AE and CD intersect at point B. Find m

The specified details of the triangle, obtained using the segments joining the midpoints of the sides of the triangle ΔADG and trapezoid ACFG indicates that we get;

4. [tex]\overline{CE}[/tex] is a midsegment of ΔBDF

[tex]\overline{BF}[/tex] is the midsegment of trapezoid ACFG

5. CE = 12 cm, AG = 36 cm

6. m∠2 = 116°, m∠3 = 32°, m∠4 = 58°, m∠5 = 58°, m∠6 = 64°

The midpoint of a segment or the side of a triangle is a point that divides the segment into two parts of the same length.

4. The details of the diagram indicates that the segment [tex]\overline{CE}[/tex] is the midsegment of triangle ΔBDF

[tex]\overline{BF}[/tex] is the midsegment of trapezoid ACFG

5. [tex]\overline{CD}[/tex] is congruent to [tex]\overline{BC}[/tex] by the definition of the midpoint of [tex]\overline{BD}[/tex], similarly;

[tex]\overline{BC}[/tex] is congruent to [tex]\overline{AB}[/tex], by the definition of midpoint of [tex]\overline{AC}[/tex], therefore;

[tex]\overline{CE}[/tex] is the midsegment of triangle ΔBDF, therefore;

CE = (1/2) × BF

CE = (1/2) × 24 cm = 12 cm

CE = 12 cm

ΔBDF and ΔADG and ΔCDE are similar triangles, therefore;

[tex]\overline{BD}[/tex] = (2/3) × [tex]\overline{AD}[/tex]

Similarly, by the relationship between similar triangles we get;

[tex]\overline{BF}[/tex] = (2/3) × [tex]\overline{AG}[/tex]

BF = 24 cm, therefore;

24 = (2/3) × AG

AG = (3/2) × 24 = 36

AG = 36 cm

6. The length of a median of a right triangle, drawn from the right angled vertex, is half the length of the hypotenuse side.

Therefore; ΔACM and ΔABM are an isosceles triangles

m∠1 = m∠3 = 32°

m∠2 = 180° - (32° + 32°) = 116°

m∠2 = 116°

m∠3 = 32°

m∠4 = m∠5 = 90° - m∠1

m∠4 = m∠5 = 90° - 32° = 58°

m∠4 = 58°

m∠5 = 58°

m∠6 = 180° - (m∠4 + m∠5)

m∠6 = 180° - (58° + 58°) = 64°

m∠6 = 64°

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To write the equation y = -13x + 102 in irrational form, we need to isolate x on one side of the equation.

First, let's subtract y from both sides to get:

-y + y2 = -13x + y2 + 102

Next, let's divide both sides by -13 to get:

x = (-1/13)y2 + (1/13)y - (102/13)

Therefore, the irrational equation of y2 = -13x + 102 is:

x = (-1/13)y^2 + (1/13)y - (102/13)

Applying the laws of cosine, in the second section of her ride, Andariel traveled about 3.012 km, as rounded to 2 decimal places.

The law of cosines is a mathematical formula used to determine the unknown length or angle of a triangle when two sides and an angle or all three sides are known.

Hence, we can think of it as trying to know Andariel's travel distance around a big triangle.

Thus to calculate, using the law of cosines, we have:

[tex]c^2 = a^2 + b^2 - 2ab*cos(C)[/tex]

Where in our case:

If we substitute the values above into the cosine formula, we get:

[tex](5.5)^2 = (6)^2 + (x)^2 - 2(6)(x)*cos(55)[/tex]

[tex]30.25 = 36 + x^2 - 12.0627x[/tex]

Simplifying and rearranging the equation further:

[tex]x^2 - 12.0627x + 5.75 = 0[/tex]

Applying the quadratic formula to simply:

[tex]x = (12.0627 ± sqrt(12.0627^2 - 415.75))/2[/tex]

x = 9.05 or x =3.012.


Remember, we are told Andariel turned left twice and ended up at her starting position, we know that she traveled in a closed loop.

Therefore, the distance she traveled in the second section of her ride must be less than 6 km (the distance she traveled east in the first section). Thus, the distance she traveled last or second section of her ride was 3.012 km.

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There are 8 ounces of cereal left in the box.

Dena ate 1/6 of the cereal, leaving 5/6 of the box for Joey.

Joey then ate 2/3 of the box, which is equivalent to (2/3) × (5/6) = 10/18 of the box.

