Which of the following is the correct expansion of the binomial (x + y)6?
Answers
Answer:
x^6+6x^5y+15x^4y^2+20x^3y^3+15x^2y^4+6xy^5+y^6
Step-by-step explanation:
expansion of the binomial (x + y)^6
USe Pascals triangle
6th row in pascals triangle is
1 6 15 20 15 6 1
Now we do the expansion using the above row.
nCr (x)^n-r (y)^r
1 (x)^6(y)^0+ 6(x)5(y)^1+ 15(x)^4(y)^2+20(x)^3(y)^3+15(x)^2(y)^4+6(x)^1(y)^5+1(x)^0(y)^6
Pascal Triangle:
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
1 6 15 20 15 6 1
x^6+6x^5y+15 x^4y² +20 x^3y^3 + 15 x²y^4+6 x y^5 +y^6
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Answers
Area of the rectangle= 202. 52 square inches
Area of the square={202.52}
Length of the square= 14.23 units
(Algebra 1)
Answers
Answer: y = 1/2x+3
Step-by-step explanation:
7x + 6y = 31
Answers
The solution is, (1,4) is the solution of the system of equations and choose the correct ordered pair.
4x + 3y = 16
7x + 6y = 31
What is equation?
An equation is a mathematical statement that is made up of two expressions connected by an equal sign. In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.
here, we have,
given that,
equation: 1
4x+3y=16
y=(16-4x)/3
equation: 2
7x+6y=31
y=(31-7x)/6
now, we have,
(16-4x)/3 = (31-7x)/6
6(16-4x) = 3(31-7x)
96-24x=93-21x
3=3x
x=1
we get,
4x+3y=16, x=1
4(1)+3y=16
4+3y=16
3y=12
y=4
so, we have,
x=1, y=4
therefore the answer is B (1,4)
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y=(16-4x)/3 y=(31-7x)/6
(16-4x)/3 = (31-7x)/6
6(16-4x) = 3(31-7x)
96-24x=93-21x
3=3x
x=1
4x+3y=16, x=1
4(1)+3y=16
4+3y=16
3y=12
y=4
x=1, y=4 therefore the answer is B (1,4)
(14x3y2z)4
Answers
Final answer:
The result of raising the polynomial (14x3y2z) to the 4th power is 38416x12y8z4. This is calculated by individually multiplying each part of the polynomial by itself 4 times.
Explanation:
The problem is asking you to calculate the result of raising a polynomial (14x3y2z) to the 4th power.
The operation refers to using the rule of powers which states that any base with an exponent is multiplied by itself the amount of times indicated by the exponent. The result should therefore be calculated as follows:
(14x3y2z)4 = 38416x12y8z4
To find the answer, we raised each part of the polynomial to the 4th power. 144 equals 38416, (x3)4 results in x12 because you multiply the exponents, (y2)4 results in y8 for the same reason and z4 because anything to the power of 4 is itself raised 4 times.
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A.4y = 2x – 6
B.3x + 5y = 7
4x = 2y – 5
C.2y = 4x + 2
D.2x = 5y + 4
15y = 6x – 12
Answers
Answer : D
2x=5y+4
15y=6x-12
Solve 2x=5y+4 for x
Divide both sides by 2
2x/2=(5y+4)/2
x = 5/2 y +2
Substitute 5/2 y +2 for x in 15y=6x-12
15y= 6x-12
15y= 6(5/2 y +2 ) -12
Simplify both sides of the equation
15y=15y
Add -15y to both sides
15y-15y= 15y-15y
0=0
Hey Lily , I hope this help and if you have question(s) please let me know . Thanks
–4
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27
Answers
If the equation of the line is written in slope-intercept form, y = mx + b, then the value of b is -21 and is denoted as option A.
What is Slope?
This is also referred to as the gradient of a line and measures its steepness and direction.
Slope = (y₂ - y₁) / (x₂ - x₁)
Parameters
J(-4, -5) and K(-6, 3)
= (3 - (-5)) / (-6 - (-4))
= (3 + 5) / (-6 + 4)
= 8 / -2
= -4
Substitute one of the coordinates into the formula to solve for b
y = mx + b
y = -4x + b
3 = -4(-6) + b
3 = 24 + b
3 - 24 = b
b = - 21
Read more about Slope of a line here brainly.com/question/20848
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Find the slope that passes between the points.
(y₂ - y₁) / (x₂ - x₁)
J(-4, -5)
K(-6, 3)
(3 - (-5)) / (-6 - (-4))
(3 + 5) / (-6 + 4)
8 / -2
-4
Now slap that slope into the formula and substitute on of the coordinates to the formula to solve for b (I'll take point K's coordinate):
y = mx + b
y = -4x + b
3 = -4(-6) + b
3 = 24 + b
3 - 24 = b
- 21 = b
b = -21