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2 years ago

What is the solution to the system of equations graphed below?

Mathematics

1 answer:

barxatty [35]2 years ago

7 0

Answer:

(4,2)

Step-by-step explanation:

Solving the system of equations means to find the dot where both the lines intersect. We know by the graph that the point where the both intersect is (4,2).

Please mark me as brainliest and I hope you do well on your assignment!

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a 56 inch board is to be cut into three pieces so that the second piece is three times as long as the first piece and a third pi

wolverine [178]

X + 3x + 4x = 56
8x = 56
x = 7

The shortest piece is 7 inches
The middle piece is 7*3 = 21 inches.
The longest piece is 4*7 = 28 inches

Check
7 + 21 + 28 = 56 It does check and the lengths are correct.

7 0

3 years ago

I have 30 photos to post on my website. I'm planning to post these on two web pages, one marked "Friends" and the other marked "

Sergio039 [100]

Answer:a) 870

b) 435

Step-by-step explanation:

number of photos to be posted =n = 30

number of web pages on which they would be posted is 2

Since the order in which the photos appear on the web pages matters,

Number of ways = 30 permutation 2

=870 ways

Since the order in which the photos appear on the web pages does not matter,

Number of ways = 30 combination 2

= 435 ways

6 0

3 years ago

) Use the Laplace transform to solve the following initial value problem: y′′−6y′+9y=0y(0)=4,y′(0)=2 Using Y for the Laplace tra

artcher [175]

Answer:

$y(t)=2e^{3t}(2-5t)$

Step-by-step explanation:

Let Y(s) be the Laplace transform Y=L{y(t)} of y(t)

Applying the Laplace transform to both sides of the differential equation and using the linearity of the transform, we get

L{y'' - 6y' + 9y} = L{0} = 0

(*) L{y''} - 6L{y'} + 9L{y} = 0 ; y(0)=4, y′(0)=2

Using the theorem of the Laplace transform for derivatives, we know that:

$\large\bf L\left\{y''\right\}=s^2Y(s)-sy(0)-y'(0)\\\\L\left\{y'\right\}=sY(s)-y(0)$

Replacing the initial values y(0)=4, y′(0)=2 we obtain

$\large\bf L\left\{y''\right\}=s^2Y(s)-4s-2\\\\L\left\{y'\right\}=sY(s)-4$

and our differential equation (*) gets transformed in the algebraic equation

$\large\bf s^2Y(s)-4s-2-6(sY(s)-4)+9Y(s)=0$

Solving for Y(s) we get

$\large\bf s^2Y(s)-4s-2-6(sY(s)-4)+9Y(s)=0\Rightarrow (s^2-6s+9)Y(s)-4s+22=0\Rightarrow\\\\\Rightarrow Y(s)=\frac{4s-22}{s^2-6s+9}$

Now, we brake down the rational expression of Y(s) into partial fractions

$\large\bf \frac{4s-22}{s^2-6s+9}=\frac{4s-22}{(s-3)^2}=\frac{A}{s-3}+\frac{B}{(s-3)^2}$

The numerator of the addition at the right must be equal to 4s-22, so

A(s - 3) + B = 4s - 22

As - 3A + B = 4s - 22

we deduct from here

A = 4 and -3A + B = -22, so

A = 4 and B = -22 + 12 = -10

It means that

$\large\bf \frac{4s-22}{s^2-6s+9}=\frac{4}{s-3}-\frac{10}{(s-3)^2}$

and

$\large\bf Y(s)=\frac{4}{s-3}-\frac{10}{(s-3)^2}$

By taking the inverse Laplace transform on both sides and using the linearity of the inverse:

$\large\bf y(t)=L^{-1}\left\{Y(s)\right\}=4L^{-1}\left\{\frac{1}{s-3}\right\}-10L^{-1}\left\{\frac{1}{(s-3)^2}\right\}$

we know that

$\large\bf L^{-1}\left\{\frac{1}{s-3}\right\}=e^{3t}$

and for the first translation property of the inverse Laplace transform

$\large\bf L^{-1}\left\{\frac{1}{(s-3)^2}\right\}=e^{3t}L^{-1}\left\{\frac{1}{s^2}\right\}=e^{3t}t=te^{3t}$

and the solution of our differential equation is

$\large\bf y(t)=L^{-1}\left\{Y(s)\right\}=4L^{-1}\left\{\frac{1}{s-3}\right\}-10L^{-1}\left\{\frac{1}{(s-3)^2}\right\}=\\\\4e^{3t}-10te^{3t}=2e^{3t}(2-5t)\\\\\boxed{y(t)=2e^{3t}(2-5t)}$

5 0

3 years ago

PLEASE HELP!!! A blueprint for a fence has a scale of 1:40. The fence in the blueprint is 6in. What is the length of the actual

EastWind [94]

1 : 40 = 6 : 240

On the ground the fence would be 240 inches long

240 / 12 = 20 feet long fnce

4 0

3 years ago

How can you find the value of x? in 3x= 2 1/4

tino4ka555 [31]

Answer:Tap for more steps... By the Sum Rule, the derivative of x 4 + 3 x 2 x 4 + 3 x 2 with respect to x x is d d x [ x 4] + d d x [ 3 x 2] d d x [ x 4] + d d x [ 3 x 2]. Differentiate using the Power Rule which states that d d x [ x n] d d x [ x n] is n x n − 1 n x n - 1 where n = 4 n = 4.

Step-by-step explanation:

6 0

3 years ago