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natali 33 [55]
2 years ago
7

The coordinates of the vertices of quadrilateral HIJK are H (-2, -1), I (2, 1), J (5, 0), and K (-1, -3). Isabella states that q

uadrilateral HIJK is a parallelogram. Is Isabella correct? Support your answer and show all work.
Mathematics
1 answer:
Firlakuza [10]2 years ago
7 0

Answer:

Step-by-step explanation:

You might be interested in
The perimeter of a square garden is (20k+36) feet. Write an expression
sertanlavr [38]

Answer:

5k+9

Step-by-step explanation:

Since it's a square, all four sides are equal so divide the equation of the total by 4.

20k/4=5k

36/4=9

The length of one side of the garden can be represented by the expression:

5k+9

5 0
2 years ago
Find the function y1 of t which is the solution of 121y′′+110y′−24y=0 with initial conditions y1(0)=1,y′1(0)=0. y1= Note: y1 is
strojnjashka [21]

Answer:

Step-by-step explanation:

The original equation is 121y''+110y'-24y=0. We propose that the solution of this equations is of the form y = Ae^{rt}. Then, by replacing the derivatives we get the following

121r^2Ae^{rt}+110rAe^{rt}-24Ae^{rt}=0= Ae^{rt}(121r^2+110r-24)

Since we want a non trival solution, it must happen that A is different from zero. Also, the exponential function is always positive, then it must happen that

121r^2+110r-24=0

Recall that the roots of a polynomial of the form ax^2+bx+c are given by the formula

x = \frac{-b \pm \sqrt[]{b^2-4ac}}{2a}

In our case a = 121, b = 110 and c = -24. Using the formula we get the solutions

r_1 = -\frac{12}{11}

r_2 = \frac{2}{11}

So, in this case, the general solution is y = c_1 e^{\frac{-12t}{11}} + c_2 e^{\frac{2t}{11}}

a) In the first case, we are given that y(0) = 1 and y'(0) = 0. By differentiating the general solution and replacing t by 0 we get the equations

c_1 + c_2 = 1

c_1\frac{-12}{11} + c_2\frac{2}{11} = 0(or equivalently c_2 = 6c_1

By replacing the second equation in the first one, we get 7c_1 = 1 which implies that c_1 = \frac{1}{7}, c_2 = \frac{6}{7}.

So y_1 = \frac{1}{7}e^{\frac{-12t}{11}} + \frac{6}{7}e^{\frac{2t}{11}}

b) By using y(0) =0 and y'(0)=1 we get the equations

c_1+c_2 =0

c_1\frac{-12}{11} + c_2\frac{2}{11} = 1(or equivalently -12c_1+2c_2 = 11

By solving this system, the solution is c_1 = \frac{-11}{14}, c_2 = \frac{11}{14}

Then y_2 = \frac{-11}{14}e^{\frac{-12t}{11}} + \frac{11}{14} e^{\frac{2t}{11}}

c)

The Wronskian of the solutions is calculated as the determinant of the following matrix

\left| \begin{matrix}y_1 & y_2 \\ y_1' & y_2'\end{matrix}\right|= W(t) = y_1\cdot y_2'-y_1'y_2

By plugging the values of y_1 and

We can check this by using Abel's theorem. Given a second degree differential equation of the form y''+p(x)y'+q(x)y the wronskian is given by

e^{\int -p(x) dx}

In this case, by dividing the equation by 121 we get that p(x) = 10/11. So the wronskian is

e^{\int -\frac{10}{11} dx} = e^{\frac{-10x}{11}}

Note that this function is always positive, and thus, never zero. So y_1, y_2 is a fundamental set of solutions.

8 0
2 years ago
Solve for x.<br> -5x + 12x - 8x = -24<br> x = _________a0
hichkok12 [17]

Answer:

x=24

Step-by-step explanation:

-5x+12x-8x=-24

Add like terms

12x-13x=-24

-x=-24

divide by 1

x=24

5 0
3 years ago
I need help on my homework
soldi70 [24.7K]

Answer:

\displaystyle m\angle AED=32.5^\circ

Step-by-step explanation:

<u>Angles in a Circle</u>

An exterior angle of a circle is an angle whose vertex is outside a circle and the sides of the angle are secants or tangents of the circle.

Segments AE and DE are secants of the given circle. They form an exterior angle called AED.

The measure of an exterior angle is equal to half the difference of the measure of their intercepted arcs.

Intercepted arcs in the given circle are AD=113° and BC=48°. The exterior angle is:

\displaystyle m\angle AED=\frac{AD-BC}{2}

\displaystyle m\angle AED=\frac{113^\circ-48^\circ}{2}=\frac{65^\circ}{2}

\displaystyle m\angle AED=32.5^\circ

8 0
2 years ago
An audio cable is 14.5 dm long. How long is the cable in meters?
Oduvanchick [21]

Answer:

1.45 meters

Step-by-step explanation:

7 0
2 years ago
Read 2 more answers
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