If #f(x) = 3x + 5# and #g(x) = x^2#, what is #f(x) + g(x)#?

What is the equation of the line passing through the point (4, 6) and parallel to the line y= 1/4x + 4?

How do you evaluate f(2) given #f(x)=x^24#?

How do I convert 101 degrees fahrenheit into degrees celsius?

How do you graph #y=sqrt(x1)# and how does it compare to the parent function?

How do you solve #\frac { 4a + 5} { a + 8} = \frac { 4a + 6} { a + 9}#?

How do you find the x and y intercepts and slope if they exist and graph the line 2x + 7y = 14?

How can I find the horizontal intercept of the equation #y=4x^28x+12# algebraically?

The sum of the two numbers is 12. The difference between them is 4. Find the numbers?

Suppose in a right triangle, cos(t)=3/4. How do you find: cot(t)?

How do you graph #y=x7# by plotting points?

Integrate 1/9+cosx dx?

Can the quadratic formula be used with functions of the form #f(x)=ae^(bx)+ce^((b/2)x)+d#? Why or why not?

If a circle has center (0,0) and a point on the circle (2,4) write the equation of the circle.?

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