6-3 practice proving that a quadrilateral is a parallelogram

Answer:

Step-by-step explanation:

thats hard

The given equation is of form : x1+x2+...+xn = k, where x1>=m1, x2>=m2 and so on, this is typical equation which can be mapped to questions like :

Q)You have n candies and you want to distribute it to k children where each child gets at least m candies or in other words n same candies in k different boxes, where each box must have certain number of candies.

In your case m1=m2=...=mn= 0(or 1 based on your definition of natural numbers, lets first solve for condition where lower bound is 0).

This solution is simple, (n-1+k C k) which gives (3-1+11 C 11) = 78 as answer.

Now, the case for which we start natural numbers with 1 :

First we need to reduce it to previous formula. This can be done by making the lower bounds as 0 or to say lets first distribute minimum number of candies to children.Now we are left with k-m1-m2...-mn candies, so equation reduces to :

x1+x2+...+xn = k-m1-m2...-mn

or in your case x1+x2+x3 = (11-3) = 8

Now, using the previous formula (3-1+8 C 8) = 45.Which is required solution.

A linear equation in two variables is an equation of the form ax + by + c = 0 where a, b, c ∈ R, a, and b ≠ 0. When we consider a system of linear equations, we can find the number of solutions by comparing the coefficients of the variables of the equations. Also, we can find the number of solutions by the graphical method.

Consider the pair of linear equations in two variables x and y.

a1x + b1y + c1 = 0

a2x + b2y + c2 = 0

Here a1, b1, c1, a2, b2, c2 are all real numbers.

Note that, a12 + b12 ≠ 0, a22 + b22 ≠ 0

1. If (a1/a2) ≠ (b1/b2), then there will be a unique solution. If we plot the graph, the lines will intersect. This type of equation is called a consistent pair of linear equations.

2. If (a1/a2) = (b1/b2) = (c1/c2), then there will be infinitely many solutions. The lines will coincide. This type of equation is called a dependent pair of linear equations in two variables

3. If (a1/a2) = (b1/b2) ≠ (c1/c2), then there will be no solution. If we plot the graph, the lines will be parallel. This type of equation is called an inconsistent pair of linear equations.

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Farmer brown had ducks and cows having a total of 13 heads and 46 feet, which means there are 10 cows and 3 ducks.

This is an algebraic problem that can be solved using a system of equations.

Let x be the number of cows and y be the number of ducks. We know from the problem statement that:

x + y = 13 (the number of heads)

4x + 2y = 46 (the number of feet)

We can use the first equation to solve for one of the variables in terms of the other.

For example, if we subtract y from both sides of the equation we get:

x = 13 - y

We can substitute this expression for x into the second equation:

4(13 - y) + 2y = 46

Simplifying, we get:

52 - 4y + 2y = 46

which gives us:

-4y = -6

then we get:

y=3

Now we can use this value of y to solve for x in terms of y:

x = 13 - y

x = 13 - 3

x = 10

Therefore, there are 10 cows and 3 ducks.

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Note that in the above problem,  m∠Y > 72°. This problem can be approached with logic and Physics. (Option A)

Usually, you would require at least two sides to solve for an angle. However, without out that information lets examine what we know.

1) It is given that in Δ UVW, the side opposite UW is 36cm;

2) we know that in ΔXYZ the side opposite XZ is 39cm.

3) we know that both triangles are similar in that they are scalene triangles

4) we know that they have similar sides that is:

UV ≅ XY; and

VW ≅ YZ

5) ∠V = 72°

Given item 4, since all other factors between both triangles are similar, the logic of physics suggests that extending XZ will increase ∠Y and vice versa.

Since we know that XZ is 39cm (that is 3cm longer than UW), it therefore is logical to expect m∠Y to be larger than the angle to which it is similar in  ΔUVW which is ∠V.

Thus, the correct answer is m∠Y> 72° (Option A)

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Answer:

domain : - 4 ≤ x ≤ 6

Step-by-step explanation:

the domain is the values of x that cover the graph

the solid black circles indicate that x can equal these values, in this case x = - 4 and x = 6

all other values of x between these points are included in the domain, so

domain : - 4 ≤ x ≤ 6

The speed of the car is 100 kilometers per hour, since it traveled 200 kilometers in 2 hours.

