point a is at -4 and point b is at 6 one way to find the point that divides a b into a 3:2 ratio brainly

Please help me with these questions

Scrat [10]

3. Answer: y = 4

Step-by-step explanation:

Need to find the slope (m):

$\dfrac{y_2-y_1}{x_2-x_1}$

$\dfrac{4 - 4}{-3-1}$

= $\dfrac{0}{-4}$

= 0

Now input ONE of the points (1, 4) and the slope (m = 0) into the Point-Slope formula:

y - y₁ = m(x - x₁)

y - 4 = 0(x - 1)

y - 4 = 0

y = 4

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4. Answer: $\bold{y = \dfrac{2}{3}x + 3}$

Step-by-step explanation:

$y - y_1 = m(x - x_1)$

$y - 1 = \dfrac{2}{3}(x - (-3))$

$y - 1 = \dfrac{2}{3}(x + 3)$

$y - 1 = \dfrac{2}{3}x + 2$

$y = \dfrac{2}{3}x + 3$

3 0

3 years ago

What is the sum of the first 51 consecutive odd positive integers?

Angelina_Jolie [31]

We call:

$a_{n}$ as the set of the first 51 consecutive odd positive integers, so:

 $a_{n} = \{1, 3, 5, 7, 9...\}$

Where:
$a_{1} = 1$
$a_{2} = 3$
$a_{3} = 5$
$a_{4} = 7$
$a_{5} = 9$
and so on.

In mathematics, a sequence of numbers, such that the difference between two consecutive terms is constant, is called Arithmetic Progression, so:

3-1 = 2
5-3 = 2
7-5 = 2
9-7 = 2 and so on.

Then, the common difference is 2, thus:

 $a_{n} = \{ a_{1} , a_{1} + d, a_{1} + d + d,..., a_{1} + (n-2)d+d\}$

Then:

 $a_{n} = a_{1} + (n-1)d$

So, we need to find the sum of the members of the finite series, which is called arithmetic series:

There is a formula for arithmetic series, namely:

 $S_{k} = ( \frac{a_{1} + a_{k}}{2} ).k$

Therefore, we need to find:
 $a_{k} = a_{51}$

Given that $a_{1} = 1$ , then:

$a_{n} = a_{1} + (n-1)d = 1 + (n-1)(2) = 2n-1$

Thus:
$a_{k} = a_{51} = 2(51)-1 = 101$

Lastly:

$S_{51} = ( \frac{1 + 101}{2} ).51 = 2601$

4 0

3 years ago

4,11,7,14,10,17,.....?

jek_recluse [69]

Answer:

4,11,7,14,10,17,13,20,16,23,19,26........

8 0

3 years ago

Can anybody explain how to do this? The answer I keep getting isn't one of the options.

Nastasia [14]

I think is D

5^-2*25^-1
5^-2*5^-2
5^-4
1/5^4
1/625
0,0016, 5^-4

3 0

3 years ago

HELP!!!!!!!!!!!!!!!!!!!!!!!!!! Can U Answer All These.

mash [69]

QUESTION 1

In figure A, the area of the bigger square is $625\:units^2$ . This means that the length of this square is the hypotenuse of the right angle triangle formed, which is $25\:units$ .

The area of the two smaller squares are $576\:units^2$ and $49\:units^2$ .

The length of these two squares form the two shorter legs of the right angle triangle, which are $24$ and $7$ units respectively.

Therefore we can write the equation, $576+49=625$ .

This implies that, $24^2+7^2=25^2$

We can see that the sum of the squares of the two shorter legs equals the square of the longer side which is the hypotenuse and this what the Pythagoras theorem says.

But in fig. B,

$5^2+4^2\ne 6^2$