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
Murljashka [212]
3 years ago
14

Patanna bought some red and blue bricks. She bought a total or 100 bricks. The red bricks cost $5 each and the blue bricks cost

$7 each. She spent a total of $560. How many red bricks and how many blue bricks did she buy?
Mathematics
1 answer:
klasskru [66]3 years ago
6 0

Let...

x=the number of red bricks

y=the number of blue bricks

Since she bought a total of 100 bricks... x+y=100.

Because the total cost is $560... 5x+7y=560.

Using these two equations, we can use the substitution method to solve for x and y.

x+y=100 ------------------------> x=100-y

        subtract y on both sides

Because x=100-y...

                                                                  this is x

5x+7y=560 (second equation) equals 5( 100 - y )+7y=560  

This equation we created has only one variable so we can solve it.

5(100-y)+7y=560

500-5y+7y=560

2y+500=560

2y=60

y=30 blue bricks

Because x=100-y... x=100-30=70 red bricks.

You might be interested in
Simplify fraction 40/85
Leona [35]
Divide both the numerator and denominator by 5 and you get 8/17. your answer is 8/17.
7 0
3 years ago
(X^2+y^2+x)dx+xydy=0<br> Solve for general solution
aksik [14]

Check if the equation is exact, which happens for ODEs of the form

M(x,y)\,\mathrm dx+N(x,y)\,\mathrm dy=0

if \frac{\partial M}{\partial y}=\frac{\partial N}{\partial x}.

We have

M(x,y)=x^2+y^2+x\implies\dfrac{\partial M}{\partial y}=2y

N(x,y)=xy\implies\dfrac{\partial N}{\partial x}=y

so the ODE is not quite exact, but we can find an integrating factor \mu(x,y) so that

\mu(x,y)M(x,y)\,\mathrm dx+\mu(x,y)N(x,y)\,\mathrm dy=0

<em>is</em> exact, which would require

\dfrac{\partial(\mu M)}{\partial y}=\dfrac{\partial(\mu N)}{\partial x}\implies \dfrac{\partial\mu}{\partial y}M+\mu\dfrac{\partial M}{\partial y}=\dfrac{\partial\mu}{\partial x}N+\mu\dfrac{\partial N}{\partial x}

\implies\mu\left(\dfrac{\partial N}{\partial x}-\dfrac{\partial M}{\partial y}\right)=M\dfrac{\partial\mu}{\partial y}-N\dfrac{\partial\mu}{\partial x}

Notice that

\dfrac{\partial N}{\partial x}-\dfrac{\partial M}{\partial y}=y-2y=-y

is independent of <em>x</em>, and dividing this by N(x,y)=xy gives an expression independent of <em>y</em>. If we assume \mu=\mu(x) is a function of <em>x</em> alone, then \frac{\partial\mu}{\partial y}=0, and the partial differential equation above gives

-\mu y=-xy\dfrac{\mathrm d\mu}{\mathrm dx}

which is separable and we can solve for \mu easily.

-\mu=-x\dfrac{\mathrm d\mu}{\mathrm dx}

\dfrac{\mathrm d\mu}\mu=\dfrac{\mathrm dx}x

\ln|\mu|=\ln|x|

\implies \mu=x

So, multiply the original ODE by <em>x</em> on both sides:

(x^3+xy^2+x^2)\,\mathrm dx+x^2y\,\mathrm dy=0

Now

\dfrac{\partial(x^3+xy^2+x^2)}{\partial y}=2xy

\dfrac{\partial(x^2y)}{\partial x}=2xy

so the modified ODE is exact.

Now we look for a solution of the form F(x,y)=C, with differential

\mathrm dF=\dfrac{\partial F}{\partial x}\,\mathrm dx+\dfrac{\partial F}{\partial y}\,\mathrm dy=0

The solution <em>F</em> satisfies

\dfrac{\partial F}{\partial x}=x^3+xy^2+x^2

\dfrac{\partial F}{\partial y}=x^2y

Integrating both sides of the first equation with respect to <em>x</em> gives

F(x,y)=\dfrac{x^4}4+\dfrac{x^2y^2}2+\dfrac{x^3}3+f(y)

Differentiating both sides with respect to <em>y</em> gives

\dfrac{\partial F}{\partial y}=x^2y+\dfrac{\mathrm df}{\mathrm dy}=x^2y

\implies\dfrac{\mathrm df}{\mathrm dy}=0\implies f(y)=C

So the solution to the ODE is

F(x,y)=C\iff \dfrac{x^4}4+\dfrac{x^2y^2}2+\dfrac{x^3}3+C=C

\implies\boxed{\dfrac{x^4}4+\dfrac{x^2y^2}2+\dfrac{x^3}3=C}

5 0
4 years ago
Prove: If a^2-a is even then a is even.
Alla [95]

This is not always true. Consider a=3. Then 3^2-3=9-3=6 is even, but a is odd.

6 0
3 years ago
-9p-17=10 pls help I do Connexus
marshall27 [118]
P would equal negative three.
7 0
3 years ago
A store owner puts in an order for product x and product y for a total of 4,000 units. it costs $0.10 per item to ship of produc
galben [10]

The system of equations can be used to determine how much of product x and product y the store owner bought is x + y = 4,000

0.10x + 0.04y = 352

<h3>Simultaneous equation</h3>

  • product x
  • Product y
  • Total units of x and y = 4,000 units
  • Cost of shipping each product x = $0.10
  • Cost of shipping each product y = $0.04
  • Total cost of shipping = $352

The equation:

x + y = 4,000

0.10x + 0.04y = 352

Therefore, the system of equations can be used to determine how much of product x and product y the store owner bought is x + y = 4,000

0.10x + 0.04y = 352

Learn more about simultaneous equation:

brainly.com/question/16863577

#SPJ4

6 0
2 years ago
Other questions:
  • Assume red and green are equally likely occurrences. Using Pascal’s triangle, what is the probability that you will get one gree
    8·1 answer
  • Is 17 0.02 irrational or rational
    7·1 answer
  • The square root of a product of two positive real numbers is the product of their square roots. Write an algebraic expression ba
    12·1 answer
  • If a certain roundabout has diameter of 96 feet,
    13·1 answer
  • Please proved explanation for answer.
    7·1 answer
  • What two properties of a Cepheid variable star do we need to know in order to calculate the approximate distance from Earth?
    6·1 answer
  • HELP ASAP PLEASE A LOT OF POINTS!!! I WILL 5 STAR YOU IF RIGHT
    10·1 answer
  • An alternating voltage of 240V,50HZ is connected across an impedance of (60-j100) Ω. Determine:
    6·1 answer
  • What is the value of 2cos2(105⁰) − 1?
    6·2 answers
  • Solve using matrix inverse method 3x 2y 3x-2y+3z=8 , 2x+ y - z = 1, 4x-3y + 2z =4
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!