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Gala2k [10]
3 years ago
7

Given the trinomial, what is the value of the coefficient B in the factored form? 2x2 + 4xy − 48y2 = 2(x + By)(x − 4y) −12 12 −6

6
Mathematics
1 answer:
Sonja [21]3 years ago
3 0

Answer:

B is 6.

Step-by-step explanation:

We are trying to find a value for B such that:

2x^2+4xy-48y^2=2(x+By)(x-4y) is true for every x,y.

So let's choose x=0,y=1:

2(0)^2+4(0)(1)-48(1)^2=2(0+B(1))(0-4(1))

2(0)+0-48=2(B)(-4)

0-48=-8B

-48=-8B

Divide both sides by -8:

\frac{-48}{-8}=B

6=B

B=6

Note: I didn't want to choose y to be 0 because the value of B would disappear from the equation. So you should be able to have chosen any x and y except for y=0 to solve the equation for B.

Check:

So let's check and use foil to multiply out the right hand side.

(x+6y)(x-4y)

x(x)+x(-4y)+6y(x)+6y(-4y)

x^2-4xy+6xy-24y^2

x^2+2xy-24y^2

There was a 2 in front of that multplicapltiation:

2(x+6y)(x-4y)

2(x^2+2xy-24y^2)

2x^2+4xy-48y^2

This is exactly what we have on the left hand side of your given equation.

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2 years ago
One angle of a right triangle measures 70 degrees. What is the other acute angle?
Sunny_sXe [5.5K]

Answer:

20 degrees

Step-by-step explanation:

A triangle's angles should 180 degrees added together, so 90 + 70 = 160, leaving 20 for the last angle.

4 0
3 years ago
How can the average rate of change be identified for a function?
Digiron [165]

Answer:

Rateofchange=\frac{f(x_2)-f(x_1)}{x_2-x_1}

where x₁ and x₂ are values in the interval [x,y] respectively

Step-by-step explanation:

Well, first to determine the average rate of change of a function, you should have the interval of the values of x for the function.

So lets assume you have a function;

f(x)=x^3-4x

And the interval as [1,3]

Then the average rate of change for the function f(x) will be;

=\frac{f(x_2)-f(x_1)}{x_2-x_1}

where x₁ and x₂ are the interval coordinates x,y respectively. In this case x₁=1 and x₂=3

To find the average rate of change in this example will be;

=\frac{f(x_2)-f(x_1)}{x_2-x_1} \\\\=f(x_2)=f(3)=3^3-4(3)=27-12=15\\\\=f(x_1)=f(1)=1^3-4(1)=1-4=-3\\\\\\=x_2-x_1=3-1=2\\\\\\=\frac{15--3}{2} \\\\=\frac{18}{2} =9

8 0
3 years ago
Please help!!As soon as possible!!
pychu [463]

Answer: Their equations have different y-intercept but the same slope

Step-by-step explanation:

Since, the slope of the line passes through the points (2002,p) and (2011,q) is,

m_1 = \frac{q-p}{2011-2002} = \frac{q-p}{9}

Similarly, the slope of the line asses through the points (2,p) and (11,q) is,

m_2 = \frac{q-p}{11-2} = \frac{q-p}{9}

Since, m_1 = m_2

Hence, both line have the same slope.

Now, the equation of the line one having slope m_1 and passes through the point (2002,p) is,

y - p = \frac{q-p}{9}(x-2002)

Put x = 0 in the above equation,

We get, y = \frac{2000(p-q)}{9}+p

The y-intercept of the line one is (0, \frac{2000(p-q)}{9}+p)

Also, the equation of second line having slope m_2 and passes through the point (2,p)

y-p=\frac{q-p}{9}(x-2)

Put x = 0 in the above equation,

We get, y = \frac{2(p-q)}{9}+p

The y-intercept of the line one is (0, \frac{2(p-q)}{9}+p)

Thus, both line have the different y-intercepts.

⇒ Third option is correct.

6 0
3 years ago
What is the difference between 2a + 5 and 2(a + 5)? Give an English expression to describe each of
Sergio [31]

Answer:

without brackets, the two is only multiplying the a. with brackets, you distribute the 2, making the equation 2a+10

Step-by-step explanation:

6 0
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