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dusya [7]
2 years ago
14

There is a number that is three-fifths the total of the other number. When four is added to one of the numbers their sum will be

equal to the other number. There are two pairs of numbers that satisfy these descriptions. What are they?
Mathematics
1 answer:
gogolik [260]2 years ago
6 0

Answer:

-10, -6

6, 10

Step-by-step explanation:

Let the one number be x.

One number is 3/5 of the other number.

The numbers are x and 3x/5.

Add 4 to one number, the sum equals the other number.

There are two possibilities.

A) x + 4 = 3x/5

B) 3x/5 + 4 = x

Solve A)

5x + 20 = 3x

2x = -20

x = -10

Solve B)

3x + 20 = 5x

2x = 20

x = 10

According to A)

x = -10

3x/5 = -6

According to B)

x = 10

3x/5 = 6

Answer:

-10, -6

6, 10

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A certain number of sixes and nines is added to give a sum of 126; if the number of sixes and nines is interchanged, the new sum
galina1969 [7]

Answer:

Original number of sixes = 6

Original number of nines = 10

Step-by-step explanation:

We are told in the question that:

A certain number of sixes and nines is added to give a sum of 126

Let us represent originally

the number of sixes = a

the number of nines = b

Hence:

6 × a + 9 × b = 126

6a + 9b = 126.....Equation 1

If the number of sixes and nines is interchanged, the new sum is 114.

For this second part, because it is interchanged,

Let us represent

the number of sixes = b

the number of nines = a

6 × b + 9 × a = 114

6b + 9a = 114.......Equation 2

9a + 6b = 114 .......Equation 2

6a + 9b = 126.....Equation 1

9a + 6b = 114 .......Equation 2

We solve using Elimination method

Multiply Equation 1 by the coefficient of a in Equation 2

Multiply Equation 2 by the coefficient of a in Equation 1

6a + 9b = 126.....Equation 1 × 9

9a + 6b = 114 .......Equation 2 × 6

54a + 81b = 1134 ........ Equation 3

54a + 36b = 684.........Equation 4

Subtract Equation 4 from Equation 3

= 45b = 450

divide both sides by b

45b/45 = 450/45

b = 10

Therefore, since the original the number of nines = b,

Original number of nines = 10

Also, to find the original number of sixes = a

We substitute 10 for b in Equation 1

6a + 9b = 126.....Equation 1

6a + 9 × 10 = 126

6a + 90 = 126

6a = 126 - 90

6a = 36

a = 36/6

a = 6

Therefore, the original number of sixes is 6

7 0
3 years ago
Choose one of the factors of 500x3 + 108y18
sammy [17]

Answer:

Option C

Therefore, one of the factors of 500x^3 +108y^\left (18\right ) is (5x+3y^6).

Step-by-step explanation:

Given: 500x^3 +108y^\left (18\right )

the common factor from 500x^3 and 108y^\left (18\right ) is 4.

therefore, 4\cdot \left ( 125x^3+27y^\left (18\right ) \right )

4\cdot \left ( (5x)^3+(3y^6)^3 \right))

Now, use the formula for above expression: (a^3+b^3)=(a+b)(a^2-ab+b^2)

here, a=5x and b=3y^6

( (5x)^3+(3y^6)^3 \right))=(5x+3y^6)(25x^2-15xy^6+9y^12)

Therefore, we have

500x^3 +108y^\left (18\right )=4\cdot (5x+3y^6)\left (25x^2-15xy^6+9y^\left ( 12 \right )  \right )

Therefore, one of the factors of 500x^3 +108y^\left (18\right ) is (5x+3y^6).








7 0
3 years ago
Read 2 more answers
Factor the expression below.4x2 - 1
marusya05 [52]

Answer:

C. (2x – 1)(2x + 1)

Step-by-step explanation:

4x² – 1 = (2x)(2x) – 1 = (2x – 1)(2x + 1)

5 0
2 years ago
Read 2 more answers
–10 = –6 + 2c <br><br><br><br> –8<br><br><br> 1<br><br><br> –2<br><br><br> 2
guapka [62]

–10 = –6 + 2c

+ 6     + 6          Add 6 to cancel out -6

-4 = 2c

/2    /2              Divide by 2 to get c variable alone

-2 = c               Choice C is the correct answer

6 0
3 years ago
Help! <br> Is the data skewed or symmetric?
KATRIN_1 [288]

Answer:

i believe it is skewed. sorry if its wrong

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
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