Algebraic proofs geometry

Therefore, DM = 0, which means that the plane is directly above point D. Pythagorean theorem The vertical distance from the plane to point D is simply the altitude of the plane.

The Pythagorean Theorem is the fundamental Euclidean geometry relationship between the three sides of a right triangle. According to this rule, the area of a square with the hypotenuse side equals the sum of the areas of squares with the other two sides.

drawing a diagram

  A ------ 3 miles ------ D ----- x miles ------ C

  |                                               |

  |                                               |

  6 miles                                         6 miles

  |                                               |

  |                                               |

  B -----------------------------------------------

[tex]AC^2 = AD^2 + DC^2\\BC^2 = BD^2 + DC^2\\AD^2 + DC^2 = BD^2 + DC^2\\AD^2 = BD^2[/tex]

So, the plane must be directly above the midpoint of AB. Let's call this point M:

  A ------ 3 miles ------ D ----- x miles ------ C

  |                                               |

  |                                               |

  6 miles                           3 miles        6 miles

  |                                               |

  |                                               |

  B -----------------------------------------------

                     |

                     |

                     M

Now, let's use Pythagoras' theorem again to find the distance from the plane to point D:

[tex]DM^2 = AD^2 - AM^2\\DM^2 = AD^2 - 3^2\\DM^2 = 3^2 - 3^2\\DM^2 = 0[/tex]

Therefore, DM = 0, which means that the plane is directly above point D. The vertical distance from the plane to point D is simply the altitude of the plane.

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After spending 60% of his money Joseph has rs. 600., He has 1500 in the beginning.

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the word percent means. The letter "%" stands for it.

Let the total amount be x

He spent 60% of his money

So, Money spent = 60% x=0.6x

Remaining amount = x- 0.6 x = 0.4x

We are given that Now he has Rs.600

[tex]0.4x=600\\\\x=\frac{600}{0.4}\\\\x=1500[/tex]

Hence He has Rs.1500 at the beginning

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Answer:

Complex or Imaginary solutions

Step-by-step explanation:

In the Quadratic Formula, the discriminant is the part that is inside of the radical (square root symbol).

So there are three cases, the discriminant can be:

-positive, OR

-zero, OR

-negative

If its positive, there are two real solutions.

If its zero, there is one real solution.

If its negative, there are two complex (imaginary) solutions.



The factorized terms of the given expression  ax - a + x - 1 by grouping the terms in pairs is given by  (x - 1)(a + 1) .

Expression is equal to,

ax - a + x - 1

To factorize the expression ax-a+x-1 by grouping terms in pairs.

First group the first two terms and the last two terms together we get,

⇒ ax - a + x - 1 = ( ax - a ) + ( x - 1 )

Now factor out the common factor of 'a' from the first group.

And the common factor of '1' from the second group we get,

⇒ ax - a + x - 1 = a(x - 1) + 1(x - 1)

Both the groups have a common factor of (x - 1).

Take out  common factor we have,

⇒ ax - a + x - 1 = (x - 1)(a + 1)

Therefore, the factorized expression is equal to,

 ax - a + x - 1 = (x - 1)(a + 1)

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If the credit limit on the card is amount $1,000, then you should aim to keep the balance owing on the card at amount $300 or less.

It depends on the acceptable debt ratio. Generally, to maintain a good credit rating, it is recommended to keep a debt-to-credit ratio of 30% or less, meaning that you should have an amount owing on the card equal to or less than amount 30% of the credit limit.

If the credit limit on the card is $1,000, then you should aim to keep the balance owing on the card at $300 or less. So, if the balance owing at the end of the month is over $300, you would need to make a payment of at least the difference between the balance owing and the acceptable debt ratio.

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The probability of getting 2 kings out of 25 cards is approximately 0.044 or 4.4%.

Drawing cards from a standard deck of 52 cards is a random process, and the probability of getting 2 kings out of 25 cards depends on the total number of possible outcomes.

There are 4 kings in a deck of 52 cards,

So, The probability of drawing a king on the first draw = 4/52.

Since the deck is not replaced,

The probability of drawing another king on the second draw = 3/51.

Therefore,

The probability of getting 2 kings out of 25 cards can be calculated by combining these two probabilities.
The probability of drawing 2 kings = [tex](4/52) * (3/51) * (25C2)[/tex]

Where,

25C2 = The number of ways to select 2 cards out of 25.

After calculating this expression, the probability of getting 2 kings out of 25 cards is approximately 0.044 or 4.4%.

