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2 years ago

Find the equation (in terms of x) of the line through the points (-2,1) and(2,9) Y=

Mathematics

2 answers:

TiliK225 [7]2 years ago

8 0

Answer:

y = 2x + 5

Step-by-step explanation:

There are 2 ways to find this equation:

The first way: We have: y = ax + b (this is the line, right?)

The line is through the point (-2, 1) so we have:

1 = (-2)a + b (1)

The line is also through the point (2, 9) so we have:

9 = 2a + b. (2)

From (1) and (2) we get a equals 2, b equals 5. Then:
y = 2x + 5

The second way:

Let A(-2, 1) and B(2, 9), then AB = (4, 8).

=> The normal vector of this line is n = (-2, 1).

The line that is through the points A(-2, 1) and B(2, 9), and has the normal vector n=(-2, 1) has the equation:

$-2(x - 2) + 1(y - 9) = 0$

$-2x + y - 5 =0\\ < = > y = 2x + 5$

I am Lyosha [343]2 years ago

5 0

Answer:

Step-by-step explanation:

gradient =y² -y¹ /x²-x¹

=9-1/2--2

=8/4

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In a random sample of students who took the SAT test, 427 had paid for coaching courses and the remaining 2733 had not. Calculat

Dvinal [7]

Answer:

The 95% confidence interval for the proportion of students who get coaching on the SAT is (0.1232, 0.147).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the z-score that has a p-value of $1 - \frac{\alpha}{2}$ .

427 had paid for coaching courses and the remaining 2733 had not.

This means that $n = 427 + 2733 = 3160, \pi = \frac{427}{3160} = 0.1351$

95% confidence level

So $\alpha = 0.05$ , z is the value of Z that has a p-value of $1 - \frac{0.05}{2} = 0.975$ , so $Z = 1.96$ .

The lower limit of this interval is:

$\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.1351 - 1.96\sqrt{\frac{0.1351*0.8649}{3160}} = 0.1232$

The upper limit of this interval is:

$\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.1351 + 1.96\sqrt{\frac{0.1351*0.8649}{3160}} = 0.147$

The 95% confidence interval for the proportion of students who get coaching on the SAT is (0.1232, 0.147).

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3 years ago

3x(x − 2) + 2 x=6<br> i really need help

neonofarm [45]

This equation if finding x would be 88

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3 years ago

A dot plot titled Number of runs scored going from 0 to 5. 0 has 2 dots, 1 has 4 dots, 2 has 6 dots, 3 has 4 dots, 4 has 2 dots,

BaLLatris [955]

Answer:

abdef (those are the answers)

Step-by-step explanation:

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3 years ago

Gina, Sam, and Robby all rented movies from the same video store. They each rented some dramas, comedies, and documentaries. Gin

weqwewe [10]

Solve using equations:

Gina 11 = a+b+c
Sam 27 = 2a+3b+2c
Robby 19= a+2b+2c

Gina *2 give 22=2a+2b+2c (subtract this from Sam to give)
b=5

the subtract Robby from Gina *2 to give a=3

[Question 1]
let d = number of dramas Gina rented, c = # of comedies, and t = # of documentaries:

[equation a] d + c + t = 11
[equation b] 2d + 3c + 2t = 27
[equation c] d + 2c + 2t = 19

if we subtract [a] from [c] we get:
[equation d] c + t = 8

if we subtract [c]*2 from [b] we get:
[equation e] -c - 2t = -11 or
[equation e] c + 2t = 11

Now we can subtract [e] from [d] to solve for t:
t = 3

Now put in 3 for t in [d] or [e] to solve for c:
c + 2(3) = 11
c + 6 = 11
c = 5

So she rented 5 comedies and 3 documentaries which leaves 3 dramas (which is answer A)

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3 years ago

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Determine the constant of variation for the direct variation given.

Flura [38]

The formula is y= k x where k is the constant of variation, so plug a coordinate in the formula to find value of k, lets get (3,12) you have 12 = 3k, then k = 4, if you get (9,36) then you have 36 = 9k where k = 4

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3 years ago

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