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Vesnalui [34]
3 years ago
13

Use the identity (x+y)(x−y)=x2−y2 to find the difference of two numbers if the sum of the numbers is 12 and the difference of th

e squares of the numbers is 48.
Enter your answer as a number, like this: 42
Mathematics
2 answers:
Natalka [10]3 years ago
8 0

Answer:

The difference of two numbers using identity (x+y)(x-y)=x^2-y^2 is 4.

Step-by-step explanation:

Given:  The sum of the numbers is 12 and the difference of the squares of the numbers is 48.

To find the difference of two numbers using identity (x+y)(x-y)=x^2-y^2

Let the two numbers be a and b, then

Given that the sum of the numbers is 12

that is a + b = 12 .........(1)

Also, given the difference of the squares of the numbers is 48.

that is a^2-b^2=48     ..........(2)

Using given identity  (x+y)(x-y)=x^2-y^2

We have (a+b)(a-b)=a^2-b^2

Substitute the known values, we have,

12(a-b)=48

Divide both side 12 , we have,

(a-b)=4

Thus, the difference of two numbers using identity (x+y)(x-y)=x^2-y^2 is 4.

krok68 [10]3 years ago
7 0

Answer:

The difference of two numbers is 7.

Step-by-step explanation:

We have given that

The sum of the numbers is 12

x+y = 12

The difference of the squares of the numbers is 48.

x²-y² = 48

We have to find the difference of two numbers.

x-y = ?

Given formula is:

(x+y)(x-y) = x²-y²

Putting values in above formula, we have

(12)(x-y) = 48

x-y = 48 / 12

The difference of two numbers =  x-y = 4 which is the answer.

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Which functions are the same as their inverse functions? please help!!!
Whitepunk [10]
Case a)
f(x)=[x-1]/[x+5]
step 1
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y=[x-1]/[x+5]
step 2
exchange x for y and y for x
y=[x-1]/[x+5]------> x=[y-1]/[y+5]----> x*[y+5]=[y-1]----> xy+5x=y-1
step 3
clear the variable y
xy+5x=y-1-----> y-xy=5x+1----> y*[1-x]=[5x+1]----> y=[5x+1]/[1-x]
step 4
f(x)-1= [5x+1]/[1-x]
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case b)
g(x)=[x-2]/[x-1]
step 1
g(x)=y
y=[x-2]/[x-1]
step 2
exchange x for y and y for x
y=[x-2]/[x-1]------> x=[y-2]/[y-1]----> x*[y-1]=[y-2]----> xy-x=y-2
step 3 
clear the variable y
xy-x=y-2-----> xy-y=-2+x----> y*[x-1]=[x-2]----> y=[x-2]/[x-1]
step 4
g(x)-1= [x-2]/[x-1]
the function and the inverse function are  the same

case c)
h(x)=[x+3]/[x-2]
step 1
h(x)=y
y=[x+3]/[x-2]
step 2
exchange x for y and y for x
y=[x+3]/[x-2]------> x=[y+3]/[y-2]----> x*[y-2]=[y+3]----> xy-2x=y+3
step 3 
clear the variable y
xy-2x=y+3-----> xy-y=3+2x----> y*[x-1]=[2x+3]----> y=[2x+3]/[x-1]
step 4
h(x)-1= [2x+3]/[x-1]
the function and the inverse function are not the same

case d)
k(x)=[x+1]/[x-1]
step 1
k(x)=y
y=[x+1]/[x-1]
step 2
exchange x for y and y for x
y=[x+1]/[x-1]------> x=[y+1]/[y-1]---> x*[y-1]=[y+1]----> xy-x=y+1
step 3 
clear the variable y
xy-x=y+1-----> xy-y=x+1----> y*[x-1]=[x+1]----> y=[x+1]/[x-1]
step 4
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7 0
3 years ago
........................
andreyandreev [35.5K]

First expression: (-7)/(-4)

Divide. Note that two negative numbers divided will result in a positive answer

(-7)/(-4) = 7/4 = 1.75

First expression: Greater than 1.

-----------------------------------------------------------------------------------------------------------------

Second expression: -(3/2)

Simplify: 3/2 = 1.5

-(1.5) = -1.5

Second expression: Less than -1

--------------------------------------------------------------------------------------------------------------

Third expression: (-8/5) x (-5/8)

Note that two negatives = one positive answer when multiplying

8/5 x 5/8 = 40/40 = 1

Third expression: Neither

----------------------------------------------------------------------------------------------------------------

Fourth Expression: (-5)/(-3)

Divide: (-5)/(-3) = 5/3 = ~1.67

Fourth Expression: Greater than 1

----------------------------------------------------------------------------------------------------------------

Fifth Expression: (-9)/6

Divide: (-9)/6 = -1.5

Fifth expression: Less than -1

----------------------------------------------------------------------------------------------------------------

hope this helps

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Answer:

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ihnc

6 0
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3 0
3 years ago
Steve made $50 raking leaves and $75 mowing lawns he gave 60% of his earnings to his mother how much did Steve give to his mothe
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Answer:

Steve gave his mother $75.

Step-by-step explanation:

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0.60($125) = $75

Steve gave his mother $75.

3 0
3 years ago
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