In 2013, the population of China was estimated to be 1,360,760,100. Round off the number of people

What are the solutions of the equation x4 + 6x2 + 5 = 0? Use u substitution to solve.

tester [12383]

The solutions to the equation are $x=\pm i, x=\pm \sqrt{5}i$

Explanation:

Given the equation $x^{4}+6 x^{2}+5=0$

, we aim to find the solutions of the equation.

Let us use $x^{2} =u$ and $x^4=u^2$

Thus, the equation transforms into

$u^{2}+6 u+5=0$

Factoring the equation results in:

$(u+1)(u+5)=0$

$u=-1, u=-5$

Inserting back $x^{2} =u$ and allows us to solve for x.

Initially, we will substitute $u=-1$

Consequently, we find;

$x^{2} =-1$

$x=\sqrt{-1}$

$x=\pm i$

Similarly, by substituting $u=-5$ , we derive;

$x^{2} =-5$

$x=\sqrt{-5}$

$x=\pm \sqrt{5}i$

Thus, the solutions to the equation are $x=\pm i, x=\pm \sqrt{5}i$

6 0

1 month ago

Toby goes on holiday to Geneva, Switzerland. In Geneva, Toby sees a watch costing 193.75 CHF (Swiss Francs). In Manchester, an i

lawyer [12517]

The watch is less expensive in Geneva, Switzerland by £20. Step-by-step explanation: To identify the city where the watch is cheaper, we need to convert the watch's price to the same currency. Since pounds are utilized in part b of the question, using this currency would simplify the calculations. In Geneva, the watch's price is 193.75 CHF from our conversion: £1 = 1.55 CHF, thus, £x = 193.75 CHF. By cross-multiplying, we solve for x: (193.75 * 1) / 1.55 = 193.75/1.55 = £125. This demonstrates that the watch is cheaper in Geneva and more expensive in Manchester. To find out by how much, we simply deduct the Geneva price from the Manchester price: 145 - 125 = £20 cheaper.

3 0

1 month ago

Toyota advertises that their Toyota Highlander Hybrid provide 28 MPG. To test this, an experiment involving a sample of 20 Toyot

Inessa [12570]

We opt to accept the null hypothesis. Given the following details provided: the Sample mean equals 28.8 miles per gallon, Sample size n is 120, and Alpha α is 0.01 with a sample standard deviation of 6.89 miles per gallon. Initially, we set up the null and alternative hypotheses. Utilizing a two-tailed t-test facilitates this hypothesis testing. By substituting the relevant values we calculate, and eventually conclude that we fail to reject the null hypothesis, endorsing that the average MPG for the Toyota Highlander Hybrid vehicles is indeed 28 miles per gallon.

5 0

2 months ago

Angelica is working with function machines. She has the two machines at shown at the right. She wants to put them in order so th

Leona [12618]

To achieve the desired output, first use the machine with the function y = x^2 - 6, followed by the machine that computes y = sqrt(x-5). This way, when you input 6, the output from the first machine is calculated as x = 6, yielding y = 6^2 - 6, resulting in 30 as the input for the second machine. The second machine then processes this to provide the final output of sqrt(30 - 5), which equals sqrt(25) = 5. Alternatively, to obtain a negative final output, you should first utilize the machine with the function y = sqrt(x-5). Assuming you start with the value x = 9, the first machine computes this to sqrt(9-5), which is sqrt(4) = 2. Then, the second machine converts y to 2^2 - 6, leading to a result of 4 - 6 = -2.

3 0

2 months ago