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zavuch27 [327]
2 years ago
8

Help me with this one

Mathematics
1 answer:
Artist 52 [7]2 years ago
5 0

9514 1404 393

Answer:

  "complete the square" to put in vertex form

Step-by-step explanation:

It may be helpful to consider the square of a binomial:

  (x +a)² = x² +2ax +a²

The expression x² +x +1 is in the standard form of the expression on the right above. Comparing the coefficients of x, we see ...

  2a = 1

  a = 1/2

That means we can write ...

  (x +1/2)² = x² +x +1/4

But we need x² +x +1, so we need to add 3/4 to the binomial square in order to make the expressions equal:

  x^2+x+1\\\\=(x^2+x+\frac{1}{4})+\frac{3}{4}\\\\=(x+\frac{1}{2})^2+\frac{3}{4}

_____

Another way to consider this is ...

  x² +bx +c

  = x² +2(b/2)x +(b/2)² +c -(b/2)² . . . . . . rewrite bx, add and subtract (b/2)²*

  = (x +b/2)² +(c -(b/2)²)

for b=1, c=1, this becomes ...

  x² +x +1 = (x +1/2)² +(1 -(1/2)²)

  = (x +1/2)² +3/4

_____

* This process, "rewrite bx, add and subtract (b/2)²," is called "completing the square"—especially when written as (x-h)² +k, a parabola with vertex (h, k).

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A vendor at the State Fair has learned that, by pricing his deep fried bananas on a stick at $1.00, sales will reach 82 bananas
Tasya [4]

Answer:

Y=-40x+122

Step-by-step explanation:

hello

Due to the nature of the data, it is most convenient to model this problem as a linear function.

To solve this problem we must use the equation that defines a line, then start assigning the corresponding values

y1=82bananas per day

X1=1 dolar

y2=52bananas per day

x2=1.75dolar

line ecuation

y − y 1 = m(x − x 1 )

where

m=slope=\frac{y2-y1}{x2-x1} =\frac{52-82}{1.75-1}=-40

solving:

Y-82=-40(x-1)

Y=-40x+40+82

Y=-40x+122

let's try the result!

Price =1dolar

Y=-40(1)+122=82bananas per day

Price=1.75dolar

Y=-40(1.75)+122=52bananas per day

7 0
3 years ago
A rectangle has an area of 10x^2-29x-21 square units. Which of the following could represent the primeter of the rectangle in te
nata0808 [166]
Area=LW
<span>10x^2-29x-21=area
factor and those are the lengh and width
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5 0
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