ABC is an isosceles triangle of vertex A. D is the symmetric of A with respect to (BC) and E the symmetric of A with respect to B. 1) Prove that ACDB is a rhombus. 2") Prove that BCDE is a parallelogram.

i need help with question 1
also if they say, "D symmetric of Awith respect to (BC)" does it mean that Any point on BC or the midpoint of BC?​

ΔVWX ≅ ΔZYX, to justify the statement SAS property is used.

Correct option is: 3

Congruent triangles exist if its two sides and also included angles are identical to that of other triangle's two sides and also included angle.

The triangles are considered to be congruent when all three pairs of matching sides are. Side-side-side is the name of this congruence shortcut (SSS). Side-angle-side (SAS) is an alternative simplification if two sets of side as well as the angles between them is known to just be congruent.

When determining if a collection of triangles is congruent, the Side-Angle-Side rule is utilized. According to the SAS rule, two sides and the included angle of one triangle must equal two sides and the included angle of another triangle in order for the two triangles to be considered congruent. An angle produced by two specified sides is called an included angle.

Correct option: 3

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Answer:

  4/9

Step-by-step explanation:

If Maggie reads 1/3 of a book in 3/4 weeks, you want to know how many books per week Maggie reads.

To find Maggie's reading rate in books per week, divide books by weeks:

  (1/3 book)/(3/4 week) = (1/3)/(3/4) book/week

  = (1/3) · (4/3) book/week = 4/9 book per week

Maggie reads 4/9 books per week.

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Answer:

The number of cars of a particular model produced by the factory between 2006 and 2010 are:

2006: 35,000

2007: 40,000

2008: 45,000

2009: 30,000

2010: 35,000

No data is available for 2012.

The total distance travelled by the ball after dropping from a height of 16 feet and rebounds 0.81 feet is equal to 168.4 feet.

Balls from a height = 16 feet

Rebounds = 0.81feet

It form a geometric progression pattern :

16 + 16(0.81) + 16(0.81)² + 16(0.81)³ + ......+ ∞

Using sum of geometric progression :

S = a / 1 - r

here a = 16

r = 0.81

S represents the sum .

The total distance travelled by the ball is double of the sum .

S = 16 / ( 1 - 0.81 )

  = 16 / ( 0.19)

  = 84.2 feet

Total distance travelled by the ball  = 2 × 84.2 feet

                                                           = 168.4 feet

Therefore, the total distance travelled by the ball as per given situation is equal to 168.4 feet.

The above question is incomplete, the complete question is:

A ball is dropped from a height of 16 feet. Each time it drops h feet, it rebounds 0.81h feet. Find the total distance traveled by the ball .

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Answer:

Step-by-step explanation:

well 6.4 converted to a fraction is 32/5 so i hope this helps.

The equation in function notation to represent Ainsley's salary is y = $24,500 * (1 + 0.03x) and  Ainsley's salary will be $26,940 when she begins her fourth year working at the bookstore.

What is an equation in function notation?

An equation involving x and y, which is also a function, can be written in the form y = “some expression involving x”; that is, y = f ( x). This last expression is read as “ y equals f of x” and means that y is a function of x.

a. Let y be Ainsley's salary after x years of working at the bookstore.

The equation representing Ainsley's salary as a function of the number of years she has been working at the bookstore is y = $24,500 * (1 + 0.03x).

b. To find Ainsley's salary when she begins her fourth year working at the bookstore, we need to plug in x = 3 into the equation:

y = $24,500 * (1 + 0.03x)

y = $24,500 * (1 + 0.03 * 3)

y = $24,500 * 1.09

y = $26,940.

Hence, The equation in function notation to represent Ainsley's salary is y = $24,500 * (1 + 0.03x) and  Ainsley's salary will be $26,940 when she begins her fourth year working at the bookstore.

