Solve the slope for the table.

Simplify. x^2-3x-18/x+3

andre [41]

Answer:

1. Option C is correct

2. Option A is correct

3. Option C is correct

4. Option B is correct

5. Option D is correct

Step-by-step explanation:

1. x^2-3x-18/x+3

Factorize the numerator

x^2-6x+3x-18/x+3

x(x-6)+3(x-6)/x+3

(x+3)(x-6)/x+3

x-6

x-6 where x≠6

Option C is correct.

2. x-2/x^2+4x-12

Factorizing the denominator

x-2/x^2+6x-2x-12

x-2/x(x+6)-2(x+6)

x-2/(x-2)(x+6)

1/x+6

1/x+6 where x≠-6

Option A is correct.

3. 5x^3/7 x^3+x^4

5x^3/7x^3+x^4

5x^3/x^3(7+x)

5/7+x

Option C is correct

5/7+x where x≠-7

4. Simplify x/6x-x^2

x/6x-x^2

x/x(6-x)

1/6-x

Option B is correct

1/6-x where x≠6

5. 2/3a * 2/a^2

Multiplying both terms

4/3a^3

Option D is correct.

4/3a^3 where a≠0

7 0

3 years ago

25 points+brainliest!

STatiana [176]

Answer:

an= 10n+90

a10= 190

8 0

3 years ago

Read 2 more answers

What is the equation of the line perpendicular to 3x+y= -8that passes through -3,1? Write your answer in slope-intercept form. S

Gekata [30.6K]

Slope intercept form of a line perpendicular to 3x + y = -8, and passing through (-3,1) is $y=\frac{1}{3} x+2$

Solution:

Need to write equation of line perpendicular to 3x+y = -8 and passes through the point (-3,1).

Generic slope intercept form of a line is given by y = mx + c

where m = slope of the line.

Let's first find slope intercept form of 3x + y = -8

3x + y = -8

=> y = -3x - 8

On comparing above slope intercept form of given equation with generic slope intercept form y = mx + c , we can say that for line 3x + y = -8 , slope m = -3

And as the line passing through (-3,1) and is perpendicular to 3x + y = -8, product of slopes of two line will be -1 as lies are perpendicular.

Let required slope = x

$\begin{array}{l}{=x \times-3=-1} \\\\ {=>x=\frac{-1}{-3}=\frac{1}{3}}\end{array}$

So we need to find the equation of a line whose slope is $\frac{1}{3}$ and passing through (-3,1)

Equation of line passing through $(x_1 , y_1)$ and having lope of m is given by

$\left(y-y_{1}\right)=\mathrm{m}\left(x-x_{1}\right)$

$\text { In our case } x_{1}=-3 \text { and } y_{1}=1 \text { and } \mathrm{m}=\frac{1}{3}$

Substituting the values we get,

$\begin{array}{l}{(\mathrm{y}-1)=\frac{1}{3}(\mathrm{x}-(-3))} \\\\ {=>\mathrm{y}-1=\frac{1}{3} \mathrm{x}+1} \\\\ {=>\mathrm{y}=\frac{1}{3} \mathrm{x}+2}\end{array}$

Hence the required equation of line is found using slope intercept form

4 0

3 years ago

What is the distance between M(9, −5) and N(−11, 10)?

lesya692 [45]

Answer:

$\boxed{ \bold{ \huge{ \boxed{ \sf{25 \: units}}}}}$

Step-by-step explanation:

Let M ( 9 , -5 ) be ( x₁ , y₁ ) and N ( - 11 , 10 ) be ( x₂ , y₂ )

Finding the distance between these points

$\boxed{ \sf{distance = \sqrt{ {(x2 - x1)}^{2} + {(y2 - y1)}^{2} } }}$

$\longrightarrow{ \sf{ \sqrt{ {( - 11 - 9)}^{2} + {(10 - ( - 5))}^{2} } }}$

$\longrightarrow{ \sf{ \sqrt{ {( - 20)}^{2} + {(10 + 5)}^{2} } }}$

$\longrightarrow{ \sf{ \sqrt{ {( - 20)}^{2} + {(15)}^{2} } }}$

$\longrightarrow{ \sf{ \sqrt{400 + 225}}}$

$\longrightarrow{ \sf{ \sqrt{625}}}$

$\longrightarrow{ \sf{ \sqrt{ {(25)}^{2} } }}$

$\longrightarrow{ \sf{25 \: units}}$

Hope I helped!

Best regards! :D

7 0

3 years ago

The average cost of tuition, room and board at small private liberal arts colleges is reported to be $8,500 per term, but a fina

Vlada [557]

Answer:

The test statistic for this test is 3.82.

Step-by-step explanation:

The null hypothesis is:

$H_{0} = 8500$

The alternate hypotesis is:

$H_{1} > 8500$

Our test statistic is:

$t = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$

In which X is the sample mean, $\mu$ is the value tested at the null hypothesis, $\sigma$ is the standard deviation of the population and n is the size of the sample.

In this question:

$X = 8745, \mu = 8500, \sigma = 1200, n = 350$

So

$t = \frac{8745 - 8500}{\frac{1200}{\sqrt{350}}} = 3.82$

The test statistic for this test is 3.82.

5 0

4 years ago