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Firdavs [7]
3 years ago
8

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Mathematics
1 answer:
WARRIOR [948]3 years ago
5 0

Answer:

2\,(x-1)^2=4

which is the first option in the list of possible answers.

Step-by-step explanation:

Recall that the minimum of a parabola generated by a quadratic expression is at the vertex of the parabola, and the formula for the vertex of a quadratic of the general form:

y=ax^2+bx+c

is at   x_{vertex}=\frac{-b}{2\,a}

For our case, where a=2\,\,, b=-4\,\,,\,\,and \,\,c=-2  we have:

x_{vertex}=\frac{-b}{2\,a}\\x_{vertex}=\frac{4}{2\,*\,2}\\x_{vertex}=1

And when x = 1, the value of "y" is:

y(x)=2x^2-4x-2\\y(1)=2(1)^2-4(1)-2\\y(1)=2-6\\y(1)=-4\\y_{vertex}=-4

Recall now that we can write the quadratic in what is called: "vertex form" using the coordinates (x_{vertex},y_{vertex)of the vertex as follows:

y-y_{vertex}=a\,(x-x_{vertex})^2

Then, for our case:

y-(-4)=2\,(x-1)^2\\y=2\,(x-1)^2-4

Then, for the quadratic equal to zero as requested in the problem, we have:

y=2\,(x-1)^2-4=0\\2\,(x-1)^2-4=0\\2\,(x-1)^2=4

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If i= square root of -1, what is the value of i^3
Ber [7]

Answer:

- i

Step-by-step explanation:

Set up equation.

i {}^{3}  = y

{i}^{2 }  \times i = y

- 1 \times i = y

- i = y

6 0
3 years ago
Mariah bought nine yards of fabric for a project she used three yards on the first day what fraction of the fabric did she use t
JulsSmile [24]

1/3 because on total has to be 1 or 9/9 but if she use 3 yards of 9/9 then she use 3/9 and if you simplify is 1/3

3 0
3 years ago
Turner measured the floor of his storage unit, which is rectangular. It is 48 feet wide and 52 feet from one corner to the oppos
saveliy_v [14]

Answer:

<u>The storage unit is 20 feet long.</u>

Step-by-step explanation:

1. Let's use the Pythagorean Theorem to find the unknown side or length of the storage unit:

With the information given, we have a right triangle with 52 feet of hypotenuse and 48 feet as one of its sides and width of the storage unit.

Length of the storage unit ² = Hypotenuse ² - Width of the storage unit ²

Replacing with the real values:

Length of the storage unit ² = 52² - 48²

Length of the storage unit ² = 2,704 - 2,304

Length of the storage unit ² = 400

√Length of the storage unit ² = √400

<u>Length of the storage unit = 20 feet</u>

4 0
3 years ago
A water dunking tank at a carnival is in the shape of a right circular cylinder. Its height is 5 feet, and the radius of each ba
bagirrra123 [75]

Answer:

141.37 ft^3

Step-by-step explanation:

No question was asked, but based off of the given information, I will assume you want to know the volume of the circular cylinder.

The volume of a circular cylinder is: v=(π)(r^2)(h)

r=3

h=5

v=(π)(3^2)(5)

v = 141.37

5 0
2 years ago
Which of the following must be true in order for SAND to be in a rhombus? Select all that apply
Ahat [919]

Answer:

Consecutive sides must be congruent.

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Step-by-step explanation:

Rhombus:

1. Sides: all 4 sides are congruent.

Then consecutive sides must be congruent.

2.Diagonals : Diagonals bisect each other at 90°.

So, second option is wrong.

3. Sum of interior angle is 360°.

7 0
3 years ago
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