write an equivalent expression to the expression b+b+b+b+b and a sum of two terms

The indicated congruency of the angles ∠BEC and ∠AED (∠BEC ≅ ∠AED) and ∠BEA and ∠CED (∠BEA ≅ ∠CED), according to the alternate interior angles postulate, shows that [tex]\overline{AB}[/tex]║[tex]\overline{CD}[/tex] and  [tex]\overline{BC}[/tex]║[tex]\overline{AC}[/tex] are parallel.

Two segments on a plane are parallel if the distance between the segments remain the same, through the lengths of the segments.

The specified details of the dimensions of the segments in ABCD are;

Segments [tex]\overline{AC}[/tex] bisects segment [tex]\overline{BD}[/tex] and vice versa

Required to prove that [tex]\overline{AB}[/tex] ║ [tex]\overline{CD}[/tex] and [tex]\overline{BC}[/tex] ║ [tex]\overline{AD}[/tex]

The two column consisting of the statements and reasons to prove that the specified sides are parallel is presented as follows;

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

1.    [tex]{}[/tex]   [tex]\overline{AC}[/tex] and [tex]\overline{BD}[/tex] bisect each other           Given

2. [tex]{}[/tex]    [tex]\overline{BE}[/tex] ≅ [tex]\overline{ED}[/tex] and  [tex]\overline{CE}[/tex] ≅ [tex]\overline{AE}[/tex]                   Definition of bisected segments

3.   ∠BEC ≅ ∠AED and  ∠BEA ≅ ∠CED     Vertical angles theorem

4. [tex]{}[/tex] ΔBCE ≅ ΔADE and ΔBEA ≅ ΔCED      SAS congruency rule

5.  [tex]{}[/tex] ∠EBC ≅ EDA and ∠EBA ≅ ∠EDC        CPCTC

6.  [tex]{}[/tex] [tex]\overline{AB}[/tex] ║ [tex]\overline{CD}[/tex] and [tex]\overline{BC}[/tex] ║ [tex]\overline{AD}[/tex]                     Converse of alt. int. ∠s theorem

The details of the reasons in the above table are;

Vertical angles theorem

The vertical angle theorem states that the vertical angles formed by two intersecting straight lines are congruent.

SAS congruency rule

The SAS (acronym for Side-Angle-Side) congruency rule states that if two sides and an included angle in one triangle are congruent to two sides and an included angle in a second triangle, the two triangles are congruent

CPCTC

CPCTC is an acronym for Corresponding Parts of Congruent Triangle are Congruent.

Converse Alt, Int, ∠s theorem

The converse of the alt. int. ∠s (abbreviation for alternate interior angles) theorem state that if the the alternate interior angles formed by two lines and a common transversal are congruent, then the two lines are parallel

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The consecutive numbers are 21 and 22.

Consecutive numbers are numbers that follow each other in order and they have a difference of 1 between every two numbers. 

We shall represent the consecutive numbers with n and (n + 1) so that:

3(n + 1) = 2n + 24 {open bracket}

3n + 3 = 2n + 24

3n - 2n = 24 - 3 {collect like terms}

n = 21

since the lesser number is 21, then the greater number is 21 + 1= 22.

Therefore, the two consecutive numbers such that 3 times the greater number exceeds twice the lesser by 24 are 21 and 22.

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Answer:

Step-by-step explanation:

poop

Answer:

Step-by-step explanation:

System I: This system has one solution. To solve, you would need to first solve for one of the variables, say x. Then, substitute the value of x into the other equation to solve for y.

System II: This system has an infinite number of solutions. To solve, you would need to first solve for one of the variables, say x. Then, substitute the value of x into the other equation to solve for y. Since both equations are linear, they will have an infinite number of solutions.

The domain and range of the the function are given below -

Domain → [-5, 10)

Range → [-3, 3)

Given is a graph of the function.

The domain of a function f(x) is the set of all values for which the function is defined, and the range of the function is the set of all values that function takes. So, we can write the domain as -

Domain → [-5, 10)

Range → [-3, 3)

Therefore, the domain and range of the the function are given below -

Domain → [-5, 10)

Range → [-3, 3)

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Answer:

Step-by-step explanation:

The company breaks even, meaning the profits are $0, only when it sells 10,000 boxes.

Using sum of angles in a triangle theorem and sine law, the angle x is 20 degrees, while the length of y and z are 25.83 and 26 respectively.

Sine law is a mathematical law that states that the ratio of the lengths of two sides of a triangle to the sines of the angles opposite to them is constant. It is also known as the sine rule or the law of sines.

This is represented mathematically as;

x /sin X = y / sin Y = z / sin Z

To find angle X, we can simply use the theorem of sum of angles in a triangle.

