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3 years ago

Ten times the sum of half a number and 6 is 8

1 answer:

5 0

Even though we don't know the number yet, we need to give it some kind of label
so that we can work with it. We can call it anything. I'd like to call it ' G '.

The number we're looking for is ' G '.

Half of it is 1/2 G

The sum of that and 6 is 1/2 G + 6

Ten times that is 10 (1/2 G + 6)

The question says that's 8.
So   10 (1/2 G + 6) = 8

Divide each side by 10 : 1/2 G + 6 = 0.8

Subtract 6 from each side: 1/2 G = - 5.2

Multiply each side by 2 : G = - 10.4

That seems like a weird answer. We should check it.

The number:    -10.4
Half the number:    - 5.2
The sum of half the number and 6: -5.2 + 6 = +0.8
Ten times that sum: 8

Yep ! By golly, sho nuff, dV-dT and E to the X !
Everything checks out, and the mystery number is - 10.4

You might be interested in

The owner of a stereo store wants to advertise that he has many different sound systems in stock. The store carries 6 different

Orlov [11]

Answer: 540

Step-by-step explanation:

Given : The owner of a stereo store wants to advertise that he has many different sound systems in stock.

Number of different CD players =6

Number of different receivers= 10

Number of different speakers = 9

We are assuming that a sound system consists of one of each .

Then by Fundamental principle of counting , we have

The number of different sound systems can he advertise = (Number of different CD players)x (Number of different receivers) x(Number of different speakers)

= 6 x10 x 9 =540

Hence, the number of different sound systems can he advertise =540

6 0

3 years ago

Which equation is y = –6x^2 + 3x + 2 rewritten in vertex form? y = negative 6 (x minus 1) squared + 8 y = negative 6 (x + one-fo

mart [117]

Answer:

$y = -6(x - \frac{1}{2})^2 -\frac{7}{2}$

Step-by-step explanation:

Given:

$y = -6x^2 + 3x + 2$

Required

Rewrite in vertex form

The vertex form of an equation is in form of: $y = a(x - h)^2+ k$

Solving: $y = -6x^2 + 3x + 2$

Subtract 2 from both sides

$y - 2 = -6x^2 + 3x + 2 - 2$

$y - 2 = -6x^2 + 3x$

Factorize expression on the right hand side by dividing through by the coefficient of x²

$y - 2 = -6(x^2 + \frac{3x}{-6})$

$y - 2 = -6(x^2 - \frac{3x}{6})$

$y - 2 = -6(x^2 - \frac{x}{2})$

Get a perfect square of coefficient of x; then add to both sides

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

Rough work

The coefficient of x is $\frac{-1}{2}$

It's square is $(\frac{-1}{2})^2 = \frac{1}{4}$

Adding inside the bracket of $-6(x^2 - \frac{x}{2})$ to give: $-6(x^2 - \frac{x}{2} + \frac{1}{4})$

To balance the equation, the same expression must be added to the other side of the equation;

Equivalent expression is: $-6(\frac{1}{4})$

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

The expression becomes

$y - 2 -6(\frac{1}{4})= -6(x^2 - \frac{x}{2} + \frac{1}{4})$

$y - 2 -\frac{6}{4}= -6(x^2 - \frac{x}{2} + \frac{1}{4})$

$y - 2 -\frac{3}{2}= -6(x^2 - \frac{x}{2} + \frac{1}{4})$

Factorize the expression on the right hand side

$y - 2 -\frac{3}{2}= -6(x - \frac{1}{2})^2$

$y - (2 +\frac{3}{2})= -6(x - \frac{1}{2})^2$

$y - (\frac{4+3}{2})= -6(x - \frac{1}{2})^2$

$y - (\frac{7}{2})= -6(x - \frac{1}{2})^2$

$y +\frac{7}{2} = -6(x - \frac{1}{2})^2$

Make y the subject of formula

$y = -6(x - \frac{1}{2})^2 -\frac{7}{2}$

Solved

7 0

4 years ago

Read 2 more answers

Each letter of the English alphabet is written on a scrap of paper and put in a hat p(j)= 1/26 what type of probability is illus

Marysya12 [62]

In the situation 'Each letter of the English alphabet is written on a scrap of paper and put in a hat p(j)= 1/26', the type of probability illustrated is classical or mathematical probability. This is because 1 represents the number of expected outcomes of the event while 26 represents the total number of outcomes.

8 0

4 years ago

Read 2 more answers

(10 POINTS) answer ASAP if you can

erma4kov [3.2K]

Answer:

Step-by-step explanation:

Because it's 340 meters per second

5 0

3 years ago

Select all the true statements.

Temka [501]

Answer:

-2+2=0

4+-4=0

are true statement

6 0

3 years ago