Solve this in an equality 8z+3-2z <51

Answers

Answer 1

Answer: Answer: x < 8

8z+3-2z<51

Collect like terms.

6z+3<51

Move constant to the right side and change its sign.

6z<51-3

Subtract the numbers.

6z<48

Divide both sides of the inequality by 6.

z < 8

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

Solving Quadratic Equations by Factoring : brainly.com/question/12182022
Determine the Discriminant : brainly.com/question/4600943
Formula of Quadratic Equations : brainly.com/question/3776858

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.

What is the answer? Pls helpp

Answers

There would be 18 separate outcomes, since the spinner has three numbers and the dice has six numbers. Since the spinner has all odd numbers then an even number must be rolled on the dice for the answer to be odd. And since half of the numbers on a dice are even then half of the answers will be odd, aka 50%

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