What is the square root of 2?

Answers

Answer 1
Answer: Hi There!

What is the square root of 2?

The answer is 1.4 or 1.41421356237
Answer 2
Answer: The answer is not 1.4

The answer is 2

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Which represents a quadratic function?f(x) = −8x^3 − 16x^2 − 4x

f (x) = 3/4 x ^2 + 2x − 5

f(x) = 4/x^2 - 2/x + 1

f(x) = 0x^2 − 9x + 7

Answers

A quadratic equation is of the format:

ax² + bx + c = 0,  where a ≠ 0.

The first option is not quadratic, it is a cubic, it has highest power of 3.

The second option f (x) = 3/4 x ^2 + 2x − 5, is quadratic, that is the answer.

The third f(x) = 4/x^2 - 2/x + 1, doesn't qualify because of the 2/x.

The last f(x) = 0x^2 − 9x + 7 , doesn't qualify because of the a = 0, and the rule is that a ≠ 0.

Therefore  f (x) = 3/4 x ^2 + 2x − 5 represents a quadratic function.

I hope this helps.
Hello,

a quadratic function has y=ax²+bx+c with a!=0 for equation.
Thus the only answer is f(x)=3/4 x²+2x-5

Is negative 5 a rational number

Answers

its a rational number but also a integer and could never be a whole number because its a negative and whole numbers are always positive
 

Quadrilateral ABCD is located at A(−2, 2), B(−2, 4), C(2, 4), and D(2, 2). The quadrilateral is then transformed using the rule (x − 2, y + 8) to form the image A'B'C'D'. What are the new coordinates of A', B', C', and D'? Describe what characteristics you would find if the corresponding vertices were connected with line segments.

Answers

The new coordinates are A(-4, 10), B (-4, 12), C (0, 12) and D (0, 10). If you were to connect these, it would take the shape of a rectangle. 

The domain of a function is given by {-4,2,8}. If the function is defined by y= x +1 /3 ,then which of the following values is a member of the range?

Answers

Answer:

{-1, 1, 3}

Step-by-step explanation:

Given the function

y = (x + 1)/3

The domain are the input value x while the range are the output values given the input value x;

Given the domain {-4, 2, 8}

when x = -4;

y = (-4+1)/3

y = -3/3

y = -1

when x = 2;

y = (2+1)/3

y = 3/3

y = 1

when x = 8;

y = (8+1)/3

y = 9/3

y = 3

Hence the member of the range are {-1, 1, 3}

The graph of which function has an axis of symmetry at x =-1/4 ?f(x) = 2x2 + x – 1

f(x) = 2x2 – x + 1

f(x) = x2 + 2x – 1

f(x) = x2 – 2x + 1

Answers

The graph of which function has an axis of symmetry at x = -1/4 is :

f(x) = 2x² + x – 1

Further explanation

Discriminant of quadratic equation ( ax² + bx + c = 0 ) could be calculated by using :

D = b² - 4 a c

From the value of Discriminant , we know how many solutions the equation has by condition :

D < 0 → No Real Roots

D = 0 → One Real Root

D > 0 → Two Real Roots

Let us now tackle the problem!

An axis of symmetry of quadratic equation y = ax² + bx + c is :

\large {\boxed {x = (-b)/(2a) } }

Option 1 :

f(x) = 2x² + x – 1 → a = 2 , b = 1 , c = -1

Axis of symmetry → x = (-b)/(2a) = (-1)/(2(2)) = -(1)/(4)

Option 2 :

f(x) = 2x² – x + 1 → a = 2 , b = -1 , c = 1

Axis of symmetry → x = (-b)/(2a) = (-(-1))/(2(2)) = (1)/(4)

Option 3 :

f(x) = x² + 2x – 1 → a = 1 , b = 2 , c = -1

Axis of symmetry → x = (-b)/(2a) = (-2)/(2(1)) = -1

Option 4 :

f(x) = x² – 2x + 1 → a = 1 , b = -2 , c = 1

Axis of symmetry → x = (-b)/(2a) = (-(-2))/(2(1)) = 1

Learn more

Answer details

Grade: High School

Subject: Mathematics

Chapter: Quadratic Equations

Keywords: Quadratic , Equation , Discriminant , Real , Number

The graph of function \boxed{f(x)=2x^(2)+x-1} has an axis of symmetry as \boxed{x=-(1)/(4)}.

