Answer:
7. (4x +10)/(x^3 +3x^2 -16x -48)
9. -320/93
Step-by-step explanation:
7. As with adding any fractions, first you find a common denominator. When the fractions are rational expressions, it often helps to factor the denominators.
6/(x^2 -16) -2/(x^2 -x -12) = 6/((x -4)(x +4)) -2/((x -4)(x +3))
= (6(x +3) -2(x +4))/((x -4)(x +3)(x +4)) . . . . . using a common denominator
= (6x +18 -2x -8)/((x -4)(x +3)(x +4))
= (4x +10)/((x^2 -16)(x +3))
= (4x +10)/(x^3 +3x^2 -16x -48)
_____
9. First you simplify the denominator:
2/25 -5/16 = (2·16 -5·25)/(25·16) = -93/400
Then you perform the division. This can be done by multiplying by the inverse of the denominator.
(4/5)/(2/5 -5/16) = (4/5)·(-400/93) = -320/93
The value of y is 40 degree , Option B is the correct answer.
<h3>What is Angle Sum Property ?</h3>
According to angle sum property, the sum of all angles of a triangle is equal to 180 degree.
It is given in the question a triangle , here
the angles given are 2y , y+10 , 50 degree
From the property ,
2y + y + 10 +50 = 180
3y +60 = 180
3y = 120
y = 40 degree
Therefore The value of y is 40 degree , Option B is the correct answer.
To know more about Angle Sum Property
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The two linear equations represented in system A as :
3 x + 2 y =3 -------(1)
- 2 x - 8 y = -1 ------(2)
(1) × 2 + (2) × 3 gives
⇒ 6 x + 4 y - 6 x - 24 y = 6 -3
⇒ - 20 y = 3
⇒ y = 
Putting the value of y in equation (1), we get
Two linear equation represented in system B is:
3. -x - 14 y =1
4. - 2 x - 8 y = -1
-2 ×Equation (3) + Equation (4)=
2 x +28 y- 2 x - 8 y= -2 -1
⇒ 20 y = -3
⇒y =
Putting the value of y in equation (3),we get
As Two system , that is system (A) and System (B) has same solution.
By looking at all the options , i found that Option (D) is correct. The two system will have the same solution because the first equation of System B is obtained by adding the first equation of System A to 2 times the second equation of System A.
A) (0,1), (1,-2), (-1,4), (2,-5)
b) (0,4), (-1,2), (-2,0), (1,6)
c) (-2,-7), (-1, -7), (0,-7), (1, -7)
Answer:
Step-by-step explanation:
Instead, since the divisor is in the form of 
, use what is called Synthetic Division. Remember, in this formula, 
gives you the OPPOSITE terms of what they really are, so do not forget it. Anyway, here is how it is done:
4| 1 −5 7 −12
↓ 4 −4 12
_______________
1 −1 3 0 →
You start by placing the 
in the top left corner, then list all the coefficients of your dividend [x³ - 5x² + 7x - 12]. You bring down the original term closest to then begin your multiplication. Now depending on what symbol your result is tells you whether the next step is to subtract or add, then you continue this process starting with multiplication all the way up until you reach the end. Now, when the last term is 0, that means you have no remainder. Finally, your quotient is one degree less than your dividend, so that 1 in your quotient can be an 
, the −1 [
] follows right behind it, and bringing up the rear, comes the 3, giving you the quotient of .
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