X + Y + Z = 180°

X + 79 + 81 = 180

X = 20°

Using sine law

x / sin X = y / sin Y

9 / sin 20 = y / sin 79

y = (9 * sin 79) / sin 20

y = 25.83

Using sine rule again

z / sin Z = x / sin X

z / sin 81 = 9 / sin 20

z = (9 * sin 81) / sin 20

z = 25.99≅ 26

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[tex]\textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \sqrt{c^2 - b^2}=a \qquad \begin{cases} c=\stackrel{hypotenuse}{12}\\ a=adjacent\\ b=\stackrel{opposite}{9}\\ \end{cases} \\\\\\ \sqrt{12^2 - 9^2}=a\implies \sqrt{144 - 81}=a\implies \sqrt{63}=a[/tex]

Answer:

square root 27

Step-by-step explanation:

3³/² =

(3×3×3 )½ =27½

Answer:

19.7

Step-by-step explanation:

A^2 + B^2 = C^2

8^2 + 18^2 = sqrt(388)

Answer: A. AB = BC can be proven true.

An isosceles triangle has two equal side lengths, and since the vertex angle is angle C, it means that sides AB and BC are the equal sides.

B. angle A = angle B can be proven true.

In an isosceles triangle, since the two sides are equal, the base angles are also equal.

D. segment BC = segment AC can be proven true.

In an isosceles triangle, since the two sides are equal, the base segments are also equal.

E. segment AB = segment AC can be proven true.

In an isosceles triangle, since the two sides are equal, the base segments are also equal.

C. angle B = angle C is not true.

Because the vertex angle is angle C, and it is formed by the two base segments, so it will be different than angle B and angle A.

Step-by-step explanation:

Answer:

  B, D

Step-by-step explanation:

You want to know what you can prove, given that the vertex angle of isosceles triangle ABC is angle C.

A triangle is isosceles if it has two congruent sides or two congruent angles. In either case, the angles opposite the congruent sides are congruent, and vice versa.

The vertex angle is opposite the "base" of the isosceles triangle. The sides of the vertex angle are the congruent sides, and the angles that are not the vertex angle are the congruent angles.

These sides share point B, which is not the vertex. This cannot be proven.

These are the base angles of the triangle, hence congruent. This can be proven.

These angles cannot be proven congruent using the given information. This will be true if and only if the isosceles triangle is also an equilateral triangle.

These sides share point C, which is the vertex. This can be proven.

These sides share point A, which is not the vertex. This cannot be proven.

The angles forming the triangle must be equal to prove that they are parallel.

Two triangles are similar if they have the same ratio of corresponding sides and equal pair of corresponding angles.

Given here: AX/AB=XY/BC=AY/AC

Thus the triangles are similar (ΔAXY≈ABC)

Therefore ∠x=∠B & ∠Y=∠C , so we can conclude that the two lines (XY||BC)

Hence, The angles forming the triangle must be equal to prove that they are parallel.

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Answer:

It can be represented as a fraction, 276/1000. It isn't non-terminating.

0.276 is a rational number because we can write it as a fraction, where both denominator and numerator are integers.

The point corresponding to the transformed function y=f(x/x)+1 is approximately (-4, 4.25), (-2, 2.5), (0, 1), (1, -0.5), (3, 1). 

we need to substitute x/x = 1 for the argument of the function f(x) and add 1 to the result.

Transformed point on point y on f(x) = f(x/x) + 1

(x, f(x)) (x, f(x/x) + 1)

(-4, 5) (-4, f(-2) + 1) ≒ (-4, 4.25)

(-2, 3) (-2, f(-1) + 1) ≈ (-2, 2.5)

(0, 0) (0, f(0) + 1)

= (0, 1)

(1, -2) (1, f(1) + 1) ≈ (1, -0.5)

(3, -4) (3, f(3/3) + 1) ≈ (3, 1)

Note that for the point (-4,5) you have to substitute x/x = -1/2 instead of x/x = 2. This gives x = -8. So the corresponding transformed point is (-4, f(-8) + 1) ≈ (-4, 2.75).

So the point corresponding to the transformed function y=f(x/x)+1 is approximately

(-4, 4.25), (-2, 2.5), (0, 1), (1, -0.5), (3, 1). 

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Answer: To solve for t in terms of P, I and r, we'll use algebraic manipulation of the given formula:

I = Prt

To solve for t, we'll divide both sides of the equation by Pr:

I/Pr = t

So, t = I/Pr

So we can say that the time (in years) is the ratio of the interest earned over the product of principal and the interest rate.

Step-by-step explanation:

Answer:

I/Pt

Step-by-step explanation:

bottom one wrong ash

Answer:

3/2

Step-by-step explanation:

8 ratio 12 would be 2/3. but to get the right ratio sequence, we switch up the fraction to give the right answers. so 3/2 as in 12 ratio 8.

