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3 years ago

50 POINTS! Show All Work!

Mathematics

2 answers:

olasank [31]3 years ago

7 0

Let the number of chickens = c.

Let the number of pigs = p.

A chicken has 1 head and 2 legs.

c number of chickens have c heads and 2c legs.

A pig has 1 head and 4 legs.

p number of pigs have p heads and 4p legs.

There are 40 heads.

Equation for heads:

c + p = 40

There are 110 legs.

Equation for legs:

2c + 4p = 110

System of equations:

c + p = 40

2c + 4p = 110

Solve the first equation of the system of equations for c:

c = 40 - p

Substitute 40 - p for c in the second equation:

2c + 4p = 110

2(40 - p) + 4p = 110

80 - 2p + 4p = 110

80 + 2p = 110

2p = 30

p = 15

Now substitute p = 15 in the first equation to find c.

c + p = 40

c + 15 = 40

c = 25

There are 25 chickens and 15 pigs.

vichka [17]3 years ago

4 0

Answer:

There are 25 chickens and 15 pigs. I did my research/work outside of brainly. Don't worry, the person above me also got the same answer so we're all good. Either way, I hope this helps you! :)

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Help with 30 please. thanks.

Svet_ta [14]

Answer:

See Below.

Step-by-step explanation:

We have the equation:

$\displaystyle y = \left(3e^{2x}-4x+1\right)^{{}^1\! / \! {}_2}$

And we want to show that:

$\displaystyle y \frac{d^2y }{dx^2} + \left(\frac{dy}{dx}\right) ^2 = 6e^{2x}$

Instead of differentiating directly, we can first square both sides:

$\displaystyle y^2 = 3e^{2x} -4x + 1$

We can find the first derivative through implicit differentiation:

$\displaystyle 2y \frac{dy}{dx} = 6e^{2x} -4$

Hence:

$\displaystyle \frac{dy}{dx} = \frac{3e^{2x} -2}{y}$

And we can find the second derivative by using the quotient rule:

$\displaystyle \begin{aligned}\frac{d^2y}{dx^2} & = \frac{(3e^{2x}-2)'(y)-(3e^{2x}-2)(y)'}{(y)^2}\\ \\ &= \frac{6ye^{2x}-\left(3e^{2x}-2\right)\left(\dfrac{dy}{dx}\right)}{y^2} \\ \\ &=\frac{6ye^{2x} -\left(3e^{2x} -2\right)\left(\dfrac{3e^{2x}-2}{y}\right)}{y^2}\\ \\ &=\frac{6y^2e^{2x}-\left(3e^{2x}-2\right)^2}{y^3}\end{aligned}$

Substitute:

$\displaystyle y\left(\frac{6y^2e^{2x}-\left(3e^{2x}-2\right)^2}{y^3}\right) + \left(\frac{3e^{2x}-2}{y}\right)^2 =6e^{2x}$

Simplify:

$\displaystyle \frac{6y^2e^{2x}- \left(3e^{2x} -2\right)^2}{y^2} + \frac{\left(3e^{2x}-2\right)^2}{y^2}= 6e^{2x}$

Combine fractions:

$\displaystyle \frac{\left(6y^2e^{2x}-\left(3e^{2x} - 2\right)^2\right) +\left(\left(3e^{2x}-2\right)^2\right)}{y^2} = 6e^{2x}$

Simplify:

$\displaystyle \frac{6y^2e^{2x}}{y^2} = 6e^{2x}$

Simplify:

$6e^{2x} \stackrel{\checkmark}{=} 6e^{2x}$

Q.E.D.

6 0

3 years ago

Note: Enter your answer and show all the steps you use to solve this problem in the space provided.

Alex Ar [27]

Answer:

(67/100)×(3/10)= (67x3)/(100×10)=201/1000=201/1000=0.201

7 0

3 years ago

G is the centroid of triangle ABC.

AleksAgata [21]

Answer:

x = 37
DG = 22
AG = 44
AD = 66

Step-by-step explanation:

We presume your "centroid ratio theorem" tells you that AG = 2·DG, so ...

(x+7) = 2(x -15)

x + 7 = 2x - 30 . . . . eliminate parentheses

37 = x . . . . . . . . . . .add 30-x

Then AG = 37+7 = 44

and DG = 37-15 = 22.

Of course, AD = AG +GD = 44 +22 = 66

7 0

3 years ago

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Ribbon sells for $3.75 per yard. Find the cost, in dollars, for 48 inches of ribbon.

Leto [7]

Answer:

4.9875

if rounding then 5 dollars

Step-by-step explanation:

7 0

4 years ago

Simone saved $65.35 more than her brother Dan and $37.50 less than her sister Carly. Carly saved $127.75. Write and solve equati

elena55 [62]

Siamone has $65.32 + DAN
Dan has CARLY - $37.50
CARLY = $127.75
Plug Carly into Dan's equation...
$127.75 - $37.50 = $90.20
DAN = $90.20
Plug Dan into Siamone's equation
$65.32 + $90.20 = $155.57

5 0

3 years ago

Read 2 more answers