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V to Inlogic

1. ABCD is a parallelogram

2. AB II CD

3. D is the midpoint of BE

4. AD II BC

5. ∠BAD = ∠CDE

6. AB = CD

7. BD = CE

8. AABD ACDE

A parallelogram is a four-sided shape with two pairs of parallel sides. Its opposite sides are equal in length, and its opposite angles are also equal. Its interior angles add up to 360 degrees. The defining property of a parallelogram is that both pairs of its opposite sides are parallel, meaning they never intersect. This is in contrast to a rectangle, which has four right angles and four sides of equal length, but its opposite sides are not parallel. A parallelogram is also different from a rhombus, which has all sides of equal length, but its opposite sides are not parallel.

Proof:  1. Given: ABCD is a parallelogram

2. Given: AB II CD

3. Given: D is the midpoint of BE

4. Since D is the midpoint of BE, BD = CE

5. Since ABCD is a parallelogram, AD II BC

6. Since AB II CD and AD II BC, ∠BAD = ∠CDE [Angle-Angle Postulate]

7. Since AB II CD and BD = CE, AB = CD [Side-Side-Side Postulate]

8. Therefore, AABD ACDE [Consecutive Angles Postulate]

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According to the question the Statement and the Reasons is given below:

A statement is an assertion or declaration made by a person or group. It is a fact, opinion, or belief that is expressed as a sentence or short phrase. Statements are typically used to communicate ideas, opinions, facts, or beliefs. They can be used to make an argument, express a point of view, or inform someone of something. Statements can be found in a variety of contexts, including speeches, reports, documents, interviews, and conversations.

      Statement                      |                 Reasons.

1. ABCD, AB|CD                    | Given

2. D is the midpoint of BE    | Given

3. AD = DB                            | Definition of midpoint

4. AB + BD = AE                   | Segment addition postulate

5. AB + AD = AE                  | Substitution 3

6. AABD = ACDE                 | Segment addition postulate. Subtraction                
                                              postulate. Substitution 5.

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For the given analogous polygons, in exercise 37 x = 32, y = 18, and in exercise 38, x = 5, y = 166 °.

A polygon is an unrestricted polygonal chain made up of line parts that are connected to produce an area plane figure in figure. The borders or sides of an unrestricted polygonal chain are the individual pieces. The polygon's vertices or corners are the places where two lines meet. A solid polygon's body is its Centre. A polygon is a geometric object with two confines and a limited number of sides. A polygon's sides are made up of pieces of straight lines that are joined end to end. As a result, a polygon's line pieces are appertained to as its sides or edges. Vertex or angles relate to the crossroad of two-line parts, where an angle is created. Having three edges makes a triangle apolygon.What's a commen surable relationship? Proportional connections are connections between two variables where their rates are original. Another way to suppose about them is that, in a commensurable relationship, one variable is always a constant value times the other. That constant is known as the" constant of proportionality".

In the given question.

for exercise 37,[tex]39/(x-6)=27/y=24/1839/(x-6) =24/18=3/2[/tex]

on solving,[tex]3x-18= 78x=3227/y=3/23x=54y=18[/tex]

For exercise 38on comparing,[tex]x=5y-73=360-(61+116+90)y-73=93y=166degree[/tex]

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Answer:

slope of 3/4 = line C

undefined slope = line A

Step-by-step explanation:

remember that slope is [tex]\frac{rise}{run}[/tex]. Pick any two points on the graph and count up and over to find the rise/run.

OR

use the slope formula [tex]m=\frac{y_{2} -y_{1} }{x_{2}-x_{1} }[/tex] to plug the two points into and find the slope.

- vertical lines are always undefined.

- horizontal lines have a slope of 0

Answer:

Give me time to figure this out hold on

Step-by-step explanation:

12

As the two triangles are congruent by AAS congruence rule, the segments AB is equivalent to FG.

If two triangles are the same size and shape, they are said to be congruent.

To establish that two triangles are congruent, not all six matching elements of either triangle must be located.There are five requirements for two triangles to be congruent, according to studies and trials.

The congruence properties are SSS, SAS, ASA, AAS, and RHS.

Now in the given figure,

D is the midpoint, so CE = BG.

