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Sladkaya [172]
3 years ago
5

Derrick has a total of 9 nickels and quarters in his pocket. The total amount of money he has in coins is $1.45. How many nickel

s and how many quarters does Derrick have? A. 3 nickels and 6 quarters B. 6 nickels and 3 quarters C. 4 nickels and 5 quarters D. 5 nickels and 4 quarters
Mathematics
2 answers:
Alexeev081 [22]3 years ago
7 0

Answer:

<u>Option C. 4 nickels and 5 quarters</u>

Step-by-step explanation:

let the number of nickels = x, and the number of quarters = y

Derrick has a total of 9 nickels and quarters in his pocket

So, x + y = 9

∴ y = 9 - x ⇒(1)

1 nickel = 5 cent = $0.05

1 quarter = 25 cent = $0.25

The total amount of money he has in coins is $1.45

So, 0.05 x + 0.25 y = 1.45

Multiply the both sides by 100

∴ 5x + 25y = 145 ⇒(2)

Substitute with y from (1) at (2)

∴ 5x + 25(9-x) = 145

Solve for x

5x + 225 - 25x = 145

-20x = 145 - 225 = -80

x = -80/-20 = 4

Substitute with x at (1)

y = 9 - 4 = 5

So, The number of nickels = 4 , and the number of quarters = 5

<u>The answer is option C. 4 nickels and 5 quarters</u>

zepelin [54]3 years ago
4 0

Answer: 4 nickels and 5 quarters

Step-by-step explanation:

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I'm confused on how to do this. Please explain step by step. If you respond with just the answer I WILL report you. I would like
Tcecarenko [31]

Answer:

Exact Form:

√2−1

Decimal Form:

0.41421356

…

Step-by-step explanation:

Since  9π/8  is not an angle where the values of the six trigonometric functions are known, try using half-angle identities.

9π/8  is not an exact angle

First, rewrite the angle as the product of  1/2  and an angle where the values of the six trigonometric functions are known. In this case,  9π/8  can be rewritten as

(1/2)*  9π/8 tan ((1/2)*  9π/8)

Use the half-angle identity for tangent to simplify the expression. The formula states that  

tan (0/2)=sin(0)/1+cos(0) sin(9π/4)/1+cos(9π/4)

Simplify

Remove full rotations of  2π  until the angle is between  0  and  2π.

sin(π/4)/1+cos(9π/4)

The exact value of sin(π/4) is √2/2

√2/2/1+cos(9π/4)

Simplify the Denominator

Remove full rotations of  2π  until the angle is between  0  and  2π.√2/2/1+cos(π4)

The exact value of cos(π/4)   is  √2/2.√2/2/1+√2/2

To write  1/1  as a fraction with a common denominator, multiply by  2/2  .√2/2/1/1⋅2/2+√2/2

Write each expression with a common denominator of  2, by multiplying each by an appropriate factor of  1.

Combine.

√2/2/1⋅2/1⋅2+√2/2

Multiply 2 by 1

√2/2/1⋅2/2+√2/2

Combine the numerators over the common denominator.

√2/2/1⋅2+√2/2

Multiply 2 by 1

√2/2/2+√2/2

Multiply the numerator by the reciprocal of the denominator

√2/2  ⋅  2/2+√2

Cancel the common factor of  2  .

Factor out the greatest common factor  2

√2/2⋅1  ⋅  2⋅1/2+√2

Cancel the common factor

√2/2⋅1  ⋅  2⋅1/2+√2

Rewrite the expression.

√2/1  ⋅  1/2+√2

Simplify

Multiply  √2/1  and  1/2+√2

√2/2+√2

Multiply  √2/2+√2  by  2−√2/2−√2

Combine

√2(2−√2)/(2+√2)(2−√2)

Expand the denominator using the FOIL method.

√2(2−√2)/4−2√2+√2⋅2−√2^2

Simplify

√2(2−√2)/2

Apply the distributive property

√2⋅2+√2(−√2)/2

Move  2  to the left of the expression  √2⋅2.

2⋅√2+√2(−√2)/2

Simplify  

√2(−√2)  .

Raise  √2  to the power of  1  .

2⋅√2−(√2^1√2)/2

Raise  √2  to the power of  1  .

2⋅√2−(√2^1√2^1)/2

Use the power rule  a^m  a^n=a^m+n  to combine exponents.

2⋅√2−√2^1+1/2

Add  1  and  1  .

2⋅√2−√2^2/2

Simplify each term.

Multiply  2  by  √2  .

2√2−√2^2/2

Rewrite  √2^2  as  2  .

2√2−1⋅2/2

Multiply  −1  by  2.

2√2−2/2

Reduce the expression by cancelling the common factors.

Factor  2  out of  2√2.

2(√2)−2/2

Factor  2  out of  −2.

2(√2)+2⋅−1/2

Factor  2  out of  

2(√2)+2(−1)2(√2−1)/2

Cancel the common factors.

Factor  2  out of  2  .

2(√2−1)/2(1)

Cancel the common factor.

2(√2−1)/2⋅1

Rewrite the expression.

√2−1/1

Divide  √2−1  by  1  .

√2−1

The result can be shown in multiple forms.

Exact Form:

√2−1

Decimal Form:

0.41421356…

Hope it help. Good luck.

4 0
3 years ago
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