Ryann Hart

2023-03-15

How to solve the equation for ${x}^{2}-3x=0$?

Sterling Cameron

Beginner2023-03-16Added 6 answers

${x}^{2}-3x=0$

$x\cdot (x-3)=0$ ($x$ was a common factor to both the terms)

In general, if $a\cdot b=0,$ then either $a=0\phantom{\rule{1ex}{0ex}}\text{or}\phantom{\rule{1ex}{0ex}}b=0$

So here,

$x=0\phantom{\rule{1ex}{0ex}}\text{or}\phantom{\rule{1ex}{0ex}}x-3=0$

$x=0\phantom{\rule{1ex}{0ex}}\text{or}\phantom{\rule{1ex}{0ex}}x=3$ is the correct Solution.

$Note$ :

Here's a classic $Mistake$ that many students make:Transpose $3x$ to the right hand side

${x}^{2}=3x$

Divide both sides by $x$ will give us $x=3$ (Incorrect/Incomplete)

This is a $mistake$ because we CANNOT divide by $x$ unless we are sure about it not being equal to zero.

$x\cdot (x-3)=0$ ($x$ was a common factor to both the terms)

In general, if $a\cdot b=0,$ then either $a=0\phantom{\rule{1ex}{0ex}}\text{or}\phantom{\rule{1ex}{0ex}}b=0$

So here,

$x=0\phantom{\rule{1ex}{0ex}}\text{or}\phantom{\rule{1ex}{0ex}}x-3=0$

$x=0\phantom{\rule{1ex}{0ex}}\text{or}\phantom{\rule{1ex}{0ex}}x=3$ is the correct Solution.

$Note$ :

Here's a classic $Mistake$ that many students make:Transpose $3x$ to the right hand side

${x}^{2}=3x$

Divide both sides by $x$ will give us $x=3$ (Incorrect/Incomplete)

This is a $mistake$ because we CANNOT divide by $x$ unless we are sure about it not being equal to zero.

Anastasia Macdonald

Beginner2023-03-17Added 4 answers

We must first factorize the equation in order to determine $x$.

${x}^{2}-3x=0$

As $x$ is the common factor between the 2 values, we factorize the equation by taking $x$ out of ${x}^{2}-3x=0$

${x}^{2}-3x=0$

$x(x-3)=0$

Any value that is multiplied by 0, will give 0 as the answer.

$1\times 0=0\phantom{\rule{0ex}{0ex}}2\times 0=0\phantom{\rule{0ex}{0ex}}3\times 0=0$

From here, we know that in $x(x-3)=0$,

$x=0$ and $(x-3)=0$

$(x-3)=0$

$x=3$

Hence $x=0$ and $x=3$

${x}^{2}-3x=0$

As $x$ is the common factor between the 2 values, we factorize the equation by taking $x$ out of ${x}^{2}-3x=0$

${x}^{2}-3x=0$

$x(x-3)=0$

Any value that is multiplied by 0, will give 0 as the answer.

$1\times 0=0\phantom{\rule{0ex}{0ex}}2\times 0=0\phantom{\rule{0ex}{0ex}}3\times 0=0$

From here, we know that in $x(x-3)=0$,

$x=0$ and $(x-3)=0$

$(x-3)=0$

$x=3$

Hence $x=0$ and $x=3$

Find the volume V of the described solid S

A cap of a sphere with radius r and height h.

V=??

Whether each of these functions is a bijection from R to R.

a) $f(x)=-3x+4$

b) $f\left(x\right)=-3{x}^{2}+7$

c) $f(x)=\frac{x+1}{x+2}$

?

$d)f\left(x\right)={x}^{5}+1$In how many different orders can five runners finish a race if no ties are allowed???

State which of the following are linear functions?

a.$f(x)=3$

b.$g(x)=5-2x$

c.$h\left(x\right)=\frac{2}{x}+3$

d.$t(x)=5(x-2)$ Three ounces of cinnamon costs $2.40. If there are 16 ounces in 1 pound, how much does cinnamon cost per pound?

A square is also a

A)Rhombus;

B)Parallelogram;

C)Kite;

D)none of theseWhat is the order of the numbers from least to greatest.

$A=1.5\times {10}^{3}$,

$B=1.4\times {10}^{-1}$,

$C=2\times {10}^{3}$,

$D=1.4\times {10}^{-2}$Write the numerical value of $1.75\times {10}^{-3}$

Solve for y. 2y - 3 = 9

A)5;

B)4;

C)6;

D)3How to graph $y=\frac{1}{2}x-1$?

How to graph $y=2x+1$ using a table?

simplify $\sqrt{257}$

How to find the vertex of the parabola by completing the square ${x}^{2}-6x+8=y$?

There are 60 minutes in an hour. How many minutes are there in a day (24 hours)?

Write 18 thousand in scientific notation.