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Harman [31]
3 years ago
15

Please help me so confused Solve. x^2 + 3x − 7 = 0 Enter your answers, as exact values, in the boxes. x = or x =

Mathematics
2 answers:
Rzqust [24]3 years ago
6 0

Answer:

x = -1/2 ( 3±sqrt(37))

Step-by-step explanation:

x^2 + 3x − 7 = 0

Add 7 to each side

x^2 + 3x =7

Using complete the square

Taking the coefficient of x

3

Divide by 2

3/2

Square it

(3/2)^2 = 9/4

Add this to each side

x^2 + 3x+ 9/4 = 7+9/4

( x+ 3/2) ^2 = 28/4 + 9/4

( x+ 3/2) ^2 = 37/4

Take the square root of each side

x+3/2 = ±sqrt(37/4)

x+3/2 = ±sqrt(37) / sqrt(4)

x+ 3/2 = ±sqrt(37) / 2

Subtract 3/2 from each side

x = -3/2 ±sqrt(37) / 2

x = -1/2 ( 3±sqrt(37))

igomit [66]3 years ago
5 0

Answer:

-1.5 -√9.25 or -1.5 +√9.25

Step-by-step explanation:

x^2 + 3x - 7 = 0

This will not factor so we can use completing the square:

x^2 + 3x = 7

(x + 1.5)^2 - 2.25 = 7

(x + 1.5)^2 = 9.25

x + 1.5 = ±√9.25

x = -1.5 ±√9.25

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Un campo de fútbol mide de largo 105m y de ancho 65m¿cuál es el área total del campo de fútbol?​
Jet001 [13]

Answer:

6825

Step-by-step explanation:

area=largo X ancho

area= 105 x  65=  6825

7 0
2 years ago
Find the absolute maximum and minimum values of the function below. f(x) = x3 − 9x2 + 3, − 3 2 ≤ x ≤ 12 Solution Since f is cont
Neko [114]

Answer:

There are an absolute minimum (x = 6) and an absolute maximum (x = 12).

Step-by-step explanation:

The correct statement is described below:

Find the absolute maximum and minimum values of the function below:

f(x) = x^{3}-9\cdot x^{2}+ 3, 2 \leq x \leq 12

Given that function is a polynomial, then we have the guarantee that function is continuous and differentiable and we can use First and Second Derivative Tests.

First, we obtain the first derivative of the function and equalize it to zero:

f'(x) = 3\cdot x^{2}-18\cdot x

3\cdot x^{2}-18\cdot x = 0

3\cdot x \cdot (x-6) = 0 (Eq. 1)

As we can see, only a solution is a valid critical value. That is: x = 6

Second, we determine the second derivative formula and evaluate it at the only critical point:

f''(x) = 6\cdot x -18 (Eq. 2)

x = 6

f''(6) = 6\cdot (6)-18

f''(6) =18 (Absolute minimum)

Third, we evaluate the function at each extreme of the given interval and the critical point as well:

x = 2

f(2) = 2^{3}-9\cdot (2)^{2}+3

f(2) = -25

x = 6

f(6) = 6^{3}-9\cdot (6)^{2}+3

f(6) = -105

x = 12

f(12) = 12^{3}-9\cdot (12)^{2}+3

f(12) = 435

There are an absolute minimum (x = 6) and an absolute maximum (x = 12).

6 0
3 years ago
Jorge is asked to build a box in the shape of a rectangular prism. The maximum girth of the box is 20 cm. What is the width of t
MariettaO [177]

Answer:

The width of the box is 6.7 cm

The maximum volume is 148.1 cm³

Step-by-step explanation:

The given parameters of the box Jorge is asked to build are;

The maximum girth of the box = 20 cm

The nature of the sides of the box = 2 square sides and 4 rectangular sides

The side length of square side of the box = w

The length of the rectangular side of the box = l

Therefore, we have;

The girth = 2·w + 2·l = 20 cm

∴ w + l = 20/2 = 10

w + l = 10

l = 10 - w

The volume of the box, V = Area of square side × Length of rectangular side

∴ V = w × w × l = w × w × (10 - w)

V = 10·w² - w³

At the maximum volume, we have;

dV/dw = d(10·w² - w³)/dw = 0

∴ d(10·w² - w³)/dw = 2×10·w - 3·w² = 0

2×10·w - 3·w² = 20·w - 3·w² = 0

20·w - 3·w² = 0 at the maximum volume

w·(20 - 3·w) = 0

∴ w = 0 or w = 20/3 = 6.\overline 6

Given that 6.\overline 6 > 0, we have;

At the maximum volume, the width of the block, w = 6.\overline 6 cm ≈ 6.7 cm

The maximum volume, V_{max}, is therefore given when w = 6.\overline 6 cm = 20/3 cm  as follows;

V = 10·w² - w³

V_{max} = 10·(20/3)² - (20/3)³ = 4000/27 = 148.\overline {148}

The maximum volume, V_{max} = 148.\overline {148} cm³ ≈ 148.1 cm³

Using a graphing calculator, also, we have by finding the extremum of the function V = 10·w² - w³, the coordinate of the maximum point is (20/3, 4000/27)

The width of the box is;

6.7 cm

The maximum volume is;

148.1 cm³

5 0
3 years ago
Please help! A six-pack of soda is on for $2.46. Find the cost of one can of soda and drop the appropriate value into the answer
Gala2k [10]

Answer:

0.41 cents

Step-by-step explanation:

2.46/6 = 0.41

4 0
3 years ago
Sarah is a cliff driver she starts 75 feet above the water dives and dives to 20 feet below the water jada also starts at 75 fee
Murljashka [212]

Answer:

sarah=55ft Jada=58ft

Step-by-step explanation:

7 0
3 years ago
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