1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Lostsunrise [7]
3 years ago
12

A piggy bank contains $5.45 in dimes and quarters. If the bank contains 29 coins, how many quarters are in the bank?

Mathematics
2 answers:
soldier1979 [14.2K]3 years ago
6 0
.1x + .25y = 5.45
x + y = 29

Multiply the second equation by -.1
 .1x + .25y = 5.45
-.1x - .1y  = -2.9  Now add the equations together, the x's will cancel.
------------------------
       .15y  = 2.55  Divide both sides by .15
         y = 17
29 - 17 = 12
12 dimes and 17 quarters

CHECK
12 * .1 + 17*.25 = $5.45
fredd [130]3 years ago
5 0
There are 12 dimes in there
 and 17 quaters
You might be interested in
For each of the following vector fields F , decide whether it is conservative or not by computing curl F . Type in a potential f
Phantasy [73]

The key idea is that, if a vector field is conservative, then it has curl 0. Equivalently, if the curl is not 0, then the field is not conservative. But if we find that the curl is 0, that on its own doesn't mean the field is conservative.

1.

\mathrm{curl}\vec F=\dfrac{\partial(5x+10y)}{\partial x}-\dfrac{\partial(-6x+5y)}{\partial y}=5-5=0

We want to find f such that \nabla f=\vec F. This means

\dfrac{\partial f}{\partial x}=-6x+5y\implies f(x,y)=-3x^2+5xy+g(y)

\dfrac{\partial f}{\partial y}=5x+10y=5x+\dfrac{\mathrm dg}{\mathrm dy}\implies\dfrac{\mathrm dg}{\mathrm dy}=10y\implies g(y)=5y^2+C

\implies\boxed{f(x,y)=-3x^2+5xy+5y^2+C}

so \vec F is conservative.

2.

\mathrm{curl}\vec F=\left(\dfrac{\partial(-2y)}{\partial z}-\dfrac{\partial(1)}{\partial y}\right)\vec\imath+\left(\dfrac{\partial(-3x)}{\partial z}-\dfrac{\partial(1)}{\partial z}\right)\vec\jmath+\left(\dfrac{\partial(-2y)}{\partial x}-\dfrac{\partial(-3x)}{\partial y}\right)\vec k=\vec0

Then

\dfrac{\partial f}{\partial x}=-3x\implies f(x,y,z)=-\dfrac32x^2+g(y,z)

\dfrac{\partial f}{\partial y}=-2y=\dfrac{\partial g}{\partial y}\implies g(y,z)=-y^2+h(y)

\dfrac{\partial f}{\partial z}=1=\dfrac{\mathrm dh}{\mathrm dz}\implies h(z)=z+C

\implies\boxed{f(x,y,z)=-\dfrac32x^2-y^2+z+C}

so \vec F is conservative.

3.

\mathrm{curl}\vec F=\dfrac{\partial(10y-3x\cos y)}{\partial x}-\dfrac{\partial(-\sin y)}{\partial y}=-3\cos y+\cos y=-2\cos y\neq0

so \vec F is not conservative.

4.

\mathrm{curl}\vec F=\left(\dfrac{\partial(5y^2)}{\partial z}-\dfrac{\partial(5z^2)}{\partial y}\right)\vec\imath+\left(\dfrac{\partial(-3x^2)}{\partial z}-\dfrac{\partial(5z^2)}{\partial x}\right)\vec\jmath+\left(\dfrac{\partial(5y^2)}{\partial x}-\dfrac{\partial(-3x^2)}{\partial y}\right)\vec k=\vec0

Then

\dfrac{\partial f}{\partial x}=-3x^2\implies f(x,y,z)=-x^3+g(y,z)

\dfrac{\partial f}{\partial y}=5y^2=\dfrac{\partial g}{\partial y}\implies g(y,z)=\dfrac53y^3+h(z)

\dfrac{\partial f}{\partial z}=5z^2=\dfrac{\mathrm dh}{\mathrm dz}\implies h(z)=\dfrac53z^3+C

\implies\boxed{f(x,y,z)=-x^3+\dfrac53y^3+\dfrac53z^3+C}

so \vec F is conservative.

4 0
3 years ago
The dimensions of a rectangular prism are shown below:
GuDViN [60]

Answer:

...........

Step-by-step explanation:

...........

5 0
2 years ago
Read 2 more answers
What is 4 divided by 888
const2013 [10]

Answer:

0.0045045045

Step-by-step explanation:

Have a good day I hope this helps! :)

3 0
2 years ago
Work out the value of x when <br> 2^30 / 8^9 =2^x
vesna_86 [32]
X=3 lollllllllllllllll
6 0
2 years ago
a set of angles has a ratio of 5:2 if the larger angle measures 105 degrees then what is the measure of the smaller angle?
Sphinxa [80]
42 degrees. Divide 105 by 5 and get 21 and then multiply it by 2.
7 0
3 years ago
Read 2 more answers
Other questions:
  • The flag of a country contains an isosceles triangle.​ (Recall that an isosceles triangle contains two angles with the same​ mea
    9·1 answer
  • Multiply or divide as indicated. p^8 • p^-3 • p^2
    15·1 answer
  • Simplify the following expression.
    9·2 answers
  • Find the value of y. Express in simplest radical form.
    5·1 answer
  • How do I get a common denominator
    7·1 answer
  • 50 POINTS!! Please help!!! In the bold portion of the narrative, the author tries to use a flashback to develop tension. However
    13·1 answer
  • I need help with this did I get this right
    13·1 answer
  • (10 POINTS) Rectangle ABCD is dilated with center at (0, 0) and scale factor 2. Select the three statements that are true about
    14·1 answer
  • Given: a=b+2c, b=3c. What is the average of numbers a, b and c?
    9·1 answer
  • Ab + 2b²<br> where<br> a = 7 b=4
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!