Missing lenght on the right side. solve for c. 8", 6" =c

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

GEO, TRIGONOMETRY! 45 POINTS AND BRAINLIEST FOR CORRECT ANSWER. NEED HELP ASAP PLEASE :) Isabell is standing at the top of a wat

IRINA_888 [86]

Answer:

h ≈ 39 ft

Step-by-step explanation:

When we draw out a picture, we should see that we have to use cos∅ to solve this:

cos31.66° = x/46

46cos31.66° = x

x = 39.1542

5 0

3 years ago

Simplify these fraction 9 1/3-5 3/4

poizon [28]

Answer : 3 7/12

Hope it helps yah (◕ᴗ◕✿)

8 0

3 years ago

Read 2 more answers

Two times the sum of a number and three is not equal to eight

jarptica [38.1K]

Could be the sum is 1 and then 2 times 2 which equals 4 then 5 then plus 3 it is 8 so wrong

8 0

3 years ago

Please help .... Jeff is traveling from Atlanta to Columbia and then to Charleston. He decides to plot the cities on a coordinat

Crazy boy [7]

Answer:

The answer is C

Step-by-step explanation:

Use the Pythagoras theorem which states that a2 = b2 + c 2

For easier understanding imagine a straight line along the x axis. At (0,0) we have Atlanta. Moving 21 units to our right we have Columbia. This is represented on the coordinate system by (21, 0). To go from Colombia to Charleston, which is located at (24, -11), we need to travel 3 units right along the x- axis to reach ‘24’ and ‘11’ units down along the y- axis to reach (24, -11). Starting from Colombia we can make an imaginary triangle with its perpendicular being the y- component and its base being the x- component, which as we have stated above is ‘-11’ and ‘3’ respectively

Now applying the Pythagoras theorem to calculate the hypothesis and hence the distance between Colombia and Charleston.

a, which represents the distance between Colombia and Charleston would be

a² = b² + c²

a² = (3)² + (-11)²

a = √[(3)² + (-11)²]

Hence the answer is C

5 0

3 years ago