Write a rational
expression that is
equal to the followi
rational expression
when x doesn’t = 3 or -
(x+2)(x-6)/
(x-3)(x+2)

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.

Learn more about AAS congruency of triangles from the given link

https://brainly.com/question/3168048

#SPJ1

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

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.

Learn more about no solution equation at https://brainly.com/question/14603452.

#SPJ4

If g(x) is obtained by shifting f(x) down by 7 units, the value of k is 7.

In Mathematics, the translation of a geometric figure or graph downward simply means subtracting a digit from the value on the y-coordinate (y-axis) of the pre-image or function.

Mathematically, a horizontal translation to the left is modeled by this mathematical expression g(x) = f(x + k) while a vertical translation to the negative y-direction (downward) is modeled by this mathematical expression g(x) = f(x) - k.

Where:

By comparison based on the graph of f(x) = (0.5)^x and g(x) = (0.5)^x − k, we can logically deduce that the value of k is equal to 7.

Read more on translation here: brainly.com/question/26869095

#SPJ1

The average rate of change on the given interval [0, 2] is:

r = 1.5

For any function y = f(x), we define the average rate of change on an interval [a, b] as:

r = ( f(b) - f(a))/(b - a)

Here we want to find the average rate of change of the graphed function on the interval [0, 2]

Then we will have:

r = ( f(2) - f(0))/(2 - 0) = ( f(2) - f(0))/2

Using the graph, we can see that:

f(0) = 1

f(2) = 4

Replacing that in the equation above we will get:

r = (4 - 1)/2

r = 3/2

r = 1.5

Learn more about average rates of changes:

https://brainly.com/question/8728504

#SPJ1

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.

(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.

Learn more about distributive property

https://brainly.com/question/2807928

#SPJ1

Answer:

f(-3) = -42

Step-by-step explanation:

Substitute X in the function definition:

f(-3) = -(-3)² + 5(-3) - 18
f(-3) = -9 - 15 - 18
f(-3) = -42

To simplify, you must add the exponents. To add or subtract fractions, the denominator must be the same.

In expression [tex]a^\frac{5}{3}[/tex] and [tex]a^\frac{1}{4}[/tex]  if you have to solve this you have to first add them according to the rule of indices ([tex]a^2 * a^4 = a^6[/tex]).

[tex]a^\frac{5}{3} * a^\frac{1}{4} = a^\frac{5*4 + 3*1 }{4*3} \\\\a^\frac{20 + 3}{12} \\\\a^\frac{23}{12}[/tex]

The components of a number array are described using index notation in both mathematics and computer programming. Using indices has varying degrees of formality depending on the subject. Specifically, depending on whether one is writing a formal academic article for publication or when one is building a computer program, there are several ways to refer to the components of a list, a vector, or a matrix.

Exponentiation is a mathematical operation that involves the base b and the exponent or power n. It is written as bⁿ and is pronounced as "bⁿ." Exponentiation corresponds to base multiplication when n is a positive integer; therefore, bⁿ is the result of multiplying n bases:

Learn more about Exponents :

https://brainly.com/question/11975096

#SPJ4

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

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 value of the side ST or p is equal to 3

A trapezoid is also known as a trapezium is a four-sided polygon or a quadrilateral. It has one set of opposite sides which are parallel and a set of non-parallel sides. The parallel sides are known as the bases and the non-parallel sides are known as the legs of the trapezoid.

Given here: A trapezoid STVW and ST=p and UX=4p-3 and VW=2p+9 with U and X are midpoints.

The length of the midsegment is the sum of the two bases divided by 2.

Now we know that the mid segment UX is given by    

UX= ST+VW / 2

thus substituting the values we get

4p-3= p+2p+9 /2

8p-6=3p+9

5p=15

p=3

Hence, The value of p is equal to 3

Learn more about the trapezoid here:

https://brainly.com/question/8643562

#SPJ1

The price per quart of water would be = $2.35

The equivalent of a quart means the total amount of cups of water that can be found in a quart after conversation.

The equivalence of a quart of water would be = 4 cups

Therefore, if 6 cups = $ 3.52

4 cups = X

Make X the subject of formula;

X = 4 × 3.52/6

X = 14.08/6

X = 2.35

Therefore, a the price per quart of water = $2.35.

Learn more about addition here:

https://brainly.com/question/25421984

#SPJ1

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)

Learn more about Logic:
https://brainly.com/question/2141979
#SPJ1

The scale factor of AABC dilation of ADEF with center (0, 0) is 3.