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Answer:

(-3,-5)

Step-by-step explanation:

2x+1=x-2

subtract 3 from both sides

x=(-3)

sub the value of x back into one of the equations

y=2(-3) + 1=-5

Answer:

B, C, E, F

Step-by-step explanation:

Solve for the missing angle first (which is 42°)

Listing all of the basic trig ratios (sohcahtoa):

sin x = opp/hyp

cos x = adj/hyp

tan = opp/adj

sin 48° = a/c

cos 48° = b/c

tan 48 = a/b

sin 42° = b/c

cos 42° = a/c

tan 42° = b/a

There were 37 pupils that completed push-ups. The maximum number of push-ups allowed is 32.

A line chart, also known as a curve chart, is a type of chart that presents information as a succession of data points called "markers" that are connected by straight line segments. It is a simple form of chart that is used in many disciplines. A line plot is a linear graph that displays data frequency distributions along a number line. It is useful for analyzing data with a single specified value. Line plots are sometimes known as dot plots. A line plot depicting the distance traveled by 17 turtles in one hour is shown below (we know it is 17 turtles because there are 17 dots on the line plot).

Here,

Mr. Anderson's class=20

Mrs. Brown's class=17

Number of students who did push-ups is 37. Maximum number of push-ups is 32.

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The tangent of the corners of this right-angle triangle is 4/3.

The Pythagorean theorem states, "In a right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides." The sides of this triangle were called the perpendicular, the base, and the hypotenuse.

The tangent of a right triangle angle is equal to the ratio of the opposite side to the adjacent side. So if we call the other side "x", we can set the following formula:

tan(θ) = 8/x

where θ is the angle from height 8. We can find the value of x using the Pythagorean theorem.

[tex]x^2 + 8^2 = 10^2\\x^2 = 100 - 64\\x^2 = 36\\x = 6[/tex]

So the tangent values ​​are:

tan(θ) = 8/6 = 4/3

Therefore, the tangent of the corners of this right triangle is 4/3.  

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Answer:  £13,741.69 will be the value in 4 years

Step-by-step explanation:

formula: present value * (1-depreciation rate)^years

15095*(1-0.0275)^4

=13,741.69

The number of socks you pull out to have two black socks is 3 socks

Total number of pairs of socks in a drawer = 10

Number of black pairs of socks = 5

Number of blue pairs of socks  = 5

A. If you picked 2 socks [black] and [blue] 3rd pick guarantees you will have one pair of either blue or black

The number of socks you pull out to guarantee that you have a pair of one color is 3 socks

B. If you want to pick 2 good pairs and your 6 picks are the worst case, so 7th pick of the socks will give you good pair of two colors.

The number of socks you pull out to have two good pairs is 7 socks

C. If you want to have a pair of black socks your worst case will be you pick all 10 blue socks so another 2 socks must be black.

Therefore, the number of socks you pull out to have two black socks is 12 socks.

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Answer:

cos^2 (x)

Step-by-step explanation:

Use two of the Pythagorean Identities. See image.

You can rearrange the Pyth Identities. Like subtract the same thing from both sides.

Your question simplifies in just two steps. See image.

The probability of a flight will not arrive on time is 231/1000

Probability is the function that measures the chances that an outcome of a random event will be as expected. In this way you can measure how likely it is that an event will happen.

Probability requested is equivalent to:

Flights arrive on time= 769

Total flights = 1000

P(arrive on time) = Flights arrive on time / Total flights

P(arrive on time) = 769/1000

P (not arrive on time) = 1 - 769/1000

P (not arrive on time) = (1000 - 769)/1000

P (not arrive on time) = 231/1000

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Answer:

Step-by-step explanation:

We have two values i.e., 6*10^6 and 4*10^4
we divide both of them
i.e., =6*10^6/4*10^4
we shift the 10^4 to the numerator which becomes 10^-4.
=6*10^6*10^-4/4

=6*10^2/4

=600/4

=150
so, 6*10^6 is 150 times greater than 4*10^4

Answer:

x=42

Step-by-step explanation:

Step 1) 105=3x-21

Step 2) 126= 3x

Step 3) 42=x

The value of x = 25 % (option b) in 79% of 8400 + 66.66% of 4800 = 120% of 7200+ x% of 4784. by converting the percentages.

