Answer:
Step-by-step explanation:
f(x) = x^2 + 4x + 4
f(x + a) = (x + a)^2 + 4(x + a) + 4
f(x + a) = x^2 + 2ax + a^2 + 4x + 4a + 4 Now combine like terms and use the distributive property.
f(x + a) = x^2 + (2a + 4)x + a^2 + 4a + 4
We are told that f(x + a) = x^2 - 6x + 9
So that means that
2a + 4 = - 6 Subtract 4 from both sides.
2a = - 6 - 4
2a = - 10 Divide by 2
a = - 10/2
a = - 5.
But you are not finished. You have to check the last part.
a^2 + 4x + 4 = 9
(a + 2)^2 = 9
Take the square root of both sides
sqrt(a+ 2)^2 = +/- 3
a+2 = 3
a = 1.
Does this work or is it extraneous? It is extraneous because it will not work for 2(a) + 4 = - 6
You get 6 = - 6 which is not correct. But you did give the second best answer.
a + 2 = - 3
a = - 3 - 2
a = - 5 which agrees with your previous answer.
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This is an extremely hard or tricky or sneaky problem. It takes a lot of conniving to get the right answer and 1 is not a left field answer. It just does not happen to be correct.
Answer:
2X
Step-by-step explanation:
bill has X and Ben has twice X so Ben has 2X
Answer: The polynomial 3x2 is of one variable with a degree of 2.
The polynomial x2y + 3xy2 + 1 is of two variables a with a degree of 3.
Step-by-step explanation: For this case we have the following polynomials:
3x2
x2y + 3xy2 + 1
We have then:
For 3x2:
Classification: polynomial of one variable:
Degree: 2
For x2y + 3xy2 + 1:
Classification: polynomial of two variables
Degree: 2 + 1 = 3
Answer:
Addition property of equality
Step-by-step explanation:
3/4 was added to each side
Answer:
Pedro pagó $448
Step-by-step explanation:
Sea P el precio inicial de un objeto.
Si aplicamos un descuento del X%, entonces el nuevo precio del objeto es:
NP = P*(1 - X%/100%)
y lo que estamos ahorrando es:
P - NP
En este caso, primero tenemos un descuento del 30%, entonces:
NP = P*(1 - 30%/100%) = P*(1 - 0.3)
Luego tenemos otro descuento, esta vez del 20%, entonces:
NP' = NP*(1 - 20%/100%) = P*(1 - 0.3)*(1 - 20%/100%) = P*(1 - 0.3)*(1 - 0.2)
Lo que Pedro ahorra es igual a $352
entonces:
P - NP' = $352
P - P*(1 - 0.3)*(1 - 0.2) = $352
P*(1 - (1 - 0.3)*(1 - 0.2)) = $352
P*(1 - 0.56) = $352
P = $352/(1 - 0.56) = $800
Esto significa que el precio original era $800.
Y lo que pedro pago esta dado por la ecuación:
NP' = P*(1 - 0.2)*(1 - 0.3) = $800*(1 - 0.2)*(1 - 0.3) = $448.
