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3 years ago

Find the y-coordinate of the vertex of the parabola whose equation is y=x^2-x+2

2 answers:

meriva3 years ago

8 0

To find a vertex of a parabola, use the equation -b / 2a to find the AOS.

$y = x^{2} -x + 2$

$\frac{-1}{2}$

If the x - coordinate of the equation is $-\frac{1}{2}$ , then plug that value of x in:

$y = \frac{1}{4} + \frac{1}{2} + 2$

The y-coordinate is $\frac{11}{4}$

a_sh-v [17]3 years ago

3 0

Answer:

2 and 1/4

Step-by-step explanation:

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If a/b < c/d with b > 0, d > 0, prove that a+c / b+d lies between the two fractions a/b and c/d .

Tems11 [23]

Divide through everything by b :

$\dfrac{a+c}{b+d} = \dfrac{\dfrac ab + \dfrac cb}{1 + \dfrac db}$

Since a/b < c/d, it follows that

$\dfrac{a+c}{b+d} < \dfrac{\dfrac cd+\dfrac cb}{1 + \dfrac db}$

Multiply through everything on the right side by b/d to get

$\dfrac{a+c}{b+d} < \dfrac{\dfrac{bc}{d^2}+\dfrac cd}{\dfrac bd+1} = \dfrac{\dfrac cd\left(\dfrac bd+1\right)}{\dfrac bd+1} = \dfrac cd$

and so (a + c)/(b + d) < c/d.

For the other side, you can do something similar and divide through everything by d :

$\dfrac{a+c}{b+d} = \dfrac{\dfrac ad + \dfrac cd}{\dfrac bd + 1}$

and a/b < c/d tells us that

$\dfrac{a+c}{b+d} > \dfrac{\dfrac ad + \dfrac ab}{\dfrac bd + 1}$

Then

$\dfrac{a+c}{b+d} > \dfrac{\dfrac ab + \dfrac{ad}{b^2}}{1 + \dfrac db} = \dfrac{\dfrac ab\left(1+\dfrac db\right)}{1 + \dfrac db} = \dfrac ab$

and so (a + c)/(b + d) > a/b.

Then together we get the desired inequality.

5 0

3 years ago

-8.0 is classified as?Select all that apply * Natural Number Whole Number Integer Rational Number

grigory [225]

Answer:

Integer and Rational Number

Step-by-step explanation:

Natural numbers are positive numbers starting at 1 and going onward. Since -8.0 is not a positive number, it is not a natural number.

Whole numbers are natural numbers and 0 altogether. -8 is not greater than zero or positive, so it is not a whole number.

A rational number is a number that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q. Since q may be equal to 1, every integer is a rational number. -8.0 can also be written as -8/1, so it is a rational number and an integer, since every integer is a number over 1 and also a rational number.

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3 years ago

at fish world,clownfish are on sale for $5 off with a maximum of 6 fish per customer. Rudy buys 6 clownfish on sale plus 3 more

ICE Princess25 [194]

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3 years ago

A regular hexagon has a perimeter of 72 feet. How long is each side?

Lena [83]

Step-by-step explanation:

a hexagon has 6 sides

so it's only 72/6

so each side is 12ft

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4 years ago