MATHEMATICS HIGH SCHOOL

Solve for x. Express the answer in simplest form.
2/1= 8x-2/9

Answers

Answer 1
Answer: First, you put known numbers apart ( numbers without x ) and unknown numbers apart (numbers with x ), and of course don't forget that when you move a number from a part to another, his sign change, So you get: 
(2)/(1) = 8x - (2)/(9)
(2)/(1) + (2)/(9) = 8x

Now, you need to have the same denominator so you can add 2/1 and 2/9. So, you multiply 2/1 by 9, so you get:
(2*9)/(1*9) + (2)/(9) = 8x
(18)/(9) + (2)/(9) = 8x

Then you add the 2 fractions and you get:
(20)/(9) = 8x

Now, you divide each term by 8, so you get:
( (20)/(9) )/(8) = (8x)/(8)

in (8x)/(8), you removed 8 and 8 and you get x, so you get:
( (20)/(9) )/(8) = x

as you know, 8 = 8/1, and when you got a division of 2 fractions, you multiply the first by the inverse of the second, which means you get:
(20)/(9) * (1)/(8) = x

And now you multiply, so you get:
(20*1)/(9*8)
(20)/(72)

20 and 72 have a common factor, so you divide each by 4, and you get:
(20/4)/(72/4)
(5)/(18)

So, x = (5)/(18)

Hope this Helps! :D
Answer 2
Answer: 2/1= 8x-2/9
2= 8x-2/9
18=72x-2
20=72x
x=20/72
x= 5/18

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The sum of two consecutive odd integers is equal to 43 more than 1/3 the larger number. Find both numbers. PLZ HELP

Answers

x and y

consecutive odd are 2 apart
x=2+y
x=larger number


sum is 43 more than 1/3 or larger
x+y=43+(x/3)
x=2+y
2+y+y=43+((2+y)/3)
2+2y=43+((2+y)/3)
minus 43 both sides
-41+2y=(2+y)/3
times 3 both sides
-123+6y=2+y
minus y both sides
-123+5y=2
add 123 both sides
5y=125
divide by 5
y=25

sub
x=2+y
x=2+25
x=27

the numbers are 25 ad 27

The first term of an arithmetic progression is -3 and the common difference is 8. What is the 28th term? 213
226
229
220

Answers

Hello,

a(28)=a(0)+27*8=-3+27*8=213

Answer A

A hospital employs a total of 77n nurses and doctors. The ratio of nurses to doctors is 9:2. How many nurses are employed at the hospital? How many doctors are employed at the hospital.

Answers

Answer:

number of nurses employed at the hospital is 9x = 9 * (7n/9) = 7n, and the number of doctors is 2x = 2 * (7n/9) = (14n/9).

Step-by-step explanation:

Given the ratio of nurses to doctors is 9:2, we can express this as:

Number of nurses (9x) : Number of doctors (2x)

Now, you've mentioned that the total number of nurses and doctors employed at the hospital is 77n. So, we can set up an equation:

9x + 2x = 77n

Combine like terms:

11x = 77n

Now, to find the number of nurses (9x) and the number of doctors (2x), we need to divide both sides by 11:

9x = (77n) / 11

9x = 7n

Now, we can solve for x:

x = (7n) / 9

So, the number of nurses employed at the hospital is 9x = 9 * (7n/9) = 7n, and the number of doctors is 2x = 2 * (7n/9) = (14n/9).

In summary:

- Number of nurses = 7n

- Number of doctors = (14n/9)

solved by MG

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