The amount of cereal left in the box is therefore 18 - 10 = 8 ounces.

Therefore, there are 8 ounces of cereal left in the box.

Answer:

150+92+168=410

Step-by-step explanation:

Answer: (28 / 4) + 3 = x; x = the regular price of a notebook not on sale.

Step-by-step explanation: The price of the notebook on sale is $7 and the price of a notebook regularly is $10 (not on sale). Therefore, the equation "(28 / 4) + 3 = x" explains how to come to that value.

There is a 1/3 chance, or around 0.333, that a randomly chosen passenger will have to wait longer than 10 minutes during one of these times.

What is probability?

Calculating the likelihood of experiments happening is one of the branches of mathematics known as probability. We can determine everything from the likelihood of receiving heads or tails when tossing a coin to the likelihood of making a research blunder, for instance, using a probability.

Since waiting times follow a uniform distribution on the interval from 0 to 15 minutes, the probability density function (PDF) is:

f(x) = 1/15, for 0 ≤ x ≤ 15

The probability that a randomly selected passenger has to wait more than 10 minutes is:

P(X > 10) = ∫10¹⁵ f(x) dx

P(X > 10) = ∫10¹⁵ 1/15 dx (since f(x) = 1/15 for 0 ≤ x ≤ 15)

P(X > 10) = [x/15]10¹⁵

P(X > 10) = (15 - 10)/15

P(X > 10) = 5/15

P(X > 10) = 1/3

Therefore, there is a 1/3 chance, or around 0.333, that a randomly chosen passenger will have to wait longer than 10 minutes during one of these times.

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The number of touchdowns are 4, field goals are 2 and safeties are 2 for the given system of equation.

A system of equations in algebra consists of two or more equations and looks for common answers to the equations. "A collection of equations fulfilled by the same set of variables is called a system of linear equations." Finding the values of the variables employed in a system of equations entails solving the set of equations. By keeping the equations balanced on both sides, we compute the values of the unknown variables. Finding the value of the variable that makes the condition of all the provided equations true is the primary goal when solving an equation system.

Let us suppose touchdowns = x.

Let us suppose field goals = y.

Let us suppose safeties = z.

Given that, they score point 8 times, thus:

x + y + z = 8

The total points scored are 38 thus,

7x + 3y + 2z = 38

Also,

x = (y + z)

Substituting the value of y + z in equation 1 we have:

x + x = 8

2x = 8

x = 4

Substitute the value of x in second equation:

7(4) + 3y + 2z = 38

28 + 3y + 2z = 38

3y + 2z = 10

Now, using x = (y + z). we have:

4 - z = y

Substitute the value of y:

3y + 2z = 10

3(4 - z) + 2z = 10

12 - 3z + 2z = 10

-z = -2

z = 2

Substitute the value of x and z:

x = (y + z)

4 = y + 2

y = 2

Hence, the number of touchdowns are 4, field goals are 2 and safeties are 2 for the given system of equation.

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Answer:

no. four

Step-by-step explanation:

Price of the oranges per pound..

Answer:

Step-by-step explanation:

Type of orange

Answer:

A/C/E/F/G/H

Step-by-step explanation:

all of them have the same rotations there just have been turned around

Answer:

0.03

Step-by-step explanation:

Answer:

.03

Step-by-step explanation:

x = .24(1/8)

x = .24/8

x = .03

Helping in the name of Jesus.

The degree of the polynomial is 2, and the leading coefficient is 3. The polynomial has two terms, so we classify it as a binomial.

What is the polynomial equation?

A polynomial equation is an equation in which the variable(s) are raised to non-negative integer powers and the coefficients are constants. In other words, it is an equation in which the terms involve only addition, subtraction, multiplication, and positive integer exponents.

The expression is 7 + 3p²

To write the polynomial in standard form, we need to arrange the terms in descending order of degree:

3p² + 7

hence, The degree of the polynomial is 2, and the leading coefficient is 3. The polynomial has two terms, so we classify it as a binomial.

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The compound interest on birr 5006 at 5% for 4 years compounded annually​ is $1,078.82.

Compound interest is a type of interest that is calculated not only on the initial principal amount but also on the accumulated interest of previous periods.

In other words, the interest earned during each period is added to the principal amount, and the interest for the next period is calculated on the sum of the principal and the accumulated interest.

