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Brut [27]
1 year ago
7

A system of equations is shown below. Solve for x. y = x² - 6x + 4 y = x + 1

Mathematics
1 answer:
rjkz [21]1 year ago
6 0

The value of x in the given quadratic equations is either -2.7 or -11.3.

<h3>What are quadratic equations?</h3>

A quadratic equation is a second-degree algebraic equation in x. ax² + bx + c = 0, where a and b are coefficients, x is the variable, and c is the constant term, is the quadratic equation in its simplest form.

Given first equation, y = x²- 6x + 4 second equation, y = x +1

Put the value of y in the first equation to get

x + 1 = x² - 6x + 4

Solving this equation

x² - 7x + 3 = 0

Using quadratic formula,

x = - b ± \frac{\sqrt{(b^{2}- 4ac)}}{2a}

x = - 7 ±  \frac{\sqrt{(-7)^{2}- 4(3)}}{2}

x = - 7 ± 4.3

Therefore in the given quadratic equations, the value of x can be either -2.7 or -11.3

For more information on quadratic equations, visit:

brainly.com/question/1863222

#SPJ13

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Charra [1.4K]

Answer:

Point in Quadrant I

Step-by-step explanation:

the lines will overlap in quadrant I (the positive quadrant)

3 0
3 years ago
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A company wants to find out if the average response time to a request differs across its two servers. Say µ1 is the true mean/ex
lorasvet [3.4K]

Answer:

a) The null and alternative hypothesis are:

H_0: \mu_1-\mu_2=0\\\\H_a:\mu_1-\mu_2\neq 0

Test statistic t=0.88

The P-value is obtained from a t-table, taking into acount the degrees of freedom (419) and the type of test (two-tailed).

b)  A P-value close to 1 means that a sample result have a high probability to be obtained due to chance, given that the null hypothesis is true. It means that there is little evidence in favor of the alternative hypothesis.

c) The 95% confidence interval for the difference in the two servers population expectations is (-0.372, 0.972).

d) The consequences of the confidence interval containing 0 means that the hypothesis that there is no difference between the response time (d=0) is not a unprobable value for the true difference.

This relate to the previous conclusion as there is not enough evidence to support that there is significant difference between the response time, as the hypothesis that there is no difference is not an unusual value for the true difference.

Step-by-step explanation:

This is a hypothesis test for the difference between populations means.

The claim is that there is significant difference in the time response for the two servers.

Then, the null and alternative hypothesis are:

H_0: \mu_1-\mu_2=0\\\\H_a:\mu_1-\mu_2\neq 0

The significance level is 0.05.

The sample 1, of size n1=196 has a mean of 12.5 and a standard deviation of 3.

The sample 2, of size n2=225 has a mean of 12.2 and a standard deviation of 4.

The difference between sample means is Md=0.3.

M_d=M_1-M_2=12.5-12.2=0.3

The estimated standard error of the difference between means is computed using the formula:

s_{M_d}=\sqrt{\dfrac{\sigma_1^2}{n_1}+\dfrac{\sigma_2^2}{n_2}}=\sqrt{\dfrac{3^2}{196}+\dfrac{4^2}{225}}\\\\\\s_{M_d}=\sqrt{0.046+0.071}=\sqrt{0.117}=0.342

Then, we can calculate the t-statistic as:

t=\dfrac{M_d-(\mu_1-\mu_2)}{s_{M_d}}=\dfrac{0.3-0}{0.342}=\dfrac{0.3}{0.342}=0.88

The degrees of freedom for this test are:

df=n_1+n_2-1=196+225-2=419

This test is a two-tailed test, with 419 degrees of freedom and t=0.88, so the P-value for this test is calculated as (using a t-table):

\text{P-value}=2\cdot P(t>0.88)=0.381

As the P-value (0.381) is greater than the significance level (0.05), the effect is not significant.

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that there is significant difference in the time response for the two servers.

<u>Confidence interval </u>

We have to calculate a 95% confidence interval for the difference between means.

The sample 1, of size n1=196 has a mean of 12.5 and a standard deviation of 3.

The sample 2, of size n2=225 has a mean of 12.2 and a standard deviation of 4.

The difference between sample means is Md=0.3.

The estimated standard error of the difference is s_Md=0.342.

The critical t-value for a 95% confidence interval and 419 degrees of freedom is t=1.966.

The margin of error (MOE) can be calculated as:

MOE=t\cdot s_{M_d}=1.966 \cdot 0.342=0.672

Then, the lower and upper bounds of the confidence interval are:

LL=M_d-t \cdot s_{M_d} = 0.3-0.672=-0.372\\\\UL=M_d+t \cdot s_{M_d} = 0.3+0.672=0.972

The 95% confidence interval for the difference in the two servers population expectations is (-0.372, 0.972).

7 0
3 years ago
If QRST is a rectangle with QT = 30 and RS = 4x + 10, find x.
ArbitrLikvidat [17]
The opposite side pairs in a rectangle are congruent, so basically QT would be congruent to RS when you draw the rectangle and label the points.
4x+10=30
4x=20
x=5
4 0
3 years ago
What value of x makes the equation shown true? Show or explain what you did to get your answer. 5x – 1 = 19
Advocard [28]
5x-1=19
1st you add the one over to the 19 and you'll get 20
then you do 5x=20
divide the 5x over to the 20 and your final answer is 4.
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3 years ago
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Determine the median of the data. 2, 3, 3, 4, 5, 7, 9
satela [25.4K]
The median is 4 because 2 x’s out 9, 3 x’s out 7, 3 x’s out 5, and 4 is the only remaining number.
3 0
3 years ago
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