What does x equal in x+4=2x-3

Flauer [41]

2272in^3 because volume is always measured in ^3

6 0

3 years ago

Four darts are thrown at this dartboard. If all four darts hit the board, how many different point totals are possible. (Dartboa

jonny [76]

Answer:

Different point total are possible = 497

Step-by-step explanation:

Given - Four darts are thrown at this dartboard. Dartboard regions are

1, 4, 7, 10 points

To find - If all four darts hit the board, how many different point totals are

possible.

Proof -

Are given there are 4 regions -

1st region - 1 point

2nd region - 4 points

3rd region - 7 points

4th region - 10 points

Case I :

If all the darts hit the different region -

Total points possible are - 1 + 4 + 7 + 10 = 22 points

Case II :

If all the darts hit the same region -

It means either they hit 1 region or 2nd region or 3rd region or 4th region

If they all 4 hit first region , points are - 1+1+1+1 = 4

If they all 4 hit second region , points are - 4+4+4+4= 16

If they all 4 hit third region , points are - 7+7+7+7 = 28

If they all 4 hit fourth region , points are - 10+10+10+10 = 40

So,

the Total points possible are - 4 + 16 + 28 + 40 = 88

Case III :

If 3 darts hit the same region -

Sub-case 1 :

If 1 dart hit 1st region, other 3 dart hit 2nd region

Points are - 1 + 4 + 4+ 4 = 13

Sub-case 2 :

If 1 dart hit 1st region , other 3 dart hit 3rd region

Points are - 1 + 7 + 7 + 7 = 22

Sub-case 3 :

If 1 dart hit 1st region , other 3 dart hit 4th region

Points are - 1 + 10 + 10 + 10 = 31

Sub-case 4 :

If 1 dart hit 2nd region , other 3 dart hit 1st region

Points are - 4 + 1 + 1 + 1 = 7

Sub-case 5 :

If 1 dart hit 2nd region , other 3 dart hit 3rd region

Points are - 4 + 7 + 7 + 7 = 25

Sub-case 6 :

If 1 dart hit 2nd region , other 3 dart hit 4th region

Points are - 4 + 10 + 10 + 10 = 34

Sub-case 7 :

If 1 dart hit 3rd region , other 3 dart hit 1st region

Points are - 7 + 1 + 1 + 1 = 10

Sub-case 8 :

If 1 dart hit 3rd region , other 3 dart hit 2nd region

Points are - 7 + 4 + 4 + 4 = 19

Sub-case 9 :

If 1 dart hit 3rd region , other 3 dart hit 4th region

Points are - 7 + 10 + 10 + 10 = 37

Sub-case 10 :

If 1 dart hit 4th region , other 3 dart hit 1st region

Points are - 10 + 1 + 1 + 1 = 13

Sub-case 11 :

If 1 dart hit 4th region , other 3 dart hit 2nd region

Points are - 10 + 4 + 4 + 4 = 22

Sub-case 12 :

If 1 dart hit 4th region , other 3 dart hit 3rd region

Points are - 10 + 7 + 7 + 7 = 31

So,

Total points possible are - 13+22+21+7+25+34+10+19+37+13+22+31 = 254

Case IV :

If 2 darts hit the same region -

Sub-case 1:

If 2 darts hits 1st region , other 2 darts hit 2nd region

Points are - 1 + 1 + 4 + 4 = 10

Sub-case 2:

If 2 darts hits 1st region , other 2 darts hit 3rd region

Points are - 1 + 1 + 7 + 7 = 16

Sub-case 3:

If 2 darts hits 1st region , other 2 darts hit 4th region

Points are - 1 + 1 + 10 + 10 = 23

Sub-case 4:

If 2 darts hits 2nd region , other 2 darts hit 3rd region

Points are - 4 + 4 + 7 + 7 = 22

Sub-case 5:

If 2 darts hits 2nd region , other 2 darts hit 4th region

Points are - 4 + 4 + 10 + 10 = 28

Sub-case 6:

If 2 darts hits 3rd region , other 2 darts hit 4th region

Points are - 7 + 7 + 10 + 10 = 34

So,

Total points possible are - 10 + 16 + 23 + 22 + 28 + 34 = 133

Case V :

If 1 darts hit the same region -

This case is include in the Case III.

∴ we get

Different point total are possible = Points in Case I + II + III + IV

= 22 + 88 + 254 + 133

= 497

⇒Different point total are possible = 497

4 0

3 years ago

An aeroplane flies 1860 miles in 4 hours. What is its average speed?

nexus9112 [7]

Answer:

The average speed is 465 mph

Step-by-step explanation:

1860/4 = 465

6 0

3 years ago

Read 2 more answers

6.7.37

posledela

Answer:

a. The start-up cost for the teenagers company is $50

b. The number of mugs the teenager must sell to break even are 5 mugs or 25 mugs

c. The number of mugs that will give maximum profit is 15 mugs

d. The profit if she sells 10 mugs is $30

Step-by-step explanation:

The given profit function for selling <em>x</em> number of mugs is presented as follows;

f(x) = -0.4·x² + 12·x - 50

a. The start-up cost in dollars is given by the value of the profit function at the start, where, x = 0, as follows;

Start-up cost = f(0) = -0.4×0² + 12×0 - 50 = -50

The negative sign represents amount put in the business

The start-up cost = (The initial) $50 put into the business.

b. The break even point is the point where, the revenue and costs are equal

At break even point; Revenue = Cost

∴ Profit, at break even point, f(x) = Revenue - Cost = 0

From the profit function, we get;

At the break even point, f(x) = 0 = -0.4·x² + 12·x - 50

Dividing by -0.4 gives;

0/(-0.4) = 0 = (-0.4·x² + 12·x - 50)/(-0.4) = x² - 30 + 125

0 = x² - 30 + 125

∴ (x - 25)·(x - 5) = 0

The number of mugs the teenager must sell before she breaks even, x = 5 mugs or x = 25 mugs.

c. From the general form of a quadratic equation, which is; y = a··x² + b·x + c, the formula for the x-values at the maximum point is; x = -b/(2·a)

Comparing the profit function to the general form of the quadratic equation we have at the maximum point;

x = -12/(2×(-0.4)) = 15

Therefore, the number of mugs that will give maximum profit, x = 15 mugs.

d. The profit from selling 10 mugs, f(10) is given as follows;

f(10) = -0.4 × 10² + 12 × 10 - 50 = 30

The profit from selling 10 mugs, f(10) = $30

4 0

3 years ago

Find all zeros and write the answers in factored form<br> (x-5)(3x^2-8x+6) =0

katen-ka-za [31]

Answer:

x-5=0

x=5

3x2-8x+6=0

d= 64 - 4*3*6= -8

=>

x≠R

answer: only x=5

3 0

3 years ago