Factor completely 6x^4y^3 + 21x^3y^2 − 9x^2y.3xy(2x^3y^2 + 7xy − 3x)
3x^2y(2x^2y^2 + 7xy − 3)
3x^2y3&(2x^2 + 7xy − 3)
3x^2y(2x^2y + 7xy − 3y)
Answers
=3x^2y(2x^2y^2+7xy-3)
Final answer:
The simplest factored form of the expression 6x^4y^3 + 21x^3y^2 − 9x^2y is 3x^2y(2x^2y^2 + 7xy - 3), derived by taking the greatest common factor (GCF) out from each term.
Explanation:
The task here is to completely factor the polynomial 6x^4y^3 + 21x^3y^2 − 9x^2y. Initially, you look for the greatest common factor (GCF) in the terms. In this case, the GCF is 3x^2y. So we factor that out from each term:
3x^2y(2x^2y^2 + 7xy - 3)
The factored form of the original expression is therefore 3x^2y(2x^2y^2 + 7xy - 3). This result represents the simplest factored form of the expression.
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4cd×10×2p÷50d+20q=??
Answers
Let's start by breaking down the problem so that it's not overwhelming.
For now, we're only going to focus on the very beginning of the problem -- 4c.
When a number is next to a letter with no signs in between (in terms of this kind of math), the number is called a coefficient and the letter is called a variable. When you see this in math, it means that the coefficient is being multiplied by the variable. But how do you know what the variable is?
In other examples of math, you'd have to solve for the variable, but in this case, they already give it to you! Look back at the top... what does C equal? It equals 4! This means that 4c is actually 4x4, or 4(4)!
What we just did there, changing 4c to 4 multiplied by 4, is called substitution. You just substituted the c with 4. Now you know that to solve this, you need to use the method of substitution. What do you get if you substitute all of the variables with the numbers they equal (as shown above)...?
((4*-4)*5)((10(2*2))/(50(5)))+20(-1). You didn't use parentheses to separate the term /50d + 20q, so I'm assuming that the first part of the problem is only divided by just 50d, and not 50d+20q. In the future, be sure to clarify with parentheses. Anyway...
((4*-4)*5)((10(2*2))/(50(5)))+20(-1). Do NOT let this scare you. All the parentheses do is help you see what is being multiplied. All that's left is simple order of operations! You should get -340 as your answer.
~ y = -(1/20)x²
~ x = (1/20)y²
Answers
The equation of parabola will be y=(1/20)x² .
Given,
Focus : (0, 5)
Directrix : y = -5
Now,
The standard equation of parabola is : x² = 4ay or y² = 4ax .
Focus is above directrix, it opens up
x²=4ay
a is distance from directrix to vertex
Since it opens up, a is positive
from -5 to 0 is 5 units
x²=4(5)y
x²=20y
solve for y
divide both sides by 20
y=(1/20)x²
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we see that we have to go up and down
therfor it opens up or down
since focus is above directix, it opens up
x^2=4Py
p is distance from directix to vertex
since it opens up, P is positive
from -5 to 0 is 5 units
x^2=4(5)y
x^2=20y
solve for y
divide both sides by 20
y=(1/20)x^2
first one
Equation 2: x = 20
A.
multiplication property of equality
B.
division property of equality
C.
subtraction property of equality
D.
addition property of equality
Answers
That will be your 100% sure answer!
Answer:
Step-by-step explanation:
On A.- Multiplication property of equality is multiplying both sides of an equation by the same number it does not change the equation.
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On B. - Division property of equality is dividing both sides of an equation by the same non-zero number it does not change the equation.
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On C.- Subtraction property of equality is subtracting the same number from both sides of an equation it does not change the equation.
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On D.- Addition property of equality is adding the same number to both sides of an equation it does not change the equation.
x-6=14
First you had to add by six from both sides of an equation form.
x-6+6=14+6
Then simplify by equation.
x=20
Final answer:
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Hope this helps!
And thank you for posting your question at here on brainly, and have a great day.
-Charlie
Answers
Answers
Add x on both sides.
3 - x + x = 5 + x
3 = 5 + x
Subtract 5 on both sides
3 - 5 = 5 - 5 + x
3 - 5 = x
x = 3 - 5
x = -2
b)30t people per year^2
c)600t people per year
d)36t people per year^2
Answers
The acceleration in the population t years from 1996 is 60t people per year^2.
What is a Function?
A function assigns the value of each element of one set to the other specific element of another set.
It is given that a population grows from an initial size of 10 people to an amount P(t), given by P(t)=10(3+0.5t+t³) where t is measured in years from 1996.
Now, in order to find the acceleration in the population t years from 1996, we need to find the second derivative of the populationfunction, therefore,
Hence, the acceleration in the population t years from 1996 is 60t people per year^2.
Learn more about Function:
The first derivative has to be determined first.
dP(t)/dt = 10(0.5+3t^2)
Next, the second derivative can be determined using the first derivative:
d2P(t) = 10(6t) = 60t
Since it's acceleration, the unit is per year^2
THE ANSWER IS a) 60t people per year^2