Plz help 10points Quick

The length of a rectangle is 5 centimeters less than twice its width. The perimeter of the rectangle is 80 cm. What are the dime

Nat2105 [25]

Let the width be x

The length would be 2x-5

So, 2(x+2x-5)=80

3x-5=40

3x=45

x=15.

So the width is 15 and the length would be 25.

8 0

3 years ago

What is the y-intercept of a line that passes through (-3,3) and (1,-5)

shepuryov [24]

Answer:

The point-slope formula states:

(

y

−

y

1

)

=

m

(

x

−

x

1

)

Where

m

is the slope and

(

x

1

y

1

)

is a point the line passes through.

Substituting the slope and values from the point in the problem gives:

(

y

−

1

)

=

3

5

(

x

−

3

)

(

y

+

1

)

=

3

5

(

x

+

3

)

If you want the equation in the somewhat more familiar slope-intercept form we can solve this equation for

y

. The slope-intercept form of a linear equation is:

y

=

m

x

+

b

Where

m

is the slope and

b

is the y-intercept value.

y

+

1

=

(

3

5

⋅

x

)

+

(

3

5

⋅

3

)

y

+

1

=

3

5

x

+

9

5

y

+

1

−

1

=

3

5

x

+

9

5

−

1

y

+

0

=

3

5

x

+

9

5

−

5

y

=

3

5

x

+

4

5

The point-slope formula states:

(

y

−

y

1

)

=

m

(

x

−

x

1

)

Where

m

is the slope and

(

x

1

y

1

)

is a point the line passes through.

Substituting the slope and values from the point in the problem gives:

(

y

−

1

)

=

3

5

(

x

−

3

)

(

y

+

1

)

=

3

5

(

x

+

3

)

If you want the equation in the somewhat more familiar slope-intercept form we can solve this equation for

y

. The slope-intercept form of a linear equation is:

y

=

m

x

+

b

Where

m

is the slope and

b

is the y-intercept value.

y

+

1

=

(

3

5

⋅

x

)

+

(

3

5

⋅

3

)

y

+

1

=

3

5

x

+

9

5

y

+

1

−

1

=

3

5

x

+

9

5

−

1

y

+

0

=

3

5

x

+

9

5

−

5

y

=

3

5

x

+

4

5

Step-by-step explanation:

7 0

2 years ago

988,18<br> is divisible by 6.

zheka24 [161]

988,188 is divisible by 6

5 0

3 years ago

The logistic equation for the population (in thousands) of a certain species is given by:

Eva8 [605]

Answer:

a.

b. 1.5

c. 1.5

d. No

Step-by-step explanation:

a. First, let's solve the differential equation:

$\frac{dp}{dt} =3p-2p^2$

Divide both sides by $3p-2p^2$ and multiply both sides by dt:

$\frac{dp}{3p-2p^2}=dt$

Integrate both sides:

$\int\ \frac{1}{3p-2p^2} dp =\int\ dt$

Evaluate the integrals and simplify:

$p(t)=\frac{3e^{3t} }{C_1+2e^{3t}}$

Where C1 is an arbitrary constant

I sketched the direction field using a computer software. You can see it in the picture that I attached you.

b. First let's find the constant C1 for the initial condition given:

$p(0)=3=\frac{3e^{0} }{C_1+2e^{0} } =\frac{3}{C_1+2}$

Solving for C1:

$C_1=-1$

Now, let's evaluate the limit:

$\lim_{t \to \infty} \frac{3e^{3t} }{2e^{3t}-1 } \\\\Divide\hspace{3}the\hspace{3}numerator\hspace{3}and\hspace{3}denominator\hspace{3}by\hspace{3}e^{3t} \\\\ \lim_{t \to \infty} \frac{3 }{2-e^{-3x} }$

The expression $-e^{-3x}$ tends to zero as x approaches ∞ . Hence:

$\lim_{t \to \infty} \frac{3e^{3t} }{2e^{3t}-1 } =\frac{3}{2} =1.5$

c. As we did before, let's find the constant C1 for the initial condition given:

$p(0)=0.8=\frac{3e^{0} }{C_1+2e^{0} } =\frac{3}{C_1+2}$

Solving for C1:

$C_1=1.75$

Now, let's evaluate the limit:

$\lim_{t \to \infty} \frac{3e^{3t} }{2e^{3t}+1.75 } \\\\Divide\hspace{3}the\hspace{3}numerator\hspace{3}and\hspace{3}denominator\hspace{3}by\hspace{3}e^{3t} \\\\ \lim_{t \to \infty} \frac{3 }{2+1.75e^{-3x} }$

The expression $-e^{-3x}$ tends to zero as x approaches ∞ . Hence:

$\lim_{t \to \infty} \frac{3e^{3t} }{2e^{3t}+1.75 } =\frac{3}{2} =1.5$

d. To figure out that, we need to do the same procedure as we did before. So, let's find the constant C1 for the initial condition given:

$p(0)=2=\frac{3e^{0} }{C_1+2e^{0} } =\frac{3}{C_1+2}$

Solving for C1:

$C_1=-\frac{1}{2} =-0.5$

Can a population of 2000 ever decline to 800? well, let's find the limit of the function when it approaches to ∞:

$\lim_{t \to \infty} \frac{3e^{3t} }{2e^{3t}-0.5 } \\\\Divide\hspace{3}the\hspace{3}numerator\hspace{3}and\hspace{3}denominator\hspace{3}by\hspace{3}e^{3t} \\\\ \lim_{t \to \infty} \frac{3 }{2-0.5e^{-3x} }$

The expression $-e^{-3x}$ tends to zero as x approaches ∞ . Hence:

$\lim_{t \to \infty} \frac{3e^{3t} }{2e^{3t}-0.5 } =\frac{3}{2} =1.5$

Therefore, a population of 2000 never will decline to 800.

6 0

3 years ago

Leah and Ashley go to the movie theater and purchase refreshments for their friends

klasskru [66]

Answer:

The required system of equations is:

5 m+ 7 n = 113.75

6 m + 14 n = 185.50

The price of 1 bag of popcorn = $10.5

The price of 1 drink = $8.75

Step-by-step explanation:

Let us assume the cost of 1 bag of popcorn = $ m

And, the cost of 1 drink = $ n

Now, Leah spends a total of 113.75 on 5 bags of popcorn and 7 drinks.

Cost of 5 bags + 7 drinks = 5 m + 7 n = $ 113.75

⇒ 5 m+ 7 n = 113.75 .. (1)

Also, Ashley spends a total of 185.50 on 6 bags of popcorn and 14 drinks

Cost of 6 bags + 14 drinks = 6 m + 14 n = $185.50

⇒ 6 m + 14 n = 185.50 .. (2)

So, here the system of equations that can be used to find the price of one bag of popcorn (m) and the price of one drink (n) are

5 m+ 7 n = 113.75 .. (1)

6 m + 14 n = 185.50 .. (2)

Now, to solve this, Multiply (1) with -2 and add with 2, we get:

-10m + 6m - 14 n + 14 n = 185.5 - 227.5

or, - 4 m = -42 , or m = 42/4 = 10.5

Putting the value of m = 10.5 in 5 m+ 7 n = 113.75 , we get n = 8.75

Hence, the price of 1 bag of popcorn = m = $10.5

And the price of 1 drink = n = $8.75

6 0

3 years ago