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3 years ago

Express the fraction in simplest form 9/12

Mathematics

2 answers:

Ratling [72]3 years ago

6 0

9/12 dividing both the numerator and the denominator by 3

9/3=3
12/3=4

this reduces down to 3/4

Roman55 [17]3 years ago

4 0

Just like they said you find the factors of both of them that they have in common like in this problem ×3 so you divide that 3 with your numerator and your denominator and t gets shorter
9÷3=3
12÷3=4
3/4

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How many integers between 10 and 60, inclusive, can be evenly divided by neither 2 nor 3?

erastovalidia [21]

Find total number of integers.

$a_1=10,a_n=60,d=1 \\a_n=a_1+(n-1)d \\60=10+(n-1)1 \\n-1=50 \\n=51$

Find how many integers is divisible by 2.

$a_1=10,a_n=60,d=2
\\a_n=a_1+(n-1)d
\\60=10+(n-1)2
\\2(n-1)=50
\\n-1=25
\\n=26$

Eliminate even numbers.

11, 13, 15,..., 57, 59

This array contains 51 - 26 = 25 numbers.

Eliminate numbers before the first number divisible by 3 and after the last number divisible by 3.

15, 17, 19,..., 55, 57

This array contains 25 - 3 = 22 numbers.

Now we should eliminate numbers divisible by 3: 15, 21, 27...

$a_1=15,a_n=57,d=6,n=?
\\a_n=a_1+(n-1)d
\\57=15+(n-1)6
\\6(n-1)=42
\\n-1=7
\\n=8$

There are 8 such numbers.

Therefore, there are 25 - 8 = 17 numbers that <span>can be evenly divided by neither 2 nor 3</span>

6 0

3 years ago

Simplify the expression:<br> 9v–4v+7v

EleoNora [17]

Step-by-step explanation:

9v-4v+7v

= 5v+7v

= 12v

The answer is 12v

7 0

3 years ago

Solve Sine inverse x +sine inverse 2x = π/3 <br> Please solve it faster..

LuckyWell [14K]

Arcsin x + arcsin 2x = π/3

arcsin 2x = π/3 - arcsin x

sin[arcsin 2x] = sin[π/3 - arcsin x] (remember the left side is like sin(a-b)

2x = sinπ/3 cos(arcsin x)-cosπ/3 sin(arc sinx)

2x = √3/2 . cos(arcsin x) - (1/2)x)

but cos(arcsin x) = √(1-x²)===>2x = √3/2 .√(1-x²) - (1/2)x)

Reduce to same denominator:

(4x) = √3 .√(1-x²) - (x)===>5x = √3 .√(1-x²)

Square both sides==> 25x²=3(1-x²)

28 x² = 3 & x² = 3/28 & x =√(3/28)

3 0

2 years ago

Mr. McBride ordered 6 cheese pizzas and 7 pepperoni pizzas and paid $153.50 for his son's birthday party. He realized he was goi

Marat540 [252]

Let x = cost of one cheese pizza.

Let y = cost of one pepperoni pizza.

Set up a system of equations.

6x + 7y = 153.50

2x + 2y = 47.00.

Multiply the second equation by -3

6x + 7y = 153.50

-6x - 6y = -141.00.

Add the equations together

y = $12.00.

Plug 12 into one of our original equations.

2x + 2(12) = 47.

Simplify the left side.

2x + 24 = 47.

Subtract 24 from each side.

2x = 23.

Divide each side by 2

x = $11.50

In conclusion, one pepperoni pizza costs $12.00

8 0

3 years ago

The table below shows the number of points Josh scored in each basketball game of the season.

MrRissso [65]

Answer:

◻️B. The value of the mode is the least value of the data.

Step-by-step explanation:

The mode is the data value that appears most often

5,7,9,5,18,6,8,5

Arranging the data from smallest to largest

5,5,5,6,7,8,9,18

The number that appears most often is 5

This is the smallest value of the data

5 0

2 years ago