What is the total cost of a $12.49 item with a sales tax of 5%?

Answers

Answer 1

Answer:

Answer: $13.11

Step-by-step explanation:

hope this helps!

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HELP! What is the solution to the following system of equations?

Answers

Answer:

it is 2,4

Step-by-step explanation:

The point that they meet is 2,4 . It means X+ is 2 and Y+ is 4 .

You can write a as their meet point . you should answer like this a(2,4) .

How would I solve 16x^4-41x^2+25=0 ???

Answers

$16{ x }^( 4 )-41{ x }^( 2 )+25=0$

${ x }^( 4 )={ ({ x }^( 2 )) }^( 2 )\n \n 16{ ({ x }^( 2 )) }^( 2 )-41{ x }^( 2 )+25=0$

First of all to make our equation simpler, we'll equal $x^(2)$ to a variable like 'a'.

So,

${ x }^( 2 )=a$

Now let's plug $x^(2)$ 's value (a) into the equation.

$16{ ({ x }^( 2 )) }^( 2 )-41{ x }^( 2 )+25=0\n \n { x }^( 2 )=a\n \n 16{ (a) }^( 2 )-41{ a }+25=0$

Now we turned our equation into a quadratic equation.

(The variable 'a' will have a solution set of two solutions, but 'x' , which is the variable of our first equation will have a solution set of four solutions since it is a quartic equation (fourth-degree equation) )

Let's solve for a.

The formula used to solve quadratic equations ;

$\frac { -b\pm \sqrt { { b }^( 2 )-4\cdot t\cdot c } }{ 2\cdot t }$

The formula is used in an equation formed like this :

$t{ x }^( 2 )+bx+c=0$

In our equation,

t=16 , b=-41 and c=25

Let's plug the values in the formula to solve.

$t=16\quad b=-41\quad c=25\n \n \frac { -(-41)\pm \sqrt { -(41)^( 2 )-4\cdot 16\cdot 25 } }{ 2\cdot 16 } \n \n \frac { 41\pm \sqrt { 1681-1600 } }{ 32 } \n \n \frac { 41\pm \sqrt { 81 } }{ 32 } \n \n \frac { 41\pm 9 }{ 32 }$

So the solution set :

$\frac { 41+9 }{ 32 } =\frac { 50 }{ 32 } \n \n \frac { 41-9 }{ 32 } =\frac { 32 }{ 32 } =1\n \n a\quad =\quad \left\{ \frac { 50 }{ 32 } ,\quad 1 \right\}$

We found a's value.

Remember,

${ x }^( 2 )=a$

So after we found a's solution set, that means.

${ x }^( 2 )=\frac { 50 }{ 32 }$

and

${ x }^( 2 )=1$

We'll also solve this equations to find x's solution set :)

${ x }^( 2 )=\frac { 50 }{ 32 } \n \n \frac { 50 }{ 32 } =\frac { 25 }{ 16 } \n \n { x }^( 2 )=\frac { 25 }{ 16 } \n \n \sqrt { { x }^( 2 ) } =\sqrt { \frac { 25 }{ 16 } } \n \n x=\quad \pm \frac { 5 }{ 4 }$

${ x }^( 2 )=1\n \n \sqrt { { x }^( 2 ) } =\sqrt { 1 } \n \n x=\quad \pm 1$

So the values x has are :

$\frac { 5 }{ 4 }$ , $-\frac { 5 }{ 4 }$ , $1$ and $-1$

Solution set :

$x=\quad \left\{ \frac { 5 }{ 4 } \quad ,\quad -\frac { 5 }{ 4 } \quad ,\quad 1\quad ,\quad -1 \right\}$

I hope this was clear enough. If not please ask :)

16x⁴ - 41x² + 25 = 0
16x⁴ - 16x² - 25x² + 25 = 0
16x²(x²) - 16x²(1) - 25(x²) + 25(1) = 0
16(x² - 1) - 25(x² - 1) = 0
(16x² - 25)(x² - 1) = 0
(16x² + 20x - 20x - 25)(x² - x + x - 1) = 0
(4x(4x) + 4x(5) - 5(4x) - 5(5))(x(x) - x(1) + 1(x) - 1(1)) = 0
(4x(4x + 5) - 5(4x + 5))(x(x - 1) + 1(x - 1)) = 0
(4x - 5)(4x + 5)(x + 1)(x - 1) = 0
4x - 5 = 0 or 4x + 5 = 0 or x + 1 = 0 or x - 1 = 0
    + 5 + 5    - 5 - 5 - 1 - 1 + 1 + 1
   4x = 5 4x = -5 x = -1    x = 1
      4    4    4 4
   x = 1¹/₄ x = -1¹/₄

The solution set is equal to {(1¹/₄, -1¹/₄, -1, 1)}.

Ayuda por favor en la actividad 3 , Funciones, Matemáticas

Answers

Answer:

y = 1

y = 16

y = 20

y = 0

Step-by-step explanation:

Por cada valor de x intercambialo con su valor nuevo.

Edward is playing a game where he draws cards with integers on them from a deck of cards. If the integer is positive he moves forward that many steps, if the integer is negative he moves back that many steps. Edward drew the following cards: 3, -3, -4, 5, 10, -7. Where does Edward end up in relation to where he started? A) 4 steps behind where he started. B) 4 steps in front of where he started. C) 32 steps behind where he started. D) 32 steps in front of where he started.