Scale factor is a numerical value used to indicate the proportional change in the size of an object or image. It is often expressed as a fraction or ratio, for example 1:2, where the first number (1) represents the original size, and the second number (2) represents the new size. This is also referred to as a "scaling factor," since it indicates how much larger or smaller the new size is compared to the original size. Scale factors can be used to resize objects in different directions, such as width, height, and depth.

This means that each point of ADEF was scaled up by a factor of 3. This means that the length and width of ADEF were multiplied by 3 to make the new figure AABC. For example, if the length of ADEF was 6, then the length of AABC would be 18. Similarly, if the width of ADEF was 9, then the width of AABC would be 27.

To know more about scale factor click-
https://brainly.com/question/2826496
#SPJ1

Jacki is correct, that one number is correct nineties, which is number 97

Prime number - In mathematics, the prime numbers are the numbers which can be divisible by 1 and the number itself. In other words prime numbers are the numbers which has only two factors.

Composite Number - In mathematics, the composite numbers are the numbers which can be divisible by 1 and number itself and other numbers as well.

Given statements,

Marla says that every number in the nineties is composite

Jackie says that one number in the nineties is prime

Lets check,

91 is divisible by 7, 1, 91, 13

92 is divisible by 2, 1, 91, 46

93 is divisible by 3, 31, 1, 93

94 is divisible by 2, 1, 94, 47

95 is divisible by 5, 1, 95, 13

96 is divisible by 2, 1, 96, 48

97 is PRIME, is only divisible by 1 & 97

98 is divisible by 2, 1, 98, 49

99 is divisible by 3, 1, 99, 33

To know more about numbers check:

https://brainly.com/question/17429689

#SPJ1

Answer: 4/12

Step-by-step explanation: Simplified into 1/4                                         :)

Answer:

4/12 chance of getting striped card

Step-by-step explanation:

There are 4 striped cards, out of 12 cards, so that would be 4/12

One albino laboratory rat is an independent variable.

To investigate how alcohol affects reaction times, sixty participants were randomly split into two groups. Those in one group drank a certain amount of alcohol, while those in the other group drank non-alcoholic beverages. Both groups' reaction times were timed before and after the beverage.

Know more about reaction time

https://brainly.com/question/24016399

#SPJ4

The question is incomplete and wrong:

Sixty albino laboratory rats were randomly divided into two groups as part of a study on the effects of alcohol on reaction time. Each member of one group consumed a specified amount of alcohol and members of the other group had a non-alcoholic beverage. The reaction time of both groups was measured before and after taking the beverage/alcoholic drink. What is the INDEPENDENT VARIABLE?

a. Amount of alcohol

b. Reaction time

c. One albino laboratory rat

d. Sixty albino laboratory rats​

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.

Learn more about vector at https://brainly.com/question/13322477.

#SPJ4

Answer:

The dimensions of the rectangle are 22 and 55 feet

Step-by-step explanation:

We can set the Width to be X and the Length to be 3x-11 since it is 11 less than 3 times the width.

the perimeter is 2 widths plus 2 lengths so x + x + 3x-11 + 3x-11 or 8x -22
since the perimeter is also 154, we get that 8x-22 = 154, we can add 22 to both sides and get that 8x = 176 if we divide both sides by 8 we get that X or the width is 22 and since the length is 3 times the width minus 11 it is

66-11 or 55.

Answer:2x3=5

Step-by-step explanation:3x8=1234

The volume of the rectangular box is equal to 36 1/4 or 36.25 cubic inches.

Mathematically, the volume of a rectangular prism can be calculated by using this formula:

Volume = L × W × H

Where:

Substituting the given parameters into the formula for the volume of a rectangular prism, we have;

Volume of rectangular prism = 3 5/8 × 2 1/2 × 4

Volume of rectangular prism = 29/8 × 5/2 × 4

Volume of rectangular prism = 580/16

Volume of rectangular prism = 36 1/4 or 36.25 cubic inches.

Read more on prism here: brainly.com/question/21012007

#SPJ1

Answer:

A ≈ 561.2 yd²

Step-by-step explanation:

the area (A) of an equilateral triangle is calculated as

A = [tex]\frac{s^2\sqrt{3} }{4}[/tex] ( where s is a side of the triangle )

here s = 36 , then

A = [tex]\frac{36^2\sqrt{3} }{4}[/tex] = [tex]\frac{1296\sqrt{3} }{4}[/tex] = 324[tex]\sqrt{3}[/tex] ≈ 561.2 yd²

The degree of the given polynomial is 4 and the number of terms from the above given polynomial is 2 .

