Look at the table representing the growth of the circumference of a tree, and then complete the sentences.

A collection of 20 coins made up of only nickels, dimes, and quarters has a total value of $3.35. If the dimes were nickels, the

Kay [80]

Answer: The required number of quarters in the collection is 11.

Step-by-step explanation: Given that a collection of 20 coins made up of only nickels, dimes and quarters has a total value of $3.35.

If the dimes were nickels, the nickels were quarters and the quarters were dimes, the collection of coins would have a total value of $2.75.

We are to find the number of quarters in the collection.

Let x, y and z represents the number of nickels, dimes and quarters respectively in the collection.

We will be using the following values of nickels, dimes and quarters in form of dollar :

1 nickel = $ 0.05, 1 dime = $ 0.10 and 1 quarter = $0.25.

Then, according to the given information, we have

$x+y+z=20\\\\\Rightarrow x=20-y-z~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\0.05x+0.10y+0.25z=3.35\\\\\Rightarrow 5x+10y+25z=335\\\\\Rightarrow x+2y+5z=67~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)\\\\0.05y+0.25x+0.10z=2.75\\\\\Rightarrow 5y+25x+10z=275\\\\\Rightarrow y+2z+5x=55~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iii)$

Substituting the value of x from equation (i) in equations (ii) and (iii), we have

$(20-y-z)+2y+5z=67\\\\\Rightarrow y+4z=47\\\\\Rightarrow y=47-4z~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iv)$

and

$y+2z+5(20-y-z)=55\\\\\Rightarrow -4y-3z=-45\\\\\Rightarrow y=\dfrac{45-3z}{4}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(v)$

Comparing the values of y from equations (iv) and (v), we get

$47-4z=\dfrac{45-3z}{4}\\\\\Rightarrow 188-16z=45-3z\\\\\Rightarrow 16z-3z=188-45\\\\\Rightarrow 13z=143\\\\\Rightarrow z=\dfrac{143}{13}\\\\\Rightarrow z=11.$

Thus, the required number of quarters in the collection is 11.

7 0

2 years ago

What is the measure of angle P? Round only your final answer to the nearest hundredth.

Svetradugi [14.3K]

Answer:

i think its 130

Step-by-step explanation:

hope this helps? :|

5 0

3 years ago

Which is a stretch of an exponential decay function? f(x) = O f(x) = O Rx) = O f(x)=

zhannawk [14.2K]

B I think but I don’t know

7 0

2 years ago

Read 2 more answers

Solve the equation. And write all solutions in general form.

Amiraneli [1.4K]

Answer:

x = pi/2 + 2 pi n x = pi + 2 pi n where n is an integer

x = 5pi /3 + 2 pi n

Step-by-step explanation:

8 cos^2 x + 4 cos x-4 = 0

Divide by 4

2 cos^2 x + cos x-1 = 0

Let u = cos x

2 u^2 +u -1 =0

Factor

(2u -1) ( u+1) = 0

Using the zero product property

2u-1 =0 u+1 =0

u = 1/2 u = -1

Substitute cosx for u

cos x = 1/2 cos x = -1

Take the inverse cos on each side

cos ^-1(cos x) = cos ^-1(1/2) cos ^-1( cos x) =cos ^-1( -1)

x = pi/2 + 2 pi n x = pi + 2 pi n where n is an integer

x = 5pi /3 + 2 pi n

8 0

3 years ago

If D=20 miles when T=15 minutes, write a proportion to find D for T=20 minutes

Igoryamba

D/20=20/15

d=400/15

d=80/3

d=26 2/3 miles

8 0

2 years ago