∠ABC ≅ ∠FGE

That gives us, AB ≈ FG as sides corresponding to equivalent sides are also equivalent to each other.

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The probability that their two sons will both have hemophilia is 0%.

Hemophilia is a sex-linked recessive disorder, which means that it is passed from mother to son. Since the woman does not have the disorder, she does not carry the gene for it and therefore her sons would not be affected by the disorder.

However, her daughters could be carriers of the disorder and could pass it on to their sons.

In order for a son to be affected by hemophilia, his mother must carry the gene for the disorder and the father must also have the gene. If the father does not have the gene, then the son will not have hemophilia.

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Answer:

To calculate a percentage decrease, first, work out the difference (decrease) between the two numbers you are comparing. Next, divide the decrease by the original number and multiply the answer by 100. The result expresses the change as a percentage—i.e., the percentage change.

Promotion 50√2 (or about 70.7) coupons need to be sent in order to get 100 customers to make a purchase.

The given problem states that around 80% of customers who receive a promotion coupon will visit the store. But only 20% of those in the store will make a purchase.

The problem asks us to determine how many promotion coupons have to be sent in order to get 100 customers to make a purchase.

Therefore, let the number of coupons to be sent be x.

Then, 80% of x people will visit the store. Therefore, the number of people who will visit the store is

(80/100)x or (4/5)x people.

However, only 20% of those in the store will make a purchase.

Therefore, the number of customers who make a purchase is (20/100) x (4/5)x = (1/25)x² customers.

We need to find x such that (1/25)x² = 100.

Therefore, x² = 25 × 100. Hence, x = √2500 or x = 50√2.

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The amount of work (in foot-pounds) done in stretching a spring from its natural length to 0.8 feet beyond its natural length is 24.

so we have W=6lbs*(0.8ft-0.6ft)

=6lbs*0.2ft

=24ft-lbs.

Work is the measure of the amount of energy required to move an object over a certain distance, so to stretch the spring 0.8 feet beyond its natural length, 24 foot-pounds of work is done.

This can also be understood as the product of the force (6lbs) and the displacement (0.2ft). Work is a scalar quantity, meaning it only has magnitude and not direction.

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Answer:

The three correct ways to describe an angle with a measure of 13° are:

Thirteen degrees

An acute angle with a measure of 13°

An angle that is less than a right angle and has a measure of 13°

Answer:

Step-by-step explanation:

a. 100 divided by 75 = 1.3333333333333333333333333333333

1.3333333333333333333333333333333 times 43 = 57.333333333333333333333333333332

round it to the nearest whole number: ≅ 57%

Answer:

True

False

72

72

96

30

See below.

Step-by-step explanation:

First statement: True

A unit cube is a cube with an edge length of 1 unit.

Its volume is (1 unit)³ = 1 unit³

Second Statement: False

A unit cube cannot be used to measure the volume of "other 2D shapes" since a 2D shape has no volume. Only a 3D shape can have a volume. The word "other" is also used incorrectly.

Problems:

9 × 2 × 4 = 72; 72 cubic units

6 × 3 × 4 = 72; 72 cubic units

Length = 4; Width = 4; Height = 6

4 × 4 × 6 = 96; 96 cubic units

Length = 3; Width = 5; Height = 2

3 × 5 × 2 = 30; 30 cubic units

The evaluations of the composite functions expressions and operations are presented as follows;

1. (f + g)(x) = 2·x² + 7·x + 3

(f - g)(x) = 7·x + 21

(f · g)(x) = x⁴ + 7·x³ + 3·x² - 63·x - 108

(f/g)(x) = f(x)/g(x) = (x² + 7·x + 12)/(x² - 9)

2. (f + x)(x) = 3·x - 2

(f - g)(x) = x + 4

(f · g)(x) = f(x) × g(x) = (2·x + 1) × (x - 3) = x⁴ + 7·x³ + 3·x² - 63·x - 108

(f/g)(x) = (2·x + 1)/(x - 3)

3. f[h(-9)] = 25

4. h[f(4)] = 20

5. g[h(-2)] = 10

6. The composite function that converts inches into miles is; n/63360

Composite function is a function that is applied to the result of another function.