Speed = Distance/Time

Speed = 200 kilometers/2 hours

Speed = 100 kilometers/hour

The speed of a car is determined by dividing the distance traveled by the amount of time it took to travel that distance. In this case, the car traveled 200 kilometers in 2 hours. To calculate the speed of the car, we divide the distance (200 kilometers) by the time (2 hours). This gives us 100 kilometers per hour, which is the speed of the car. In other words, the car traveled 100 kilometers in 1 hour.

The speed of a car is an important factor in determining how fast a car can go. It is also important to consider other factors such as the weight of the car, the type of fuel it uses, and the road conditions. All of these factors can affect the speed of the car and should be taken into account when calculating the speed of a car. Knowing the speed of the car can help drivers make better decisions about their speed and can help prevent accident

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Answer:

D is similar, because if you slightly turn it around it will shape out like a diamond as how the bottom one is set

Answer: 1. A, B, D, 2. A, D

Step-by-step explanation:

Substitute the points into the equation:

1. A, B, D,

2. A, D

Answer:

22

Step-by-step explanation:

It is proved that triangle ABC≅ triangle DEC. The solution has been obtained using the AAS congruency of triangles.

What is AAS congruency of triangles?

Angle-Angle-Side is referred to as AAS. The triangles are said to be congruent if two of a triangle's angles and one of its non-included sides are equal to the equivalent angles and sides of another triangle.

We are given ∠BAC ≅ ∠EDC

And, BC ≅ CE

We know that the vertically opposite angles are equal,

So, ∠ACB ≅ ∠DCE

Thus, by angle-angle-side congruency,

Triangle ABC≅ Triangle DEC

Hence, triangle ABC≅ triangle DEC by AAS congruency.

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Since, there are multiple questions so the question I answered is attached below.

Answer:

A

Step-by-step explanation:

A

first add the distanity of the hours and miles next add the numbers in the chart then divide and subtract the final number

Answer:

y = -3/4x + 9

Step-by-step explanation:

first, find the slope by taking the difference of the y-values / difference of the x-values

(-3-12) / (16-(-4)) which equals -15/20 or -3/4

now use that value to represent the 'm' in the formula in order to find 'b'

y = mx + b

-3 = -3/4(16) + b

-3 = -12 + b

9 = b

y = -3/4x + 9

Answer:

Rate of Change: 7 for Jake

Step-by-step explanation:

84 goes to 91 by adding 7 and if added 7 again, U will get 98.

The MLE’s of the means of X and Y in a bivariate normal distribution, given the variances of X and Y and the correlation between X and Y, can be found by solving the equations ∑(Xn-µx)/σx2 = 0 and ∑(Yn-µy)/σy2 = 0 for µx and µy. The solutions are µx = (1/n)∑Xn and µy = (1/n)∑Yn.

Let µx and µy be the means of X and Y, respectively.

The MLE of µx and µy can be found by maximizing the joint likelihood function:

L(µx, µy) = (2πσxσy√(1-ρ2))-n/2  exp{-1/2[∑(Xn-µx)2/σx2 + ∑(Yn-µy)2/σy2 - 2ρ(∑(Xn-µx)(Yn-µy)/(σxσy))]}

Taking the partial derivatives of L with respect to µx and µy and setting them to zero yields the equations

∑(Xn-µx)/σx2 = 0

∑(Yn-µy)/σy2 = 0

Solving these equations yields the MLE’s of µx and µy:

µx = (1/n)∑Xn

µy = (1/n)∑Yn

The MLE’s of the means of X and Y in a bivariate normal distribution, given the variances of X and Y and the correlation between X and Y, can be found by solving the equations ∑(Xn-µx)/σx2 = 0 and ∑(Yn-µy)/σy2 = 0 for µx and µy. The solutions are µx = (1/n)∑Xn and µy = (1/n)∑Yn.

The complete question is :

Suppose that the two-dimensional vectors (X1, Y1), (X2, Y2),. , (Xn, Yn) form a random sample from a bivariate normal distribution for which the means of X and Y are unknown but the variances of X and Y and the correlation between X and Y are known. Find the M. L. E. ’s of the means of X and Y.

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Answer:

Sinigang is a sour soup native to the Philippines. This recipe uses pork as the main ingredient. Other proteins and seafood can also be used.

Step-by-step explanation:

Answer:

2.65

Step-by-step explanation:

Using a calculator's square root key, we get √7 = 2.64575....

To the nearest hundredth, that'd be √7 = 2.65.

