##### Questions

##### Question type

Use these controls to find questions to answer

Dear friends, Please read our latest blog post for an important announcement about the website. ❤, The Socratic Team

Featured 4 months ago

Full details shown. With practice you will be able to do this calculation type with very few lines.

Lets split it into two parts

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The gradient for part is the same as the gradient for all of it

Gradient (slope)

Set point

Set point

Set point

The gradient ALWAYS reads left to right on the x-axis (for standard form)

So we read from

Set gradient

Negative 1 means that the slope (gradient) is downward as you read left to right. For 1 across there is 1 down.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Determined that

Multiply both sides by (-8)

Add 8 to both sides

Featured 4 months ago

We can solve this quadratic with the strategy **factoring by grouping**. Here, we will rewrite the

This is equivalent to the following:

Notice, I only rewrote

We can factor a

Since

We now set both factors equal to zero to get:

Our factors are in blue. Hope this helps!

Featured 4 months ago

The distance is

The easiest way is to use the distance formula, which is kinda tricky:

That looks really complex, but if you take it slowly, I'll try and help you through it.

So let's call

Let's call

Let's plug these numbers into the distance formula:

This is quite the hard subject, and is best taught by someone who knows how to explain well! This is a really good video about the distance formula:

Khan Academy distance formula video

Featured 3 months ago

Answer:-#" "color(red)(1/n)# and#color(red)(1/m#

If the roots of an equation

#color(red)(ax^2+bx+c=0# is#color(blue)(alpha,beta# , then we can write as per rule that

#color(red)(alpha+beta)=-b/a# #color(red)(alpha cdot beta)=c/a# As per given condition, we can write that

#color(red)(m+n)=-b/a# #color(red)(m cdot n)=c/a# We will determine some values now for further use.

#color(red)(-b/c)=(-b/a)/(c/a)=(m+n)/(m cdot n)# #color(red)(a/c)=1/(m cdot n# If the roots of the equation

#color(red)(cx^2+bx+a=0# is#color(blue)(alpha,beta# , then,

#color(red)(alpha+beta)=-b/c=(m+n)/(m cdot n)" "...(1)# #color(red)(alpha cdot beta)=a/c=1/(m cdot n#

#color(red)(alpha-beta)#

#=sqrt((alpha+beta)^2-4 cdot alpha cdot beta)#

#=sqrt(((m+n)/(m cdot n))^2-4 /(m cdot n))#

#=(m-n)/(m cdot n)" "...(2)#

- From
#(1)" & " (2)# ,

#color(red)(alpha)=((m+n)/(m cdot n)+(m-n)/(m cdot n))/2=1/n# #color(red)(beta)=((m+n)/(m cdot n)-(m-n)/(m cdot n))/2=1/m# Hope this helps....

Thank you...

Featured 1 month ago

Kate has 50 pens.

If Jimmy gives 7 pens to Kate, that means Kate got 7 pens from Jimmy. Let the number of pens Jimmy and Kate have be

From the question, we can deduce that

From equation 1,

From equation 2,

Since

Hence,

Solve,

Featured 1 month ago

To simplify this, we will use PEMDAS, shown here:

This is a common method to simplify expressions, and you can remember it using:

**Please Excuse My Dear Aunt Sandy**

We also start from inside to outside.

First thing we do is simplify the **parenthesis**:

**Exponent**:

**Multiplication**:

**Subtract on numerator**:

**Division**:

**Multiplication**:

And lastly, **subtraction**:

Hope this helps!

Ask a question
Filters

×

Use these controls to find questions to answer

Unanswered

Need double-checking

Practice problems

Conceptual questions