11 Mark the givens in the diagram. Then copy the proof on paper, and fill in the blanks to complete the proof. Chapter Reference c Given that AR ∩ DC = M, AD = RC and ∠A ≅ ∠R, prove that △MAD ≅ △MRC. A D M R C 1. AD = ____ 1. Given 2. ∠A ≅ ∠____ 2. Given 3. ∠AMD ≅ ∠____ 3. ________ 4. △MAD≅ △____ 4. ________ Answer: 1. AD = RC 1. Given 2. ∠A≅∠ 2. Given 3. ∠ AM D = ∠ 3. 4. △ MAD ≅△ 4.

A 3-regular graph is called a cubic graph. A strongly regular graph is a regular graph where every adjacent pair of vertices has an equal number of neighbors in common, and every non-adjacent pair of vertices has an equal number of neighbors in common.

In the mathematical field of graph postulate, a cubic graph is a graph in which all vertices have a degree of three. In other terms, a cubic graph is a 3-regular graph. Cubic graphs are also known as trivalent graphs.

A bicubic graph is called a cubic bipartite graph.

In graph theory, a regular graph is a graph where each vertex has an equal number of neighbors; i.e. every vertex has an equal degree or valency.

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The remainder when N is divided by 1000 is 106.

The Principle of Inclusion-Exclusion, often known as PIE, offers a method/formula for organizing information about the size of each set, the number of elements in the union of a given set of sets, and the size of all potential set intersections.

From the question,

First, we think about all the possible divisions of the 7×1 board. Since we require at least one tile of each color, we exclude the cases of just one or two pieces.

Three pieces = 5+1+1 , 4+2+1 , 4+1+2 etc (6C2) = 15 ways

Four pieces = 6C3 = 20

Five pieces = 6C4 = 15

Six pieces = 6C5 = 6

Seven pieces =6C6 = 1

Now, we apply the Principle of Inclusion-Exclusion to consider how many ways to color them:

Three pieces : 3³ - 3 × 2³ + 3 = 6

Four pieces: 3⁴ - 3 × 2⁴ + 3 = 36

Five  pieces : 3⁵ - 3 × 2⁵ + 3 = 150

Six pieces : 3⁶ - 3 × 2⁶ + 3 = 540

Seven pieces : 3⁷ - 3 × 2⁷ + 3 = 1806

Adding them together, we get

15×6 + 20×36 + 15×150 + 6×540 + 1×1806 = 8106

Hence, the remainder when it is divided by 1000 is 106.

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Answer:

106

Step-by-step explanation:

12 cups of water should be mixed to 6 scoops of fruit mix and the unit rate is 0.5 scoops per cup

Unit rate is the ratio of two different units, with denominator as 1. For example, kilometer/hour, meter/sec, miles/hour, salary/month, etc. Arithmetic is probably the most basic and ancient branch of mathematics and is quite commonly used in our day-to-day life.

Given here: Ryan is making a fruit drink. The directions say to mix 3 cups of water with 1 1/2 scoops of powdered fruit mix.

Thus the ratio of the number of cups of water to scoops of powdered fruit mix is equal to 3:3/2=2:1

∴ With 6 scoops of fruit mix we will be required to mix 12 cups of water.

Again unit rate ( scoops of fruit mix / cup of water)= 1.5/3

                                                                                   =0.5 scoops/cup of water

The unit rate means the number of scoops that are required to be mixed with  a cup of water.

Hence, 12 cups of water should be mixed to 6 scoops of fruit mix and the unit rate is 0.5 scoops per cup

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The linear equation that correctly represents how much Martina collects for one night of stay in her homey is 25 + 10x - 5z

The linear equation to represent how much Martina collects for one night of stay in her home is:

y = 25 + 10x - 5z

where:

y is the total amount collected in dollars

x is the number of additional guests (besides the first one)

z is the number of hours the guests check out late

This equation represents the flat fee of $25 per night for the first guest, the additional fee of $10 per person per night for additional guests, and the extra fee of $5 per hour for late checkouts.

Therefore, The linear equation that correctly represents how much Martina collects for one night of stay in her homey is 25 + 10x - 5z

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0.1728 suburban park users bike on the park trail.