Part 1: Operations of Functions

1. f(x) = x² + 7·x + 12 and g(x) = x² - 9, therefore;

(f + g)(x) = f(x) + g(x) = (x² + 7·x + 12) + (x² - 9) = 2·x² + 7·x + 3

(f - g)(x) = f(x) - g(x) = (x² + 7·x + 12) - (x² - 9) = 7·x + 21

(f · g)(x) = f(x) × g(x) = (x² + 7·x + 12) × (x² - 9) = x⁴ + 7·x³ + 3·x² - 63·x - 108

(f/g)(x) = f(x)/(g(x)) = (x² + 7·x + 12)/(x² - 9)

2. f(x) = 2·x + 1 and g(x) = x - 3

(f + g)(x) = f(x) + g(x) = 2·x + 1 + (x - 3) = 3·x - 2

(f - g)(x) = f(x) - g(x) = 2·x + 1 - (x - 3) = x + 4

(f · g)(x) = f(x) × g(x) = (2·x + 1)·(x - 3) = 2·x² - x - 3

(f/g)(x) = f(x)/(g(x)) = (2·x + 1)/(x - 3)

Part 2; 3. f(x) = x², g(x) = 5·x, and h(x) = x + 4

f[h(-9)] = (h(-9))² = (-9 + 4)² = 25

4. f(x) = x², g(x) = 5·x, and h(x) = x + 4

h[f(4)] = (f(4) + 4) = (16 + 4) = 20

5. f(x) = x², g(x) = 5·x, and h(x) = x + 4

g[h(-2)] = (h(-2) × 5) = (-2 + 4) × 5 = 10

6. The formula F = n/12 converts n inches into feet f, and m = f/5280 converts feet to miles m.

Let F(N) represent the function that converts inches to feet and let G(F) represent the function that converts feet to miles. Then the composition function that converts inches to miles is G(F(N))

G(F(N)) = G(n/12) = (n/12)×(1/5280) = n/63360

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Answer:

We know that 1 yard is equal to 3 feet. Therefore, 7 yards is equal to:

7 yards = 7 × 3 feet = 21 feet

So, 7 yards is greater than 20 feet.

To complete the table to model the answer, we can write:

Quantity Value

20 feet 20 ft

7 yards 21 ft

Comparing the values, we can see that 7 yards is greater than 20 feet.

Answer:

t=36°

Step-by-step explanation:

90-54=36

opposite angles are equal so t=36°

The remainder when a 90-digit number 9999 is divided by 89 is 0, as the result of applying the divisibility rule of 89, which involves reversing the digits of the number and subtracting the smaller from the larger.

To find the remainder when a 90-digit number 9999 is divided by 89, we can use the divisibility rule of 89. The rule states that for any integer n, the number obtained by reversing the digits of n and subtracting the smaller from the larger is divisible by 89.

In this case, we reverse the digits of 9999 to get 9999 again, and subtract the smaller from the larger to get 0. Since 0 is divisible by any number, including 89, the remainder when 9999 is divided by 89 is 0.

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Answer:

multiply the length of the rectangle by the width of the rectangle.

Step-by-step explanation:

I'm tired for this

Answer:

226.865 square inches.

Step-by-step explanation:

The equation for the area of a circle is [tex]\pi r^2[/tex]. Let's use 3.14 for pi. The radius can be found by dividing 17/2 = 8.5. 8.5 squared is 72.25. Finally, multiply by pi to get 226.865.

In circle , arc length is  18.84 ft and sector area = 75.36 ft .

What is arc?

In mathematics, an arc is referred to as a section of a circle's or curve's perimeter. The term "open curve" can also be used to describe it. The circumference, also known as the perimeter, is the measurement around a circle that defines its edge.

Length of an arc = Angle/360 * pi * diameter

                      =  135/360 * 3.14 * 16

                      = 18.84 ft

sector area = Angle/360 * π * r²

                    = 135/360 * 3.14 * 8 * 8

                   = 75.36 ft

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The probability that the second chip drawn is red is 1/3.

The probability of drawing a red chip on the first draw is 6/10, or 3/5. After one chip is discarded, there are 9 chips remaining, 3 of which are red. So the probability of drawing a red chip on the second draw, given that a chip has already been discarded, is 3/9, or 1/3.

