Which path is a Hamiltonian circuit?

The equation of the parabola with the vertex at (2,7) and passing through (-1,3) is y = -(4/9)(x - 2)^2 + 7, found by substituting the given points into the vertex form of a parabola's equation.

To find the equation of a parabola given its vertex and a point it passes through, we use the vertex form of a parabola's equation, which is y = a(x - h)^2 + k, where (h, k) is the vertex of the parabola.

Given the vertex at (2,7) and a point (-1,3) through which the parabola passes, we substitute these values into the vertex form to find the value of 'a'.

Substituting the vertex, we have:

y = a(x - 2)^2 + 7

Then, substituting the point (-1,3) into the equation, we get:

3 = a(-1 - 2)^2 + 7

Solving for 'a', we get:

3 = a(3)^2 + 7 \n3 = 9a + 7 \n-4 = 9a \na = -4/9

Therefore, the equation of the parabola is:

y = -(4/9)(x - 2)^2 + 7

The equation of the parabola with the vertex at (2,7) and passing through (-1,3) is y = -(4/9)(x - 2)2 + 7, found by substituting the given points into the vertex form of a parabola's equation.

To find the equation of a parabola given its vertex and a point it passes through, we use the vertex form of a parabola's equation, which is y = a(x - h)2 + k, where (h, k) is the vertex of the parabola.

Given the vertex at (2,7) and a point (-1,3) through which the parabola passes, we substitute these values into the vertex form to find the value of 'a'.

Substituting the vertex, we have:

y = a(x - 2)2 + 7Then, substituting the point (-1,3) into the equation, we get:

3 = a(-1 - 2)2 + 7

Solving for 'a', we get:

3 = a(3)2 + 7n3 = 9a + 7n-4 = 9ana = -4/9

Therefore, the equation of the parabolais: y=-(4/9)(x-2)2+7

Given is the side length of a cube = 6 inches.

It says that the dimensions of this cube are divided into half, so the side length of new cube would be 3 inches.

We know the formula for volume of cube is given as follows :-

Volume of new cube  = Side x Side x Side.

Volume of new cube  = 3 inches x 3 inches x 3 inches.

Volume of new cube  = 27 cubic inches.

Hence, 27 cubic inches is the answer.

The speed of the slower car is 84 km/h. This was calculated by using the distance equals rate times time formula, setting up an equation based on the combined distance both cars travel and the time they take to meet, and solving for the unknown rate.

Two cars leave towns 360 kilometers apart and travel toward each other; one car travels at a rate 12 kilometers per hour slower than the other. They meet in 2 hours, so we need to find the rate of the slower car. To solve this, we'll use the formula for distance which is rate × time. Let's denote the rate of the faster car as r and the rate of the slower car as r - 12. Since they meet in 2 hours, the faster car would have traveled 2r kilometers and the slower 2(r - 12) kilometers. The total distance covered by both cars should add up to 360 km, which gives us the equation 2r + 2(r - 12) = 360.

Simplifying the equation gives 4r - 24 = 360, and adding 24 to both sides gives 4r = 384. Dividing both sides by 4, we get r = 96. Therefore, the speed of the slower car, which is 12 km/h less than the faster car, is 96 - 12 = 84 km/h.

To convert 1,700 meters to feet, we multiply by the conversion factor of 3.28 feet per meter, resulting in a length of 5,576 feet for the train.

To find the length of the train in feet, we need to convert meters to feet using the conversion factor provided. Given that 1 meter is approximately 3.28 feet, we can calculate the length of the train in feet by multiplying the length of the train in meters (1,700 meters) by the conversion factor (3.28 feet per meter).

The calculation would be as follows:

1,700 meters × 3.28 feet/meter = 5,576 feet

Therefore, the length of the train is 5,576 feet.

