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Discover Frequently Asked Math Questions and Their Answers

• How do you write the quadratic function #y=x^2+14x+11# in vertex form?
• How many points does #y=-2x^2+x-3# have in common with the vertex and where is the vertex in relation to the x axis?
• How do you solve #4x^4 - 16x^2 + 15 = 0#?
• How do you solve #2x^2+3x-2=0#?
• How do you solve #7(x-4)^2-2=54# using any method?
• How do you solve #x^2 + 5x + 6 = 0# algebraically?
• How do you use factoring to solve this equation #3x^2/4=27#?
• What is the vertex of # y = (1/8)(x – 5)^2 - 3#?
• How do you solve #| x^2+3x-2 | =2#?
• How do you solve #2x²+3x=5 # using the quadratic formula?
• How do you find the derivative of #y=tan(3x)# ?
• How do you differentiate #f(x)= 1/ (lnx)# using the quotient rule?
• How do you differentiate #(3+sin(x))/(3x+cos(x))#?
• What is the derivative of this function #sin^-1(x/4)#?
• What is the derivative of this function #y=sin^-1(2x)#?
• What is the derivative of this function #arcsec(x^3)#?
• What is the derivative of #y=sin(tan2x)#?
• How do you differentiate #cos(pi*x^2)#?
• What is the derivative of #f(x)=(x^2-4)ln(x^3/3-4x)#?
• What is the derivative of #y=3sin(x) - sin(3x)#?
• A triangle has corners at #(5 ,1 )#, #(2 ,9 )#, and #(4 ,3 )#. What is the area of the triangle's circumscribed circle?
• How can we find the area of irregular shapes?
• A triangle has vertices A, B, and C. Vertex A has an angle of #pi/2 #, vertex B has an angle of #( pi)/3 #, and the triangle's area is #24 #. What is the area of the triangle's incircle?
• An isosceles triangle has sides A, B, and C with sides B and C being equal in length. If side A goes from #(7 ,1 )# to #(8 ,5 )# and the triangle's area is #27 #, what are the possible coordinates of the triangle's third corner?
• A triangle has corners at #(7 , 9 )#, #(3 ,7 )#, and #(4 ,8 )#. What is the radius of the triangle's inscribed circle?
• Circle A has a center at #(2 ,3 )# and a radius of #1 #. Circle B has a center at #(0 ,-2 )# and a radius of #4 #. Do the circles overlap? If not, what is the smallest distance between them?
• A parallelogram has sides A, B, C, and D. Sides A and B have a length of #2 # and sides C and D have a length of # 7 #. If the angle between sides A and C is #pi/4 #, what is the area of the parallelogram?
• What is a quadrilateral that is not a parallelogram and not a trapezoid?
• Your teacher made 8 triangles he need help to identify what type triangles they are. Help him?: 1) #12, 16, 20# 2) #15, 17, 22# 3) #6, 16, 26# 4) #12, 12, 15# 5) #5,12,13# 6) #7,24,25# 7) #8,15,17# 8) #9,40,41#
• A triangle has corners A, B, and C located at #(3 ,5 )#, #(2 ,9 )#, and #(4 , 8 )#, respectively. What are the endpoints and length of the altitude going through corner C?
• What is the GCF of the set #64, 16n^2, 32n#?
• How do you write the reciprocal number of 5?
• Jeanie has a 3/4 yard piece of ribbon. She needs one 3/8 yard piece and one 1/2 yard piece. Can she cut the piece of ribbon into the two smaller pieces? Why?
• How do you find the GCF of #25k, 35j#?