A mathematical comparison of two numbers is called a proportion.

It is an equation or statement used to depict that two ratios or fractions are equal.

According to proportion, two sets of provided numbers are said to be directly proportional to one another if they increase or decrease in the same ratio. "::" or "=" are symbols used to indicate proportions.

The proportion (p) is calculated as:

p = bike the trail/number of residents

Given that,

The number of users who bike the trail = 42

The number of residents using the park trails = 243

Thus,

p = 42/243 = 0.1728

Therefore, 0.1728 suburban park users bike on the park trail.

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The required solution of the given simultaneous equation is x = 5 and y = -9.

Simultaneous linear equations are two- or three-variable linear equations that can be solved together to arrive at a common solution.

here,
Given a system of equations,
6x + 5y = -15 - - - - -(1)
-4x - y = -11 - - - - (2)

Multiply equation 1 by 1 and multiply equaiton 2 by 5 then add both the equation,
6x + 5y -20x -5y = -15 -55
-14x = -70
x = 5

Now,
-4(5) - y = -11
-20 - y = -11
-y = -11 +20
y = -9

Thus, the required solution of the given simultaneous equation is x = 5 and y = -9.

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Answer:

-2

a open bracket

and then a and - a negate each other to give -2

By completing squares in both the variables and try to get the general equation of the form:

(x - a)^2 + (y - b)^2 = R^2

A general circle equation for a circle whose center is (a, b) and the radius is R, is:

(x - a)^2 + (y - b)^2 = R^2

So, if we have an equation like:

x^2 + cx + d + y^2 + h*y + l = m

We just need to complete squares in both x and y, such that we end with an equation of the form of:

(x - a)^2 + (y - b)^2 = R^2

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Answer: A,9

Step-by-step explanation:

g(7) = 4 and f(4) = 9

When you see something like f(g(x)) it is just asking you to find g(x) and plug that number in as x for f(x).

There are 22 different types of functions based on range, element, equation, and domain.

Based on the range it includes Modulus Function, rational function, signum function, even and odd functions, periodic functions, greatest integer function, inverse function, and composite functions. On the basis of elements, it includes One One function, many one functions, onto function, one one and onto function, into function, and constant function. On the basis of the equation, it includes the identity function, linear function, quadratic function, cubic function, and polynomial functions. On the basis of the domain, it has algebraic functions, trigonometric functions, and logarithmic functions.

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Answer:

price is now $24.64

and it was $3.36 off

Step-by-step explanation:

Mean, because there are no outliers that affect the center

third period: 3,2,3,1,3, 4, 2, 4, 3, 1, 0, 2, 3, 1, 2

Sorted values : 0, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4

The mean = ΣX / n

n = sample size, n = 15

Mean = 34 / 15 = 2.666

The median = 1/2(n+1)th term.

1/2(16)th term = 8th term.

The 8th term = 2

The best measure of centre is the mean because the values for the second period has no outliers that might have affected the centre of the distribution.

Both interquartile range and standard deviation are measures of spread and not measures of centre.

complete question

A survey was taken of students in math classes to find out how many hours per day students spend

on social media. The survey results for the first., second-, and third-period classes are as follows:

First period: 2,4,3,1,0, 2, 1, 3, 1,4,9,2,4,3,0

Second period: 3,2,3,1,3, 4, 2, 4, 3, 1, 0, 2, 3, 1, 2

Third period: 4,5, 3, 4, 2, 3, 4, 1, 8, 2, 3, 1, 0, 2, 1,3

Which is the best measure of center for second period and why? (5 points)

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Peer-reviewed (refereed or scholarly) journals: Before an article is published in a journal, it is examined by a number of other experts in the subject to guarantee that it is of a high caliber. (The paper is more likely to be valid from a scientific standpoint, draw fair conclusions, etc.)

Peer review has been conducted on the publications in a refereed journal. The papers were evaluated for quality by reputable academics or subject-matter experts before being approved for publication, so this tells us that they are of a high caliber. Also known as "scholarly" or "peer-reviewed," these pieces are published in journals.

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On solving the provided question, we can say that by equation  it cost to buy the material assuming you can buy a piece exactly the right size = $350.

