All categories

3 years ago

Which system of equations can you use to find the roots of the equation 2x3 + 4x2 – x + 5 = –3x2 + 4x + 9?

Mathematics

2 answers:

Viefleur [7K]3 years ago

7 0

Answer:

C is the answer

Step-by-step explanation:

Degger [83]3 years ago

3 0

Answer:

$y=2x^3+4x^2-x+5$

$y=-3x^2+4x+9$

Step-by-step explanation:

The given equation is in the form $2x^3+4x^2-x+5=-3x^2+4x+9$

We have to evaluate the correct system of equations which can be used to find the roots of the equation.

We can find the root of the equation by plotting the graph of the equations. In order to graph, we can assume the left and right hand side of the given equation as two separate equations.

Therefore, we have

$y=2x^3+4x^2-x+5$

$y=-3x^2+4x+9$

Now, we plot the graph of these two equations in the same coordinate plane. The intersection point (s) would be the roots of the given equation.

Hence, the system of equation that we can use to find the root of the given equation is

$y=2x^3+4x^2-x+5$

$y=-3x^2+4x+9$

Last option is correct.

You might be interested in

A rectangle is 3 1/3 ft long and 2 1/3 feet wide. What is the distance around the rectangle?

Sonja [21]

3 1/3= 10/3
2 1/3= 7/3
7/3 + 10/3= 17/3
17/3 (2)+ 34/3
34/3= 11 1/3
final answer = 11 1/3

8 0

4 years ago

Read 2 more answers

An element with mass 780 grams decays by 16.3% per minute. How much of the element is remaining after 16 minutes, to the nearest

vitfil [10]

Exponential decay is a very common process especially when we are talking about radioactive materials. So, there is already a common formula for this type of behavior which is written below:

A = Pe^-rt
where
A is the amount left after time t
P is the initial amount at t=0
r is the rate

Substituting the values,
A = (780 g)(e^-0.163*16)
A = 57.5 g

8 0

4 years ago

The bar graph shown here provides the numbers of scoops of different ice cream flavors that were sold during school lunch today.

Mila [183]

C is the answer because 10 - 6 = 4 and 6 + 4 = 10

3 0

3 years ago

Read 2 more answers

A simple random sample of items resulted in a sample mean of . The population standard deviation is . a. Compute the confidence

Varvara68 [4.7K]

Answer:

(a): The 95% confidence interval is (46.4, 53.6)

(b): The 95% confidence interval is (47.9, 52.1)

(c): Larger sample gives a smaller margin of error.

Step-by-step explanation:

Given

$n = 30$ -- sample size

$\bar x = 50$ -- sample mean

$\sigma = 10$ --- sample standard deviation

Solving (a): The confidence interval of the population mean

Calculate the standard error

$\sigma_x = \frac{\sigma}{\sqrt n}$

$\sigma_x = \frac{10}{\sqrt {30}}$

$\sigma_x = \frac{10}{5.478}$

$\sigma_x = 1.825$

The 95% confidence interval for the z value is:

$z = 1.960$

Calculate margin of error (E)

$E = z * \sigma_x$

$E = 1.960 * 1.825$

$E = 3.577$

The confidence bound is:

$Lower = \bar x - E$

$Lower = 50 - 3.577$

$Lower = 46.423$

$Lower = 46.4$ --- approximated

$Upper = \bar x + E$

$Upper = 50 + 3.577$

$Upper = 53.577$

$Upper = 53.6$ --- approximated

So, the 95% confidence interval is (46.4, 53.6)

Solving (b): The confidence interval of the population mean if mean = 90

First, calculate the standard error of the mean

$\sigma_x = \frac{\sigma}{\sqrt n}$

$\sigma_x = \frac{10}{\sqrt {90}}$

$\sigma_x = \frac{10}{9.49}$

$\sigma_x = 1.054$

The 95% confidence interval for the z value is:

$z = 1.960$

Calculate margin of error (E)

$E = z * \sigma_x$

$E = 1.960 * 1.054$

$E = 2.06584$

The confidence bound is:

$Lower = \bar x - E$

$Lower = 50 - 2.06584$

$Lower = 47.93416$

$Lower = 47.9$ --- approximated

$Upper = \bar x + E$

$Upper = 50 + 2.06584$

$Upper = 52.06584$

$Upper = 52.1$ --- approximated

So, the 95% confidence interval is (47.9, 52.1)

Solving (c): Effect of larger sample size on margin of error

In (a), we have:

$n = 30$ $E = 3.577$

In (b), we have:

$n = 90$ $E = 2.06584$

Notice that the margin of error decreases when the sample size increases.

4 0

3 years ago

The wheel of a bike has a diameter of 27 inches. Find the circumference of the wheel. Round your answer to the nearest whole num

Readme [11.4K]

By definition, the circumference is given by:
C = 2 * pi * R
Where,
R: Radio
Substituting values we have:
C = 2 * pi * (27/2)
C = 84.82300165 in
Round to the nearest whole number:
C = 85 in
Answer:
The circumference of the wheel is:
B. about 85 inches

4 0

3 years ago

Read 2 more answers