Answer:

To determine whether the three points P, Q, and R are colinear, we can calculate the distances between pairs of points using the distance formula:

d(P,Q) = √((-8 - (-7))^2 + (4 - 6)^2 + (-11 - (-8))^2) = √((-1)^2 + (-2)^2 + (-3)^2) = √14

d(Q,R) = √((-9 - (-8))^2 + (3 - 4)^2 + (-14 - (-11))^2) = √((-1)^2 + (-1)^2 + (-3)^2) = √9

d(P,R) = √((-9 - (-7))^2 + (3 - 6)^2 + (-14 - (-8))^2) = √((-2)^2 + (-3)^2 + (-6)^2) = √19

If the three points are collinear, the distance between any two points should be a multiple of the distance between the other two points. Since √14, √9, and √19 are not multiples of each other, it can be concluded that the three points P, Q, and R are not collinear.

Answer:

It means there is no solution.

Step-by-step explanation:

When you work on a system of equations and the variable falls out of the equation and you're left with a false statement...that means there is no solution.

Answer:

2^6009 + 6^2003 / 49 ig lol

Answer:

  see attached

Step-by-step explanation:

You want a parallelogram with angles of 20° and 160°.

The drawing will start with a line for one side. An angle of 20° can be drawn using a protractor, geometry app, or by approximating its slope.

The slope of a line 20° from the x-axis is tan(20°) ≈ 0.36397. A line with a slope of 4/11 = 0.3636... will have an angle of about 19.983° from the x-axis. For accuracy you can expect in a hand-drawn figure, this is "close enough." It is probably closer to 20° than you could draw using a protractor.

A parallelogram with the required angles is shown in the attachment. Point B is 11 units right and 4 units up from point A, so the angle at A is 20° when rounded to the nearest tenth.

__

Additional comment

Another very close approximation of tan(20°) is 9.9/27.2. A line with that slope makes an angle of 20.00002° with the x-axis.

When the triangle has a base of 3 inches and an area of 5 square inches, its height is 3.33 inches.

Since a polygon has number of sides and three vertices, it is a polygon. It is a fundamental geometric shape. Triangle ABC is the moniker given to a pyramid that has vertices A, B, and C. When the three factors are not collinear, a singular plane and triangle are found in Euclidean geometry. A triangle is a polygon if it has three sections and three corners. The points where the three sides meet are known as the triangle's corners. The product of three triangle angles is 180 degrees.

given

triangle's surface area is equal to 1/2 * b*h

5 = 1/2 * 3 * h

10 = 3h

h = 3.33 inches.

When the triangle has a base of 3 inches and an area of 5 square inches, its height is 3.33 inches.

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Answer:

Step-by-step explanation:

Let's start by labeling the sides of the triangle ABC:

A = 12

B = x

C = 10

Using the Law of Cosines, we can write the following equation:

C² = A² + B² - 2ABcos(C)

Substituting the values we have, we get:

10² = 12² + x² - 2(12)(x)cos(10)

Simplifying, we get:

100 = 144 + x² - 24xcos(10)

Rearranging, we get:

x² - 24xcos(10) + 44 = 0

Solving for x, we get:

x = [24cos(10) ± √(576cos²(10) - 176)]/2

Calculating the values, we get:

x = [24cos(10) + √(5232)]/2 ≈ 18.3

x = [24cos(10) - √(5232)]/2 ≈ 7.7

Therefore, BC = 18.3 or BC = 7.7

Refer to the image attached.

The value of x in this equation is found to be 8±4√7.

What is Pythagoras theorem?

The hypotenuse's square is equal to the sum of the squares of the other two sides if a triangle has a straight angle (90 degrees), according to the Pythagoras theorem. Keep in mind that BC2 = AB2 + AC2 in the triangle ABC signifies this. Base AB, height AC, and hypotenuse BC are all used in this equation. The longest side of a right-angled triangle is its hypotenuse, it should be emphasized.

Here given in the question that one side of the wall 5 feet

So as it is a rectangular bedroom it can be split into 2 right-angled triangles.

So the hypotenuse of the triangle is 13 feet

Now using the Pythagoras theorem we can find out the length of the other wall

b²=h²-p²

(x-4)²+(x+6)² = (x+10)²

x²+16-8x+x²+36+12x = x²+100+20x

x²-16x-48=0

x= 8±4√7.

Hence The value of x in this equation is found to be 8±4√7.

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The correct statements about the graph are given as follows:

The rise and the run of a graph are defined as follows:

The slope of a line is given by the change in y divided by the change in x, hence it's equation is given as follows:

Slope = Rise/Run.

For the first triangle, the rise and the run are given as follows:

Hence the slope is of:

Slope = -6/3 = -2.

For the second triangle, the rise and the run are given as follows:

Hence the slope is of:

Slope = -2/1 = -2.

