Solving Equations
The solution to the equation
b-12=3
What is
b=15
A number that stands alone, like the 4 in the expression 13x+4 or the -9 in the equation 4x=5x-9
What is a constant?
The standard form equivalent of 4(7p-5), which can be found by applying the distributive property.
What is
28p-20
The value of f(6) for the function
f(x)=9x-11
What is 43?
Five more than the number dogs (d) at the park.
What is
5+d
The value of two quarters and a dime.
What is 60 cents?
The solution to the equation
4x-3=21
What is
x=6
A quantity being multiplied by a variable, like the -3 in the expression 1.2-3b , or the 5.8 in the equation 7.2=5.8k+14.2 .
What is a coefficient?
The prime factorization of 45.
What is
3*3*5
The value of g(-2) for the function g(t)=4t-9.5
What is -17.5?
The total cost of 4 drinks and 3 snacks, where the cost of each drink is d and the cost of each snack is s.
What is
4d+3s
A banking card that allows you to use money from your checking account to pay for things.
What is a debit card?
The solutions to the equation
(x-4)(x+9)=0
What is
x={4,-9}
A polynomial with three terms, like 15x^4-20x^2+85 , not to be confused with a binomial, which has two terms, like 2n-1 .
What is a trinomial?
The fully simplified fraction form of (40c^2)/(60c^5) .
What is (2)/(c^3) ?
The value of q(-10) for the function q(p)=2p^2+5p-32 .
What is 118?
The amount of money in Susana's piggy bank after she started with $5 and added $2 every week for w weeks.
What is
2w+5
The monthly payment a tenant pays to a landlord, which is ideally no more than 25% of the tenant's income, even though that can be hard to achieve in the greater Boston area.
What is rent?
The solutions to the equation
(2x-3)(5x+1)=0
What is
x={3/2,-1/5}
The process of rewriting an expression in an equivalent form to emphasize the components that are being multiplied, such as rewriting 48 as 2*2*2*2*3 , or rewriting 6m^2+23m+20 as (2m+5)(3m+4) .
What is factoring/factorizing?
The equation 5^n=k , rewritten as a logarithmic equation.
What is
log_5k=n
The value of h(4) for the function h(x)=400*2^(-x)+85 .
What is 110?
If phone plan A costs $25 per month plus a $50 sign-up fee, and phone plan B costs $30 per month plus a $2 sign-up fee, this inequality models when plan A is cheaper than plan B.
What is
25m+50<30m+2
A percentage of a balance that gets paid to the account owner; you want it high for your savings account, and low for loans.
What is interest?
The solutions to the equation
x^2+11=60
What is
x={-7,7}
The field of mathematics that studies unknown quantities (variables), taken from the name of Al-Khwarizmi's great book: Ilm al-jabr wa l-muqābala (the Compendious Book on Calculation by Completion and Balancing).
What is algebra?
The factored form equivalent of x^2+10x+21 .
What is (x+3)(x+7) ?
The value of r(5) for the function r(d)=(6d)/(35-7d)+(14d)/(35+7d)
What is undefined?
The balance of a savings account with 3% interest compounded continuously after t years if you initially deposited $2,000.
What is
2000*e^(.03*t)
The money that your employer sets aside from your paycheck to pay for services like social security and Medicare.
What are (federal income tax) withholdings?