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marin [14]
3 years ago
9

A collection of 30 coins worth $5.50 consists of nickels, dimes and quarters. There are twice as many dimes as nickels. How many

quarters are there?
Mathematics
1 answer:
MAVERICK [17]3 years ago
4 0
<span>Let N equal the number of nickels.
Let D equal the number of dimes.
Let Q equal the number of quarters.

We know that .05N + .10D + .25Q = 5.50.
We also know that N + D + Q = 30.
We also know that D = 2N.

Therefore, Q = 30 - (N + D) = 30 - (N + 2N) = 30 - 3N

So...

5.50 = .05N + .10(2N) + .25(30 - 3N)
= .05N + .20N + 7.50 - .75N

Therefore (moving all N's to the left of the equals sing, and all constants to the right of the equals sign)...

.5N = 2.

Therefore, N = 4. There are four nickels, eight dimes, and 18 quarters.

Checking our work...
Four nickels is 0.20.
Eight dimes is 0.80.
18 quarters is 4.50.

That sums to 5.50, and is 30 coins.</span>
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Find the local maximum and minimum values and saddle point(s) of the function. If you have three-dimensional graphing software,
vichka [17]

Answer:

A(-1,0) is a local maximum point.

B(-1,0)  is a saddle point

C(3,0)  is a saddle point

D(3,2) is a local minimum point.

Step-by-step explanation:

The given function is  

f(x,y)=x^3+y^3-3x^2-3y^2-9x

The first partial derivative with respect to x is  

f_x=3x^2-6x-9

The first partial derivative with respect to y is  

f_y=3y^2-6y

We now set each equation to zero to obtain the system of equations;

3x^2-6x-9=0

3y^2-6y=0

Solving the two equations simultaneously, gives;

x=-1,x=3  and y=0,y=2

The critical points are

A(-1,0), B(-1,2),C(3,0),and D(3,2).

Now, we need to calculate the discriminant,

D=f_{xx}(x,y)f_{yy}(x,y)-(f_{xy}(x,y))^2

But, we would have to calculate the second partial derivatives first.

f_{xx}=6x-6

f_{yy}=6y-6

f_{xy}=0

\Rightarrow D=(6x-6)(6y-6)-0^2

\Rightarrow D=(6x-6)(6y-6)

At A(-1,0),

D=(6(-1)-6)(6(0)-6)=72\:>\:0 and f_{xx}=6(-1)-6=-18\:

Hence A(-1,0) is a local maximum point.

See graph

At B(-1,2);

D=(6(-1)-6)(6(2)-6)=-72\:

Hence, B(-1,0) is neither a local maximum or a local minimum point.

This is a saddle point.

At C(3,0)

D=(6(3)-6)(6(0)-6)=-72\:

Hence, C(3,0) is neither a local minimum or maximum point. It is a saddle point.

At D(3,2),

D=(6(3)-6)(6(2)-6)=72\:>\:0 and f_{xx}=6(3)-6=12\:>\:0

Hence D(3,2) is a local minimum point.

See graph in attachment.

3 0
3 years ago
Janine has job offers at two companies. one company offers a starting salary of $28,000 with a raise of $3000 each year . the ot
ollegr [7]
After nine years the salaries will be the same
28000   3600031000   3800034000   4000037000   4200040000   4400043000   4600046000   4800049000   5000052000   52000
7 0
3 years ago
HELP ASAP!!!!!!
WARRIOR [948]

Answer:

x=26

C = 91

Step-by-step explanation:

The sum of the angles of a triangle add to 180 degrees

A + B+ C = 180

35+ 52+ 3(x+5) = 180

Distribute

35+52+3x+15 = 180

Combine like terms

102 +3x = 180

Subtract 102 from each side

102-102 +3x=180-102

3x= 78

Divide by 3

3x/3 = 78/3

x=26

Now we need to find angle C

c = 3(x+5)

C = 3(26+5)

     3(31)

     93

6 0
3 years ago
9. Rusty can ride his bicycle 21 miles in 3 hours. Find the unit rate of the
pashok25 [27]

Rate = distance / time

Rate = 21 miles / 3 hours

Rate = 7 miles / hour

The answer is choice A. Hope this helps.

6 0
3 years ago
96=-8k solve <br> Show work
larisa86 [58]

Answer:

k = -12

Step-by-step explanation:

<u>Step 1:  Divide both sides by -8</u>

<u />96 / -8 = -8k / -8

-12 = k

Answer: k = -12

3 0
3 years ago
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