An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.

the floor costs  =  3.50 per square foot

assuming we can buy a piece exactly the right size = x

then cost =

x * 3.50

let x be 100

cost = $350

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If [tex]$f$[/tex]is bounded and [tex]$\displaystyle\lim_{x \rightarrow c} g(x)$[/tex] exists, then the limit of function[tex]$f(x)g(x)$[/tex]as [tex]$x$[/tex] approaches domain[tex]$c$[/tex]also exists and is equal to [tex]$Lf(c)$[/tex]

Let [tex]$M$[/tex]be an upper bound of [tex]$f$[/tex] on the domain . Since [tex]$\displaystyle\lim_{x \rightarrow c} g(x)$[/tex] exists, there exists a number [tex]$L$[/tex] such that for all [tex]$\epsilon > 0$[/tex] there exists a [tex]$\delta > 0$[/tex] such that for [tex]$x \in A$[/tex] with [tex]$0 < |x - c| < \delta |g(x) - L| < \epsilon[/tex].

Now let [tex]\epsilon > 0Then $|f(x)g(x) - Lf(x)| = |f(x)||g(x) - L| < M\epsilon[/tex]

for all [tex]x \in A$ with $0 < |x - c| < \delta$[/tex]. So [tex]\displaystyle\lim_{x \rightarrow c} f(x)g(x)$ exists and is equal to $Lf(c)[/tex]

If [tex]$f$[/tex] is bounded and [tex]$\displaystyle\lim_{x \rightarrow c} g(x)$[/tex] exists, then the limit of [tex]f(x)g(x)$[/tex]as [tex]$x$[/tex]approaches[tex]$c$[/tex]also exists and is equal to [tex]$Lf(c)$[/tex].

The complete question is:

Let [tex]$f$[/tex] and [tex]$g$[/tex] be functions defined on a domain[tex]$A$[/tex]. Prove that if [tex]$f$[/tex] is bounded, and [tex]$\displaystyle\lim_{x \rightarrow c} g(x)$[/tex]exists, then [tex]$\displaystyle\lim_{x \rightarrow c} f(x)g(x)$[/tex] exists.

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If a translation of (x,y) → (x+6,y-10) is applied to figure ABCD, the coordinates of D are (1,-12).

What is translation?

A translation in mathematics does not turn a shape; instead, it moves it left, right, up, or down. They are congruent if the translated shapes (or the image) seem to be the same size as the original shapes.

The points of the original image is -

A(-3,4), B(3,4), C(1,-2), D(-5,-2)

The translation of (x,y) → (x+6,y-10) is applied -

A(-3,4) = (-3+6,4-10) = (3,-6)

B(3,4) =  (3+6,4-10) = (9,-6)

C(1,-2) = (1+6,-2-10) = (7,-12)

D(-5,-2) = (-5+6,-2-10) = (1,-12)

Therefore, the new points are -

A'(3,-6), B'(9,-6), C'(7,-12) and D'(1,-12).

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One of the most popular dance types of the sixteenth century was the pavane, another one are galliard and allemande.

Instruments in math are tools or processes used to perform mathematical operations and calculations. Examples of instruments in math include calculators, rulers, compasses, protractors, and computers. These instruments can be used to solve problems, analyze data, and understand mathematical concepts. Additionally, instruments in math can be used to teach students about problem-solving and allow them to gain a deeper understanding of mathematics.

This was a slow, stately dance, usually in duple meter, that was popular in courts and societies across Europe. It was usually accompanied by lute or harpsichord and sometimes with viols. The pavane was often used as a ceremonial dance in courts and was usually performed by couples.

Another popular dance type of the sixteenth century was the galliard. This was a lively, energetic dance, usually in triple meter, that was popular in courts and societies across Europe. It was usually accompanied by lute or harpsichord and sometimes with viols. The galliard was often used as a dance for entertainment and was usually performed by couples.

The third popular dance type of the sixteenth century was the allemande. This was a slow, stately dance, usually in duple meter, that was popular in courts and societies across Europe. It was usually accompanied by lute or harpsichord and sometimes with viols. The allemande was often used as a ceremonial dance and was usually performed by couples. It was usually danced in a line or circle formation, with each dancer taking the lead in turn.

