Which of the options is a solution for the following system of inequalities 2x+y>3 and x-y>1?

Which of the following represent(s) an equation of the line passing through the points A(5, 6) and B(4, 8). Select all that appl

andriy [413]

Answer:

The equations that represent the equation of the line are:

y = -2x + 16 ⇒ A

2x + y = 16 ⇒ D

y - 6 = -2(x - 5) ⇒ E

Step-by-step explanation:

The slope intercept form of the linear equation is y = m x + b, where

m is the slope of the line
b is the y-intercept (y at x = 0)

The formula of the slope is $m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

∵ The line is passing through points (5 , 6) and (4 , 8)

∴ $x_{1}$ = 5 and $x_{2}$ = 4

∴ $y_{1}$ = 6 and $y_{2}$ = 8

- Substitute them in the formula of the slope to find it

∵ $m=\frac{8-6}{4-5}=\frac{2}{-1}$

∴ m = -2

- Substitute it in the form of the equation

∴ y = -2 x + b

- To find b substitute x and y in the equation by the coordinates

of any point in the line

∵ x = 5 and y = 6

∴ 6 = -2(5) + b

∴ 6 = -10 + b

- Add 10 to both sides

∴ 16 = b

∴ y = -2 x + 16

∴ The equation of the line is y = -2x + 16

∴ A represents the equation of the line

∵ 2x + y = 16

- Subtract 2x from both sides

∴ y = -2x + 16

∴ D represents the equation of the line

∵ y - 6 = -2(x - 5)

∴ y - 6 = -2x + 10

- Add 6 to both sides

∴ y = -2x + 16

∴ E represents the equation of the line

The equations that represent the equation of the line are:

y = -2x + 16 ⇒ A

2x + y = 16 ⇒ D

y - 6 = -2(x - 5) ⇒ E

7 0

3 years ago

Rewrite the equation by completing the square. 4 x^{2} +20x +25 =0

Ede4ka [16]

Answer:

(x+5/2)^2 = 0

Step-by-step explanation:

4 x^{2} +20x +25 =0

Divide by 4

4/4 x^{2} +20/4x +25/4 =0

x^2 +5x +25/4 =0

Subtract 25/4 from each side

x^2 +5x +25/4 -25/4 =-25/4

x^2 +5x =-25/4

Take the coefficent of x

5

Divide by 2

5/2

Square it

25/4

Add it to each side

x^2 +5x +25/4 =-25/4+25/4

(x+5/2)^2 = 0

Take the square root of each side

x+5/2 = 0

x = -5/2

8 0

3 years ago

Read 2 more answers

The number of entrees purchased in a single order at a Noodles & Company restaurant has had an historical average of 1.7 ent

SOVA2 [1]

Answer:

$t=\frac{2.1-1.7}{\frac{1.01}{\sqrt{48}}}=2.744$

$p_v =P(t_{(47)}>2.744)=0.0043$

If we compare the p value and the significance level given $\alpha=0.02$ we see that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, and we can conclude that the true mean is higher than 1,7 entrees per order at 2% of signficance.

Step-by-step explanation:

Data given and notation

$\bar X=2.1$ represent the mean

$s=1.01$ represent the sample standard deviation

$n=48$ sample size

$\mu_o =1.7$ represent the value that we want to test

$\alpha=0.02$ represent the significance level for the hypothesis test.

t would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the mean is higher than 1.7, the system of hypothesis would be:

Null hypothesis: $\mu \leq 1.7$

Alternative hypothesis: $\mu > 1.7$

If we analyze the size for the sample is > 30 but we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

Calculate the statistic

We can replace in formula (1) the info given like this:

$t=\frac{2.1-1.7}{\frac{1.01}{\sqrt{48}}}=2.744$

P-value

The first step is calculate the degrees of freedom, on this case:

$df=n-1=48-1=47$

Since is a one side test the p value would be:

$p_v =P(t_{(47)}>2.744)=0.0043$

Conclusion

If we compare the p value and the significance level given $\alpha=0.02$ we see that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, and we can conclude that the true mean is higher than 1,7 entrees per order at 2% of signficance.

4 0

3 years ago

Read 2 more answers

Given: Line Segment AC ≅ Line Segment DC, ∠B≅∠D

Neporo4naja [7]

Answer:

See Below.

Step-by-step explanation:

Statements Reasons:

$1)\text{ } AC\cong DC$ Given