All categories

2 years ago

What are the solutions?8x^2-12x-23=-5

Mathematics

1 answer:

erastova [34]2 years ago

4 0

Answer:

x = 3/4 + (3 sqrt(5))/4 or x = 3/4 - (3 sqrt(5))/4

Step-by-step explanation:

Solve for x over the real numbers:

8 x^2 - 12 x - 23 = -5

Divide both sides by 8:

x^2 - (3 x)/2 - 23/8 = -5/8

Add 23/8 to both sides:

x^2 - (3 x)/2 = 9/4

Add 9/16 to both sides:

x^2 - (3 x)/2 + 9/16 = 45/16

Write the left hand side as a square:

(x - 3/4)^2 = 45/16

Take the square root of both sides:

x - 3/4 = (3 sqrt(5))/4 or x - 3/4 = -(3 sqrt(5))/4

Add 3/4 to both sides:

x = 3/4 + (3 sqrt(5))/4 or x - 3/4 = -(3 sqrt(5))/4

Add 3/4 to both sides:

Answer: x = 3/4 + (3 sqrt(5))/4 or x = 3/4 - (3 sqrt(5))/4

You might be interested in

Mason wants to host a housewarming party. The following equation represents how the cost of party depends on the number of atten

mestny [16]

The answer I got was a=5. Hope this is correct and hope it helped

4 0

3 years ago

Solve the right triangle. round your answers to the nearest tenth. help.

hammer [34]

Answer:

19.2

Step-by-step explanation:

Cosine rule :

$\sqrt{a^{2} +b^{2} ﹣2abcos(angle ) }$

c will always be the hypotenuse.

a and b can be any if the opposite or the adjacent.

${15}^{2} + 12^{2} - 2 \times 15 \times 12 \times \cos(90) = 369$

\sqrt{369}=19.20937...

8 0

2 years ago

As a bowl of soup cools, the temperature of the soup is given by the twice-differentiable function H for 0<img src="https://tex.

Aleks04 [339]

The rate of change of temperature with time at a point in time is given by

the derivative of the function for the temperature of the soup.

The correct responses are;

a) H'(5) is approximately -2.6 degrees Celsius per minute.

b) Yes

c) The equation for the line tangent is y = -3.6·t + 90.8
The approximate value of C(5) is 72.8 °C

d) The rate of change of the temperature of the soup at t = 3 minutes is -3.6 degrees Celsius per minute.

Reasons:

a) From the data in the table, we have;

The approximate value of H'(5) is given by the average value of the rate of

change of the temperature with time between points, t = 3, and t = 8

Therefore;

$\displaystyle H'(5) = \mathbf{\frac{H(8) - H(3)}{8 - 3}}$

Which gives;

$\displaystyle H'(5) = \frac{80 - 67}{8 - 3} = \mathbf{2.6}$

Therefore, H'(5) = -2.6°C per minute

b) Given that the function is twice differentiable over the interval, 0 ≤ t ≤ 12, the function for the change in temperature is continuous in the interval 0 ≤ t ≤ 12

At t = 0, H(0) = 90 °C

At t = 12, H(12) = 58 °C

58 °C < 60 < 90 °C

Therefore, there exist a temperature, of 60 °C between 90° C and 58 °C

c) The given derivative of C is, $C'(t) = \mathbf{-3.6 \cdot e^{-0.05 \cdot t}}$

At t = 3, we have;

$The \ slope \ at \ t = 3 \ is \ C'(3) = -3.6 \cdot e^{-0.05 \times 3} \approx -3.1$

Therefore, we have;

y - 80 ≈ -3.1 × (x - 3)

The equation for the tangent is; y = -3.6 × (x - 3) + 80

y = -3.6·x + 10.8 + 80 = -3.6·x + 90.8

The equation for the tangent is; y = -3.6·x + 90.8

The value of C(5) is approximately, C(5) ≈ -3.6 × 5 + 90.8 = 72.8

C(5) ≈ 72.8°

d) Based on the the model above, the rate at which the temperature of the

soup is changing at t = 3 minutes is -3.6 degrees per minute.

Learn more about calculus and concepts here:

brainly.com/question/20336420

8 0

2 years ago

A marketing research company desires to know the mean consumption of milk per week among people over age 30. They believe that t

Nitella [24]

Answer:

651 is the minimum number of people over age 30 they must include in their sample.

Step-by-step explanation:

We are given the following information:

Confidence level = 90%

Significance level = 10%

Maximum error = 0.09

Variance = 1.96

$\text{Standard Deviation} = \sqrt{\text{Variance}} = \sqrt{1.96} = 1.4$

Formula:

$\text{Error} = z_{critical}\dfrac{\sigma}{\sqrt{n}}$

Putting all the values,

$z_{critical}\text{ at}~\alpha_{0.05} = \pm 1.64$

$0.09 = 1.64\times \dfrac{1.4}{\sqrt{n}}\\\\n = (\dfrac{1.64\times 1.4}{0.09})^2 = 650.81 \approx 651$

651 is the minimum number of people over age 30 they must include in their sample.

7 0

3 years ago

Circle S is shown. Line segment R T is a diameter. The length of S T is 4. Sector R S T is shaded. The measure of central angle

ad-work [718]

Answer: 8π (Option B)

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

What are the solutions?8x^2-12x-23=-5​

What are the solutions?8x^2-12x-23=-5