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Answer:

x = 2, -6

Step-by-step explanation:

3x + 6 = ±12
=> If 3x + 6 = 12
3x = 6
x = 2
=> If 3x + 6 = -12
3x = - 18
x = -6

Answer: 2

Step-by-step explanation: To find the value of x, we need to use the order of inverse operations. Inverse operation(s) means to do the opposite of the operations used. So, instead of adding, we subtract, instead of multiplying, we'll divide. So, the opposite of 6 + 12 is 12 - 6. So, that's 6. Now, instead of multiplying 6 by 3, we need to divide 6 by 3. That's 2. Therefore x = 2. Now, to check our answer, we plug 2 in for 6. So, | 3(2) + 6 | is the positive value of 3(2) + 6, which is 6 + 6.

12 = 12

So, therefore the absolute value of |3x+6|=12 is 2. I hope this helped!

Answer: [tex]y=3[/tex]

Step-by-step explanation:

The intersection point of the graphs is the solution. So, you need to find the [tex]y[/tex]-coordinate of the intersection point.

The congruent angles, ∠ACD and ∠BCD formed by the angle bisector [tex]\overline{DC}[/tex] the congruent segments [tex]\overline{AC}[/tex] and [tex]\overline{BC}[/tex], and the segment [tex]\overline{DC}[/tex] (congruent to itself, indicates that ΔACD ≅ ΔBCD by SAS

The SAS (Acronym for Side-Angle-Side) congruency rule states that two triangles, A and B are congruent if two sides and an included angle of the triangle A are congruent to the two sides and an included angle of the other triangle B.

The specified information are;

The bisector of ∠ACB = [tex]\overline{DC}[/tex]

Segment [tex]\overline{AC}[/tex] ≅ [tex]\overline{BC}[/tex]

Required; to prove that ΔACD ≅ ΔBCD

The two-column method can be used to prove the congruency of the triangles as follows;

Step     [tex]{}[/tex]             Statement            [tex]{}[/tex]        Reasons

1.  [tex]{}[/tex]                    [tex]\overline{DC}[/tex] bisects ∠ACB          Given

                 [tex]{}[/tex]      [tex]\overline{AC}[/tex] ≅ [tex]\overline{BC}[/tex]

2.  [tex]{}[/tex]                  ∠ACD ≅ ∠BCD              Definition of bisected angles

3.                [tex]{}[/tex]    [tex]\overline{CD}[/tex] ≅ [tex]\overline{CD}[/tex]                       Reflexive property of congruency

4. [tex]{}[/tex]                   ΔACD ≅ ΔBCD               SAS congruency rule

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The provided statement indicates that the differential equation's solution will be y = c₁ + c₂ e⁻ˣ - 1/2 cos x

Equations with General Differential. Consider the differential equation y′=3x2, which has a derivative and is an illustration of a differential equation. The variable x and y are related because y is an unidentified function of x. The component of y is also on the equation's left-hand side.

The analytical solution is, given that.

⇒ y'' + y = sin x

Now,

The system of equations as follows:

The difference between these two is,

⇒ y'' + y = sin x

Find its auxiliary equation as;

⇒ m² + m = 0

⇒ m (m + 1) = 0

⇒ m = 0 or m = - 1

Therefore, the auxiliary equation is c1 e0 + c2 ex.

                                     = c₁ + c₂ e⁻ˣ

And, Particular integral = 1/(D² + D) (sin x)

                                  = 1/2D (sin x)

                                  = 1/2 (- cos x)

                                  = - 1/2 cos x

Consequently, the differential equation's solution will be;

⇒ y = A.E + P.I

⇒ y = c1 + c2 e x - cos x / 2

As a result, the differential equation's solution is;

⇒ y = c1 + c2 e x - cos x / 2

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The complete question is-

Solve the differential equation by variation of parameters.

y'' + y = sin x

The limit exists, where limx→+∞ ex=+∞  and  limx→+∞ arctanx=π\2

This problem can be solved by dividing it into smaller parts.

Let f(x)=ex and g(x)=arctan(x)

The range of the function arctan(ex) is equal to the intersection of the ranges of f(x) and g(x).

