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4 years ago

If x2 – 49 = (x+a) (x – a), what is the value of a?

Mathematics

2 answers:

Ivenika [448]4 years ago

7 0

Answer:

a = 7 & a = −7

Explanation:

Rewrite the equation as

(x+a)(x−a)=x^2−49

Simplify (x+a)(x−a)

x^2−a^2=x^2−49

Move all terms not containing a to the right side of the equation.

−a^2=−49

Multiply each term in −a^2=−49 by −1

a^2=49

Take the square root of both sides of the equation to eliminate the exponent on the left side.

a=±√49

The complete solution is the result of both the positive and negative portions of the solution.

a=7,−7

vaieri [72.5K]4 years ago

5 0

Answer:

a is 7

Step-by-step explanation:

x²-49

so you are finding the difference of squares

and if you look closely, you can see that the equation has squares.

49 has the square root of 7, but the rules on squares state that the squared number comes in both positive and negative numbers.

so a is equal to both -7 and +7

PS i hope this helps

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Two pumps are filling a pool. One of them is high power and can fill the pool alone in 2 hours less time than the other can do s

KatRina [158]

Answer:

9.1 hours

Step-by-step explanation:

Make a Chart.

Column 1 is Time it takes to do the job alone

Column 2 is Rate of Work ( 1 over the expression in Column 1)

Column 3 is Time it takes to do the job together

Column 4 is Part of the Job done ( Columns 2 and 3 multiplied together )

Row 1 is the First pipes info.

Row 2 is the Second pipes info.

The equation comes from column 4. Part of the Job from Pipe 1 + Part of the Job from Pipe 2 = 1 (the whole job)

So Row 1 for Pipe 1, the small pipe, would look like this: x , 1/x , 4 , 4/x

Row 2 for Pipe 2, the larger pipe, would look like this: x - 2 , 1/x-2 , 4 , 4/(x-2)

So, the equation would be: 4/x + 4/(x-2) = 1

Solve this equation by first multiplying both side by x(x-2) to clear the denominators.

So the equation becomes: 4(x-2) + 4x = x(x-2)

Distribute and combine like terms, then get everything on one side of the equation.

So the equation becomes: x^2 - 10x + 8 = 0

Use the quadratic equation to solve for x. Solutions are x = 9.1 and x = .9

.9 hours does not make sense so throw that solution out (with the dirty pipe water :) )

9.1 hours makes sense for how long it would take the smaller pipe working alone to fill the pool.

3 0

3 years ago

Read 2 more answers

The negative sign in 15t-2t belongs to the term____?

alexdok [17]

The expression 15t – 2t not equivalent to 2t – 15t because the negative sign in 15t – 2t belongs to the term 2t.

Solution:

Given expressions are 15t – 2t and 2t – 15t.

To determine 15t – 2t is equivalent to 2t – 15t or not.

Substitute t = 2 in above two expressions.

15t – 2t = 15(2) – 2(2)

= 30 – 4

= 26

2t – 15t = 2(2) – 15(2)

= 4 – 30

= –26

The values of the expressions are different when t = 2.

So, 15t – 2t is not equivalent to 2t – 15t.

Hence the expression 15t – 2t not equivalent to 2t – 15t because the negative sign in 15t – 2t belongs to the term 2t.

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3 years ago

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VladimirAG [237]

Equation: 19-2(3x-1)/5 = x + 2

Solution:

1. Find x

(5) - 2 = (x + 2) - 2

x = 3

2. Plug in X and solve

19-2(3(3)-1)/3

19-2(9-1)/3

19-2(8)/3

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3 years ago

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swat32

Answer:

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Step-by-step explanation:

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