What is the value of z in the equation 4(2z + 3) = 12?<br><br> −13<br> 12<br> 0<br> 12

The sum of a number, 1/6 of that number, 2 1/2 of that number, and 7 is 12 1/2. Find the number.

Tema [17]

Answer:

2 $\frac{1}{16}$

Step-by-step explanation:

The question state that; the sum of a number, 1/6 of that number, 2 1/2 of that number, and 7 is 12 1/2. Find the number.

First, we need to interpret and represent this statement mathematically

Let n be the number.

The sum means 'addition'

1/6 of that number is 1/6 of n = 1/6 × n = $\frac{n}{6}$

2 1/2 of that number is 2 1/2 of n = 2 1/2 × n = 5/2 × n = $\frac{5n}{2}$

So the question says that, when we add; $\frac{n}{6}$ , $\frac{5n}{2}$ and 7 all together, the value is 12 1/2

That is;

$\frac{n}{6}$ + $\frac{5n}{2}$ + 7 = 12 1/2

$\frac{n}{6}$ + $\frac{5n}{2}$ + 7 = $\frac{25}{2}$ ( changing 12 1/2 to improper fraction will give $\frac{25}{2}$ )

So we can now go ahead and solve for n

$\frac{n}{6}$ + $\frac{5n}{2}$ + 7 = $\frac{25}{2}$

subtract 7 from both-side of the equation

$\frac{n}{6}$ + $\frac{5n}{2}$ = $\frac{25}{2}$ - 7

$\frac{n + 15n}{6}$ = $\frac{25 -14}{2}$

$\frac{16n}{6}$ = $\frac{11}{2}$

$\frac{16n}{6}$ can be reduced to give us $\frac{8n}{3}$

$\frac{8n}{3}$ = $\frac{11}{2}$

Cross multiply

8n × 2 = 11× 3

16n = 33

Divide both-side of the equation by 16

$\frac{16n}{16}$ = $\frac{33}{16}$

(On the left-hand side of the equation, 16 will cancel-out 16 leaving us with just, while on the right-hand side of the equation 33 will be divided by 16)

n = $\frac{33}{16}$ = $2\frac{1}{16}$

Therefore the number is $2\frac{1}{16}$

5 0

3 years ago

8x – 65 = - x2<br> [pease help me

Leya [2.2K]

Answer: x=5 or x=−13

Step-by-step explanation:

8x−65=−x2

8x−65−(−x2)=−x2−(−x2)

x2+8x−65=0

(x−5)(x+13)=0

x−5=0 or x+13=0

x=5 or x=−13

4 0

3 years ago

|3x-7|-7=x solve the equation for all values of x

romanna [79]

The solutions to the given equation containing absolute value term |3x-7| - 7 = x are 0 and 7.

<h3>What are the solutions to the given equation?</h3>

Given the equation in question;

|3x-7| - 7 = x

First, add 7 to both sides.

|3x-7| - 7 + 7 = x + 7

|3x-7| = x + 7

Next, remove the absolute value term, this creates a ± on the right side of the question.

|3x-7| = x + 7

3x-7 = ±( x + 7 )

The complete solution is the result of both the negative and positive portions of the solution.

For the first solution, use the positive of ±.

3x-7 = ( x + 7 )

3x - 7 = x + 7

3x - x = 7 + 7

2x = 14

x - 14/2

x = 7

For the second solution, use the negative of ±.

3x-7 = -( x + 7 )

3x-7 = -x - 7

3x + x = -7 + 7

4x = 0

x = 0/4

x = 0

Therefore, the solutions to the given equation containing absolute value term |3x-7| - 7 = x are 0 and 7.

Learn to solve more equation involving absolute value term here: brainly.com/question/28635030

#SPJ1

4 0

1 year ago

Help! Me solve this problem please

snow_tiger [21]

Answer: 2 1/4

Step-by-step explanation:

5 0

2 years ago

The population of the world in 1987 was 5 billion and the annual growth rate was estimated at 2 percent per year. Assuming that

Vinvika [58]

Answer:

Population in 1998 year = 6.22 billion

Step-by-step explanation:

Given:-

- The population in year 1987, Po = 5 billion

- Growth rate, r = 2%

- World population follows an exponential growth model

Find:-

The projected world population in 1998.

Solution:-

- The exponential growth model is mathematically expressed as:

Population in x year = Po* ( 1 + r/100)^( x - xo )

Where, xo: The base year.

- Plug in the values and solve for the projected population in year 1998:

Population in 1998 year = 5,000,000,000* ( 1 + 2/100)^( 1998 - 1987 )

Population in 1998 year = 5,000,000,000* ( 1 + 0.02)^( 11 )

= 5,000,000,000* ( 1.02 )^( 11 )

= 6.22 billion

8 0

3 years ago

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What is the value of z in the equation 4(2z + 3) = 12? −13 12 0 12