Ask question

Ask question

All categories

3 years ago

10

Mark has twice as many quarters as nickels and three more dimes than nickels. He has 4.20 in all. How many of each type of coin

does he have?

1 answer:

Firlakuza [10]3 years ago

5 0

Answer:

Number of nickels = 6

number of dimes = 9

number of quarters =12

Step-by-step explanation:

Let 'q' be the number of quarters and 'n' be the number of nickels

and 'd' be the number of dimes

twice as many quarters as nickels

$q=2n$

three more dimes than nickels.

$d=3+n$

1 nickel = 5 cents

1 dime = 10 cents

1 quarter = 25 cents

4.20 dollars = 420 cents

$5n+10d+25q=420$

replace q and d in the above equation

$5n+10(3+n)+25(2n)=420$

$5n+30+10n+50n=420$

$65n+30=420$

Subtract 30 from both sides

$65n=390$

divide both sides by 65

n=6

Number of nickels = 6

number of dimes = $3+n=3+6=9$

number of quarters = $2n=2(6)= 12$

You might be interested in

What is the solution to the equation 6y –2(y + 1) = 3(y – 2) + 6?

AleksAgata [21]

Answer: y=2

Step-by-step explanation:

Distribute the numbers -2 and 3...

6y-2y-2=3y-6+6

The -6 and 6 cancel each other out...

6y-2y-2=3y

Combine like terms....

4y-2=3y

Move 4y over....

-2=-y

Multiply both sides by -1.....

2=y

That’s your solution! Hope this helps!

8 0

4 years ago

b) y= 5/x What happens to the value of y if the value of x triples? Select your answer. A. x2 B. x3 C. /2 D. /3

jeyben [28]

Answer:

D.)

Step-by-step explanation:

y = 5/x

so when the value of x triples, the new X becomes;

X = 3x

So,

Y = 5/ X

=> Y = 5/3x

=> Y = 1/3 . 5/x

=> Y = 1/3 . y

so the new value of y ( Y ) is 1/3 times original y.

Hence, D. is the answer

3 0

3 years ago

Which polynomial function has a leading coefficient of3 and roots -4, i, and 2, all with multiplicity 1?

andreyandreev [35.5K]

Answer:

Step-by-step explanation:

f(x) = 3(x + 4)(x – i)(x + i)(x – 2)

7 0

3 years ago

Find , , and if and terminates in quadrant .

ioda

sin2x =12/13

cos2x = 5/13

tan2x = 12/5

STEP - BY - STEP EXPLANATION

What to find?

• sin2x

,

• cos2x

,

• tan2x

Given:

tanx = 2/3 = opposite / adjacent

We need to first make a sketch of the given problem.

Let h be the hypotenuse.

We need to find sinx and cos x, but to find sinx and cosx, first determine the value of h.

Using the Pythagoras theorem;

hypotenuse² = opposite² + adjacent²

h² = 2² + 3²

h² = 4 + 9

h² =13

Take the square root of both-side of the equation.

h =√13

This implies that hypotenuse = √13

We can now proceed to find the values of ainx and cosx.

Using the trigonometric ratio;

$\sin x=\frac{opposite}{\text{hypotenuse}}=\frac{2}{\sqrt[]{13}}$ $\cos x=\frac{adjacent}{\text{hypotenuse}}=\frac{3}{\sqrt[]{13}}$

And we know that tanx =2/3

From the trigonometric identity;

sin 2x = 2sinxcosx

Substitute the value of sinx , cosx and then simplify.

$\sin 2x=2(\frac{2}{\sqrt[]{13}})(\frac{3}{\sqrt[]{13}})$ $=\frac{12}{13}$

Hence, sin2x = 12/13

cos2x = cos²x - sin²x

Substitute the value of cosx, sinx and simplify.

$\begin{gathered} \cos 2x=(\frac{3}{\sqrt[]{13}})^2-(\frac{2}{\sqrt[]{13}})^2 \\ \\ =\frac{9}{13}-\frac{4}{13} \\ =\frac{5}{13} \end{gathered}$

Hence, cos2x = 5/13

tan2x = 2tanx / 1- tan²x

$\tan 2x=\frac{2\tan x}{1-\tan ^2x}$ $=\frac{2(\frac{2}{3})}{1-(\frac{2}{3})^2}$ $=\frac{\frac{4}{3}}{1-\frac{4}{9}}$ $=\frac{\frac{4}{3}}{\frac{9-4}{9}}$ $=\frac{\frac{4}{3}}{\frac{5}{9}}$ $=\frac{4}{3}\times\frac{9}{5}=\frac{4}{1}\times\frac{3}{5}=\frac{12}{5}$

OR

$\tan 2x=\frac{\sin 2x}{\cos 2x}=\frac{\frac{12}{13}}{\frac{5}{13}}=\frac{12}{5}$

Hence, tan2x = 12/5

Therefore,

sin2x =12/13

cos2x = 5/13

tan2x = 12/5

3 0

1 year ago

For each fraction, write the equivalent percent. a. 6/100 b. 57/100 c. 357/100 d. 100/100

ddd [48]

Answer:

(A) 6%

(B) 57%

(C) 357%

(D) 100%

Step-by-step explanation:

(A) 6 / 100 = 6%

(B) 57 / 100 = 57%

(C) 357 / 100 = 357%

(D) 100 / 100 = 100%

5 0

4 years ago

Read 2 more answers