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4 years ago

Write the equation of a line that is perpendicular to the given line and that passes through the given point. y=2/3x+9;(-6,5)

Mathematics

2 answers:

STatiana [176]4 years ago

7 0

The perpendicular equation is y = -3/2x - 4.

You can find this by first realizing that perpendicular lines have opposite and reciprocal slopes. So since it starts at 2/3 we flip it and make it a negative and the new slope is -3/2. Now we can use that and the point to get the y intercept using slope intercept form.

y = mx + b

5 = (-3/2)(-6) + b

5 = 9 + b

-4 = b

And now we can use our new slope and new intercept to model the equation.

y = -3/2x - 4

WARRIOR [948]4 years ago

4 0

Hay dear friend thank you for asking the question

according to the question we know that

y = mx +b

And given that y = 5 , m = -3/2, x = -6

so

5 = -3/2×(-6) +b

5 = 9 + b

-4 = b

now we can use our new slope and new intercept model equation then,

y = (-3/2)x-4

I hope it's help you

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Describe the rule for the sequence 2, 1, 2/3, 1/2, 2/5, 1/3, 1/7,...

Triss [41]

Multiply 2 by 1/2 to get 1.

Multiply 1 by 2/3 to get 2/3.

Multiply 2/3 by 3/4 to get 6/12 = 1/2.

Multiply 1/2 by 4/5 to get 4/10 = 2/5.

Multiply 2/5 by 5/6 to get 10/30 = 1/3.

Multiply 1/3 by 6/7 to get 6/21 = 2/7. (I suspect there's a typo in the question.)

And so on, so that the nth term in the sequence is multiplied by n/(n + 1) to get the (n + 1)th term.

Recursively, the sequence is given by

$\begin{cases}a_1=2\\a_n=\dfrac{n-1}na_{n-1}&\text{for }n>1\end{cases}$

We can solve this exactly by iterating:

$a_n=\dfrac{n-1}na_{n-1}=\dfrac{n-1}n\dfrac{n-2}na_{n-1}=\dfrac{n-1}n\dfrac{n-2}{n-1}\dfrac{n-3}{n-2}a_{n-3}=\cdots$

and so on down to

$a_n=\dfrac{(n-1)\cdot(n-2)\cdot(n-3)\cdot\cdots\cdot3\cdot2\cdot1}{n\cdot(n-1)\cdot(n-2)\cdot\cdots\cdot4\cdot3\cdot2}a_1$

$a_n=\dfrac{(n-1)!}{n!}a_1$

and with lots of cancellation, we end up with

$a_n=\dfrac{a_1}n=\boxed{\dfrac2n}$

6 0

3 years ago

I need help ASAP PLEASE!!!

Nat2105 [25]

I’m just guessing but since 13/4=3.25 that means that the triangle dialated by 3.25 so you multiply 8 by 3.25 and X might be 26

6 0

4 years ago

The slope of the line whose equation is 3 x - 2 y = 4 is:

olchik [2.2K]

Answer:

c 3/2

Step-by-step explanation:

3 0

4 years ago

The Department of Transportation would like to test the hypothesis that the average age of cars on the road is less than 12 year

puteri [66]

Answer:

$z=\frac{10.6-12}{\frac{4.1}{\sqrt{45}}}=-2.29$

Step-by-step explanation:

information given

$\bar X=10.6$ represent the sample mean

$\sigma=4.1$ represent the population standard deviation

$n=45$ sample size

$\mu_o =12$ represent the value that we want to test

$\alpha=0.05$ represent the significance level for the hypothesis test.

z would represent the statistic

$p_v$ represent the p value for the test

Hypothesis to test

We want to test if the true mean is less than 12, the system of hypothesis would be:

Null hypothesis: $\mu \geq 10$

Alternative hypothesis: $\mu < 10$

The statistic is given by:

$z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}$ (1)

Replacing the info given we got:

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

$z=\frac{10.6-12}{\frac{4.1}{\sqrt{45}}}=-2.29$

8 0

4 years ago

Which inequality is shown in this graph

Katena32 [7]

ANSWER

$y \leqslant - 2x - 2$

EXPLANATION

The boundary line passes through (-2,2) and (0,-2).

The slope of this line is

$m = \frac{ - 2 - 2}{0 - - 2}$

$m = \frac{ - 4}{2} = - 2$

The y-intercept is , c=-2.

The slope-intercept form of this line is given by;

$y = mx + c$

We substitute values to obtain;

$y = - 2x - 2$

Since the lower half-plane is shaded the required inequality is

$y \leqslant - 2x - 2$

7 0

4 years ago