Given that:

First, convert R as a percent to r as a decimal

r = R/100

r = 5/100

r = 0.05 rate per year,

Then solve the equation for A

A = P(1 + r/n)^(nt)

A = 5,006(1 + 0.05/1)^(1*4)

A = 5,006(1 + 0.05)^(4)

A = $6,084.82

Compound interest =Amount - Principal

Compound interest = 6084.82 - 5006

Compound interest = $1,078.82

Therefore, The total amount accrued, principal plus interest, with compound interest on a principal of $5,006.00 at a rate of 5% per year compounded 1 time per year over 4 years is $6,084.82.

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The surface area of the triangular prism is 1152 inches square.

The triangular prism has the base as a right triangle with base of 9 inches, height of 12 inches and third side of 15 inches. The height of the prism is 29 inches.

Therefore,

surface area of a triangular prism = bh + l(s₁ + s₂ + s₃)

where

surface area of a triangular prism = 9 × 12 + 29(9 + 12 + 15)

surface area of a triangular prism = 108 + 29(36)

surface area of a triangular prism = 108 + 1044

surface area of a triangular prism = 1152 inches

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The percentage of all possible values of the variable that lie between 10 and 16 is 97.71%, the percentage of all possible values of the variable that are at least 18 is 0.01% and the percentage of all possible values of the variable that are at most 8 is 0.01%.

Given that, variable is normally distributed with mean and standard deviation .

To find the percentage of all possible values of the variable that lie between and .

We can convert the given variable to standard normal variable using Z= (X- μ )/ σ

Therefore, we get, Z1 = (10- 12)/ 1 = -2 And Z2 = (16-12)/1 = 4

Thus, the probability of values that lie between 10 and 16 is given by

P(-2 ≤ Z ≤ 4) = P(Z ≤ 4) - P(Z ≤ -2) = 0.9999 - 0.0228 = 0.9771 = 97.71%.b)

To find the percentage of all possible values of the variable that are at least .Converting the given variable to standard normal variable using Z= (X- μ )/ σ, we get,

Z = (18-12)/1 = 6

The probability of values that are at least 18 is given by

P(Z ≥ 6) = 1- P(Z ≤ 6) = 1- 0.9999 = 0.0001 = 0.01%.c)

To find the percentage of all possible values of the variable that are at most .Converting the given variable to standard normal variable using Z= (X- μ )/ σ, we get,

Z = (8-12)/1 = -4

The probability of values that are at most 8 is given byP(Z ≤ -4) = 0.0001 = 0.01%.

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Answer: -25 and 11

solution:

|x+7| - 18 = 0

|x+7| = 18
±x = 18 ± 7

x = -25, 11

Answer:119.7

Step-by-step explanation:60 divided by 15%

When b > 1, the function f (x) = bx represents exponential development. If 0 b 1, then the function f (x) = bx depicts exponential decay.

A relation is any subset of a Cartesian product.

As an illustration, a subset of is referred to as a "binary connection from A to B," and more specifically, a "relation on A."

A binary relation from A to B is made up of these ordered pairs (a,b), where the first component is from A and the second component is from B.

Every item in a set X is connected to one item in a different set Y through a connection known as a function (possibly the same set).

A function is only represented by a graph, which is a collection of all ordered pairs (x, f (x)).

Every function, as you can see from these definitions, is a relation from X.

Hence, Exponential growth and decay are the two different kinds of exponential functions.

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Answer:

Step-by-step explanation:

The point estimate of the population​ proportion, the margin of error is 0.365.

Margin of error is a statistic that expresses the amount of random sampling error in survey results. The larger the margin of error, the less confident people are that the poll results will reflect the overall census results. When the population is incompletely sampled and the resulting measure has a positive variance, the margin of error will be positive, i.e. the measures differ. The term margin of error is often used in non-survey contexts to refer to the error observed in the reporting of measured quantities.

According to the Question:

Given that:

Lower bound = 0.123​,

Upper bound = 0.607​,

n = 1000

P = Lower Bound + Upper Lower /2

  = 0.123 + 0.607/2

  = 0.73/2

  = 0.365

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a. Midpoint of AB, BC, CD, DA is (4,4), (0,-4), (-4,-4),(-4,4) respectively. b.  polygon formed by connecting the consecutive midpoints. c.  get a smaller square inside the square.

In geometry, the midpoint refers to the point that is exactly halfway between two given points, lines, or line segments. It is the point that divides a line segment into two equal parts. The midpoint is also known as the half-way point.