Answer:

In standard position, the terminal ray of angle A passes through the point (10,-4) on the coordinate plane. The distance of the point (10, -4) from the origin (0,0) is the hypotenuse of a right triangle. The horizontal distance of the point from the y-axis is the x-coordinate, which is 10, and the vertical distance of the point from the x-axis is the y-coordinate, which is -4.

The secant of an angle is the ratio of the hypotenuse (c) to the adjacent side (a). In this case, the hypotenuse is the distance between the point (10, -4) and the origin (0,0) and the adjacent side is the x-coordinate which is 10.

So sec(A) = c/a = √(10² + (-4)²)/10 = √(100+16)/10 = √116/10 = √29/5

So sec(A) = √29/5 which is the simplified form.

When expressed in "vertex form," the parabola's vertex is (h, k), and the axis of symmetry is x = h. The h stands for a horizontal shift, or how far the graph has moved left or right from x = 0. The k value for a vertical shift, or how high or low the graph has moved in relation to y = 0.

It is important to understand that what a quadratic equation can only have equal and real roots if its discriminant equals zero. To prevent errors and ensure that we obtain the proper answer for K, we need carefully employ the discriminant formula for a quadratic equation.

The equation of the second degree is a quadratic equation. This indicates that it contains a phrase that is squared, at least once. ax² + bx + c = 0, which uses constants or numerical coefficients for the variables a, b, and c, is one of the classic formulae for solving quadratic equations. Unknown variable 'x' is used here.

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Answer: i might be wronge but 9x - 4 / x^2

Step-by-step explanation:

If line segment FG = - 4x+34 and line segment CD = 48-4X, the measurement of CD is equal to: D. 28.

In Mathematics, the midpoint theorem states that in a triangle, the line segment which joins the midpoints of any two (2) sides of the triangle must be parallel to the third side and congruent to half of the length of the third side.

By applying the midpoint theorem to triangle CDE, the measurement of CD can be calculated as follows;

CD = 2(FG)

48 - 4x = 2(-4x + 34)

Next, we would open the bracket by applying the distributive property;

48 - 4x = -8x + 68

8x - 4x = 68 - 48

4x = 20

x = 20/4

x = 5.

Now, we can calculate the measurement of CD in triangle CDE;

CD = 48 - 4x

CD = 48 - 4(5)

CD = 48 - 20

CD = 28

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Step 1, when solving a two dimensional, multi-charge problem, is to define the vectors.

Step 2: calculate A and B magnitudes

Step 3: calculate x, y components

Step 4: sum vector components

Step 5: calculate magnitude of R

Step 6: calculate direction of R

A vector is a quantity or phenomenon that has two independent properties: magnitude and direction. The term also denotes the mathematical or geometrical representation of such a quantity.

Examples of vectors in nature are velocity, momentum, force, electromagnetic fields and weight. A quantity or phenomenon that exhibits magnitude only, with no specific direction, is called a scalar. Examples of scalars include speed, mass, electrical resistance and hard drive storage capacity.

Vectors are typically represented by an arrow with a beginning, or tail, and an end, or head, that is usually represented by an arrowhead. Vectors delineate the movement from point A to point B and can be defined as an entity with a designation, such as vector a.

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The location of the vertices of the image of the rectangle WXYZ, following the dilation and reflection transformations are;

a. (-7, 5), (-4, 5), (-4, 3), (-7, 3)

b. (7, 5), (4, 5), (4, 3), (7, 3)

A dilation transformation involves the scaling of the dimensions of of the pre-image to get the dimensions of the image.

The points on the rectangle WXYZ are;

W(-7, 2), X(5, 2), Y(5, -6), and Z(-7, -6)

The scale factor of the dilation = 1/4

The center of dilation = (-7, 6)

The steps to perform the calculation of the dilation are as follows;

The coordinates of the rectangle following a translation rule of (7, -6) are;

W(-7, 2) ⇒ T₍₇, ₋₆₎ ⇒ W'(0, -4)

X(5, 2) ⇒ T₍₇, ₋₆₎ ⇒ X'(12, -4)

Y(5, -6)  ⇒ T₍₇, ₋₆₎ ⇒ Y'(12, -12)

Z(-7, -6) ⇒ T₍₇, ₋₆₎ ⇒ Z'(0, -12)

Dilating the image W'X'Y'Z' by a scale factor of 1/4, centered at the origin, we get;

W'(0, -4) ⇒ [tex]D_{1/4}[/tex]  ⇒ W''(0, -1)

X'(12, -4), ⇒ [tex]D_{1/4}[/tex]  ⇒ X''(3, -1)

