Answer:
a = 2, b = - 3, c = - 8
Step-by-step explanation:
Expand f(x) = a(x + b)² + c and compare coefficients of like terms, that is
a(x + b)² + c ← expand (x + b)² using FOIL
= a(x² + 2bx + b²) + c ← distribute parenthesis by a
= ax² + 2abx + ab² + c
Compare like terms with f(x) = 2x² - 12x + 10
Compare coefficients x² term
a = 2
Compare coefficients of x- term
2ab = - 12, substitute a = 2
2(2)b = - 12
4b = - 12 ( divide both sides by 4 )
b = - 3
Compare constant term
ab² + c = 10 , substitute a = 2, b = - 3
2(- 3)² + c = 10
18 + c = 10 ( subtract 18 from both sides )
c = - 8
Then a = 2, b = - 3, c = - 8
If you divide a number by 9 then that number is repeated (1/9 = 0.111111... or 2/9 = 0.22222....)
So if we want 94 to repeat in the decimal 0.194 then we can have 94/99. But the thing is that we don't have 94 being repeated starting from the tenths place so we can possibly do 94/990.
Now we do have a tenths with a zero but we need a one to replace that zero. To do that we have to add 1/10 + 94/990 = 99/990 + 94/990 = 193/990.
<h3>Explain why it is helpful to know the basic function shapes and discuss some ways to remember them. </h3>
- Knowing the basic function shapes and discuss some ways to remember them is helpful because this is useful tools in the creation of mathematical models because we constantly make theories about the relationships between variables in nature and society. Functions in school mathematics are typically defined by an algebraic expression and have numerical inputs and outputs.
Answer:
+22
Step-by-step explanation:
Given g(x) = -x^2 + 4x - 11, g(4) is -(4)^2 + 4(4) - 11, or just -11.
Then -2 times g(4) = -2(-11) = +22
