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3 years ago

Match each expression written in standard form to the equivalent expression in factored form

Mathematics

1 answer:

den301095 [7]3 years ago

4 0

Answer:

1. 15x^7y^2 + 4x^3 => x^3(15x^4y^2 + 4)

2. 15x^7y^2 + 3x => 3x(5x^6y^2 + 1)

3. 15x^7y^2 + 6xy => 3xy(5x^6y + 2)

4. 15x^7 + 10y^2 => 5(3x^7 + 2y^2)

Step-by-step explanation:

To obtain the answer to the question, first let us factorise each expression. This is illustrated below:

1. 15x^7y^2 + 4x^3

Common factor is x^3, therefore the expression is written as:

x^3(15x^4y^2 + 4)

2. 15x^7y^2 + 3x

Common factor is 3x, therefore the expression is written as:

3x(5x^6y^2 + 1)

3. 15x^7y^2 + 6xy

Common factor is 3xy, therefore the expression is written as:

3xy(5x^6y + 2)

4. 15x^7 + 10y^2

Common factor is 5, therefore the expression can be written as:

5(3x^7 + 2y^2)

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ExtremeBDS [4]

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2 years ago

I made some brownies and cookies to sell for a local fundraiser. The cookies sold for $0.75 each and the brownies sold for $1.25

juin [17]

Answer:

Brownies made the most money

Step-by-step explanation:

Let c = cookies

b = brownies

We sold 51 items so c+b = 51

Cookies are .75 and brownies are 1.25

.75c + 1.25 b = 53.25

We have 2 equations and 2 unknowns

c = 51-b

Substituting into the second equation

.75(51-b) + 1.25b = 53.25

Distribute

38.25-.75b +1.25b = 53.25

Combine like terms

38.25+.5b = 53.25

Subtract 38.25 from each side

38.25 +.5b -38.25 = 53.25 -38.25

.5b =15

Divide each side by .5

.5b/.5 = 15/.5

b = 30

Now find c

c =51-b

c = 51-30

c = 21

They sold 30 brownies and 21 cookies

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21 cookies *.75 = 15.75

Brownies made the most money

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3 years ago

Use a net to find the surface area of the right triangular prism shown below:

AnnZ [28]

I don't exactly know what a net is, but I can figure out the surface area (maybe). When you put this pattern together, you have to make a couple of assumptions.
First of all the 2 triangles are connected to a base that's 8 by 13.
Base
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Two Triangles.
The area of any triangle is
Area = 1/2 b * h
Area = 1/2 *12 * 5
Area = 30 square feet. There are 2 triangles so ...
The total area of both is 60 square feet.

Overlap
Now we come to the tough part. how big is it from the first dotted line to the second one?
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How far across is the dotted line? The answer is 8. Why again? That's the width of the whole prism or pattern.
So the area between the two dotted lines is 5 * 8 = 40

Finally the area over the 12.
The question is how far is it from the second dotted line to the last boundary? The answer is 12. And it's width is 8
So the area = 12 * 8 = 96

Total area
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3 years ago

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3 years ago

Suppose a circle with center (14,9) passes through point (16, 12). Which equation represents the circle?

kifflom [539]

Answer:

( x - 14)^2 + ( y - 9)^2 = 13

Step-by-step explanation:

The equation of the circle with a center and a point

( x - a) ^2 + ( y - b) ^2 = r^2

( 14 , 9) - center-( a, b)

a = 14

b = 9

( 16 , 12) - point - ( x, y)

x = 16

y = 12

Step 1: substitute the center into the equation

( x - 14)^2 + ( y - 9)^2 = r^2

Step 2: substitute the point into the equation

( x - 14)^2 +( y - 9)^2 = r^2

( 16 - 14)^2 + ( 12 - 9)^2 = r^2

2^2 + 3^2 = r^2

4 + 9 = r^2

13 = r^2

Step 3: subs the radius into the equation

( x - 14)^2 + ( y - 9)^2 = r^2

( x - 14)^2 + (y - 9)^2 = 13

Therefore, the equation of the circle is

( x - 14)^2 + ( y - 9)^2 = 13

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