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2 years ago

What is 5x^2-7x-3=8 by solving using a graph???

1 answer:

3 0

Hello!

Simplifying
5x2 + -7x + -3 = 8

Reorder the terms:
-3 + -7x + 5x2 = 8

Solving
-3 + -7x + 5x2 = 8

Solving for variable 'x'.

Reorder the terms:
-3 + -8 + -7x + 5x2 = 8 + -8

Combine like terms: -3 + -8 = -11
-11 + -7x + 5x2 = 8 + -8

Combine like terms: 8 + -8 = 0
-11 + -7x + 5x2 = 0

Begin completing the square. Divide all terms by
5 the coefficient of the squared term:

Divide each side by '5'.
-2.2 + -1.4x + x2 = 0

Move the constant term to the right:

Add '2.2' to each side of the equation.
-2.2 + -1.4x + 2.2 + x2 = 0 + 2.2

Reorder the terms:
-2.2 + 2.2 + -1.4x + x2 = 0 + 2.2

Combine like terms: -2.2 + 2.2 = 0.0
0.0 + -1.4x + x2 = 0 + 2.2
-1.4x + x2 = 0 + 2.2

Combine like terms: 0 + 2.2 = 2.2
-1.4x + x2 = 2.2

The x term is -1.4x. Take half its coefficient (-0.7).
Square it (0.49) and add it to both sides.

Add '0.49' to each side of the equation.
-1.4x + 0.49 + x2 = 2.2 + 0.49

Reorder the terms:
0.49 + -1.4x + x2 = 2.2 + 0.49

Combine like terms: 2.2 + 0.49 = 2.69
0.49 + -1.4x + x2 = 2.69

Factor a perfect square on the left side:
(x + -0.7)(x + -0.7) = 2.69

Calculate the square root of the right side: 1.640121947

Break this problem into two subproblems by setting
(x + -0.7) equal to 1.640121947 and -1.640121947.

Subproblem 1
x + -0.7 = 1.640121947

Simplifying
x + -0.7 = 1.640121947

Reorder the terms:
-0.7 + x = 1.640121947

Solving
-0.7 + x = 1.640121947

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '0.7' to each side of the equation.
-0.7 + 0.7 + x = 1.640121947 + 0.7

Combine like terms: -0.7 + 0.7 = 0.0
0.0 + x = 1.640121947 + 0.7
x = 1.640121947 + 0.7

Combine like terms: 1.640121947 + 0.7 = 2.340121947
x = 2.340121947

Simplifying
x = 2.340121947

Subproblem 2
x + -0.7 = -1.640121947

Simplifying
x + -0.7 = -1.640121947

Reorder the terms:
-0.7 + x = -1.640121947

Solving
-0.7 + x = -1.640121947

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '0.7' to each side of the equation.
-0.7 + 0.7 + x = -1.640121947 + 0.7

Combine like terms: -0.7 + 0.7 = 0.0
0.0 + x = -1.640121947 + 0.7
x = -1.640121947 + 0.7

Combine like terms: -1.640121947 + 0.7 = -0.940121947
x = -0.940121947

Simplifying
x = -0.940121947

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.340121947, -0.940121947}

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Give a geometric description of the following system of equations.a. 2x−4y=12 −3x+6y=−15.b. 2x−4y=12 −5x+3y=10.a. 2x−4y=12 −3x+6

Reptile [31]

Answer:

a. No solution, parallel lines.

b. One solution.

Step-by-step explanation:

Given the system of equations:

a. $2x-4y=12$

$-3x+6y=-15$

b. $2x-4y=12$

$-5x+3y=10$

To give a geometric description of the given system of equations.

The geometric description of a system of equations in 2 variables mean the system of equations will represent the number of lines equal to the number of equations in the system given.

i.e.

Number of planes = Number of variables

Number of lines = Number of equations in the system.

Here, we are given 2 variables and 2 equation in each system.

So, they can be represented in the xy-coordinates plane.

And the number of solutions to the system depends on the following condition.

Let the system of equations be:

$A_1x+B_1y+C_1=0\\A_2x+B_2y+C_2=0$

1. One solution:

There will be one solution to the system of equations, If we have:

$\dfrac{A_1}{A_2}\neq\dfrac{B_1}{B_2}$

2. Infinitely Many Solutions: (Identical lines in the system)

$\dfrac{A_1}{A_2}=\dfrac{B_1}{B_2}= \dfrac{C_1}{C_2}$

3. No Solution:(Parallel lines)

$\dfrac{A_1}{A_2}=\dfrac{B_1}{B_2}\neq\dfrac{C_1}{C_2}$

Now, let us discuss the system of equations one by one:

a. $2x-4y=12$ OR $2x-4y-12=0$

$-3x+6y=-15$ OR $-3x+6y+15=0$

$A_1 = 2, B_1 = -4, C_1 = -12\\A_2 = -3, B_2 = 6, C_2= 15$

Here, the ratio:

$\dfrac{A_1}{A_2}=\dfrac{B_1}{B_2} = -\dfrac{2}{3}\\\dfrac{C_1}{C_2} = -\dfrac{4}{5}$

$\dfrac{A_1}{A_2}=\dfrac{B_1}{B_2}\neq\dfrac{C_1}{C_2}$

Therefore, no solution i.e. parallel lines.

b. $2x-4y=12$ OR $2x-4y-12=0$

$-5x+3y=10$ OR $-5x+3y-10=0$

$A_1 = 2, B_1 = -4, C_1 = -12\\A_2 = -5, B_2 = 3, C_2 = -10$

$\dfrac{A_1}{A_2}= -\dfrac{2}{5}\\\dfrac{B_1}{B_2} = -\dfrac{4}{3}\\\dfrac{C_1}{C_2} = -\dfrac{6}{5}$

$\dfrac{A_1}{A_2}\neq\dfrac{B_1}{B_2}$

So, one solution.

Kindly refer to the images attached for the graphical representation of the given system of equations.

6 0

2 years ago

Please help meh i dont know the answer

Savatey [412]

Answer:

3 inches

Step-by-step explanation: An equilateral triangle means all 3 sides are the same length.

A square also have the same length for all 4 sides.

So each side of the square is 6cm, to find the perimeter you do 6*4=24.

then divide the square's perimeter by 3 since triangle have 3 sides. 24/3=8

so each side of the triangle will be 8cm

7 0

2 years ago

Plz help me I need tu turn this is by midnight!!

expeople1 [14]

Answer:

The last answer.

Step-by-step explanation:

It looks to be the correct answer because for the one above you can't simplify 27 by 5.

4 0

2 years ago

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Which of the following points is a solution of the system shown? x + y ≥ 6 x ≥ 4 a.(-1, 7) b.(4, -2) c.(4, 2)

Kobotan [32]

I know none of these are actually the answer but odysseyware gave me credit for
(4,2)

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2 years ago

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Graph Ex+ 3y = 24<br> a.<br> b.<br> c.<br> d.

8090 [49]

Answer:

(b)

Step-by-step explanation:

Given

$8x + 3y = 24$

Required

The graph

First, make y the subject

$3y = 24 - 8x$

Divide through by 3

$y = 8 - \frac{8}{3}x$

Let x = 3

$y = 8 - \frac{8}{3}*3 = 8 - 8 = 0$

Let x = 6

$y = 8 - \frac{8}{3}*6 = 8 - 16 = -8$

So, we plot the graph through

$(3,0)$ and $(6,-8)$

See attachment for graph

8 0

2 years ago