Since the range of f(x) is [0,∞] and the range of g(x) is [−π/2,π/2], the intersection is [0,∞] ∩ [−π/2,π/2] or [0,π/2]

but the limit as x approaches infinity or limx→∞.

Since the highest number in the possible range is π/2, that is the limit as x approaches infinity.

if x is approaching negative infinity or limx→−∞, the answer would be the lowest value in the function's range. Therefore, it would be 0

So, as x→∞, ex→∞ so that, letting t=ex we have limx→∞ arctan(ex)=limt→∞ arctan(t)=π/2.

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Answer:

[tex]k { { { {y6444396}^{46446?} }^342{?} }^66 {6 { { {6636163 \\ }^{2} }^{2} }^{2} }^{2} {?} }^{?} \times \4166441frac{?}{?} [/tex]

Step-by-step explanation:

djdkkwkwnsjididjfjrje

Th area of parallelogram with vertices (-3, 0), b(-1, 7), c(9, 6), and d(7, -1) is 46.5 square units.

The vertices of a parallelogram are a (-3, 0), b(-1, 7), c(9, 6), and d(7, -1).

Area of triangle abc= [tex]\frac{1}{2}[/tex] [tex]\left[\begin{array}{ccc}-3&0&1\\-1&7&1\\9&6&1\end{array}\right][/tex]

=1/2[-3(7-6)-1(-6-63)]

= 1/2[-3(1)-1(-66)]

=1/2[63]

=63/2 sq. units

Area of triangle acd= [tex]\frac{1}{2}[/tex] [tex]\left[\begin{array}{ccc}-3&0&1\\9&6&1\\7&-1&1\end{array}\right][/tex]

=1/2[-3(6+1)-1(-9-42)]

= 1/2[-3(7)-1(-51)]

=1/2[-21 + 51]

=1/2[30]

=15

Area of parallelogram abcd = Area of triangle abc + Area of triangle acd

= 63/2 + 15

= (63 + 30)/2

= 46.5 sq units.

Therefore, the area of the parallelogram is 46.5 sq. units.

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Answer:

correct answer is 72

Step-by-step explanation:

(7²)⁵ * 7⁴ is equal to the expression 7²ˣ⁵ ⁺ ⁴.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

Given an expression (7²)⁵ * 7⁴

Since as per the rule of power we can add the power is base is same and also there is a rule if Power is the power of another power they will be multiplied

From the second rule

(7²)⁵ * 7⁴  = 7²ˣ⁵ * 7⁴

From the first rule of power

7²ˣ⁵ * 7⁴ = 7²ˣ⁵ ⁺ ⁴

therefore, (7²)⁵ * 7⁴ is equal to the expression 7²ˣ⁵ ⁺ ⁴.

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Answer:

there are 12 fourths in 3 .

Answer:

The length of the third side (Hypotenuse) is 7.1556411313

Step-by-step explanation:

In order to find the third side(Hypotenuse) we use a formula called the phytogorean theorem which was invented by a philosopher named Pythagoras.

[tex]a^{2} +b^{2} =c^{2}[/tex]

We now apply the given values to the equation

[tex]5.96^{2} + 3.96^{2} = c^{2}[/tex]

Squaring the numbers we get,

[tex]35.5216+15.6816 = c^{2}[/tex]

[tex]51.2032[/tex] [tex]= c^{2}[/tex]

We now find the root of the number to find the hypotenuse which is,

[tex]\sqrt{51.2032} = c[/tex]

[tex]7.1556411313 = c[/tex]

Hence ,  the length of the third side (Hypotenuse) is 7.1556411313

The maximum number of oranges he can distribute to the ground would be = group C with a total of 115 oranges.

A maximum number is defined as the number that is equal to or greater than other values in a data set.

The various number of oranges distributed by Musa include the following:

Group A Students = 100 oranges

Remaining oranges from group A = 1

Total = 101 oranges

Group B students = 105 oranges

Remaining oranges from group B = 3

Total = 108 oranges.

Group c students = 110 oranges

Remaining oranges from group C = 115 oranges.

Therefore the maximum oranges he distributed was for group C which was 115 in total number.

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