Algebraic proofs geometry

The lowest common denominator, 20, can be used to represent any fraction that can be stated as a ratio of integers with factors of 2 and 5 in the denominator. eg. 1/4, 1/2, 2/5 and 7/10

To find all the fractions that have 20 as the lowest common denominator, we need to identify all the prime factors of 20, which are 2, 2, and 5.

Then, we can express each fraction with these prime factors in the denominator, by multiplying the numerator and denominator by the missing factors. For example, for the fraction 1/4, we need to multiply both the numerator and denominator by 5 to get:

1/4 = 5/20

Similarly, for the fraction 3/5, we need to multiply both the numerator and denominator by 2 to get:

3/5 = 6/10 = 12/20

By doing this for all fractions, we can express them with the same denominator of 20. Here are some examples:

1/4 = 5/20

3/5 = 12/20

1/2 = 10/20

2/5 = 8/20

7/10 = 14/20

Therefore, any fraction that can be expressed as a ratio of integers with factors of 2 and 5 in the denominator can be written with 20 as the lowest common denominator.

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Complete Question

Write any two fractions which have 20 as the LCD (lowest common denominator)?

The sample space is 20, 24, 28, 32, 36, 40. There are 6 outcomes in the sample space.  In this case, the sample space is {20, 24, 28, 32, 36, 40}.

The sample space of the probability experiment is the set of all possible outcomes that can occur when randomly choosing a number from the multiples of 4 between 20 and 40, inclusive.

To determine the number of outcomes in the sample space, we simply count the number of elements in the set. In this case, there are 6 outcomes in the sample space.

Therefore, the sample space is {20, 24, 28, 32, 36, 40} and there are 6 outcomes in the sample space. After Randomly choosing a number from the multiples of 4 between 20 and 40, these values are found.

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The perimeter of the rectangle is (x² + 30x + 104) in² while The area of the rectangle is (x² + 30x + 104) in²

An equation is an expression that shows how two or more numbers and variables are related using mathematical operations of addition, subtraction, multiplication, division, exponents and so on.

The rectangle have a length of (0.5x + 13) and width of (2x + 8)

1) Perimeter = 2(length + width)

Perimeter = 2(0.5x + 13 + 2x + 8) = 2(2.5x + 21) = (5x + 42) inches

The perimeter of the rectangle is (x² + 30x + 104) in²

2) Area = length * width

Area = (0.5x + 13) * (2x + 8) = x² + 4x + 26x + 104

Area = (x² + 30x + 104) in²

The area of the rectangle is (x² + 30x + 104) in²

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Answer:

Side 3 is:  5x^3 - 4x^2 +3x - 12

Note that the answer options do not include this result, but it is likely that the second option is simply missing the square term for the -4x, and it should read -4x^2.

Step-by-step explanation:

The perimeter is the sum of all three sides.  To find Side 3, subtract Sides 1 and 2 from the perimeter:

5x^3 - 2x^2 +3x - 8 - (3x^2-4x-1) - (4x-x^2+5)      = Side 3

  Perimeter             -      Side 1    -     Side 2        = Side 3

5x^3 - 2x^2 +3x - 8 - 3x^2+4x+1 - 4x+x^2-5        [Remove parentheses]

5x^3 - 3x^2 +x^2 - 2x^2 +3x +4x - 4x - 8 +1 -5     [Combine like terms]

5x^3 - 4x^2 +3x - 12                       [Simplify]       = Side 3

To rotate triangle ABC 90 degrees clockwise about a point P, we can follow these steps:

Draw a line segment from each vertex of the triangle to the point P.

Measure the distance from each vertex to the point P and make note of the lengths.

Rotate each line segment 90 degrees clockwise by swapping the x and y coordinates and changing the sign of the new y-coordinate. For example, if a vertex has coordinates (x, y), the new coordinates after rotation will be (y, -x).

Use the new endpoints of the line segments to draw the new triangle, A'B'C'.

For example, suppose the coordinates of triangle ABC are A(1,2), B(3,4), and C(5,2), and the point of rotation is P(3,3). Then the distances from each vertex to the point P are:

AP = sqrt((3-1)² + (3-2)²) = sqrt(5)

BP = sqrt((3-3)² + (3-4)²) = 1

CP = sqrt((3-5)² + (3-2)²) = sqrt(5)

After rotating each vertex 90 degrees clockwise about P, we get:

A'(4,1)

B'(2,3)

C'(4,5)

Using these new coordinates, we can draw the new triangle A'B'C', which is the result of rotating triangle ABC 90 degrees clockwise about P.

Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction of the bar. ABC rotates 90 degrees clockwise about point p to from A’B’C

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The sequence of transformations that maps HIJK to ABCD is sequence B: reflection over line HÌ, then a translation 6 units to the right and 3 units down.

What is quadrilateral ?

A quadrilateral is a polygon with four sides and four vertices. The term "quadrilateral" comes from the Latin words "quadri" meaning "four" and "latus" meaning "side". Quadrilaterals can have different shapes and properties, including rectangles, squares, parallelograms, trapezoids, and kites.

Since quadrilaterals HIJK and ABCD are congruent, we can map one onto the other using a sequence of transformations. We need to determine which of the given sequences of transformations maps HIJK to ABCD.

Sequence A involves a 270° rotation about point J, followed by a translation 9 units to the right and 8 units down.

Sequence B involves a reflection over the line HÌ, followed by a translation 6 units to the right and 3 units down.

To determine which sequence maps HIJK to ABCD, we can apply each sequence to the vertices of HIJK and see if the resulting image matches the vertices of ABCD.

Starting with sequence A, we apply the rotation and translation to the vertices of HIJK:

Vertex H(-2, 1) is rotated 270° about J(-2, 2) to get H'(0, 0). Then we translate 9 units to the right and 8 units down to get H''(9, -8).

Vertex I(-3, -1) is rotated 270° about J(-2, 2) to get I'(1, -3). Then we translate 9 units to the right and 8 units down to get I''(10, -11).

Vertex J(-2, 2) is fixed by the rotation and then translated 9 units to the right and 8 units down to get J''(7, -6).

Vertex K(0, 0) is rotated 270° about J(-2, 2) to get K'(-2, -2). Then we translate 9 units to the right and 8 units down to get K''(7, -10).

The resulting image of HIJK under sequence A has vertices H''(9, -8), I''(10, -11), J''(7, -6), and K''(7, -10). We can see that these vertices do not match the vertices of ABCD, so sequence A does not map HIJK to ABCD.

Next, we apply sequence B to the vertices of HIJK:

Vertex H(-2, 1) is reflected over line HÌ to get H'(-4, 3). Then we translate 6 units to the right and 3 units down to get H''(2, 0).

Vertex I(-3, -1) is reflected over line HÌ to get I'(-1, 1). Then we translate 6 units to the right and 3 units down to get I''(5, -2).

Vertex J(-2, 2) is reflected over line HÌ to get J'(-4, 4). Then we translate 6 units to the right and 3 units down to get J''(2, 1).

Vertex K(0, 0) is reflected over line HÌ to get K'(-2, 2). Then we translate 6 units to the right and 3 units down to get K''(4, -1).

The resulting image of HIJK under sequence B has vertices H''(2, 0), I''(5, -2), J''(2, 1), and K''(4, -1). We can see that these vertices match the vertices of ABCD, so sequence B maps HIJK to ABCD.

Therefore, the sequence of transformations that maps HIJK to ABCD is sequence B: reflection over line HÌ, then a translation 6 units to the right and 3 units down.

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Hence, in answering the stated questiοn, we may say that If yοu're unitary methοd  satisfied with yοur line plοt, save it and distribute it as needed.

The unit technique is a prοblem-sοlving apprοach that invοlves finding the value οf a single unit and then multiplying that value by the needed value. Tο put it simply, the unit technique is used tο extract a single unit value frοm a given multiple. 40 pens, fοr example, wοuld cοst 400 rupees, οr the cοst οf οne pen. The prοcess fοr achieving this may be standardized. A single cοuntry. anything that has an identity element. Its adjοint and reciprοcal are equal in mathematics and algebra.

a general methοd fοr prοducing a line plοt:

First, cοllect yοur data. Stοck prices, temperature readings, and survey results are all examples οf this. The crucial thing is that yοu have a set οf values tο plοt οn a graph.

Enter yοur x and y values intο the plοt. The exact prοcedure depends οn the graphing prοgrammed yοu're using, but yοu shοuld be able tο enter yοur values intο a data table οr spreadsheet.

Make any changes yοu want tο yοur plοt. Adding labels tο the x and y axes, tweaking the plοt's scale, changing the line cοlοur οr thickness, οr adding a title are all pοssibilities.

If yοu're satisfied with yοur line plοt, save it and distribute it as needed.

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Complete question:

The actual distance of 6 cm, given the scale of the map, would be 30 km .

The distance on the map, given the actual distance on the ground and the scale, would be 6 inches .

The scale is that for every 1 cm on the map, the actual distance is 5 kilometers. When given 6 cm therefore, the actual distance is :

= 6 x 5

= 30 km

The scale of the second map is such that 1 inch on the map is 3 actual kilometers so 18 km on the ground would be :

= 18 / 3

= 6 inches

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The two primary components of an angle are the limbs and the vertex. The angle sum property of a triangle is 20+21+29=180 70x=180 x=180/70.

An angle is the result of the intersection of two lines.

An "angle" is the length of the "opening" between these two beams.

Angles are commonly measured in degrees and radians, a measurement of circularity or rotation.

In geometry, an angle can be created by joining the extremities of two rays. These rays are intended to represent the angle's sides or limbs.

The two primary components of an angle are the limbs and the vertex. The joint vertex is the common terminal of the two beams.

According to the given question,

angle sum property of triangle-

20+21+29=180

70x=180

x=180/70.

Hence, With the angle sum property of triangle, x=180/70.

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By the given parameters, Gethyn needs to drink 2 more cups of water today.

From the question, we have the following parameters that can be used in our computation:

Amount = 8 cups

Today = 48 ounces

There are 8 fluid ounces in one cup.

So, to convert 48 fluid ounces to cups, we divide by 8:

48 fluid ounces / 8 fluid ounces per cup = 6 cups

Therefore, Gethyn has already drnk 6 cups of water today.

To reach his goal of 8 cups, he still needs to drink:

8 cups - 6 cups = 2 cups

So Gethyn needs to drink 2 more cups of water today.

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If I walk 3.5 miles in 2 hours, then I can walk 14 miles in 8 hours.

If I walk 3.5 miles in 2 hours, then I can use a simple proportion to calculate how far I can walk in 8 hours. I know that in 2 hours I can walk 3.5 miles, and I want to calculate how far I can walk in 8 hours. To do this, I can set up a proportion. The fraction representing the time I spent walking and the distance I walked must be equal on both sides of the equation. On the left side of the equation, I set up 2/3.5, and on the right side I set up 8/x, where x is the unknown distance I can walk in 8 hours. I can then solve for x by cross-multiplying and dividing. After solving, I find that I can walk 14 miles in 8 hours.

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Answer:

To simplify the expression x - 15 + 2x + 6, you can combine like terms. Here are the steps to do that:

Group the x terms and the constant terms separately:

(x + 2x) + (-15 + 6)

Simplify the terms inside the parentheses:

3x - 9

So the simplified expression is 3x - 9.

Therefore, x - 15 + 2x + 6 equals 3x - 9.

Answer:

3(x-3)

Step-by-step explanation:

given : x-15+2x+6

factorize using like terms : x-15+3x+6 = 3x-9

= 3x - 9
=3(x-3)

The percentage decrease in the population after on year is found to be 19%.

The percentage decrease can be found by using the formula,

Percentage decrease = change in population/initial population x 100.

Now change in population in one year is given as final population - initial population.

Putting values, change in population = 252000 - 204120

Change in population = 47880

Now, putting all the value in the formula,

percentage decrease = 47880/252000 x 100

percentage decrease = 19%

So, the decrease in the population is found to be 19%.

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Answer:122

Step-by-step explanation:

sum of the interior angles of a rectangle is equal to 360 degrees. sum of neighbor angles is equal to 180 degrees. the if one of the neighbor angle is 90 then, other is 180-90=90.

a+76+72+90=360

a+238=360

a=122

The correct option to model the height is

h = cosine (StartFraction pi Over 6 EndFraction t) + 9.

Here the height of the tip of the hour hand of a wall clock follows a cosine function as the time progresses since the hour hand of a clock completes one full revolution in 12 hours.

We will use the general form of a cosine function to model the height has a function of time t:

Where A is the amplitude, B is the frequency and C is the vertical shift  

Here we have

The height, h, in feet of the tip of the hour hand of a wall clock varies from 9 feet to 10 feet.

Hence, the applitude A = [9+10]/2 = 0.5.

The period of a cosine function is given by 2π/B,

Since the hour hand completes one full revolution in 12 hours, the period is 12 hours or 2π.

=> B = π/6.

The vertical shift is C = 9.

Thus, the equation that models the height h as a function of time t is:

h = 0.5 cos(π/6 t) + 9.

Therefore,

The correct option to model the height is

h = cosine (StartFraction pi Over 6 EndFraction t) + 9.

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Answer:

The picture shows that the side lengths and the angle are the same because of the lines

Step-by-step explanation:

The answer is given and VS=WT but add the line symbol above that

If A, B, and C lie on a straight line, the sum of angles y, x, and z will be 180 degrees:

y + x + z = 180

Substituting the values given in the problem:

95 + x + 330 = 180

Simplifying:

425 + x = 180

Subtracting 425 from both sides:

x = -245

Therefore, x is -245 degrees.