What is the Degree of a Polynomial?

Degree of a polynomial can be defined as the highest power of the variable in a polynomial.

Given polynomial,

= 12x²y^4 - 10xy³ + 25x

The degree of the given polynomial is 4.

the number of  terms from the above given polynomial are x and y.

so the number of terms from the above given polynomial is 2 .

Hence, The degree of the given polynomial is 4 and the number of terms from the above given polynomial is 2 .

To learn more about Degree of polynomial from the given link.

https://brainly.com/question/29182596

#SPJ1

The volume of cube with edge m is,

⇒ V = m³

A cube is the solid shape or three-dimensional shape. A convex polyhedron which is bounded by six rectangular faces with eight vertices and twelve equal edges is called cube.

Given that;

A shipping box is in the shape of a cube.

Now, Let an edge of the shipping box = m

So, The volume of the shipping box is,

⇒ V = m × m × m

⇒ V = m³

Learn more about the cube visit;

https://brainly.com/question/27894163

#SPJ1

Answer:

64m^24n^12

Step-by-step explanation:

When we compare the given expression with the slope-intercept form, we get the required slope. Here, the slope is -3.

A line's slope or gradient numerically expresses its steepness and direction. It provides the ratio of how much y alters when x alters by a particular amount. Since m is the slope and c is the y-intercept, y=mx+c is the general form. This is the slope-intercept form.

Compare the given expression y=-3x-7 with the slope-intercept form. We get, the slope value as m=-3 and the intercept value as c=-7. Therefore, the required answer is -3. So the value of y changes with -3 times of x.

The complete question is -

What is the slope of any line parallel to y=-3x-7?

To know more about slope-intercept form:

https://brainly.com/question/1625868

#SPJ4

Answer: x=68

Step-by-step explanation:

The triangle equal up to 180 and 89 + 44 = 128

And 128 - 180 is 68

So x=68

Hope this help Please make me as the brainlest.

It is clear that planes q and r are parallel based on the fact that they do not intersect and remain in the same plane.

Lines a and b, however, are skew because they are not parallel, not in the same plane, and do not intersect.

This can be seen by looking at the angles formed by lines a and b, as they are not equal and are not of the same degree.

Furthermore, lines a and b cannot be in the same plane as planes q and r, as they do not intersect, and therefore they must be skew.

This is because two lines that are parallel to the same plane cannot be skew to each other. Therefore, lines a and b must be skew since they are not parallel to planes q and r.

To learn more about parallel, click here:

https://brainly.com/question/16701300

#SPJ4

A distance of 6.5 inches on the map represents 6.5*40 = 260 miles on the ground.

step1:

scales on a map =40 inch .

1 inch =40 miles .

then miles represents on the map =6/1/2 .

6/1/2=40miles .

13/2=40

80=13,

scale on the map =3/13/42

To learn more about inches represent refers to;

https://brainly.com/question/15737082

#SPJ1

On a ground-based map, 6.5 inches correspond to 6.5*40, or 260 miles.

The legend for the map includes a scale bar. It is stated as an inch-to-inch, foot-to-foot, or mile-to-mile conversion of the ground to the map.

The relationship (or ratio) between the distances shown on a map and their actual distances on the ground is referred to as the map scale.

40 inch is the scale of a map.

1 inch equals 40 miles.

then miles on the map is represented as 6/1/2, which is 40 miles.

13/2 = 40 80 = 13, and the map's scale is 3 13/42.

On a ground-based map, 6.5 inches correspond to 6.5*40, or 260 miles.

To learn more about distances refers to;

https://brainly.com/question/26550516

#SPJ1

The additional amount of money Dan will spend can be written in an inequality form such as = c >/= $15

Inequality is defined as the expression that is used to represent two values that are not equal. < less than or > great than signs are usually used for such expressions.

The least amount of money Dan can spend of gifts = $32

The amount he has spent so far = $15

The amount remaining c = 32-15 = $17

Therefore, additional amount of money Dan will spend can be written in an inequality form such as = c >/= $15

Learn more about inequality here:

https://brainly.com/question/24372553

#SPJ1