Use the definitions and theorems of this section to evaluate and simplify the following expression. Be sure to express answers with positive exponents.

Answer:

box = 30

Step-by-step explanation:

You could set this up very formally as a proportion. It would look like this.

1/5 = 6/x

Now all you have to do is cross multiiply.

1*x = 5 * 6

x = 30

So the answer that goes in the box is 30

Or you could just say to yourself. "The 1 was multiplied by 6. What do I have to multiply the 5 by to keep the ratio the same?"

The answer is 6

6 * 5 = 30

In higher math you are going to want to use the first method.

Answer:

the side length corresponding to mq is AE

Answer:

[tex]◻ \: 827 \div 1120 \\ \\ ◻ \: \frac{827}{1120} \\ \\ ◻ \: 1120 | \bar {1120}[/tex]

Answer:

12:18 and 10:12 (i think)

Step-by-step explanation:

After converting the given ratios in their simplest form, the equivalent form of 2:3 we get 12:18.

To find the simplest form of a fraction, you have to simplify the numerator and denominator to their lowest terms and keep dividing until you can no longer simplify the fraction any further.

The given ratios are,

12:18,

3:21,

10:12

For the ratio 12:18,

Simplify it by finding the greatest common divisor (GCD) of 12 and 18.

The GCD of 12 and 18 is 6.

By dividing both numbers by 6, we get the smallest ratio of 2:3.

Moving to the ratio of 3:21,

Find the GCD of 3 and 21, which is 3.

Dividing both numbers by 3 results in the smallest ratio of 1:7.

Find the smallest ratio for 10:12.

The GCD of 10 and 12 is 2.

Dividing both numbers by 2 gives us the smallest ratio of 5:6.

Hence, the simplest form of ratios for the given ratios are:

12:18 = 2:3,

3:21 = 1:7,

10:12 = 5:6.

Hence,

The ratio equivalent to 2:3 is 12:18.

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Answer:

Y is also 5 bro that is very easy question

Answer:

(-1,1) (-2,3) (1,3) (1,1)

Step-by-step explanation:

Hi

to progress in math, you must : know by heart the rules and formulas then train.

rule : a ( b+c ) = a*b + a*c.

this propertie is call distributivity .

so we have : 6 ( 9+5X)

here : a = 6

b = 9

c = 5X

so 6 ( 9+5X) = ?

I let you have a shot. Ask in comments section if you are stuck. But try first !

Answer:

1) rearrange terms:

6(9 + 5x) = 54

6(5x + 9) = 54

2) Distribution :

6(5x + 9) = 54

30x + 54= 54

3) subtract 54 from both side:

30x + 54 = 54

30x + 54 - 54 = 54 - 54

4) Simplify: subtract the numbers

30x = 0

5) Divide both side of the equation by the same term:

30x = 0

30x√30 = 0√30

6) Simplify: cancel term that are in the both numerator and denominator

x = O√30

solution :

x = 0]

Step-by-step explanation:

formula =P×(1+r/100)^2

3000×1.15^2=3967.50rs

Answer:

Step-by-step explanation:

[tex]\frac{x+3}{3} =5- \frac{x-3}{6} \\(\frac{x+3}{3}) *6 =5 - (x-3)[/tex]

[tex]2x+6 = 5 - x+3[/tex]

Answer:

none

Step-by-step explanation:

We can start by multiplying both side of the equation by 6 in order to remove the fractions.

[tex]6*\frac{x+3}{3} = 6(5 - \frac{x-3}{6})[/tex]

[tex]2(x + 3) = 30 - 6*\frac{x-3}{6}[/tex]

[tex]2x + 6 = 30 -(x - 3)[/tex]

[tex]2x + 6 = 30 - x + 3[/tex]

Now, we can try to see if this equation is equivalent to the other options.

Every option has the left side as 2x - 6. In order to get that, we need to subtract 12 on both sides:

[tex]2x - 6 = 30 - x + 3 - 12[/tex]

This simplifies to

[tex]2x-6 = 18 - x + 3[/tex]

This is not the same as any of the options shown.

We can check this by solving the equations.

2x - 6 = 18 - x + 3

3x = 6 + 18 + 3

3x = 27

x = 9

Now, the first option:

2x - 6 = 10 - x - 3

3x = 6 + 10 - 3

3x = 13

x = 13/3

The second option is the exact same as the third, so they would have the same solution:

2x - 6 = 30 - x- 3

3x = 6 + 30 - 3

3x= 33

x = 11

Since none of the options have the answer 9, they are not equivalent to the equation shown.

Answer:

she used about 2 gallons for her dining room

Step-by-step explanation:

she used a combined amount of 3 gallons in the other areas of the house so that left 2 gallons for the dining room

Answer:

B. 2 gallons

Step-by-step explanation:

[tex]5\frac{1}{4} -1\frac{1}{4}\\=4-1\frac{1}{8}\\=2\frac{7}{8}\\2\frac{7}{8}-\frac{3}{4}=2\frac{1}{8}\sim2[/tex]

Answer:

9*10=90 so 6*9=54   then answer is 90:54

Step-by-step explanation:

Answer:

3/8

Step-by-step explanation:

The probability of picking either a Queen or a Jack from each pile is always 1/2 (as there are only 2 cards).