• How do you write 132/100 in a mixed number?
• How do you evaluate the power #2^3#?
• How do you simplify #(4^6)^2 #?
• How do you convert 3.2 tons to pounds?
• How do you solve #\frac { 5} { 8} + \frac { 3} { 2} ( 4- \frac { 1} { 4} ) - \frac { 1} { 8}#?
• What are some acronyms for PEMDAS?
• How do you find all the asymptotes for function #y=(3x^2+2x-1)/(x^2-4 )#?
• How do you determine whether the graph of #y^2+3x=0# is symmetric with respect to the x axis, y axis or neither?
• How do you determine whether the graph of #y^2=(4x^2)/9-4# is symmetric with respect to the x axis, y axis, the line y=x or y=-x, or none of these?
• How do you find the end behavior of #-x^3+3x^2+x-3#?
• How do you find the asymptotes for #(2x^2 - x - 38) / (x^2 - 4)#?
• How do you find the asymptotes for #f(x) = (x^2) / (x^2 + 1)#?
• How do you find the vertical, horizontal and slant asymptotes of: #(3x-2) / (x+1)#?
• How do you find the Vertical, Horizontal, and Oblique Asymptote given #s(t)=(8t)/sin(t)#?
• How do you find vertical, horizontal and oblique asymptotes for #(x^3+1)/(x^2+3x)#?
• How do you find vertical, horizontal and oblique asymptotes for #y = (4x^3 + x^2 + x + 5 )/( x^2 + 3x)#?
• What is a pooled variance?
• What is the mean, mode median and range of 11, 12, 13, 12, 14, 11, 12?
• What is the z-score of sample X, if #n = 81, mu= 43, St. Dev. =90, and E[X] =57#?
• The camera club has five members, and the mathematics club has eight. There is only one member common to both clubs. In how many ways could a committee of four people be formed with at least one member from each club?
• How many permutations are there of the letter in the word baseball?
• How do you evaluate 6p4?
• What is the probability of #X= 6# successes, using the binomial formula?
• A lottery has a $100 000 first prize, a $25 000 second prize, and five $500 third prizes. A total of 50000 tickets are sold. What is the probability of winning a prize in this lottery?
• When a event is reported, the probability that is a negative event is 30%. What is the probability that 3 out of 5 reported events are negative?
• What is the median of 5, 19, 2, 28, 25?
• How do you solve this trigonometric equation?
• What is the frequency of #f(theta)= sin 3 t - cos2 t #?
• How do you evaluate #Sin(pi/2) + 6 cos(pi/3) #?
• How do you find the values of all six trigonometric functions of a right triangle ABC where C is the right angle, given a=9, b=40, c=41?
• How do you express (5*pi)/4 into degree?
• Solve for θ on the interval [90°,180°]:2tanθ +19 = 0?
• Prove that #((cos(33^@))^2-(cos(57^@))^2)/((sin(10.5^@))^2-(sin(34.5^@))^2)= -sqrt2# ?
• A triangle has sides A, B, and C. The angle between sides A and B is #(pi)/3# and the angle between sides B and C is #pi/6#. If side B has a length of 26, what is the area of the triangle?
• How do you write the following in trigonometric form and perform the operation given #(sqrt3+i)(1+i)#?
• A triangle has sides A, B, and C. The angle between sides A and B is #(2pi)/3#. If side C has a length of #32 # and the angle between sides B and C is #pi/12#, what is the length of side A?

