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Use the formula A = 1 2 b h to solve for h:

  1. when A = 170 and b = 17
  2. in general

h = 20 h = 2 A b

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Use the formula A = 1 2 b h to solve for b :

  1. when A = 62 and h = 31
  2. in general

  1. b = 4
  2. b = 2 A h
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In Solve Simple Interest Applications , we used the formula I = P r t to calculate simple interest, where I is interest, P is principal, r is rate as a decimal, and t is time in years.

Solve the formula I = P r t to find the principal, P :

  1. when I = $5,600 , r = 4% , t = 7 years
  2. in general

Solution

I = $5600, r = 4%, t = 7 years in general
Write the forumla. . .
Substitute any given values. . .
Multiply r t . . .
Divide to isolate P . . .
Simplify. . .
State the answer. The principal is $20,000. .
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Use the formula I = P r t .

Find t : when I = $2,160 , r = 6% , P = $12,000; in general

  1. t = 3 years
  2. t = I P r

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Use the formula I = P r t .

Find r : when I = $5,400 , P = $9,000 , t = 5 years in general

  1. r = 0.12 = 12%
  2. r = I P t

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Later in this class, and in future algebra classes, you’ll encounter equations that relate two variables, usually x and y . You might be given an equation that is solved for y and need to solve it for x , or vice versa. In the following example, we’re given an equation with both x and y on the same side and we’ll solve it for y . To do this, we will follow the same steps that we used to solve a formula for a specific variable.

Solve the formula 3 x + 2 y = 18 for y :

  1. when x = 4
  2. in general

Solution

when x = 4 in general
Write the equation. . .
Substitute any given values. . .
Simplify if possible. . .
Subtract to isolate the y -term. . .
Simplify. . .
Divide. . .
Simplify. . .
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Solve the formula 3 x + 4 y = 10 for y :

  1. when x = 2
  2. in general

  1. y = 1
  2. y = 10 3 x 4

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Solve the formula 5 x + 2 y = 18 for y :

  1. when x = 4
  2. in general

  1. y = −1
  2. y = 18 5 x 2

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In the previous examples, we used the numbers in part (a) as a guide to solving in general in part (b). Do you think you’re ready to solve a formula in general without using numbers as a guide?

Solve the formula P = a + b + c for a .

Solution

We will isolate a on one side of the equation.

We will isolate a on one side of the equation.
Write the equation. P = a + b + c
Subtract b and c from both sides to isolate a . .
Simplify. P b c = a

So, a = P b c

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Solve the formula P = a + b + c for b .

b = P a c

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Solve the formula P = a + b + c for c .

c = P a b

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Solve the equation 3 x + y = 10 for y .

Solution

We will isolate y on one side of the equation.

We will isolate y on one side of the equation.
Write the equation. 3 x + y = 10
Subtract 3 x from both sides to isolate y . .
Simplify. y = 10 3 x

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Solve the formula 7 x + y = 11 for y .

y = 11 − 7 x

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Solve the formula 11 x + y = 8 for y .

y = 8 − 11 x

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Solve the equation 6 x + 5 y = 13 for y .

Solution

We will isolate y on one side of the equation.

We will isolate y on one side of the equation.
Write the equation. .
Subtract to isolate the term with y . .
Simplify. .
Divide 5 to make the coefficient 1. .
Simplify. .

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Solve the formula 4 x + 7 y = 9 for y .

y = 9 4 x 7

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Solve the formula 5 x + 8 y = 1 for y .

y = 1 5 x 8

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Key concepts

  • Distance, Rate, and Time
    • d = r t

Practice makes perfect

Use the Distance, Rate, and Time Formula

In the following exercises, solve.

Questions & Answers

how does Neisseria cause meningitis
Nyibol Reply
what is microbiologist
Muhammad Reply
what is errata
Muhammad
is the branch of biology that deals with the study of microorganisms.
Ntefuni Reply
What is microbiology
Mercy Reply
studies of microbes
Louisiaste
when we takee the specimen which lumbar,spin,
Ziyad Reply
How bacteria create energy to survive?
Muhamad Reply
Bacteria doesn't produce energy they are dependent upon their substrate in case of lack of nutrients they are able to make spores which helps them to sustain in harsh environments
_Adnan
But not all bacteria make spores, l mean Eukaryotic cells have Mitochondria which acts as powerhouse for them, since bacteria don't have it, what is the substitution for it?
Muhamad
they make spores
Louisiaste
what is sporadic nd endemic, epidemic
Aminu Reply
the significance of food webs for disease transmission
Abreham
food webs brings about an infection as an individual depends on number of diseased foods or carriers dully.
Mark
explain assimilatory nitrate reduction
Esinniobiwa Reply
Assimilatory nitrate reduction is a process that occurs in some microorganisms, such as bacteria and archaea, in which nitrate (NO3-) is reduced to nitrite (NO2-), and then further reduced to ammonia (NH3).
Elkana
This process is called assimilatory nitrate reduction because the nitrogen that is produced is incorporated in the cells of microorganisms where it can be used in the synthesis of amino acids and other nitrogen products
Elkana
Examples of thermophilic organisms
Shu Reply
Give Examples of thermophilic organisms
Shu
advantages of normal Flora to the host
Micheal Reply
Prevent foreign microbes to the host
Abubakar
they provide healthier benefits to their hosts
ayesha
They are friends to host only when Host immune system is strong and become enemies when the host immune system is weakened . very bad relationship!
Mark
what is cell
faisal Reply
cell is the smallest unit of life
Fauziya
cell is the smallest unit of life
Akanni
ok
Innocent
cell is the structural and functional unit of life
Hasan
is the fundamental units of Life
Musa
what are emergency diseases
Micheal Reply
There are nothing like emergency disease but there are some common medical emergency which can occur simultaneously like Bleeding,heart attack,Breathing difficulties,severe pain heart stock.Hope you will get my point .Have a nice day ❣️
_Adnan
define infection ,prevention and control
Innocent
I think infection prevention and control is the avoidance of all things we do that gives out break of infections and promotion of health practices that promote life
Lubega
Heyy Lubega hussein where are u from?
_Adnan
en français
Adama
which site have a normal flora
ESTHER Reply
Many sites of the body have it Skin Nasal cavity Oral cavity Gastro intestinal tract
Safaa
skin
Asiina
skin,Oral,Nasal,GIt
Sadik
How can Commensal can Bacteria change into pathogen?
Sadik
How can Commensal Bacteria change into pathogen?
Sadik
all
Tesfaye
by fussion
Asiina
what are the advantages of normal Flora to the host
Micheal
what are the ways of control and prevention of nosocomial infection in the hospital
Micheal
what is inflammation
Shelly Reply
part of a tissue or an organ being wounded or bruised.
Wilfred
what term is used to name and classify microorganisms?
Micheal Reply
Binomial nomenclature
adeolu
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Source:  OpenStax, Prealgebra. OpenStax CNX. Jul 15, 2016 Download for free at http://legacy.cnx.org/content/col11756/1.9
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