Further explanation:

The standard form of a quadratic equation is as follows:

\boxed{f(x)=ax^(2)+bx+c}

The vertex form of a quadratic equation is as follows:

\boxed{g(x)=a(x-h)^(2)+k}

Axis of symmetry is the line which divides the graph of the parabola in two perfect halves.

The formula for axis of symmetry of a quadratic function is given as follows:

\boxed{x=-(b)/(2a)}

The first function is given as follows:

f(x)=2x^(2)+x-1

The above function is in standard form with a=2, b=1 and c=-1.

Then its axis of symmetry is calculated as,

\begin{aligned}x&=-(b)/(2a)\n&=-(1)/(2*2)\n&=-(1)/(4)\end{aligned}  

The axis of symmetry of first function is x=-(1)/(4).

Express the function f(x)=2x^(2)+x-1 in its vertex form,

\begin{aligned}f(x)&=2x^(2)+x-1\n&=(√(2)x)^(2)+\left(2* √(2)x* (1)/(2√(2))\right)-1+\left((1)/(2√(2))\right)^(2)-\left((1)/(√(2))\right)^(2)\n&=\left(√(2)x+(1)/(2√(2))\right)^(2)-1-(1)/(8)\n&=\left[√(2)\left(x+(1)/(4)\right)\right]^(2)-(9)/(8)\n&=2\left(x-\left(-(1)/(4)\right)\right)^(2)-(9)/(8)\end{aligned}

The above equation is in the vertex form with a=2, h=-(1)/(4) and k=-(9)/(8).

Therefore, its axis of symmetry is given as,

\begin{aligned}x&=h\nx&=-(1)/(4)\end{aligned}  

The graph of function f(x)=2x^(2)+x-1 is shown in Figure 1.

The second function is given as follows:

f(x)=2x^(2)-x+1

The above function is in standard form with a=2, b=-1 and c=1.

Then its axis of symmetry is calculated as,

\begin{aligned}x&=-(b)/(2a)\n&=-((-1))/(2*2)\n&=(1)/(4)\end{aligned}  

The axis of symmetry of second function is x=(1)/(4).

The third function is given as follows:

f(x)=x^(2)+2x-1

The above function is in standard form with a=1, b=2 and c=-1.

Then its axis of symmetry is calculated as,

\begin{aligned}x&=-(b)/(2a)\n&=-(2)/(2*1)\n&=-1\end{aligned}  

The axis of symmetry of third function is x=-1.

The fourth function is given as follows:

f(x)=x^(2)-2x+1  

The above function is in standard form with a=1, b=-2 and c=1.

Then its axis of symmetry is calculated as,

\begin{aligned}x&=-(b)/(2a)\n&=-(-2)/(2*1)\n&=1\end{aligned}  

The axis of symmetry of fourth function is x=1.

Therefore, the function \boxed{f(x)=2x^(2)+x-1} has an axis of symmetry as \boxed{x=-(1)/(4)}.

Learn more:

1. A problem on graph brainly.com/question/2491745

2. A problem on function brainly.com/question/9590016

3. A problem on axis of symmetry brainly.com/question/1286775

Answer details:

Grade: High school

Subject: Mathematics

Chapter: Functions

Keywords:Graph, function, axis, f(x), 2x^2+x-1, axis of symmetry, symmetry, vertex, perfect halves, graph of a function, x =- 1/4.

You are 6 feet tall and cast a 10 foot shadow. At the same time of day, your friendcasts a 9 foot shadow. How tall is your friend?

Answers

Answer:

5 feet tall

Step-by-step explanation: