428 × (-23 ) + (-428 )× (-223)= can you answer it with steps it would be a great help for me
1 answer:
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Remark
It's asking you to complete the square to find the vertex.
Solve
y = -2x^2 + x + 3 Put brackets around the first 2 terms.
y = (-2x^2 + x) + 3 Pull out the 2.
y = -2(x^2 - 1/2 x) + 3 Be especially observant of the sign on 1/2x Divide the middle term's number by 2 and square it.
y = -2(x^2 - 1/2 x + [(1/2) / 2]^2 ) + 3 [1/2 divided by 2 is 1/4. (1/4)^2 = 1/16; 2*(1/16) = 1/8
y = - 2(x^2 - 1/2 x + (1/4)^2 ) + 3 + 1/8
y = -2(x - 1/4)^2 + 3 1/8
Comment
Answer to your question. The maximum value (3 1/8) is above the y axis. That means the graph of the equation crosses the x axis twice. I'm going to include the graph because in answering the question, there is no harm in seeing the graph.
It's asking you to complete the square to find the vertex.
Solve
y = -2x^2 + x + 3 Put brackets around the first 2 terms.
y = (-2x^2 + x) + 3 Pull out the 2.
y = -2(x^2 - 1/2 x) + 3 Be especially observant of the sign on 1/2x Divide the middle term's number by 2 and square it.
y = -2(x^2 - 1/2 x + [(1/2) / 2]^2 ) + 3 [1/2 divided by 2 is 1/4. (1/4)^2 = 1/16; 2*(1/16) = 1/8
y = - 2(x^2 - 1/2 x + (1/4)^2 ) + 3 + 1/8
y = -2(x - 1/4)^2 + 3 1/8
Comment
Answer to your question. The maximum value (3 1/8) is above the y axis. That means the graph of the equation crosses the x axis twice. I'm going to include the graph because in answering the question, there is no harm in seeing the graph.
Answer:
f(x) = 1.5x - 0.5x
Step-by-step explanation:
The function of the pattern represented by the pentagonal numbers is the sum of three triangular numbers.
The triangular number general formula
x (x + 1) / 2
For example,
The sequence
1, 3, 6, 10
*
* * *
* * * * * *
* , * *, * * *, * * * *
_____________________________
The pentagonal numbers
The sequence:
1, 5, 12, 22, 35
As shown in the picture can be divided into three triangles
Triangle 2
x (x + 1) / 2
Triangle 1 and 3 (they are triangles one unit smaller than 2)
n (n + 1) / 2
n= x-1
Replacing n
(x-1) ((x-1) + 1) / 2
(x-1) (x) / 2
(x-1) x / 2
______________
Function represents the pattern
Triangle 2 + (Triangle 1 + Triangle 3)
Triangle 1 = Triangle 3
So then,
Triangle 2 + 2* Triangle 1
x (x +1) /2 + 2* (x -1) x/2
Rearranging
0.5 x (x +1) + x(x -1)
0.5x^2 + 0.5x + x^2 -x
(0.5 x^2 + x^2) + (0.5x -x )
1.5 x^2 - 0.5 x
______