The midpoint can be found using a variety of methods, but the most common one is by using the midpoint formula, which is:

Midpoint = [(x1 + x2)/2, (y1 + y2)/2]

Where (x1, y1) and (x2, y2) are the coordinates of the two points.

The midpoint is an important concept in many mathematical and scientific fields, including physics, engineering, and computer graphics. It is often used to determine the center of mass, the point of balance, or the halfway point in a process or journey.

a. We can use the midpoint formula to find the midpoint of each side of the square:

Midpoint of AB: ((0+8)/2, (8+0)/2) = (4,4)

Midpoint of BC: ((0+0)/2, (-8+0)/2) = (0,-4)

Midpoint of CD: ((-8+0)/2, (0-8)/2) = (-4,-4)

Midpoint of DA: ((-8+0)/2, (0+8)/2) = (-4,4)

b. Connecting the consecutive midpoints of each side of a square creates a smaller square inside the original square. We can see this by observing that the midpoints of opposite sides of a square form the vertices of a smaller square.

The polygon formed by connecting the consecutive midpoints of each side of the square is a square.

c. If we repeat the process of connecting consecutive midpoints one more time, we will get a smaller square inside the square formed in part (b). This smaller square will have vertices at the midpoints of the sides of the square formed in part (b). We can see this by observing that the midpoints of the sides of a square form the vertices of a smaller square inside that square.

So the polygon that would result from connecting the consecutive midpoints of each side of the polygon determined in part (b) is another square.

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Answer: /

Step-by-step explanation:

the pattern of the numbers 1,3,6,10,15,21,28,36. What is the 5857th triangular number: The unit digit of the 5857th triangular number is 8.

A series of numbers known as triangular numbers might be demonstrated as the amount of a series of positive whole numbers. The condition Tn = (n(n+1))/2 yields the nth triangular number. The initial not many triangular numbers, for example, are 1, 3, 6, 10, 15, etc. Numerous numerical and non-numerical applications exist for triangular numbers. They can be found, for example, in the investigation of math, combinatorics, and number hypothesis. They are used in calculations for information looking and arranging in fields like software engineering, where they have reasonable applications.

The nth triangular number is given by the recipe:

Tn = (n(n+1))/2

For the given arrangement 1,3,6,10,15,21,28,36, the units digit are:

1, 3, 6, 0, 5, 1, 8, 6, 5, 5, 6, 8, 1, 5, 0, 6, 3, 1, 0, 0, 1, 3, 6, 0, 5, ...

The worth of 5857 is compatible with 7 modulo 10.

Consequently, the unit digit is the seventh number in the cycle above, which is 8.

Thus, the unit digit of the 5857th triangular number is 8.

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the complete question is:

Here is the sequence of numbers called triangular numbers: 1,3,6,10,15,21,28,36, Notice the pattern -the numbers increase by one more each time. What is the unit's digit of the 5857th triangular?

Answer:

1.True

2.False

3.True

4.False

The value of cosec ( Ф/2 ) obtained using the double angles formula and half angle identity is : cosec ( Ф/2 ) = 5/√2.

In trigonometry, the double angles for trigonometric functions are dealt with via the double angle formulas. Other significant double angle formulas include:

cos Ф = 3/5

By using half angle identity:

cos( Ф/2 ) = ±  √(1 + cosФ)/2

cos( Ф/2 ) = ±  √(1 + 3/5)/2

cos( Ф/2 ) = ±  √8/10

cos( Ф/2 ) = ±  √2/5

In first quadrant:

cos( Ф/2 ) = +√2/5

Using reciprocal identity:

cosec ( Ф/2 ) = 1/ cos( Ф/2 )

cosec ( Ф/2 ) = 1/√2/5

cosec ( Ф/2 ) = 5/√2

Thus, the value of cosec ( Ф/2 ) obtained using the double angles formula and half angle identity is : cosec ( Ф/2 ) = 5/√2.

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Answer:

Should be A

Step-by-step explanation:

Answer:

158degrees

Step-by-step explanation:

2 = 68 ( vertically opposite)

4 = 90 (Vertically opposite)

6= 68 +90 = 158( exterior angle is sum of its opposite interior)

Answer : n⁸

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Answer:

The Position Vectors of points A,B,C with respect to the origin are 8i-10j, 2i+6j and -10i +4j respectively. If ABCN is a parallelogram find The Position Vector of N. /AN/ and /AB/. Acute angle between AN and AB