There are only 3 ways in which Lisa can draw two Queens and a Jack:

Queen, Queen, Jack

Queen, Jack, Queen

Jack, Queen, Queen

The probability of each one happening is 1/8

This is because there is a 1/2 chance of picking a Queen or a Jack from each pile and to calculate the probability that Lisa will pick a Queen AND a Queen AND then a Jack (for example) you multiply the probabilities together:

1/2 x 1/2 x 1/2 = 1/8

This is the same for other examples and since there are only 3 ways that Lisa can draw two Queens and a Jack you multiply 1/8 by 3 (you add 1/8 together 3 times) to get 3/8

It can be represented on a tree diagram however I am not sure how I can show images/drawings on this

Answer:

It is an irrational number, [tex]\sqrt{3}[/tex] as a decimal rounded to the tenth place is 1.7

Step-by-step explanation:

All square roots are irrational numbers

Answer:

4/15

Step-by-step explanation:

[tex]6\frac{3}{5} -6\frac{1}{3} \\\\\frac{33}{5} -\frac{19}{3} \\\\\frac{99-95}{15} =\frac{4}{15}[/tex]

The answer is : 40:10

*multiply by 2

If helpful, brainliest please !

Answer:

40:10 & 8:2

Step-by-step explanation:

20 * 2 = 40

5 * 2 = 10

8 * 2.5 = 20

2 * 2.5 = 5

2:1 does not work because only 2 * 10 = 20, but 1 *10 = 10 and there is no 10. There is only 5.

The correct equation that Jordan can use to solve the division problem 42 divided by 7 is:

? x 7 = 42

So, the correct equation is option 3) ? x 7 = 42.

Given that, Jordan has to solve this division problem: 42 divided by 7 = ?

In this case, Jordan needs to find the value of the missing factor, which represents how many times 7 can be multiplied to get 42.

Therefore, he can use the equation:

? x 7 = 42

This equation represents the inverse operation of division, which is multiplication.

When we know one factor (7) and the product (42), we can use multiplication to find the missing factor (the quotient).

By solving for the missing factor, he will find the correct answer to the division problem:

The missing factor = 42 / 7 = 6

So, the correct equation is option 3) ? x 7 = 42.

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Answer:

1a) x = -41

1b) x = -1

1c) x = 29/3, or x = 9.66 in decimal form

1d) x = -4

----------------

2a) y = -3

2b) y = -60

2c) y = -83

2d) y = -50

Step-by-step explanation:

1a) y = x  + 11

-30 = x  + 11

-11           -11

------------------

-41 = x

1b) y = -2x - 32

-30 = -2x - 32

+32         +32

----------------------

2 = -2x

/-2   /-2

----------------------

-1 = x

1c) y = -3x - 1

-30 = -3x - 1

+1             +1

-----------------

-29 = -3x

/-3     /-3

------------------

29/3 = x

9.66 = x

1d) y = 5x - 10

-30 = 5x - 10

+10         +10

----------------------

-20 = 5x

/5      /5

----------------------

-4 = x

------------------------

2a) y = x + 3

y = -6 + 3

y = -3

2b) y = -2x - 72

y = -2(-6) - 72

y = 12 - 72

y = -60

2c) y = 3x - 65

y = 3(-6) - 65

y = -18 - 65

y = -83

2d) y = 4x - 26

y = 4(-6) - 26

y = -24 - 26

y = -50

Answer:

1. 21.6

2. 54

3.16.22

Step-by-step explanation:

1. 3(1.8)(4)

2. 7.5(1.8)(4)

3. (1.4)(4) + (5.9)(1.8)

Answer:

There are 2 cups of peanuts for every cup of almonds. There are 3 cups of peanuts for every cup of cranberries.

Step-by-step explanation:

First question - 6(peanuts) / 3(almonds) = 2 cups of peanuts for every cup of almonds

Second question- 6(peanuts) / 2(cranberries) = 3 cups of peanuts for every cup of cranberries

Answer:

2 cups

Step-by-step explanation:

6 divided by 3 is 2 and secondly 6 divided by 2 is 3

Hope this helps you

Answer:

Step-by-step explanation:

J (-1,4)​  ⇒      x₁ = -1 & y₁ = 4

K(5,-3)​  ⇒      x₂ = 5  ; y₂ = -3

m : n = 1/3 : 2/3 = 1 :2

[tex]X \left(\dfrac{mx_{2}+nx_{1}}{m+n},\dfrac{my_{2}+ny_{1}}{m+n} \right)\\\\\\X \left(\dfrac{1*5+2*(-1)}{1+2},\dfrac{1*(-3)+2*4}{1+2} \right) \\\\\\X \left(\dfrac{5-2}{3},\dfrac{-3+8}{3} \right)\\\\\\X \left(\dfrac{3}{3},\dfrac{5}{3} \right)\\\\\\X \left( 1 , \dfrac{5}{3} \right)[/tex]

Answer:

P(blk sk AND gy shr)=P(blk sk)*P(gy shr)=7 /578

P(gy shr)=2/34

P(blk sk)=7/34

blk=Black

sk=Sock

gy=Grey

shr=Shirt