Algebra Homework Answers & Questions

Waiting for answer What is the algebraic expression for N cubed increased by 5?
It is ##n^3 + 5## The hard part of this is translating the English words into algebraic expressions. "n" is a variable. So we start with that: ##n## "cubed" means raising to the po...
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Waiting for answer There are 1000 grams in a kilogram. How many grams is 2.25 k...
2,250 grams Just multiply 2.25 kilograms by 1000 g/kg. ##2.25"kg"xx (1000"g")/(1"kg")="2,250 kg"##
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Waiting for answer How do you write an equation in slopeintercept form for the...
##3x5y+12=0## The two lines are perpendicular to each other, if the product of their slopes is ##1##. Hence if of one line is given as ##a/b##, slope of line perpendicular to it i...
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Waiting for answer How do you use the difference of two cubes formula to factor...
##x^6  y^3 = (x^2)^3  y^3## The Difference of Cubes Formula says ##color(blue)(a^3  b^3 = (ab)(a^2 +ab+b^2)## Hence ##(x^2)^3  y^3 = (x^2  y)((x^2)^2 +x^2y +y^2)## ## =color(green)( (x^2  y)(x^4 +x^2y + y^2)##
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Waiting for answer The sum of three consecutive odd integers is 63, what are th...
first integer##=19## second integer##=21## third integer ##=23## To solve this problem, we will need to set up an equation. But first, we need to make let statements to let others kn...
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Waiting for answer If the sales tax for the city of Los Angeles is 9.75%, how m...
You would pay $19.50 in taxes We can rewrite this problem as: What is 9.75% of $200.00 "Percent" or "%" means "out of 100" or "per 100", Therefore 9.75% can be written as ##9.75/1...
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Waiting for answer In the coordinate plane, three vertices of rectangle HIJK ar...
##(e,d)## If it is a rectangle then ##K =H+ (IH)+(KH)=I+KH=(e,d)##
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Waiting for answer Which expression is equivalent to 3/4 (2x8)? 3/2x6. 3/...
##3/2x6## Using distributive property of Rational numbers ##3/4(2x8)## = ##3/4xx2x3/4xx8## = ##3/cancel4^2xxcancel2^1x3/cancel4^1xxcancel8^2## = ##3/2x6##
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Waiting for answer All rational roots that are possible according to the ration...
According to the theorem, the possible rational roots are: ##+1##, ##+2##, ##+3##, ##+4##, ##+6##, ##+12## ##f(x) = x^334x+12## By the rational root theorem, any rational...
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Waiting for answer How do you convert from vertex form to intercept form of ##y...
The representation of the original function in intercept form is ##y=(x2)(x6)## Intercept form of a quadratic function, by definition, is a form ##y=k(xalpha)(xbeta)## It's call...
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Waiting for answer How do you find the square root of 80?
##80=4*20=4*4*5## ##sqrt80=sqrt4sqrt4sqrt5=2*2*sqrt5=4sqrt5## (Or do you want a decimal approximation?)
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Waiting for answer What is 1 over 2 to the 5th power?
##1/32## or ##0.03125## There are two ways to consider/evaluate this. One: ##("1/2")^5 = (1/2) * (1/2) * (1/2) * (1/2) * (1/2)## Two: ##(1/2^5)## Either way, in the end you get...
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Waiting for answer How many 250 ml bottles can be filled from 400 liters of wat...
##1600## such bottles Each liter of liquid is equivalent to ##1000## ##ml##. Hence in each liter, we have ##1000/250=(4cancel(1000))/(1cancel(250))## or four (##4##) ##250## ##ml##...
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Waiting for answer How do you find domain and range of a quadratic function?
For all quadratic functions, the domain is always ##RR## (double R). In interval notation, we write: ##(\infty,\infty)##. This means that any real number can be used as an input value. If the quadratic has a positive lead coefficient, like y = ##3x^2 4##, that 3 tells us that the parabola (gr...
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Waiting for answer How do you simplify square Root of 72 Minus Square Root of 1...
## = color(green)(3sqrt2## The square root of ##72## minus square root of ##18## can be expressed as ##sqrt72 sqrt18## Now, ##sqrt72 = sqrt(3^2 * 2^2 *2) = 6sqrt2## ##sqrt18 = sqr...
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Waiting for answer What is 1 1/3 as a decimal?
##1 1/3 = 1.bar3 " or " 1.dot3## Often rounded to ##1.333## ##1/3## is a fraction that cannot be equally divided, so the number goes on and on, it recurs. ##1 1/3 = 1.333##. . . (...
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Waiting for answer How do you change 1.25 into a fraction?
##1####1/4## or ##5/4## All you need to do is find ##0.25## as a fraction ##0.25=1/4##, because ##0.25/1=25/100=1/4##. Then, just write the ##1## from ##1.25## to the left of ##1/4...
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