AB is bisected by CD (TRUE). This is True because E is the midpoint between A and B and CD passes through E

CD is bisected by AB (FALSE) CD is bisected by point F and not AB

AE = 1/2 * AB (TRUE) since E is the midpoint of AB , E divides AB into two equal halves

EF = 1/2 * ED (FALSE) The true statement would have been CF = 1/2* CD

FD = EB (FALSE) sinc we do not know if CD and AB are of the same lengths

CE + EF = ED (TRUE) since F is the midpoint the sum of CE and EF is equal to ED

The statements for the line AB and CD for this condition that are true are given as:

Option A: [tex]\overline{AB}[/tex] is bisected by [tex]\overline{CD}[/tex]

Option C: [tex]AE = \dfrac{1}{2} \times AB[/tex]

Option F: CE + EF = FD

A bisector of a line bisects that considered line. Bisect means to split in two equal parts.

For this case, we see that CD passes through mid point of AB, so CD is bisector of line AB or we say that line segment AB is bisected by line segment CD.

But AB does not passes through the center of AB, thus, AB is not a bisector of CD, or we say that line segment CD is not bisected by line segment AB

AE = EB

And AE + EB = AB

Thus, AE + AE + AB

or 2AE = AB

or AE = (AB)/2 = (1/2)AB

E is not necessary to be fixed on CD, it can move between C and F. Thus any statement about length of E to any point on CD is not necessary to be true.

FD is half of CD and EB is half of AB. It is not necessary that AB and CD are of same length, thus, it is not necessary that FD and EB are going to be of same length, thus, not congruent(two line segments are called congruent (denoted by ≅) if they are of same lengths).

CE + EF = CF, and CF = FD since F is midpoint.

Thus, CE + EF = FD

Thus, the statements for the line AB and CD for this condition that are true are given as:

Option A: [tex]\overline{AB}[/tex] is bisected by [tex]\overline{CD}[/tex]

Option C: [tex]AE = \dfrac{1}{2} \times AB[/tex]

Option F: CE + EF = FD

Learn more about bisecting lines here:

https://brainly.com/question/24753075

Answer: Age of Lin is 12

Solution:

Let X= age of Maya

(X/2)+4= age of Adrian

((X/2)+4)-7= age of Lin

X+(X/2)+4+((X/2)+4-7)=61

X+.5X+4+.5X+4-7=61

2X+4+4-7=61

2x=61-8+7

2X=60

X=30 age of Maya

19= age of Adrian

Age of Lin is

=((X/2)+4)-7

=15+4-7

=12

To check if this is correct

30+19+12=61

By setting up an algebraic equation to represent the relationship between the ages of Lin, Adrian, and Maya, and using the sum of their ages, we determined that Lin is 17 years old.

To solve this problem, let's use algebra to define the ages of Lin, Adrian, and Maya. Let's assume that Maya's age is X. Based on the information provided, Adrian is 4 years older than half of Maya's age, so Adrian's age is represented as (X/2) + 4. Lin is 7 years younger than Adrian, so Lin's age is (X/2) + 4 - 7, which simplifies to (X/2) - 3. The sum of the three ages is 61, so we can now set up an equation to find Maya's age and, subsequently, Lin's age.

The equation based on the su of their ages is:

X + (X/2) + 4 + (X/2) - 3 = 61

Combining like terms and solving for X:

2X + X + 8 - 6 = 122

3X + 2 = 122

3X = 120

X = 40

Now that we know Maya's age (X), we can find Lin's age:

(40/2) - 3 = 20 - 3 = 17

Therefore, Lin is 17 years old.

The graph of the translated function is attached

To find the graph of the function, we apply the translations

Parent function: y = log(x)

1 unit right: y = log(x - 1)

2 units down: y = log(x - 1) - 2

The graph of the function: y = log(x - 1) - 2 is attached

Answer:

c  ≤  c  ≤  [tex]\frac{-14}{17}[/tex].

Step-by-step explanation:

Given : −32c + 12 ≤ −66c − 16.

To find : Solve

Solution ": We have given

−32c + 12 ≤ −66c − 16.

On subtracting both sides by 12

- 32 c  ≤ −66c − 16 - 12

- 32 c  ≤ −66c − 28

On adding both sides by 66 c

-32c +66c  ≤  − 28.

34 c ≤  − 28.