Therefore, the probability that the second chip drawn is red is 1/3. This is because the first chip drawn could be either white or red, so there are two possible scenarios. If the first chip drawn is white, there will be 6 red chips and 3 white chips left, so the probability of drawing a red chip on the second draw will be 6/9 or 2/3. If the first chip drawn is red, there will be 5 red chips and 4 white chips left, so the probability of drawing a red chip on the second draw will be 5/9. To get the overall probability of drawing a red chip on the second draw, we need to take the average of these two probabilities, weighted by the probability of the first chip being white or red, respectively.

The probability of the first chip being white is 4/10, or 2/5, and the probability of the first chip being red is 6/10, or 3/5. So the overall probability of drawing a red chip on the second draw is

(2/5) x (2/3) + (3/5) x (5/9) = 4/15 + 1/3 = 3/9 = 1/3.

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The best approximation of the volume of a cylinder with a radius of 10 mm, and a height of 5 mm using 3.14 for pi is 1,570 cubic millimeters.

The formula for calculating the volume of a cylinder is as follows:

V = πr²h

Where V is the volume, r is the radius of the cylinder, and h is the height of the cylinder.

Substituting the values given in the formula, we have :

V = πr²hV = 3.14 × (10 mm)² × (5 mm)V = 3.14 × 100 mm² × 5 mm

V = 1,570 cubic millimeters.

Therefore, the best approximation of the volume of a cylinder with a radius of 10 mm, and a height of 5 mm using 3.14 for pi is 1,570 cubic millimeters.

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The values of the expression when using the completing the square method is given below

To complete the square for x²-16x+c, we need to add and subtract the square of half the coefficient of x, which is (-16/2)² = 64. So:

x² - 16x + c = (x - 8)² - 64 + c

To complete the square, we added (-16/2)² = 64, but we subtracted it again to keep the expression equivalent. Therefore, c - 64 is the value that completes the square.

Similarly, for x² + 7x + c, we add and subtract (7/2)² = 49/4:

x² + 7x + c = (x + 7/2)² - 49/4 + c

So c - 49/4 completes the square.

For x²- 9x, we add and subtract (9/2)² = 81/4:

x² - 9x = (x - 9/2)² - 81/4

Therefore, c - 81/4 completes the square.

To factor x²- 14x, we can factor out x:

x² - 14x = x(x - 14)

To factor x² + 30x, we can factor out x:

x² + 30x = x(x + 30)

To factor x²- 9x, we can factor out x:

x² - 9x = x(x - 9)

To solve x² + 10x = 16 by completing the square, we first add and subtract (10/2)² = 25:

x² + 10x + 25 - 25 = 16

(x + 5)² = 41

x + 5 = ±√41

x = -5 ±√41

To solve x² - 3x = 7 by completing the square, we first add and subtract (3/2)² = 9/4:

x² - 3x + 9/4 - 9/4 = 7

(x - 3/2)² = 37/4

x - 3/2 = ±√(37/4)

x = 3/2 ±√(37/4)

To solve x² + 15x = 12 by completing the square, we first add and subtract (15/2)² = 225/4:

x² + 15x + 225/4 - 225/4 = 12

(x + 15/2)² = 129/4

x + 15/2 = ±√(129/4)

x = -15/2 ±√(129/4)

a. Let L be the length of the wading pool. Then its width is L - 12. The height is 1 foot, so the volume is:

V = L(L - 12)(1) = L² - 12L

b. To complete the square for the expression L² - 12L, we add and subtract (12/2)² = 36:

L² - 12L + 36 - 36 = (L - 6)² - 36

So the volume can be written as:

V = (L - 6)² - 36

To find the dimensions of the wading pool that give a volume of 108 cubic feet, we set V = 108 and solve for L:

(L - 6)² - 36

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Yes, we can say the shape of the sampling distribution for the sample mean if we know the population distribution.

However, if we do not know the population distribution, we cannot determine the exact shape of the sampling distribution for the sample mean. In this case, we can make use of the Central Limit Theorem (CLT) to make some assumptions about the shape of the sampling distribution. According to CLT, as the sample size increases, the sampling distribution of the sample mean becomes approximately normal, regardless of the shape of the population distribution, provided that the sample size is sufficiently large. Therefore, if the sample size is 19 and the population distribution is unknown, we can assume that the sampling distribution of the sample mean is approximately normal if the sample data is not heavily skewed or contains extreme outliers.

