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3 years ago

When using substitution to solve this system of equations

Mathematics

1 answer:

dlinn [17]3 years ago

3 0

Hello, find the work out in the attached image
X = 4.5
Y = -1

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F(x)=x² – 4x – 2 g(x)=x+7 Find: (f + g)(x)

dusya [7]

Answer:

(f + g)(x) = x² - 3x + 5

Step-by-step explanation:

Here we find the sum of two functions. Combine like terms in f and g, as follows:

(f + g)(x) = x² – 4x – 2 + x + 7, or

(f + g)(x) = x² - 3x + 5

8 0

3 years ago

Perform the indicated operation (-10) ÷ (-20)

sergey [27]

Remember that dividing a negative number by a negative number will result in a positive quotient:

$-10 \div -20 = 0.5$

The answer is 0.5.

5 0

3 years ago

Help help help please

Mnenie [13.5K]

True, because of the Triangle Inequality Theorem.

To test if you could construct a triangle, make sure the following inequalities are true.

9 + 4 > 11

9 + 11 > 4

4 + 11 > 9.

8 0

3 years ago

Read 2 more answers

Write an equation in slope intercept form when slope = -2 and y-intercept = -3 PLS help

SSSSS [86.1K]

Answer:

y= -2x -3

Step-by-step explanation:

Plug in the values for m and b in y=mx+b

4 0

3 years ago

A simple random sample of 28 Lego sets is obtained and the number of pieces in each set was counted.The sample has a standard de

Karo-lina-s [1.5K]

Answer:

Step-by-step explanation:

Given that:

A simple random sample n = 28

sample standard deviation S = 12.65

standard deviation $\sigma$ = 11.53

Level of significance ∝ = 0.05

The objective is to test the claim that the number of pieces in a set has a standard deviation different from 11.53.

The null hypothesis and the alternative hypothesis can be computed as follows:

Null hypothesis:

$H_0: \sigma^2 = \sigma_0^2$

Alternative hypothesis:

$H_1: \sigma^2 \neq \sigma_0^2$

The test statistics can be determined by using the following formula in order to test if the claim is statistically significant or not.

$X_0^2 = \dfrac{(n-1)S^2}{\sigma_0^2}$

$X_0^2 = \dfrac{(28-1)(12.65)^2}{(11.53)^2}$

$X_0^2 = \dfrac{(27)(160.0225)}{132.9409}$

$X_0^2 = \dfrac{4320.6075}{132.9409}$

$X_0^2 = 32.5002125$

$X^2_{1- \alpha/2 , df} = X^2_{1- 0.05/2 , n-1}$

$X^2_{1- \alpha/2 , df} = X^2_{1- 0.025 , 28-1}$

From the chi-square probabilities table at 0.975 and degree of freedom 27;

$X^2_{0.975 , 27}$ = 14.573

$X^2_{\alpha/2 , df} = X^2_{ 0.05/2 , n-1}$

$X^2_{\alpha/2 , df} = X^2_{0.025 , 28-1}$

From the chi-square probabilities table at 0.975 and degree of freedom 27;

$X^2_{0.025 , 27}=$ 43.195

Decision Rule: To reject the null hypothesis if $X^2_0 \ > \ X^2_{\alpha/2 , df} \ \ \ or \ \ \ X^2_0 \ < \ X^2_{1- \alpha/2 , df}$ ; otherwise , do not reject the null hypothesis:

The rejection region is $X^2_0 \ > 43.195 \ \ \ or \ \ \ X^2_0 \ < \ 14.573$

Conclusion:

We fail to reject the null hypothesis since test statistic value 32.5002125 lies between 14.573 and 43.195.

6 0

3 years ago