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anyanavicka [17]
3 years ago
11

What is the product of (y+3)(y^2-3y+9)

Mathematics
2 answers:
alina1380 [7]3 years ago
8 0
(y+3)(y^2-3y+9)
=y(y^2-3y+9)
+3(y^2-3y+9)
=(y^3-3y^2+9y)+(3y^2-9y+27)
=y^3-3y^2+9y+3y^2-9y+27
=y^3+27
jarptica [38.1K]3 years ago
3 0

Answer:

Option (a) is correct.

The product of the given expression \left(y+3\right)\left(y^2-3y+9\right) is y^3+27

Step-by-step explanation:

Given : Expression \left(y+3\right)\left(y^2-3y+9\right)            

We have to find the product of the given expression \left(y+3\right)\left(y^2-3y+9\right)

Consider the given expression \left(y+3\right)\left(y^2-3y+9\right)

Apply distributive law,

(a+b)(c+d)=ac+ad+bc+bd, we have,

=yy^2+y\left(-3y\right)+y\cdot \:9+3y^2+3\left(-3y\right)+3\cdot \:9

Simplify, we have,

=y^2y-3yy+9y+3y^2-3\cdot \:3y+3\cdot \:9

Also,

=y^3-3y^2+9y+3y^2-9y+27          

Adding similar terms, we have,

=y^3+27

Thus, The product of the given expression \left(y+3\right)\left(y^2-3y+9\right) is y^3+27

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By applying concepts of <em>linear</em> functions, the graphs are related to the following expressions:

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y = m · x + b     (1)

Where:

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What is the equation of the line that passes through the points (5, 3) and (-3,-1)?
Liono4ka [1.6K]

Answer:

y=1/2x+1/2

m=1/2

Step-by-step explanation:

You want to find the equation for a line that passes through the two points:

(5,3) and (-3,-1).

First of all, remember what the equation of a line is:

y = mx+b

Where:

m is the slope, and

b is the y-intercept

First, let's find what m is, the slope of the line...

The slope of a line is a measure of how fast the line "goes up" or "goes down". A large slope means the line goes up or down really fast (a very steep line). Small slopes means the line isn't very steep. A slope of zero means the line has no steepness at all; it is perfectly horizontal.

For lines like these, the slope is always defined as "the change in y over the change in x" or, in equation form:

So what we need now are the two points you gave that the line passes through. Let's call the first point you gave, (5,3), point #1, so the x and y numbers given will be called x1 and y1. Or, x1=5 and y1=3.

Also, let's call the second point you gave, (-3,-1), point #2, so the x and y numbers here will be called x2 and y2. Or, x2=-3 and y2=-1.

Now, just plug the numbers into the formula for m above, like this:

m=

-1 - 3 over

-3 - 5

or...

m=

-4 over

-8

or...

m=1/2

So, we have the first piece to finding the equation of this line, and we can fill it into y=mx+b like this:

y=1/2x+b

Now, what about b, the y-intercept?

To find b, think about what your (x,y) points mean:

(5,3). When x of the line is 5, y of the line must be 3.

(-3,-1). When x of the line is -3, y of the line must be -1.

Because you said the line passes through each one of these two points, right?

Now, look at our line's equation so far: y=1/2x+b. b is what we want, the 1/2 is already set and x and y are just two "free variables" sitting there. We can plug anything we want in for x and y here, but we want the equation for the line that specfically passes through the two points (5,3) and (-3,-1).

So, why not plug in for x and y from one of our (x,y) points that we know the line passes through? This will allow us to solve for b for the particular line that passes through the two points you gave!.

You can use either (x,y) point you want..the answer will be the same:

(5,3). y=mx+b or 3=1/2 × 5+b, or solving for b: b=3-(1/2)(5). b=1/2.

(-3,-1). y=mx+b or -1=1/2 × -3+b, or solving for b: b=-1-(1/2)(-3). b=1/2.

See! In both cases we got the same value for b. And this completes our problem.

The equation of the line that passes through the points

(5,3) and (-3,-1)

is

y=1/2x+1/2

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NNADVOKAT [17]

Answer:

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Step-by-step explanation:

I used the a^2+b^2=c^2 to get this answer. I squared all the number given and got 16 and 9. Then I subtract them to get 7. Finally square 7 off and got 2.6 as the final answer

Hope this helped

\sqrt{7}  = 2.6

3 0
2 years ago
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