Answer: 900 Km.
Step-by-step explanation: ...
Answer:
-x^3+5x^2-8x+1, which is choice A
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Work Shown:
f(x) = x^3 - x^2 - 3
f(x) = (x)^3 - (x)^2 - 3
f(2-x) = (2-x)^3 - (2-x)^2 - 3 ................ see note 1 (below)
f(2-x) = (2-x)(2-x)^2 - (2-x)^2 - 3 ........... see note 2
f(2-x) = (2-x)(4-4x+x^2) - (4-4x+x^2) - 3 ..... see note 3
f(2-x) = -x^3+6x^2-12x+8 - (4-4x+x^2) - 3 ..... see note 4
f(2-x) = -x^3+6x^2-12x+8 - 4+4x-x^2 - 3 ....... see note 5
f(2-x) = -x^3+5x^2-8x+1
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note1: I replaced every copy of x with 2-x. Be careful to use parenthesis so that you go from x^3 to (2-x)^3, same for the x^2 term as well.
note2: The (2-x)^3 is like y^3 with y = 2-x. We can break up y^3 into y*y^2, so that means (2-x)^3 = (2-x)(2-x)^2
note3: (2-x)^2 expands out into 4-4x+x^2 as shown in figure 1 (attached image below). I used the box method for this and for note 4 as well. Each inner box or cell is the result of multiplying the outside terms. Example: in row1, column1 we have 2 times 2 = 4. You could use the FOIL rule or distribution property, but the box method is ideal so you don't lose track of terms.
note4: (2-x)(4-4x+x^2) turns into -x^3+6x^2-12x+8 when expanding everything out. See figure 2 (attached image below). Same story as note 3, but it's a bit more complicated.
note5: distribute the negative through to ALL the terms inside the parenthesis of (4-4x+x^2) to end up with -4+4x-x^2
Answer:
Original number 26.
Step-by-step explanation:
xy - two-digit number
1) x + y = 8
2) Original two-digit number can be written as
10*x + y
3) If the digits interchanged yx,
then the new number can be written as
10*y + x
4) Double the original number is
2*(10*x + y)
5) New number is 10 more than double the original number
(10*y + x) - (2*(10*x + y)) = 10
6) Now we have the system of 2 equations:
x + y = 8
(10*y + x) - (2*(10*x + y)) = 10 -----> 10y + x - (20x + 2y) = 10 ---> 8y - 19x = 10
x = 8 - y
8y - 19(8 - y) = 10
8y - 152 +19y = 10
27y = 162
y = 6
x = 8 - y = 8 - 6 = 2
x = 2
So, x =2, y = 6.
Original number 26.
Check:
Original number 26.
New number 62.
Double of the original number = 2*26= 52.
New number is 10 more than double the original number :
62 - 52 = 10 True
Answer:
3
x
=
15
Step-by-step explanation:
you need to divide the 15 by 10, 3 times and the you will get five
and it says Determine which equations below have x = 15 as a solution.