However, since x represents an angle on a straight line, we can add 180 degrees to get an equivalent angle:

x + 180 = -245 + 180 = -65

Therefore, x is -65 degrees.

Values of y that corresponds with the value of x as per quadratic functions are as follows:

6

0

-2

0

6

A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. It is also known as the polynomial of degree 2 since the greatest degree term in a quadratic function is of second degree. A quadratic function must have at least one second-degree term. It performs algebraic operations.

The parent quadratic function connects the locations whose coordinates have the type f(x) = x2 and is of the kind (number, number2).

Just need to evaluate the function for each value of X.

for x=1 y=2(1-3)²-2= 6

for x=2 y=2(2-3)²-2= 0

for x=3 y=2(3-3)²-2= - 2

for x=4 y=2(4-3)²-2= 0

for x=5 y=2(5-3)²-2= 6

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Answer:

The required amount Ahmet needs to pay after 6 years is $1619.14.

What is compound interest?

Compound interest is the interest on deposits computed on both the initial principal and the interest earned over time.

Amount = principal[1 + r/n]ⁿᵃ

Principal = P rate= r Time =a  , n = compounding frequency

Here,

From the given data,

P = 700, r = 15% and t = 6 (n =1)

Now,

Amount = principal[1 + r/n]ⁿᵃ

Amount = 700(1 + 0.15)⁶

Amount = $1619.14

Thus, the required amount Ahmet needs to pay after 6 years is $1619.14.

Step-by-step explanation:

Answer:

1.  C.

2. D.

3. D.

Step-by-step explanation:

A.  Round both dimensions the nearest whole number. 8 1/3 rounds to 8,     6 3/4 rounds to 7. Multiply these two and your estimate for the tarp area is 56 sq yds. Option C.

B. Convert both mixed numbers to improper fractions. Multiply whole number by divisor and add the dividend. (8*3) + 1 = 25. First number is 25/3.(6*4) + 3 = 27. Second number is 27/4. Multiply these two numbers fractions  and get 225/4. Convert to a mixed number, 56 1/4. Option D.

C. This answer is reasonable. 56 1/4 is pretty close to our estimate of 56 sq yds. Or just choose the option that corresponds to your estimate from part A. Option D.

I think you are correct, I am not sure why. Maybe you ask your teacher and she or he made a mistake with this question.

Wilbur's flight took about 43.7 seconds.

Let x be the rate of Orville in feet per second and 2x be the rate of Wilbur in feet per second. Let t be the time it took for Orville to complete the flight and t - 6 be the time it took for Wilbur to complete the flight.

We know that the distance traveled by both brothers is the same, which we can express with the equation:

distance = rate × time

For Orville:

distance = x * t

For Wilbur:

distance = 2x * (t - 6)

Since the distance is the same for both brothers, we can set the two equations equal to each other:

x * t = 2x * (t - 6)

Expanding and simplifying the right-hand side:

xt = 2xt - 12x

12x = xt

x = t/12

So, Orville's rate is x = t/12 feet per second.

Substituting this into one of the equations for distance, we can solve for t:

distance = x * t

852 = (t/12) * t

852 = t² / 12

t² = 12 * 852

t² = 10224

t ≈ 101.1 seconds (rounded to the nearest tenth)

So, Orville's flight took about 101.1 seconds.

Now we can use the equation for Wilbur's distance to find his rate:

distance = 2x * (t - 6)

852 = 2(2x) * (101.1 - 6)

852 = 4x * 95.1

x ≈ 5.64 feet per second (rounded to the nearest hundredth)

So, Orville's rate is about 5.64 feet per second, and Wilbur's rate is twice that or about 11.28 feet per second.

To find Wilbur's time, we can use the equation for distance again:

distance = 2x * (t - 6)

852 = 2(11.28) * (t - 6)

852 = 22.56t - 135.36

22.56t = 987.36

t ≈ 43.7 seconds (rounded to the nearest tenth)

So, Wilbur's flight took about 43.7 seconds.

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Answer:

the answer to ur question is: 36

In conclusion, Amy used a snowball sampling method to collect data for her survey. This method is useful when the population is hard to locate or identify, and when other sampling methods are not possible

Amy used a snowball sampling method. Snowball sampling is a non-probability sampling method where the participants recruit other members of the population.

