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3 years ago

Which graph contains an Euler path?

Mathematics

1 answer:

Otrada [13]3 years ago

6 0

Answer:

graph 1

Step-by-step explanation:

path = 2 odd degree vertices, the rest even

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Divide the rational expressions and express in simplest form. When typing your answer for the numerator and denominator be sure

Veseljchak [2.6K]

Dividing by a fraction is equivalent to multiply by its reciprocal, then:

$\begin{gathered} \frac{3y^2-7y-6}{2y^2-3y-9}\div\frac{y^2+y-2}{2y^2+y-3^{}}= \\ =\frac{3y^2-7y-6}{2y^2-3y-9}\cdot\frac{2y^2+y-3}{y^2+y-2}= \\ =\frac{(3y^2-7y-6)(2y^2+y-3)}{(2y^2-3y-9)(y^2+y-2)} \end{gathered}$

Now, we need to express the quadratic polynomials using their roots, as follows:

$ay^2+by+c=a(y-y_1)(y-y_2)$

where y1 and y2 are the roots.

Applying the quadratic formula to the first polynomial:

$\begin{gathered} y_{1,2}=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ y_{1,2}=\frac{7\pm\sqrt[]{(-7)^2-4\cdot3\cdot(-6)}}{2\cdot3} \\ y_{1,2}=\frac{7\pm\sqrt[]{121}}{6} \\ y_1=\frac{7+11}{6}=3 \\ y_2=\frac{7-11}{6}=-\frac{2}{3} \end{gathered}$

Applying the quadratic formula to the second polynomial:

$\begin{gathered} y_{1,2}=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ y_{1,2}=\frac{-1\pm\sqrt[]{1^2-4\cdot2\cdot(-3)}}{2\cdot2} \\ y_{1,2}=\frac{-1\pm\sqrt[]{25}}{4} \\ y_1=\frac{-1+5}{4}=1 \\ y_2=\frac{-1-5}{4}=-\frac{3}{2} \end{gathered}$

Applying the quadratic formula to the third polynomial:

$\begin{gathered} y_{1,2}=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ y_{1,2}=\frac{3\pm\sqrt[]{(-3)^2-4\cdot2\cdot(-9)}}{2\cdot2} \\ y_{1,2}=\frac{3\pm\sqrt[]{81}}{4} \\ y_1=\frac{3+9}{4}=3 \\ y_2=\frac{3-9}{4}=-\frac{3}{2} \end{gathered}$

Applying the quadratic formula to the fourth polynomial:

$\begin{gathered} y_{1,2}=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ y_{1,2}=\frac{-1\pm\sqrt[]{1^2-4\cdot1\cdot(-2)}}{2\cdot1} \\ y_{1,2}=\frac{-1\pm\sqrt[]{9}}{2} \\ y_1=\frac{-1+3}{2}=1 \\ y_2=\frac{-1-3}{2}=-2 \end{gathered}$

Substituting into the rational expression and simplifying:

$\begin{gathered} \frac{3(y-3)(y+\frac{2}{3})2(y-1)(y+\frac{3}{2})}{2(y-3)(y+\frac{3}{2})(y-1)(y+2)}= \\ =\frac{3(y+\frac{2}{3})}{2(y+2)}= \\ =\frac{3y+2}{2y+4} \end{gathered}$

8 0

1 year ago

What is the difference between -1 3/4 and 5 1/2? Msg me

rewona [7]

7 1/4
that is the numerical difference between the two

5 0

3 years ago

Can someone please explain step by step how to do it pls i dont get it

bekas [8.4K]

The answer is option d) T(Q+6.5) = R

3 0

3 years ago

PLZ I REALLY NEED HELP/ i'll give brainlist and 100 points PLZZZZZ

andrew11 [14]

Answer:

Question 1: Answer would be A.

Question 2: Answer would be B.

Question 3: I cannot answer this one because an image is not provided. I do not have the image of the original triangle LMN. If you message me with a photo of this question, I will be able to answer.

Question 4: This answer may be wrong, but I believe that it would be A. I don't know how to calculate dilation transformations, but after graphing out all the points, I found that (6,4) would be the correct point because the distance between Point S and (6,4) is even and is able to be divided by two.

Question 5: Again, I cannot answer this one because an image is provided. Message me with a photo, I'll answer.

Question 6: Answer would be C.

Question 7: Again, I cannot answer this one because an image is provided. Message me with a photo, I'll answer.

Question 8: Answer would be C.

Step-by-step explanation:

Question 1 Explanation: Answer would be A because the quadrilateral was rotated 180 degrees and dilated to be larger.

Question 2 Explanation: Quadrant IV is on the bottom right, Quadrant I is on the top right. If a triangle were to be rotated from the origin (0,0), it would have to rotate 270 degrees in order to reach Quadrant I.

Question 3 Explanation:

Question 4 Explanation:

Question 5 Explanation:

Question 6 Explanation: Using a rotation calculator, I input the degree of rotation as -90.

Question 7 Explanation:

Question 8 Explanation: Using a rotation calculator, I input the degree of rotation as -180.

7 0

3 years ago

45 units and is centered at

mariarad [96]

The correct question is:

A circle has a radius of 45 units and is centered at (-2.4, -4.8).

What is the equation of this circle?

Answer:

Equation of the circle is;

(x + 2.4)² + (y + 4.8)² = 2304

Step-by-step explanation:

The standard equation of a circle is;

(x - a)² + (y - b)² = r²

where;

(a,b) is the center of the circle and r is the radius of the circle

Now, from the question, the circle is centered at (-2.4, -4.8) and the radius is 45

Thus, plugging those values into the standard form of equation of a circle, we have;

(x - (-2.4))² + (y - (-4.8))² = 48²

This gives;

(x + 2.4)² + (y + 4.8)² = 2304

3 0

3 years ago