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nikitadnepr [17]
2 years ago
14

Find the sum

Mathematics
1 answer:
lakkis [162]2 years ago
4 0

Answer:

Numerator = 2(b^2+a^2)    or equivalently 2b^2+2a^2

Denominator = (b+a)^2*(b-a), or equivalently b^3+ab^2-a^2b0-a^3

Step-by-step explanation:

Let

S = 2b/(b+a)^2 + 2a/(b^2-a^2)   factor denominator

= 2b/(b+a)^2 + 2a/((b+a)(b-a))     factor denominators

= 1/(b+a) ( 2b/(b+a) + 2a/(b-a))    find common denominator

= 1/(b+a) ((2b*(b-a) + 2a*(b+a))/((b+a)(b-a))   expand

= 1/(b+a)(2b^2-2ab+2ab+2a^2)/((b+a)(b-a))  simplify & factor

= 2/(b+a)(b^2+a^2)/((b+a)(b-a))  simplify & rearrange

= 2(b^2+a^2)/((b+a)^2(b-a))

Numerator = 2(b^2+a^2)    or equivalently 2b^2+2a^2

Denominator = (b+a)^2*(b-a), or equivalently b^3+ab^2-a^2b0-a^3

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natulia [17]

Answer:

x = 3

Step-by-step explanation:

reverse foil the denominator and find the largest solution.

x-3(x+1)

3 is the largest solution

6 0
2 years ago
joe has a piggy bank with $8.90 split upon nickels, dimes, and quarters. The piggy bank contains 76 coins in all. The number of
kozerog [31]

Answer:

There are 38 dimes, 22 nickels and 16 quarters.

Step-by-step explanation:

Let n, d and q represent the # of nickels, dimes and quarters respectively.

Then n + d + q = 76

The value of a nickel is $0.05; that of a dime is $0.10, and that of a quarter is $0.25.

Thus, the value of n nickels is $0.05n (and so on).

The total value of the coins is $0.05n + $0.10d + $0.25q = $8.90.

d = n + q allows us to eliminate d.

First, n + d + q = 76 becomes n + (n + q) + q = 76, and second:

$0.05n + $0.10(n + q) + $0.25q = $8.90.  Here we have succeeded in eliminating d from two different equations, and now we have these two different equations in two unknowns (n and q), which is solvable.

Simplifying both equations, we get:

2n + 2q = 76 and

5n + 10n + 10q + 25q = 890, or 15n + 35q = 890

Let's use the substitution method of solving linear equations:

Rewrite 2n  + 2q = 76 as n + q = 38, or n = 38 - q.  Substituting this result into the second equation, we get:

15(38 - q) + 35 q = 890, or

  570 - 15q + 35q = 890, or

   570 + 20 q = 890.  Then 20q = 890 - 570 = 320, and q = 320/20 = 16.

There are 16 quarters.  Thus, the number of nickels is n = 38 - 16 = 22.

Finally, since n + d + q = 76, 22 + d + 16 = 76, or:

22 + d = 60, or d = 60 - 22 = 38.

There are 38 dimes, 22 nickels and 16 quarters.

4 0
2 years ago
Trigonometric identities: Performance task
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#1

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\\ \sf\longmapsto 1-cos^2x

\\ \sf\longmapsto sin^2x

#2

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\\ \sf\longmapsto tan^2x-sec^2x

\\ \sf\longmapsto 1

3 0
3 years ago
Read 2 more answers
To make the expression 4x-2 + (2x + 4) equivalent to 2(6x + 7), what must be the value in the box?
podryga [215]

4x - 2 + (2x + 4) = 2(6x + 7) \\

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Simplification

6x + 2 = 12x + 14

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Simplification

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Subtract sides -12x

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Simplification

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Divided sides by -6

\frac{ - 6}{ - 6}x =  \frac{12}{ - 6} \\

x =  - 2

It is must be in the box buddy.

And we're done...♥️♥️♥️♥️♥️

5 0
3 years ago
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Viefleur [7K]

Answer:

The point on the y-axis is (0,-3) and the point on the x-axis is (6,0)

Step-by-step explanation:

Start by plotting -3 on the y-axis

Then move up 1 and over 2 from there

7 0
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