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kumpel [21]
2 years ago
15

Multiply and divide rational expressions and simplify the answer

Mathematics
1 answer:
lord [1]2 years ago
7 0

Answer:

1. 32x/15

2. 2/x-4

3. 1/10x+10

4. 3x^6/5x^9

5. (x-3)(x-9)/6

6. x^2/3

Step-by-step explanation:

multiply the Numerator with the Numerator of other number and multiply the denominator of the first with the denominator of the second. Find a common factor in both the Numerator and denominator to be able to cross out the identical factors.

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Molly's Custom Kitchen Supplies sells handmade forks and spoons. It costs the store $1.70 to buy the
scoray [572]

9514 1404 393

Answer:

  • 7 forks
  • 20 spoons

Step-by-step explanation:

Let x and y represent the numbers of forks and spoons made, respectively.

The cost of materials is ...

  1.70x + 1.30y = 37.90

The revenue from sales is ...

  5.60x + 5.40y = 147.20

You can solve these by any of your favorite methods. A graph is attached. It shows the solution is (x, y) = (7, 20).

They made 7 forks and 20 spoons.

_____

<em>Additional working out</em>

The equation coefficients are not "nice" multiples of each other, so elimination  and substitution will require multiplying both equations by some numbers. If we're going to that trouble, we may as well use Cramer's Rule or a variation of the "cross multiplication method". The latter is relatively straightforward and can be easy to remember. It tells you the solution to ...

  ax +by +c = 0

  dx +ey +g = 0

is ...

  1/(ae-db) = x/(bg-ey) = y/(cd-ga)

Here, that becomes ...

  1/(1.70·5.40-5.60·1.30) = x/(1.30·(-147.20)-5.40·(-37.90))

  = y/(-37.90·5.60-(-147.20·1.70))

  1/1.9 = x/13.3 = y/38

  x = 13.3/1.9 = 7 . . . number of forks

  y = 38/1.9 = 20 . . . number of spoons

__

The above solution formula may be more easily remembered in terms of the cross-multiplication pattern that gives the method its name. When the coefficients are written in two rows of four, with the last being a repeat of the first:

  • a b c a
  • d e g d

each of the three denominators (of 1, x, and y) is the difference of products in adjacent columns, formed in an X fashion: ae-db, bg-ec, cd-ga. Note that the equations are written in "general" form, which is similar to "standard" form, but with all of the non-zero terms on the left of the equal sign. (This has the effect of changing the sign of the constants: 1.7x+1.3y=37.9 ⇒ 1.7x+1.3y-37.9=0)

8 0
2 years ago
The expression 20l + 25g - 10 gives the number of dollars that Josie makes from mowing lawns and raking gardens.
vodka [1.7K]
20l + 25g -10
replace G with 4 and L with 3

20(3) + 25(4) - 10

60 + 100 - 10

160 - 10

150

he made $150
4 0
3 years ago
Maci is paid biweekly and earns $1500 each paycheck. What is his yearly salary?
Pachacha [2.7K]
Your answer would be 36,000 because he gets 3000 every month and every month for a year he would get your answer which would be 3000×12 which equals 36,000
5 0
3 years ago
Can somebody tell me what the answer to y-13=8 is? Please and thank you.
makvit [3.9K]

Answer:

Y=21

Step-by-step explanation:

add 13 on both sides you get Y=21

4 0
2 years ago
Given f(x) = -3x - 1, solve for f(x)= -4​
Nikitich [7]

Answer:

its 11

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
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