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Answer:

Assuming that g(x) represents the transformed function, the rule for g can be obtained by applying the translation and reflection operations in the correct order.

To translate the graph of f(x) down by 2 units, we need to subtract 2 from the function. This gives us:

h(x) = f(x) - 2 = 5^x - 2

Next, we need to reflect the graph of h(x) in the y-axis. To do this, we replace x with -x in the function. This gives us:

g(x) = h(-x) = 5^(-x) - 2

Therefore, the rule for g(x) that represents a translation 2 units down, followed by a reflection in the y-axis of the graph of

f(x) = 5^x is:g(x) = 5^(-x) - 2

Answer: His car was $415.18 in total

Step-by-step explanation: The calculation of the present value of a cash flow or other income stream that produces $1 in income over so many periods of time.

Amount borrowed = $12,500

Annual interest rate = 12.00%

Monthly interest rate = 1.00%

Period = 36 months

Let monthly payment be x

12,500 = x/1.01 + x/1.01^2 + x/1.01^3  … + x/1.01^35 + x/1.01^36

12,500 = x * (1 - (1/1.01)^36) / 0.01

12,500 = x * 30.107505

x = 12,500/30.107505  

x = 415.18

So, the monthly payment is $415.18

The doubling time of the culture is approximately 42.91 minutes.

The growth rate constant is a mathematical concept that is used to model the growth of a population. It represents the rate at which the population is increasing at any given moment. The doubling time is a measure of how long it takes for a population to double in size, and it can be calculated using the formula mentioned above.

The doubling time of a culture can be calculated using the formula: Doubling time = ln(2) / growth rate constant

Using the given growth rate constant of 0.01615468 min^-1, we can calculate the doubling time as:

Doubling time = ln(2) / 0.01615468 [tex]min^{-1}[/tex]

Doubling time ≈ 42.91 minutes

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The answer is the second one.

The -1 is shaded in, and the arrow is pointing to the ĺeft.

The surface area of the rectangular solid with length 5 inches, width 2 inches, and height 4 inches is 76 sq inch. The answer is D.

What is surface area of rectangular solid ?

The surface area of a rectangular solid (also known as a rectangular prism) is the total area of all its faces. It can be calculated using the formula:

SA = 2lw + 2lh + 2wh

where l is the length of the rectangular solid, w is its width, and h is its height.

The rectangular solid has six faces: a top face, a bottom face, a front face, a back face, a left side face, and a right side face. The formula above accounts for the area of each of these faces.

According to the question:
The formula for the surface area of a rectangular solid is:

SA = 2lw + 2lh + 2wh

We are given that the length (l) of the solid is 5 inches, the width (w) is 2 inches, and the height (h) is 4 inches. Substituting these values into the formula, we get:

SA = 2(5)(2) + 2(5)(4) + 2(2)(4)

= 20 + 40 + 16

= 76 square inches

Therefore, the surface area of the rectangular solid with length 5 inches, width 2 inches, and height 4 inches is 76 square inches. The answer is D.

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The expected adult height for a toddler who is 34 inches tall at the 30-month checkup is around 5 feet 7 inches.

To determine the expected adult height, one must multiply the current height by 1.08. Since 34 inches x 1.08 is equal to 36.72 inches, the expected adult height is 5 feet 7 inches.

The calculation for adult height is an approximation. Factors such as nutrition, genetics, and gender play a role in final height.

It is important to note that this calculation is just a guide and the actual adult height may differ from the predicted adult height.

To get a more accurate estimation of the expected adult height, it is recommended to have multiple height checks throughout childhood and take into account growth patterns.

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The value of x in the given linear equation of 4x = 28 is determined as 7.

To find the value of x in the linear equation 4x = 28, we need to isolate x on one side of the equation.

We can do this by dividing both sides of the equation by 4:

4x/4 = 28/4

Simplifying:

x = 7

Thus, identify the equation and the variable: In this case, the equation is 4x = 28, and the variable we want to solve for is x. Also simplify the linear equation by dividing both sides by 4, we get x = 7, which is the solution.

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The complete question is below:

4x = 28

find the value of x