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3 years ago

Which expression uses the greatest common factor and distributive property to find 10+50?

1 answer:

Rudiy273 years ago

3 0

Ab+ac=a(b+c) where a is the greatest common factor
find greatest common factor of 10 and 50
10=1,2,5,10
50=1,2,5,10,25,50
greatest common is 10
a=10
10(1)+10(5)=10(1+5)=10(6)=60

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What numbers are multiples of 9 and factors of 36?

Serga [27]

Answer:

9,18, and 36

Step-by-step explanation:

9*4=36 and 9*1=9

18*2=36 and 9*2=18

36*1=36 and 9*4=36

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2 years ago

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A man selling computer parts realizes that when he sells 16 computer parts, his earning is $1700. When he sells 56 computer part

natta225 [31]

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3 years ago

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The length of a rectangle is 5 meters less than twice the width. If the area of the rectangle is 273 meters, find the dimensions

AleksandrR [38]

The length of the rectangle = 16 meters

The width of the rectangle = 10.5 meters

Step-by-step explanation:

Given that,

The Area of the rectangle is 273.

Step 1 :

Let, the width of the rectangle be 'x'

The length of the rectangle is 2x - 5

Step 2 :

Area of the rectangle = length $\times$ width

273 = (2x - 5) x

273 = 2x^2 - 5x

Step 3 :

The equation formed is 2x^2 - 5x -273 = 0

a= coefficient of x^2 = 2

b= coefficient of x = -5

c = constant = -273

Find the roots of the equation, to find the width.

Step 4 :

Find the roots using factorizing method,

ac = 2 $\times$ -273 = -546 and b= -5

Factorizing -546 as -26 $\times$ 21

The product of -26 $\times$ 21 = -546

The sum of -26 + 21 = -5

Step 5 :

The roots of the equation 2x^2 - 5x -273 = 0 are x= -26/2 and x= 21/2

The values of x are x= -13 and x= 10.5

Since the width cannot be a negative value, neglect x= -13

Step 6 :

Therefore,

The width of the rectangle = 10.5 meters

The length of the rectangle = 2x-5

= 2(10.5) - 5

= 21 - 5

length = 16 meters

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3 years ago

Graph the hyperbola using the transverse axis, vertices, and co-vertices:

Reptile [31]

See attachment for the graph of the hyperbola 12x^2 - 3y^2 - 108 = 0

<h3>How to graph the hyperbola?</h3>

The equation of the hyperbola is given as:

12x^2 - 3y^2 - 108 = 0

Start by calculating the transverse axis

So, we have:

Transverse axis

The vertices of the given hyperbola are (0, 0)

This means that

(h, k) = 0

Where

a = 3 and b = 6

The transverse axis is calculated as:

y = ±b/a(x - h) + k

So, we have:

y = ±6/3(x - 0) + 0

Evaluate the difference and sum

y = ±6/3x

Evaluate the quotient

y = ±2x

This means that the transverse axes are y = 2x and y =-2x

The vertices

In the above section, we have:

The vertices of the given hyperbola are (0, 0)

This means that

(h, k) = 0

The co-vertices

In the above section, we have:

The vertices of the given hyperbola are (0, 0)

This means that

(h, k) = 0

And

a = 3 and b = 6

The co-vertices are

(h - a, k) and (h + a, k)

So, we have:

(0 - 3, 0) and (0 + 3, 0)

Evaluate

(-3,0) and (3, 0)

See attachment for the graph of the hyperbola