Consider points a, b, and c in the graph. Which point is the global maximum? Question 6 options: A) b B) c C) None of these D)

A cash box contains $74 made up of quarters, half-dollars, and one-dollar

Strike441 [17]

Answer:

25 one-dollar coins, 16 half-dollar coins, and 164 quarters

Step-by-step explanation:

First, set up equations based on the information given:

$0.25q+0.50h+1.00d=74$

$\displaystyle{h=\frac{3}{5}d+1}$

$q=4(d+h)$

Then, substitute q in the first equation with the expression from the third equation:

$0.25[4(d+h)]+0.50h+1.00d=74\\1d+1h+0.50h+1.00d=74\\2d+1.5h=74$

Next, substitute h in that equation with the expression from the second equation:

$\displaystyle{2d+1.5(\frac{3}{5}d+1)=74}$

$2d+0.9d+1.5=74\\2.9d+1.5=74$

Solve for d, the number of one-dollar coins:

$2.9d+1.5=74\\2.9d=72.5\\d=25$

Substitute 25 for d in the second equation to find h, the number of half-dollar coins:

$\displaystyle{h=\frac{3}{5}d+1}$

$\displaystyle{h=\frac{3}{5}(25)+1}$

$h=15+1\\h=16$

Substitute 25 for d and 16 for h in the third equation to find q, the number of quarters:

$q=4(d+h)\\q=4(25+16)\\q=4(41)\\q=164$

Then, verify that the coins total $74:

$0.25(164)+0.50(16)+1.00(25)=74\\41+8+25=74\\74=74\\\text{Check.}$

Next, verify that the number of half-dollar coins is one more than three-fifths of the number of one-dollar coins:

$\displaystyle{h=\frac{3}{5}d+1}$

$\displaystyle{16=\frac{3}{5}(25)+1}$

$16 = 15 + 1\\16 = 16\\\text{Check.}$

Finally, verify that the number of quarters is four times the number one-dollar and half-dollar coins together:

$q=4(d+h)\\164=4(25+16)\\164=4(41)\\164=164\\\text{Check.}$

6 0

3 years ago

If the perimeter of a square is 68 feet, find the approximate length of its diagonal.A. 17 feet B. 24 feet C. 38 feet D.

Elanso [62]

Find the side length:

Side = 68/4 = 17

Now use Pythagorean theorem:

Diagonal = sqrt(17^2 + 17^2)

Diagonal = sqrt(289 + 289)

Diagonal = sqrt(578)

Diagonal = 24 feet

The answer is B. 24 feet

8 0

2 years ago

PLEASE HELP, ILL GIVE MANY POINTS AND BRAINLIEST ANSWER TOTHE FASTEST ONE

spin [16.1K]

Answer:

WHATS THE QUESTION

Step-by-step explanation:

???rrtrttt r the r

7 0

2 years ago

What’s the distributive property of 17 x 8

Kamila [148]

Answer:

Step-by-step explanation:

Remember simple multiplication? Write the problem with 17 at the bottom:

8

* 1 7

----------

5 6 <-- this is 8*7

8 0 <-- this is 8*10 [we sometimes just shift and don't write the 0]

-------

1 3 6

So, 8*17 is the same as 8*10 + 8*7.

3 0

3 years ago

Read 2 more answers

Simplify the numerical expression. 125.7 - (-1.82).

sergey [27]

125.7 - ( - 1.82 )
125.7 + 1.82
127.52

6 0

3 years ago