Y'(12, -12)  ⇒ [tex]D_{1/4}[/tex]  ⇒ Y''(3. -3)

Z'(0, -12)    ⇒ [tex]D_{1/4}[/tex]  ⇒ Z''(0, -3)

Translating the above points, using the rule, (-7, 6), we get;

W''(0, -1)  ⇒ T₍₋₇, ₆₎  ⇒ W'''(-7, 5)

X''(3, -1)  ⇒ T₍₋₇, ₆₎  ⇒ X'''(-4, 5)

Y''(3. -3)  ⇒ T₍₋₇, ₆₎  ⇒ Y'''(-4, 3)

Z''(0, -3)  ⇒ T₍₋₇, ₆₎  ⇒ Z'''(-7, 3)

The coordinates of the rectangle WXYZ following the dilation by a scale factor of 1/4 with the center of dilation at (-7, 6) are;

b. The image following the reflection of a point (x, y), over the y-axis is (-x, y)

The coordinates of the image after a reflection across the y-axis are;

W'''(-7, 5) ⇒ [tex]R_{y-axis}[/tex] ⇒ W''''(7, 5) = R(7, 5)

X'''(-4, 5) ⇒ [tex]R_{y-axis}[/tex] ⇒ X''''(4, 5) = S(4, 5)

Y'''(-4, 3) ⇒ [tex]R_{y-axis}[/tex] ⇒ Y''''(4, 3) = T(4, 3)

Z'''(-7, 3)⇒ [tex]R_{y-axis}[/tex] ⇒ Z''''(7, 3) = U(7, 3)

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Answer:

The graph of g(x) will be shifted 4 units up and 1 unit to the right

Step-by-step explanation:

The parent function f(x) = x^3 is transformed to g(x) = (x – 1)^3 + 4

Parent function f(x)= x^3

If any number is added at the end then the graph will be shifted up

If any number is subtracted from x then graph will be shifted right

f(x)----> f(x) + a (shifted 'a' units up)

f(x) ----> f(x-a) (shifted 'a' units right)

g(x) = (x – 1)^3 + 4

The graph of g(x) will be shifted 4 units up and 1 unit to the right

the graph is attached below

Composite figure has an area of 10.5 + 7.25π square units. (Correct choice: D)

Composite figure are the result of combining two or more geometric figures. In this case we find a composite figure that is a combination of a semicircle and a right triangle, whose area formulas are described below:

Right triangle

A = 0.5 · w · l

Semicircle

A = (π / 8) · D²

Where:

First, determine the diameter of semicircle by Pythagorean theorem:

D = √(7² + 3²)

D = √58

Second, determine the area of the right triangle:

A = 0.5 · 7 · 3

A = 10.5

Third, calculate the area of semicircle:

A' = (π / 8) · (√58)²

A' = 7.25π

Fourth, find the area of composite figure:

A'' = A + A'

A'' = 10.5 + 7.25π

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Opportunity cost increases along the production possibility frontier because of the principle of diminishing returns.

Diminishing returns refer to the fact that as we allocate more resources to the production of one good, the marginal productivity of those resources decreases. In other words, as we produce more of one good, it becomes increasingly difficult and costly to produce additional units of that good.

As we move along the PPF, we are producing more and more of one good and less and less of the other. The resources that were previously used to produce the other good are now being used to produce more of the first good. As we move along the PPF, we are sacrificing more and more of the second good in order to produce additional units of the first good, and this is reflected in the opportunity cost. The opportunity cost of producing one good increases as we move along the PPF.

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(5x-3)(5x-3) is a product of two binomials, which can be expanded using the distributive property.

What is an example of distributive property?

A value is multiplied by a sum to leverage the distributive property of multiplication over addition. Take the case where you want to multiply 5 by the sum of 10 + 3. We frequently add the two sums when two terms are similar instead of multiplying by 5. However, the attribute states that you must first raise each addend by 5..

To expand, you would multiply each term in the first binomial (5x-3) by each term in the second binomial (5x-3) and then add the products.

(5x-3)(5x-3) = (5x)(5x) + (5x)(-3) + (-3)(5x) + (-3)(-3)

= 25x^2 - 15x + 15x - 9

= 25x^2 - 9

So the expanded form of (5x-3)(5x-3) is 25x^2 - 9.

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Answer:

-1 43/56

Step-by-step explanation:

Answer:

-99/56

Step-by-step explanation: i used my calc