Mathematics, 29.07.2019 02:00 bombo99

5x2=5x^2 4x2+4x^2 1. what values of a, b, and c would you use in the quadratic formula for the following equation? 5x2+9x=4 2. attachment 3. what are the approximate solutions of 2x2-x+10=0? 4. solve the equation using the quadric formula. 4x2+3x-10=0 5. solve the equation using the quadric formula. -x2+27=6x 6. which method is the best method for solving the equation? 8x2-13x+3=0 7. how many solutions are there for 5x2+7x-4=0? 8. the perimeter of a rectangle is 54 cm. the area of the same rectangle is 176 cm2. what are the dimensions of the rectangle?

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Answer from: zachcochran2007

1. The equation 5x^2+9x=4, can be rewritten as 5x^2+9x-4=0, where a=5 (the coefficient of the quadratic term), b = 9 (the coefficient of the linear term) and c = -4 (the independent term).

2. No attachment is shown.

3. To use the quadratic formula, the coefficients are: a = 2, b = -1 and c = 10. However, the discriminant, i. e., b^2 -4(a)(c) is negative, therefore, there is no real solution.

4. You have to use the quadratic formula, with a = 4, b = 3 and c = -10, as follows:

$x = \frac{-b \pm \sqrt{b^2 - 4(a)(c)}}{2(a)}$

$x = \frac{-3 \pm \sqrt{3^2 - 4(4)(-10)}}{2(4)}$

$x = \frac{-3 \pm \sqrt{169}}{8}$

$x_1 = \frac{-3 + 13}{8}$

$x_1 = \frac{5}{4}$

$x_2 = \frac{-3 - 13}{8}$

x_2 = -2

5. Rewriting the formula, so that all the terms are on one side and ordering the polynomial expression, gives: -x2-6x+27=0. Here a = -1, b = -6 and c = 27. Using the quadratic formula gives

$x = \frac{-b \pm \sqrt{b^2 - 4(a)(c)}}{2(a)}$

$x = \frac{6 \pm \sqrt{6^2 - 4(-1)(27)}}{2(-1)}$

$x = \frac{6 \pm \sqrt{144}}{-2}$

$x_1 = \frac{6 + 12}{-2}$

x_1 = -9

$x_2 = \frac{6 - 12}{-2}$

x_2 = 3

6. When the second grade polynomial has all of its coefficients (a, b and c) different than zero, like this case, the best method for solving the equation is the quadratic formula .

7. When the discriminant is greater than zero, there are two different solutions and when it is equal to zero, it has one double solution.

The discriminant for this case is 7^2 - 4(5)(-4) = 129. So, there are two different solutions .

8. Let's call the sides of the rectangle a and b.

perimeter formula: 2a + 2b = 54 cm (eq. 1)

area formula: (a)(b) = 176 cm2 (eq. 2)

Isolating a in equation 1, gives (units are omitted):

2a + 2b = 54

2a = 54 - 2b

a = 27 - b (eq. 3)

Replacing equation 3 into equation 2, gives (units are omitted):

(a)(b) = 176

(27 - b)(b) = 176

-b^2 + 27b - 176 = 0

Using quadratic formula, we get

$x = \frac{-27 \pm \sqrt{27^2 - 4(-1)(-176)}}{2(-1)}$

$x = \frac{-27 \pm \sqrt{25}}{-2}$

$x_1 = \frac{-27 + 5}{-2}$

x_1 = 11

$x_2 = \frac{-27 - 5}{-2}$

x_2 = 16

Then, there are two possible values for b, 11 cm and 16 cm. Replacing these values into equation 3 gives:

a = 27 - 11 = 16 cm

a = 27 - 16 = 11 cm

Therefore, the two sides are 11 cm and 16 cm long, despite their names.

Answer from: Quest

b: |12 – x| ≤ 0.25

step-by-step explanation:

let x be the possible lengths in inches, of the ribbons jaime cut.

we have been given that jaime is cutting strips of ribbon for a project. he tries to cut each piece to be 12 inches long, but sometimes he cuts it too long or too short by as much as 0.25 inch.

we can represent this information in an inequality as:

by the definition of absolute value function we will get,

upon combining our inequalities we will get,

therefore, the inequality describes all the possible lengths (x), in inches, of the ribbons jaime cut.

step-by-step explanation:

Answer from: Quest

The answer would he -4,-2 because the points are just on the opposite side. since the x axis is +4 it's going to he -4 and since the y axis is -2 it stays there because whaen rotated it stays in the third quadrant
Hello! could someone with this problem?

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5x2=5x^2 4x2+4x^2 1. what values of a, b, and c would you use in the quadratic formula for the follo...