As the ratios are the same, the triangles are similar, the line has a slope of -2, and the corresponding sides are proportional.

The graph is given by the image presented at the end of the answer.

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An ordered pair (x, y) that is a solution to the equation include the following: (x, y) = (-3, 0).

In Mathematics, an ordered pair is sometimes referred to as a coordinate and it can be defined as a pair of two (2) elements or data points that are commonly written in a fixed order within parentheses as (x, y), which represents the x-coordinate (abscissa) and the y-coordinate (ordinate) on the coordinate plane of any graph.

In order to determine the ordered pairs that represent points on the graph of the given function, we would plot its equation by using an online graphing calculator and then read all the ordered pairs that lie on the line.

By critically observing the graph of the given function (see attachment), the required solutions are include following;

Ordered pair = (0.75, 0).

Ordered pair = (-3, 0).

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To solve the equation for x, locate squares a, b, and c and use the quadratic formula. x= [tex]-1\±I[/tex]

A second order polynomial can be used to define a square. It has at least one term that needs to be squared, in other words. They go by the name quadratic equations as well. The quadratic equation's generic form is

[tex]ax^2\+ bx + c = 0[/tex]

Where x is an unknown variable and a, b, and c are numerical coefficients, the formula is: ax2 + bx + c = 0. An example of a quadratic equation is x2 + 2x + 1. in which a 0. The equation becomes a linear equation when this value is zero and ceases to be a quadratic equation.

bx+c=0

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a. The mean stock price of Cenovus Energy is 15.437.

b. The standard deviation for the sample prices of Cenovus Energy is

3.93.

c. The median stock price for Cenovus Energy is 14

d.  The range in Cenovus Energy's stock price is 11.5.

e. The coefficient of variation for each stock are 28.071% Cenovus Energy for % and 9% for TD Bank.

f. As the coefficient of variation is more for TD Bank it is riskier to buy.

The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers. While a high standard deviation suggests that the values are dispersed over a wider range, a low standard deviation suggests that the values tend to be close to the mean.

a. The mean stock price of Cenovus Energy is,

= (18 + 19 + 12 + 16 + 17.50 + 12 + 7.50 + 10)/8.

= 112/8.

= 14.

b. The variance for the sample prices of Cenovus Energy is,

= [tex]\frac{1}{n}\[ \sum_{i=1}^{n}[x_i - \overline{x}]^2[/tex].

= (1/8)×[(18 - 14)² + (19 - 14)² + (14 - 12)² + (16 - 14)² +(17.50 - 14)² +(14 - 12)² +(14 - 7.50)² + (14 - 7.50)² +(14 - 10)²].

= (1/8)×[16 + 25 + 4 + 4 + 12.25 + 4 + 42.25 + 16].

= (1/8)×(123.5).

= 15.437.

Standard deviation = √(15.437).

= 3.93.

c. To find the median stock price for Cenovus Energy first we have the data set in ascending order.

7.50, 10.00, 12.00, 12.00, 16.00, 17.50, 18.00, 19.00.

So, The median of the stock price for Cenovus Energy is,

= (12 + 16)/2.

= 28/2.

= 14.

d. The range in Cenovus Energy's stock price is (19.00 - 7.50).

= 11.5.

e. The coefficient of variation for each stock is,

CV = {(Standard Deviation)/(Mean)}×100%.

CV = (3.93/14)×100%.

CV = 28.071 for Cenovus Energy.

CV = (6.30/70)×100%.

CV = 9% for TD Bank.

f. TD Bank's higher coefficient of variance makes investing riskier.

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The possible lengths for the third side 8² + 11² < x²,  8² + 11² = x²

and 8² + 11² ≥ x².

If a² + b² < c² then it is an acute angle triangle.

If a² + b² = c² then it is a right-angle triangle.

If a² + b² ≥ c² then it is an obtuse angle triangle.

Given, Two sides of a triangle have lengths 8 and 11.

Let, The third side be 'x'.

Therefore, The possible lengths for the third side are,

8² + 11² < x²...(i)

8² + 11² = x²...(ii)

8² + 11² ≥ x²...(iii)

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Answer:

[tex]3x^{2}[/tex] + x + 6

Step-by-step explanation:

The function f( x ) = |cos( π x )| is differentiable everywhere on the interval ( 0 , 5 4 ) except at x= 1/2.

The correct option is (C).

In mathematics, a function is represented as a rule that produces a distinct result for each input x.

The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.

Given:

Function, f( x ) = |cos( π x )|

Now, if we plot the graph for function f( x ) = |cos( π x )|.

The graph touches the x axis at two points, x= 0.5 and x= 1.25.

We know, the function touches at point on x- axis cannot be differentiable at that point.

Hence, except x= 0.5 the function is differentiable.

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