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Mathway is the world’s smartest math calculator for algebra, graphing, calculus and more! Mathway gives you unlimited access to math solutions that can help you understand complex concepts. Simply point your camera and snap a photo or type your math homework question for step-by-step answers. If a premium subscription option is selected: • Payment will be charged to iTunes Account at confirmation of purchase • Subscription automatically renews unless auto-renew is turned off at least 24-hours before the end of the current period • Account will be charged for renewal within 24-hours prior to the end of the current period, at the same monthly or annual rate selected at the beginning of the subscription • Subscriptions may be managed by the user and auto-renewal may be turned off by going to the user's Account Settings after purchase Terms of Use: https://www.mathway.com/terms Privacy Policy: https://www.mathway.com/privacy

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Powered by Chegg, Mathway is your one-stop shop for homework help. Is your equation too complex to type? Save time with our snap and solve feature! Just take a photo and instantly see the solution. Our interactive calculator also allows you to select your class subject (now including physics!) to generate all the functions you need to solve that equation. Need more than an answer? Upgrade your subscription and get unlimited access to detailed equation breakdowns, helping you learn how to solve it one step at a time.

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Once I was doing my homework I couldn’t figure it out I asked my mom to help me and I showed her and she fell asleep so I kind of started panicking Went downstairs to the table I started struggling and thinking and thinking so I went to the App Store looked and looked and looked and looked left to right for helping your homeworkIs the best I really do recommend it it is the best it will save your life and when I mean save your life I mean really save your life nobody really understands when they say that they saved their lifeThey never understand how much that person means they don’t even know how serious the persons like saying I really do recommend this app messed up in the world five star review amazing helpful save your life get it get it now get it now it’s the best app ever students allowed teacher teachers not allowed can students really need this app so don’t get mad at them if they have this app it’s the best time with them so hope you get it

All it does is give the answer

Seriously saying, this app is literally just useless unless if you know the answer to math problems and want to check your answers. Otherwise, paying wouldn’t be a consideration for me. For those who are on a tight budget, and have a strong desire to reach their future career, I’d say paying wouldn’t be worth it, especially if you are just doing a living only as a student with no career and if you do not have enough financial support. I’ve lived a long way with this app studying all day and all night and yet there is high demand for paying just to get the work shown to get the idea why a question is answered in a certain way. This is why nowadays I read reviews from various books titled for math and read books that give a full explanation of how an answer is earned. As a life lesson it’s just good to say the fact that spending is not worth it for this app since there are various places and apps to ask questions related to learning math (at least in my area). This app should be like a substitute teacher or tutor for those who are having trouble, but the fact that there is such huge fee just ruins the reason why I should install this app. Teachers ask for showing work, and yet I’m stuck, having no idea what to do to get the right answers. This also goes to understanding how an answer is caught as well.

It works but the full version hasn’t for me

I have been using this a lot this semester so I decided to pay for the monthly subscription then I could cancel the membership at the end of the semester, but it doesn’t even work. The subscription shows in my subscriptions list in my settings but I still can’t view the steps, and when I attempt to see how the problem is solved it brings me to the menu to subscribe to the paid part of the app. Honestly though, other than that. This app works pretty great, solves problems the right way and you can select the method of how you want the problem solved. You can change what kind of math you are trying to solve, and the answers are pretty spot on. The predictive text is even really good on this, it’ll help solve word problems and you kind of don’t em have to type anything in sometimes. However, the keyboard is very buggy and you can’t type very fast. It’s also kind of hard to navigate as there are like 4 different keyboard menus to choose from, I always forget where to find things and it kind of takes a while to load the text sometimes. But it does solve the problems.

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Answered problems by math tutors.

A soccer coach wants to know how many hours a week his players spend training at home. He has 20 players and he decides to ask the first 4 players to arrive at Monday's soccer practice how many hours they spend training per week. He then calculated that they spend an average of 10 hour per week. Therefore, he assumed that all the players train 10 hours per week. Is this an example of a simple random sample? 

A No, because each student did not have an equal chance of being selected. 

B Yes, because each student had an equal chance of being selected. 

C No, because he did not sample every soccer player. 

D Yes, the minimum number of students sampled need to be four for it to be a simple random sample. 

The figure shows the graph of f. 

(b) Which of the cx-values A, B, C, D, E, F and G appear to be inflection points of f? 

The diagram shows two rectangles, A and B. 

All measurements are in centimetres. 

The area of rectangle A is equal to the area of rectangle B. 

Find an expression for y in terms of w. 

George's page contains twice as many typed words as Bill's page and Bill's page contains 50 fewer words than Charlie's page. If each person can type 60 words per minute, after one minute, the difference between twice the number of words on Bill's page and the number of words on Charlie's page is 210. How many words did Bill's page contain initially?

 Bill's page initially contained        words. 

Simplify 2sin(5x)cos(3x) - sin(2x) to one an expression containing one trigonometric function. Then graph the original function and your simplified version to verify they are identical. Enclose arguments of functions in parentheses. For example, sin(2x). 

2sin(5x)cos(3x)-sin(2x)=

A health psychologist was interested in the effects of vitamin supplements on the immune system. Three groups of adults were exposed (in a highly ethical way) to the cold virus; one group took no supplements for a week before exposure, another had vitamin C supplements, and a third had multivitamins (excluding C). The severity of the cold was measured as a percentage (0% = not contracted, 100% very severe symptoms). The psychologist also measured the number of cigarettes that each person smoked per day, as smoking suppresses the immune system. The psychologist was interested in the differences in the severity of the illnesses across different vitamin groups accounting for cigarette usage. What technique should be used to analyse these data? 

A. Two-way repeated-measures ANOVA 

B. Two-way independent ANOVA 

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What Is Reflection in Math? Definition, Examples & How-to

Whether you are just starting to explore reflections in math or need to brush up on your geometry, this simple, middle-school-friendly guide is for you.

