# 5.4 Application i - translating from verbal to mathetical expressions  (Page 2/2)

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Some phrases and sentences do not translate directly. We must be careful to read them properly. The word from often appears in such phrases and sentences. The word from means "a point of departure for motion." The following translation will illustrate this use. The word from indicates the motion (subtraction) is to begin at the point of "some quantity."

Eight less than some quantity. Notice that less than could be replaced with from .
$x-8$

## Practice set b

Translate the following phrases and sentences into mathematical expressions or equations.

A number divided by sixteen, plus one, is five.

$\frac{x}{16}+1=5$

Seven times two more than a number is twenty-one.

$7\left(2+x\right)=21$

A number divided by two more than itself is zero.

$\frac{x}{2+x}=0$

A number minus five is divided by twice the number plus three and the result is seventeen.

$\frac{x-5}{2x+3}=17$

Fifty-two is subtracted from some quantity.

$x-52$

An unknown quantity is subtracted from eleven and the result is five less than the unknown quantity.

$11-x=x-5$

## Exercises

For the following problems, translate the following phrases or sentences into mathematical expressions or equations.

A quantity less four.

$a-4$

Eight more than a number.

A number plus seven.

$b+7$

A number minus three.

Negative five plus an unknown quantity.

$-5+c$

Negative sixteen minus some quantity.

Fourteen added to twice a number.

$2d+14$

Ten added to three times some number.

One third minus an unknown quantity.

$\frac{1}{3}-e$

Twice a number is eleven.

Four ninths of a number is twenty-one.

$\frac{4}{9}f=21$

One third of a number is two fifths.

Three times a number is nine more than twice the number.

$3g=2g+9$

Five times a number is that number minus two.

Twice a number added to six results in thirty.

$2h+6=30$

Ten times a number less four results in sixty-six.

A number less twenty-five is equal to $3.019$ .

$k-25=3.019$

Seven more than some number is five more than twice the number.

When a number is divided by four, the result is sixty-eight.

$\frac{m}{4}=68$

Eleven fifteenths of two more than a number is eight.

One tenth of a number is that number less one.

$\frac{n}{10}=n-1$

Two more than twice a number is one half the number less three.

A number is equal to itself plus four times itself.

$x=x+4x$

Three fifths of a quantity added to the quantity itself is thirty-nine.

A number plus seven is divided by two and the result is twenty-two.

$\frac{Q+7}{2}=22$

Ten times a number minus one is divided by fourteen and the result is one.

A number is added to itself then divided by three. This result is then divided by three. The entire result is fifteen.

$\frac{\frac{r+r}{3}}{3}=15$

Ten divided by two more than a number is twenty-one.

Five divided by a number plus six is fourteen.

$\frac{5}{s+6}=14$

Twelve divided by twice a number is fifty-five.

Twenty divided by eight times a number added to one is nine.

$\frac{20}{8x}+1=9$

A number divided by itself, plus one, results in seven.

A number divided by ten, plus four, results in twenty-four.

$\frac{v}{10}+4=24$

A number plus six, divided by two, is seventy-one.

A number plus six, divided by two, plus five, is forty-three.

$\frac{w+6}{2}+5=43$

A number multiplied by itself added to five is thirty-one.

A quantity multiplied by seven plus twice itself is ninety.

$7y+2y=90$

A number is increased by one and then multiplied by five times itself. The result is eighty-four.

A number is added to six and that result is multiplied by thirteen. This result is then divided by six times the number. The entire result is equal to fifty-nine.

$\frac{\left(z+16\right)13}{6z}=59$

A number is subtracted from ten and that result is multiplied by four. This result is then divided by three more than the number. The entire result is equal to six.

An unknown quantity is decreased by eleven. This result is then divided by fifteen. Now, one is subtracted from this result and five is obtained.

$\frac{x-11}{15}-1=5$

Ten less than some number.

Five less than some unknown number.

$n-5$

Twelve less than a number.

One less than an unknown quantity.

$m-1$

Sixteen less than some number is forty-two.

Eight less than some unknown number is three.

$p-8=3$

Seven is added to ten less than some number. The result is one.

Twenty-three is divided by two less than twice some number and the result is thirty-four.

$\frac{23}{2n-2}=34$

One less than some number is multiplied by three less than five times the number and the entire result is divided by six less than the number. The result is twenty-seven less than eleven times the number.

## Exercises for review

( [link] ) Supply the missing word. The point on a line that is associated with a particular number is called the of that number.

graph

( [link] ) Supply the missing word. An exponent records the number of identical in a multiplication.

( [link] ) Write the algebraic definition of the absolute value of the number $a$ .

$|a|=\left\{\begin{array}{l}a,\text{i}\text{f}\text{\hspace{0.17em}}a\ge 0\\ -a,\text{i}\text{f}\text{\hspace{0.17em}}a<0\end{array}$

( [link] ) Solve the equation $4y+5=-3$ .

( [link] ) Solve the equation $2\left(3x+1\right)-5x=4\left(x-6\right)+17$ .

$x=3$

#### Questions & Answers

Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
what does nano mean?
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
it is a goid question and i want to know the answer as well
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
what is fullerene does it is used to make bukky balls
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
so some one know about replacing silicon atom with phosphorous in semiconductors device?
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
for screen printed electrodes ?
SUYASH
What is lattice structure?
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
how did you get the value of 2000N.What calculations are needed to arrive at it
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