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Answer:

Step-by-step explanation:

[tex]\frac{42}{x+5} =7[/tex]

[tex]42=7(x+5)[/tex]

[tex]42=7x+35[/tex]

[tex]7x=-7[/tex]

[tex]x=-1[/tex]

diameter = 14cm

[tex]radius \: = \frac{d}{2} = \frac{14}{2} \\ = 7cm[/tex]

Area of circle ( A1 ) = [tex]\pi {r}^{2} [/tex]

[tex] = \frac{22}{7} \times 7 \times 7 \\ [/tex]

[tex] = 154 {cm}^{2} [/tex]

Area of Square ( A2 ) = l²

= ( 14 )²

= 196cm²

Area of shaded region = A2 - A1

= 196 - 154

= 42cm²

....Thank you !! :)

0.0002

The required probability can be calculated as follows:Explanation:There are 7 different songs from 7 different artists, thus there are 7! ways of shuffling these songs. In other words, there are 7! = 5040 different playlists in which these songs can be shuffled.We need to calculate the probability of Adam Rickitt's song being played first and Phil Collins' song being played second. This can be done in two steps.Step 1: We place Adam Rickitt's song at the beginning of the playlist. There is only one way to do this. After Adam Rickitt's song has been placed, we are left with 6 remaining songs that can be shuffled. Thus, there are 6! = 720 different playlists.Step 2: We place Phil Collins' song as the second song on the playlist. There is only one way to do this as well.Therefore, the probability that Adam Rickitt's song is played first and Phil Collins' song is played second is given by the product of the probabilities of the two steps as follows:P = 1/5040 × 1 = 1/5040 = 0.000198 rounded to 4 decimal places. Thus, the probability is approximately 0.0002. Therefore, the probability that the first song is by Adam Rickitt and the second song is by Phil Collins is 0.0002.

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The probability of randomly selecting someone who does not believe that some people see the future in their dreams is 39.6%.

Probability is an area of mathematics that deals with the study of chance events.

We have, A poll showed that 60.4% of Americans say they believe that some people see the future in their dreams.

Therefore, the probability of randomly selecting someone who does not believe that some people see the future in their dreams can be calculated as follows:

P(A) = 1 - P(B)

Where,

P(A) = Probability of selecting someone who does not believe that some people see the future in their dreams.

P(B) = Probability of selecting someone who believes that some people see the future in their dreams.

P(A) = 1 - P(B)

⇒ 1 - 60.4/100

⇒39.6/100

⇒ 0.396 or 39.6%

Hence, the probability of randomly selecting someone who does not believe that some people see the future in their dreams is 39.6%.

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The percentage of of the shaded region is 74.8%

A circle is simply a round shape that has no corners or line segments. It is a closed curve shape in geometry. The enclosed body of a circle is called the circumference.

The space enclosed by the boundary of a plane figure is called its area. The area of a figure is the number of unit squares that cover the surface of a closed figure. Area is measured in squared units.

The area of a circle is expressed as :

πr²

The area of the shaded part = area of big circle - area of small circle

= 3.14(8.01²-4.02²)

= 3.14(64.16-16.16)

= 3.14( 48)

= 150.72in²

area of the big circle = 3.14 × 64.16 = 201.46

therefore the percentage of the shaded region of the point = 150.72/201.46 × 100

= 74.8% ( nearest tenth)

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The best way to design a study to measure the amount of traffic during the morning rush hour along a city street is to make video recordings of the street during rush hour every day for a year and count the number of vehicles that pass a certain point, then calculate the average using the given formula.

The best way to accurately measure the amount of traffic during the morning rush hour along a city street is to make video recordings of the street during rush hour every day for a year. After recording the video, count the number of vehicles that pass a specific point in the video. Then, calculate the average number of vehicles that pass the point each day during one year by using the following formula: Average = (Number of vehicles per day1 + Number of vehicles per day2 + ... + Number of vehicles per dayn) / n, where n is the number of days the video recording was made. This method is the most reliable way to measure the amount of traffic during the morning rush hour since it provides an average based on the data collected over a full year.

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Step-by-step explanation:

7. Cross multiply

14( 6x +1) = 7( 18x - 2)

Open the brackets

84x +14 = 126x - 14

Subract 84x from both sides

14 = 42x - 14

Add 14 to both sides

28 = 42x

Divide both sides by 42

X = 28/42

Write in simplest form

X=2/3

8. Add all the ratio 2+3+4= 9

Alana is ratio 3

3/9 x 63 candy = 21 candy

9. 3ab : 27ab

Divide both sides by 3, you have 1ab: 9ab

Divide both sides by ab, you have 1: 9

Answer:

it depends

Step-by-step explanation:

it depends on the value of n

for instance if n was = to 7 then

2+2n = 2+2(7) = 2+14 = 16

Answer: 2+2n

Step-by-step explanation:

The expression 2 + 2n can be simplified as follows:

2 + 2n = 2(1 + n)

So the expression 2 + 2n is equivalent to 2 times the quantity 1 plus n, or simply 2(1 + n). It cannot be simplified any further unless there is additional information or context provided.

Answer:

-180

Step-by-step explanation:

The measure of the angle on the attached figure is

There are two ways to measuring it

1. Counterclockwise: In this the sign is positive

So,

We can write

180°,

180°+360° = 540°,

180° + 2(360°) =180°+720° =900°,

2. Clockwise: In this, the sign is negative

So,

We can write

-180°,

-180° - 360° = -540°,

-180° - 2(360°) = -180° - 720° = -900°

the correct option is A.

Answer:

x = -2

y = -4

Step-by-step explanation:

x - 3y = 10 --------------(1)

x + 5y = -22 -----------(2)

Taking Eq. (1)

x - 3y = 10

x = 10 + 3y ------------(3)

10 + 3y + 5y = -22

8y = -22 - 10

8y = -32

y = -32/8

x = 10 + 3(-4)

x = 10 - 12

[tex]\rule[225]{225}{2}[/tex]

Answer:

Step-by-step explanation:

To solve the given system, let's begin by solving for x in x- 3y=10:-

[tex]\tt x-3y=10[/tex]

Add 3y to both sides:-

[tex]\tt x-3y+3y=10+3y[/tex]

[tex]\tt x=10+3y[/tex]

Substitute x= 10+3y into x+5y=-22:-

[tex]\tt 10+3y+5y=-22[/tex]

Simplify:-

[tex]\tt 10+8y=-22[/tex]

Now, solve for y in 10+8y=-22:-

[tex]\tt 10+8y=-22[/tex]

Subtract 10 from both sides:-

[tex]\tt \tt 10+8y-10=-22-10[/tex]

[tex]\tt 8y=-32[/tex]

Divide both sides by -8:-

[tex]\boxed{\bf y=-4}[/tex]

Now, substitute y=-4 into x=10+3y:-

[tex]\tt x=10+3y[/tex]

[tex]\tt x=10+3\times-4[/tex]

Simplify:-

[tex]\boxed{\bf x=-2}[/tex]

Therefore, x=-2 and y=-4

_________________________

Hope this helps! :)

Therefore, the maximum value of 17 is not considered an outlier as it falls within the upper limit.

what is  Median?

The median is a statistical measure that represents the central value of a dataset.

To calculate the upper limit for outliers, we can use the interquartile range (IQR) and the formula:

Upper Limit = Q3 + 1.5 * IQR

where Q3 is the third quartile, and IQR is the interquartile range.

First, we need to find the values for Q1, Q2 (median), and Q3:

1, 6, 6, 6, 7, 7, 8, 9, 13, 10, 17

Arranging the data in order:

1, 6, 6, 6, 7, 7, 8, 9, 10, 13, 17

The median is the middle value. Since there are 11 values, the median is the average of the 6th and 7th values:

Median = (7 + 8) / 2 = 7.5

To find Q1 and Q3, we need to find the medians of the lower and upper halves of the data, respectively:

Lower half: 1, 6, 6, 6, 7

Upper half: 8, 9, 10, 13, 17

Q1 is the median of the lower half, which is 6.

Q3 is the median of the upper half, which is 10.

Next, we can calculate the interquartile range:

IQR = Q3 - Q1 = 10 - 6 = 4

Finally, we can calculate the upper limit for outliers:

Upper Limit = Q3 + 1.5 * IQR = 10 + 1.5 * 4 = 16

Any value above 16 can be considered a potential outlier on the high end of the data.

Therefore, the maximum value of 17 is not considered an outlier as it falls within the upper limit.

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Approximately 491351% of the annual moisture at an altitude of 6000 feet falls as snow.

According to the given function, the percent of annual snowfall at an altitude of h feet is given by p(h) = 82 in (h) - 649. To approximate the amount of snow at the altitudes of 3000 feet and 6000 feet, we can simply plug these values into the function and solve for p(h).

At an altitude of 3000 feet, we have:

p(3000) = 82 in (3000) - 649

p(3000) = 246000 - 649

p(3000) = 245351

Therefore, approximately 245351% of the annual moisture at an altitude of 3000 feet falls as snow.

Similarly, at an altitude of 6000 feet, we have:

p(6000) = 82 in (6000) - 649

p(6000) = 492000 - 649

p(6000) = 491351

Therefore, approximately 491351% of the annual moisture at an altitude of 6000 feet falls as snow.

It's important to note that these values represent percentages and not the actual amount of snowfall in inches. To convert these percentages to the actual amount of snowfall, we would need to know the total annual moisture at each altitude. Nonetheless, we can use the given function to approximate the percentage of snowfall at different altitudes in the mountain range of California.

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The mean Depreciation of automobile for a random sample of 20 automobile models is 6626.

To find the mean of the Depreciation amounts in Car Depreciation, we can use the following formula:

mean = (sum of all values) / (number of values)

The resulting value of 6626 indicates the average depreciation amount in dollars of the 20 automobile models in the sample of standard deviation.

In statistics, the mean is a measure of central tendency that represents the average value of a dataset. It is calculated by adding up all the values in the dataset and then dividing the sum by the number of values.

The mean is commonly used as a measure of the "typical" value in a dataset and is often used to compare the values of different datasets or to track changes in a single dataset over time.

Automobile Depreciation For a random sample of 20 automobile models, we record the value of the model as a new car and the value after the car has been purchased and driven 10 miles. 1 The difference between these two is a measure of the depreciation on the car just by driving it off the lot.

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Answer:

To find the slope of the line through point B and perpendicular to line k, we need to first find the slope of line k.

If we have the equation of line k in slope-intercept form, y = mx + b, then the slope of line k is simply the coefficient of x, which is m.

Assuming we don't have the equation of line k, we can find its slope by using the slope formula, which is:

m = (y2 - y1)/(x2 - x1)

where (x1, y1) and (x2, y2) are two points on line k.

Let's say line k passes through points P and Q. Then we can write the slope of line k as:

m = (yQ - yP)/(xQ - xP)

Now, we want to find the slope of the line through point B and perpendicular to line k. We know that the product of the slopes of two perpendicular lines is -1. That is:

m1 * m2 = -1

where m1 is the slope of line k, and m2 is the slope of the line through point B and perpendicular to line k.

Therefore, we can write:

m2 = -1/m1

So we just need to find the slope of line k, and then we can use this formula to find the slope of the line through point B and perpendicular to line k.

Once we have the slope of the line through point B, we can write its equation in point-slope form:

y - yB = m2(x - xB)

where (xB, yB) is the point B.

Hope this helps with you with your question (it's not a direct answer, I think?) I'm sorry if it doesn't! If you need more help, ask me! :]

x°=46

Step-by-step explanation:

There are two methods of solving this question

Method 1:

x°+90°=136° the theorem states that "the sum of two opposite interior is equal to the exterior"

x°=136°-90°

x°=46°

or

Method 2:

136° is on a straight line which is 180°

so, let the other side of the straight line be a.

therefore, 136°+a°=180° theorem {Angle on a straight line}

a°=180°-136°

a°=44°

so, in the triangle is the sum of 180°

a°+90°+x°=180° theorem {Sum of angles in a triangle}

44°+90°+x°=180°

x=180°-134°

x°=46°

The forecasted demand for Samsung TVs at X-store for the 4th year using seasonality indexing are as follows:

A seasonal index is a tool that compares a specific season during a cycle to the average season during that cycle. By deseasonalizing data, we can predict or approximate future data values by removing seasonal fluctuations or patterns in the data.

To use seasonality indexing to forecast the values of the 4th year, we first need to calculate the average indices for each season:

Average index for Spring:

= (1500 + 1650 + 1550) / 3

= 1567

Average index for Summer:

= (1000 + 900 + 850) / 3

= 917

Average index for Fall:

= (500 + 600 + 550) / 3

= 550

Average index for Winter:

= (200 + 150 + 220) / 3

= 190

Next, we need to calculate the seasonality index for each season by dividing the average index by 100:

Seasonality index for Spring = 1567 / 100 = 15.67

Seasonality index for Summer = 917 / 100 = 9.17

Seasonality index for Fall = 550 / 100 = 5.50

Seasonality index for Winter = 190 / 100 = 1.90

To forecast the demand for the 4th year, we can use the following formula "Seasonality index x Average demand for the season".

For Spring, the Forecasted demand for Spring in year 4:

= 15.67 x (3710/4)

= 5800.175

≈ 5800 TVs

For Summer, the Forecasted demand for Summer in year 4:

= 9.17 x (3710/4)

= 3372.925

≈ 3373 TVs

For Fall, the Forecasted demand for Fall in year 4:

= 5.50 x (3710/4)

= 2031.25

≈ 2031 TVs

For Winter, the Forecasted demand for Winter in year 4:

= 1.90 x (3710/4)

= 692.75

≈ 693 TVs

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Answer:

the GCF of 270 & 360 is 90

exponent form: 3³x 2 x 5 = 270 & 3²x 2³x 5 = 360

Step-by-step explanation:

3 x 3 x 3 x 2 x 5 = 270

3 x 3 x 2 x 2 x 2 x 5 = 360

Answer:

y = (x + 2)² + 2

Step-by-step explanation:

a quadratic function in vertex form is

y = a(x - h)² + k

where (h, k ) are the coordinates of the vertex and a is a multiplier

y = x² + 4x + 6

using the method of completing the square

add/subtract ( half the coefficient of the x- term)² to x² + 4x

y = x² + 2(2)x + 4 - 4 + 6

 = (x + 2)² + 2 ← in vertex form

The linear function that best fits the data is given as follows:

y = 60x.

The slope-intercept representation of a linear function is given by the equation presented as follows:

y = mx + b

The coefficients of the function and their meaning are described as follows:

When x = 0, y = 0, hence the intercept b of the line is given as follows:

b = 0.

When x increases by 5, y increases by 300, hence the slope m of the line is given as follows:

m = 300/5

m = 60.

Hence the equation is:

y = 60x.

The points on the scatter plot are given as follows:

(0,0) and (5,300).

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The value of tan (A-B) is -203/169, when angles A and B are in Quadrant 1.

In trigonometry, the Pythagorean identity is sin² + cos² = 1, where is an angle in a right triangle. The Pythagorean theorem, which asserts that the square of the hypotenuse is equal to the sum of the squares of the legs of a right triangle, is the source of this identity. Trigonometric identities and formulae are derived from the Pythagorean identity, which is a basic idea in the subject.

The trigonometric identity is given as

tan(A-B) = (tan A - tan B) / (1 + tan A tan B)

The value of tan A and tan B is calculated as follows.

sin A = 7/25, we can use the Pythagorean identity: sin² A + cos² A = 1 to find cos A:

cos A = √(1 - sin² A) = √(1 - (7/25)²) = 24/25

Therefore, tan A = sin A / cos A = (7/25) / (24/25) = 7/24.

Similarly, since cos B = 12/37, we can use the Pythagorean identity cos² B + sin² B = 1 to find sin B:

sin B = √(1 - cos² B) = √(1 - (12/37)²) = 35/37

Therefore, tan B = sin B / cos B = (35/37) / (12/37) = 35/12.

Substituting the values:

tan(A-B) = (tan A - tan B) / (1 + tan A tan B)

= ((7/24) - (35/12)) / (1 + (7/24) x (35/12))

= (-203/288) / (169/288)

= -203/169

Therefore, the value of tan (A-B) is -203/169.

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Using ratios, we can find that the number of girls in the class are 20.

If b is not equal to 0, an ordered pair of numbers a and b, denoted as a / b, is a ratio. A proportion is an equation that equalises two ratios.

For illustration, the ratio may be expressed as follows: 1: 3 in the case of 1 boy and 3 girls (for every one boy there are 3 girls) There are 3 out of 4 girls and 1 out of 4 guys.

Now in the question, total students in class = 32.

The ratio between the boys and girls is 3:5.

So, total parts from the ratio = 3+5=8

Now 5/8 students in the class are girls.

= 5/8 × 32

= 5 × 4

= 20.

Therefore, the number of girls in the class are 20.

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The minimum number οf identical cοntainers Rene wοuld need tο make 2,000 cm³ οf ice is 4. Optiοn b is the cοrrect οptiοn.

A cylinder is a three-dimensiοnal sοlid in mathematics that maintains, at a fixed distance, twο parallel bases cοnnected by a curved surface. These bases typically have a circular shape (like a circle), and a line segment knοwn as the axis cοnnects the centers οf the twο bases.

The base οf a cοntainer is 8 centimeters. The height οf the cοntainer is 10 centimetres.

The radius οf a shape is half οf its diameter.

The radius οf  cοntainer is 8/2 = 4 cm.

The vοlume οf a cylinder is πr²h.

The vοlume οf a cοntainer is π×4²×10

= 160 × 3.14

= 502.4 cm³

Assume that Rene needs x number οf cοntainers.

The vοlume οf x number οf cοntainers is 502.4 x.

Accοrding tο the questiοn:

502.4 x = 2,000

Divide bοth sides by 502.4:

x = 2000/502.4

x = 3.98

x ≈ 4

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