Read on to find easy-to-follow definitions and explanations, solved examples, and resources to help you learn and master reflections.

What Is Reflection?

Reflection in mathematics is a geometric transformation where a shape or object is flipped across a line, known as the line of reflection . This results in a mirror image that is the same size and shape as the original but appears flipped or mirrored.

You encounter the concept of reflection every time you look in a mirror.

Try it now:

Step in front of a mirror and raise your right hand.

What hand is your mirror image raising?

If you raise your right hand in front of a mirror, your reflection, i.e. your mirror image, raises its left hand.

Transformations in Geometry

Reflection is one of the 4 types of transformations in geometry .

Other types of geometrical transformations are:

• Translation : Moving a shape without rotating or flipping it. It's like sliding the shape in a particular direction.
• Rotation : Turning a shape around a fixed point. It’s like turning a key in a lock.
• Dilation : Resizing a shape by enlarging or shrinking it evenly. It's like stretching or squeezing the shape while keeping its proportions intact, like inflating or deflating a balloon.

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Properties of Reflection

 To truly understand what reflection is and to distinguish it from other geometrical transformations, we need to know its properties.

Reflection has 5 key properties:

• Shape:  The shape of the original figure and its mirror image are identical.
• Size: The size of the original figure and its mirror image are the same.
• Orientation:  The orientation of the original figure and its mirror image are opposite.
• Distance:  The distance between any point on the original figure and the line of reflection is the same as the distance between the corresponding point on the mirror image and the line of reflection.
• Angle: Angles between intersecting lines are the same in both the original figure and its mirror image.

If any of these five properties are missing, the geometrical transformation is either not a reflection at all or is a combination  of reflection and other transformations.

Important Terms in Reflection

Let’s go over some language we use to talk about reflections.

We use these terms to explain how reflection works:

• Line of Reflection:  The imaginary line across which a shape is reflected to create its mirror image. It is also known as the axis of reflection or mirror line.
• Mirror Image: The image formed when you reflect a shape across the line of reflection. It is identical to the original shape but appears reversed.
• Congruent Figures: Two figures that have the same size and shape. In reflection, the original shape and its mirror image are always congruent.
• Symmetry: The property of a shape or object that remains unchanged when reflected across a line, known as a line of symmetry.

How to Do Reflections on the Coordinate Plane

To reflect a point or figure on the coordinate plane, we sometimes use the X-axis or Y-axis as the line of reflection.

Let’s see how each type of reflection works.

How to Do   Reflection Over the X-axis

Reflection over the x-axis is a transformation where each point in a shape or a graph is flipped across the x-axis .

If you have a point (x, y), reflecting it over the x-axis will give you the point (x, -y).

In other words, the x-coordinate (how far left or right the point is) stays the same, but the y-coordinate (how far up or down the point is) becomes its opposite.

For example, if you have the point (2, 3), reflecting it over the x-axis would give you (2, -3), because the x-coordinate remains 2, but the y-coordinate changes from 3 to -3, flipping it across the x-axis.

How to Do Reflection Over the Y-axis

In reflection over the Y-axis, each point in a shape or graph is mirrored horizontally along the Y-axis .

When you have a point (x, y), reflecting it over the Y-axis gives you the point (-x, y). To put it simply, the y-coordinate remains unchanged, but the x-coordinate changes to its negative value.

For example, let's take the point (4, -5). Reflecting it over the Y-axis results in (-4, -5).

Notice that while the y-coordinate remains -5, the x-coordinate changes from 4 to -4 as it mirrors along the Y-axis.

Here’s a visual representation of reflection over the Y-axis.

How to Do Reflection Over the Line y = x

The line y = x represents all the points where the y-coordinate is equal to the x-coordinate.

It's a diagonal line that passes from the bottom left corner to the top right corner through the origin at a 45-degree angle.

Reflection over the y = x line means flipping a point or shape across this diagonal line .

During this reflection, the x-coordinate of each point becomes its y-coordinate, and the y-coordinate becomes its x-coordinate.

For example, if you have a point (x, y), its reflection over the y = x line would be (y, x).

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What is rotation in math definition, examples & how-to guide.

Find simple definitions, key terms, solved examples, and practice materials in our middle-school-friendly guide to rotation in math.

What Is Translation in Math? Definition, Examples & How-to Guide

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