On dividing both sides by 34

c  ≤  [tex]\frac{-28}{34}[/tex].

On dividing both number by 2

c≤  [tex]\frac{-14}{17}[/tex].

Therefore, c  ≤  [tex]\frac{-14}{17}[/tex].

Final answer:

To find the number N with LCM of 48 and GCF of 8 with 16, we use the formula LCM × GCF = N × 16 which gives N = 24.

Explanation:

To find the number N when given that it has a Least Common Multiple (LCM) of 48 with the number 16 and a Greatest Common Factor (GCF), also known as the Greatest Common Divisor (GCD), of 8, we can use the relationship between LCM, GCF, and the product of the two numbers:

LCM(N, 16) × GCF(N, 16) = N × 16

Given that LCM(N, 16) = 48 and GCF(N, 16) = 8, we can substitute these values into the equation:

48 × 8 = N × 16

Solving for N:

N = × 48 × 8 / 16

N = × 24

Hence, the number N is 24.

The correct equation to solve for x, given that angle LOM (measured as (x + 15)°) and angle MON (measured as 48°) are complementary, is (x + 15)° + 48° = 90°. Thus, the answer is option D.

The subject of this question is Mathematics, specifically it refers to geometry, solving for a variable, and understanding the concept of complementary angles. Let's analyze the options provided.

Two angles are said to be complementary if the sum of their measure is 90 degrees. So, if angle LOM and angle MON are complementary, the sum of m∠LOM and m∠MON should be 90°. Since the measure of m∠LOM is given as (x + 15)° and the measure of m∠MON is given as 48°, the equation that represents this relationship is (x + 15)° + 48° = 90°.

Therefore, option D is the correct choice to solve for x.

https://brainly.com/question/15592900

#SPJ3

Answer:

  You can use either of the following to find "a":

Step-by-step explanation:

It looks like you have an isosceles trapezoid with one base 12.6 ft and a height of 15 ft.

I find it reasonably convenient to find the length of x using the sine of the 70° angle:

  x = (15 ft)/sin(70°)

  x ≈ 15.96 ft

That is not what you asked, but this value is sufficiently different from what is marked on your diagram, that I thought it might be helpful.

__

Consider the diagram below. The relation between DE and AE can be written as ...

  DE/AE = tan(70°)

  AE = DE/tan(70°) = DE·tan(20°)

  AE = 15·tan(20°) ≈ 5.459554

Then the length EC is ...

  EC = AC - AE

  EC = 6.3 - DE·tan(20°) ≈ 0.840446

Now, we can find DC using the Pythagorean theorem:

  DC² = DE² + EC²

  DC = √(15² +0.840446²) ≈ 15.023527

  a ≈ 15.02 ft

_____

You can also make use of the Law of Cosines and the lengths x=AD and AC to find "a". (Do not round intermediate values from calculations.)

  DC² = AD² + AC² - 2·AD·AC·cos(A)

  a² = x² +6.3² -2·6.3x·cos(70°) ≈ 225.70635

  a = √225.70635 ≈ 15.0235 . . . feet

The statement is false. An equation's solutions are points on a line; an inequality's solutions encompass a region on the plane.

The statement is false. The solutions to a linear equation are the points (x, y) in the plane that make the equation true, not an inequality. An equation represents a line on the coordinate plane, and every point on that line is a solution to the equation. In contrast, an inequality describes a range or region of the coordinate plane, not just a single line, and the solutions are the coordinates within that range.

For instance, the solutions to the equation y = 2x + 3 are all the points on the line where this is true. On the other hand, solutions to the inequality y > 2x + 3 would be all the points in the region above the line y = 2x + 3.

https://brainly.com/question/29068591

#SPJ12

The assertion that solutions to a linear equation are the points that make an inequality true is incorrect. It is the solutions to a linear inequality that would make the inequality true.

The statement provided in the question is false. Solutions to a linear equation are the points on the line that make the equation true, not an inequality. If we are dealing with a linear inequality, then its solutions are the points in the plane that satisfy the inequality, often forming a region, instead of just the points on a line.

https://brainly.com/question/29068591

#SPJ12