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2 years ago

What is the answer to the question

Mathematics

1 answer:

Crazy boy [7]2 years ago

8 0

(42 - 14sqrt2)/5 because rationalizing means getting the root out of the denominator, which is done by multiplying the denominator by a negative or positive root depending on the situation

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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

Which variable has the most impact on growing your money? If you could increase one of the variables in the compound interest fo

postnew [5]

Answer:

I would increase the number and multiply

Step-by-step explanation:

3 0

2 years ago

You are designing a metal sculpture that will be placed in front of your school. You sketch an initial design

choli [55]

Answer:

8 feet

Step-by-step explanation:

the length still remains the same regardless of the scale

4 0

3 years ago

How do you graph y = 2/3x ?

JulsSmile [24]

Answer:

(3,4)

Step-by-step explanation:

Start at the point (1,1) then Rise 2, and go to the right 3 which will give you the point (3, 4)

6 0

3 years ago

Is this set of numbers a Pythagorean triple? yes or no

Kaylis [27]

Answer:- No.

Explanation :-

Substitute these numbers in pythagoras theorem to check if the set of numbers is a pythagorean triplet.

Pythagoras theorem :- sq. of hypotenuse (longest side) is equal to the sum of sq.s of other two sides.

Here,

hypotenuse = 12 (as it is the longest side)

and other two sides are 6 and 9.

----> 6^2 + 9^2 = 12^2

----> 36 + 81 = 144

----> 117 = 144

Since, LHS is not equal to RHS, this set of numbers is not a pythagorean triplet.

8 0

3 years ago