It is useful when the population is difficult to locate or identify, as it relies on word of mouth or referrals from already recruited participants. In this case, Alfred was able to introduce other international students who might be interested in participating in Amy's survey. This allowed Amy to collect enough data to conduct her analysis. Snowball sampling is useful when the sample size is not known, when time is limited, or when a random selection is not possible.

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Mei worked 8 hours and Kara worked 7 hours when Mei can build a computer in 0.8 hours , and Kara can build a computer in 1 hour.

Let's use the following variables to represent the unknowns in the problem:

Let M be the number of computers Mei built

Let K be the number of computers Kara built

We can set up a system of equations based on the given information:

M + K = 17 (the total number of computers built is 17)

0.8M + K = 15 (the total time worked is 15 hours)

We can solve for one of the variables in terms of the other by using the first equation:

M = 17 - K

Now we can substitute this expression for M into the second equation:

0.8(17 - K) + K = 15

13.6 - 0.8K + K = 15

0.2K = 1.4

K = 7

So Kara built 7 computers. We can use the first equation to find how many computers Mei built:

M + 7 = 17

M = 10

Therefore, Mei built 10 computers.

Now we can find how long each girl worked by multiplying the number of computers by their respective build times:

Mei: 10 computers x 0.8 hours per computer = 8 hours

Kara: 7 computers x 1 hour per computer = 7 hours

Therefore, Mei worked 8 hours and Kara worked 7 hours.

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The complete question is :

Mei and Kara build computers from parts and sell them to make a profit. Mei can build a computer in 0.8 hours , and Kara can build a computer in 1 hour. together they worked 15 hours and built 17 hours and built 17 computers. how many hours did each girl work ?

The expected value and standard deviation of x are 1.6 and 0.66, respectively.

Given that:

Jimmy volunteers at events at the hospital each year.

The random variable x is the number of hospital events Jimmy works at each year.

We understand that he does not work for more than two events in a year

So, x can take on the values 0, 1, or 2.

From the question, we have:

Over the past ten years

So, the table is

X P(X)

0 0.1

1 0.2

2 0.7

To find the expected value, we take the sum of the products of x and P(x)

So, we have

E(x) = 0(0.1) + 1(0.2) + 2(0.7)

E(x) = 1.6

To find the standard deviation, we need to first calculate the variance:

Var(X) = E(x^2) - [E(x)]^2

Where

E(x^2) = 0^2(0.1) + 1^2(0.2) + 2^2(0.7)

E(x^2) = 3

So, we have

Var(X) = 3 - (1.6)^2

Var(X) = 0.44

This means that

SD(x) = √0.44

SD(x) = 0.66

Hence, the standard deviation is 0.66

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Answer: To find the total area of the grass that Yuri's dad needs to fertilize, we need to calculate the area of the back yard and the area of the front yard, and then add them together.

Area of the back yard:

The back yard measures 55 feet by 30 feet, so the area is:

55 feet x 30 feet = 1650 square feet

Area of the front yard:

The front yard is a square with a length of 42 feet on each side, so the area is:

42 feet x 42 feet = 1764 square feet

Total area:

To find the total area, we add the area of the back yard and the area of the front yard:

1650 square feet + 1764 square feet = 3414 square feet

Therefore, Yuri's dad needs to fertilize a total area of 3414 square feet.

Step-by-step explanation:

Answer:

Slope m = 1/3

Step-by-step explanation:

Slope of the line can be found by taking two points on the line, (x1, y1) and (x2, y2)

Find the difference in y coordinates, y2 - y1  (called rise)

Find the difference in corresponding x coordinates x2 - x1 (called run)

Rise/Run gives the slope

Two distinguishable points on the line graph are (0, 2) and (3, 3)

rise = 3 - 2 = 1

run = 3 - 0 = 3

Slope = 1/3

The domain and range of g of x equals the square root of the quantity x plus 4, g(x) = √x + 4, are equal to d: [–4, [infinity]) and r: [0, [infinity]). Thus, the right choice of answer is option (c).

We have a function g(x) and defined as square root of the quantity x plus 4, i.e.,

g(x) = √x + 4

We have to determine the domain and range of function g(x).

The domain of function is all input values of x that make the expression defined. The range is the set of all output values that valid g(x) values. A square root limits the function because we can't have negative numbers under the square root (they become imaginary numbers). Let y = g(x) = √x +4

the square root '√ 'sign must be implies ≥ 0, therefore, x + 4 ≥ 0

Subtracting the 4 from both sides

=> x + 4 -4 ≥ 0 - 4

=> x ≥ -4

The domain is x∈ [-4,+∞)

When x = -4, g(x) = 0

Therefore, The range is y∈ [0, 00)

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