What is the greatest common factor of 6x^3+9x-12

aniked [119]

FIRST QUESTION
Given points are:
A(2, -4) and B(6, 2)
Now, Use the distance formula.
distance formula = $\sqrt{ (x_{2}- x_{1})^{2} + ( y_{2} - y_{1} )^{2} }$

Now, plug the values into the formula, So,
distance = $\sqrt{ (6- 2)^{2} + ( 2 - (-4))^{2} }$

= $\sqrt{ (6- 2)^{2} + ( 2 +4))^{2} }$

= $\sqrt{ (4)^{2} + ( 6))^{2} }$

= $\sqrt{ 16+36}$

= $\sqrt{52}$

= $2 \sqrt{13}$

So, the length of AB is $2 \sqrt{13}$ .

THIRD QUESTION
Two points given are:
A(3, -2) and B(1, 1)
Also given that B is the midpoint of AC.

Let, the co-ordinates of C be C(a, b).
Now, using midpoint formula,
Midpoint = $(\frac{ x_{1}+ x_{2} }{2} , \frac{ y_{1}+ y_{2} }{2} )$

$(1, 1)=(\frac{ 3+ a }{2} , \frac{ -2+b }{2} )$

Now, equaling the ordered pair, we have,

$1=\frac{ 3+ a }{2}$ .............equation (1)

$1=\frac{ -2+b }{2}$ ................equation (2)

Now, taking equation (1)
$1=\frac{ 3+ a }{2}$

$1*2=3+a$

$2-3=a$

$a=-1$

Now, taking equation (2)
$1=\frac{ -2+b }{2}$

$1*2=-2+b$

$2+2=b$

$b=4$

So, the co ordinates of C are (a, b) which is (-1 , 4)


SECOND QUESTION:
Given equations are:
2x + 3y = 14.....................equation (1)
-4x + 2y = 4 .....................equation (2)
Taking equation (2)
-4x + 2y = 4
2y = 4 + 4x
y = (4 + 4x) / 2
y = 2 + 2x .......................equation (3)
Now, Taking equation (1)
2x + 3y = 14
Substituting the value of y from equation (3), we get,
2x + 3(2 + 2x) = 14
2x + 6 + 6x = 14
8x = 14 - 6
x = (14 - 6) / 8
x = 1

Taking equation (3)
y = 2 + 2x
Now, substituting the value of x in equation (3), we get,
y= 2 + 2 (1)
y = 2 + 2
y = 4

So, x=1 and y=4

6 0

3 years ago

Express 1.8meter in seconds given answer in scientific notation

polet [3.4K]

Answer:

Dear user,

Answer to your query is provided below

Scientific notation = 1.8x10^0

Step-by-step explanation:

This is usually expressed simply as 1.8 (Recall that 10^0 = 1.)

1.8×10^0

7 0

2 years ago

Help please !! I’m am struggling with this lol

tatyana61 [14]

Answer:

x ≈ 3.9

Step-by-step explanation:

Call the segment shared by the two triangle "y". The Pythagorean theorem tells you ...

sum of squares of sides = square of hypotenuse

y² +6² = 10²

x² +7² = y²

Substituting for y² using the second equation, we get ...

x² +7² +6² = 10²

x² = 10² -7² -6² = 100 -49 -36 = 15

Taking the square root, we find ...

x = √15 ≈ 3.9

4 0

2 years ago

Find Sn for the arithmetic series 5+7+9 + … and determine the value of n for which the series has sum 165.

SVETLANKA909090 [29]

Answer:

see explanation

Step-by-step explanation:

the sum to n terms of an arithmetic sequence is

$S_{n}$ = $\frac{n}{2}$ [2a + (n - 1)d ]

where d is the common difference and a is the first term

here d = 9 - 7 = 7 - 5 = 2 and a = 5, hence

$S_{n}$ = $\frac{n}{2}$ [(2 × 5) + 2(n - 1) ]

= $\frac{n}{2}$ (10 + 2n - 2)

= $\frac{n}{2}$ (2n + 8)

= n² + 4n

When sum = 165, then

n² + 4n = 165 ← rearrange into standard form

n² + 4n - 165 = 0 ← in standard form

(n + 15)(n - 11) = 0 ← in factored form

equate each factor to zero and solve for n

n + 15 = 0 ⇒ n = - 15

n - 11 = 0 ⇒ n = 11

but n > 0 ⇒ n = 11

4 0

3 years ago

(4.1.4) Let X and Y be Bernoulli random variables. Let Z = X + Y. a. Show that if X and Y cannot both be equal to 1, then Z is a

Fynjy0 [20]

Step-by-step explanation:

Given that,

a)

X ~ Bernoulli $(p_x)$ and Y ~ Bernoulli $(y_x)$

X + Y = Z

The possible value for Z are Z = 0 when X = 0 and Y = 0

and Z = 1 when X = 0 and Y = 1 or when X = 1 and Y = 0

If X and Y can not be both equal to 1 , then the probability mass function of the random variable Z takes on the value of 0 for any value of Z other than 0 and 1,

Therefore Z is a Bernoulli random variable

b)

If X and Y can not be both equal to 1

then,

$p_z = P(X=1$ or $Y=1)\\$