79% of 8400 = ( 79/100) x 8400

                     = 6636

66.66% of 4800 = (66.66/100)x4800

                      = 3199.68

120% of 7200 = (120/100)x7200

                       = 8640

x% of 4784  = (x/100) x 4784

we are given that, 79% of 8400 + 66.66% of 4800 = 120% of 7200+ x% of 4784. what is the value of x :

therefore, 6636 + 3199.68 = 8646 + (x/100) x 4784

                 (x/100) x 4784 = 6636 + 3199.68 - 8646

                                         = 1189.68

                                (x/100) = 1189.68/4784

                                            = 0.248

                                    x = 0.248 x 100

therefore , the value of x is equals to 24.8 % or 0.248 which is approximated to 25 % that is option (b)

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Yes, the lines AB and PQ are parallel lines and have same direction.

Coordinates of the line AB and PQ :

A = (1, 1), B = (3, 4), P = (1, 1), Q = (7, 10)

Slope =  (y₂ - y₁)/ (x₂ -x₁)

Substitute the value in the formula:

Slope of the line AB = ( 4 - 1 )/ ( 3 - 1 )

⇒ Slope of the line AB = 3 /2

Slope of the line PQ = ( 10 - 1 )/ ( 7 - 1 )

⇒ Slope of the line PQ = 9 /6

⇒ Slope of the line PQ = 3 /2

Slope of line AB and PQ are equal it implies they are parallel lines.

Therefore, both the lines AB and PQ are parallel lines to each other and are in the same direction.

The above question is incomplete , the complete question is:

Are lines AB and PQ parallel? And if so, do they point in the same direction? A = (1, 1), B = (3, 4), P = (1, 1), Q = (7, 10)

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The system of equations that can find the number of student tickets sold is:

7x + 9y = 543

x + y = 67

Defining the variables that helped write the system are:

Let x be the number of student tickets sold

Let y be the number of adult tickets sold.

First, define the variables. In this case, we can say that x will be the number of student tickets while also making y the number of adult tickets.

The first equation would be:

Revenue of student tickets sold + Revenue of adult tickets = Total revenue

7x + 9 y = 543

The second equation is:

Number of student tickets + Number of adult tickets = Number of total tickets

x + y = 67

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Answer: The answer is 7x + 9y = 543x + y = 67.

Step-by-step explanation: Please give Brainlist.

Hope this helps!!!!

The confidence interval is (84.41, 85.59), meaning that we are 85.0% confident that the true population mean, μ, lies between 84.41 and 85.59

A 85.0% confidence interval for the true population mean, μ, can be constructed using the following formula:

x¯ ± (Zα/2 * σ/√n)

where

Using the Z-score table for a confidence level of 0.85, we have

Zα/2 = 1.040.

Substitute the known values in the above equation, so, we have the following representation

CI = 85.0 ± (1.040 * 5.5/√94)

Evaluate

CI = 85.0 ± 0.59

This gives

CI = 84.41 to 85.59

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The result is true, the number is forbidden.

This rule can be expressed mathematically as:

10 ≤ x < 19

This statement is saying that any number x must be greater than or equal to 10, but less than 19. So if x is set to any number between 10 and 19, the statement will be false. For example, if x is set to 15, the statement becomes:

10 ≤ 15 < 19

Which is false. So any number between 10 and 19 is forbidden.

This can be calculated by first subtracting 10 from the number. For example, if the number is 17, we would subtract 10 to get 7. Since 7 is less than 19, the number is forbidden. We can also use this equation to check any given number:

x − 10 < 19

If the result is true, then the number is forbidden. For example, if x is set to 17, the equation becomes:

17 - 10 < 19

Which is true, so 17 is forbidden.

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Complete question:

What is the sum of any two numbers between 10 and 19?

The amount of money each person gets is $12.

For a total amount of $36, each person gets a fraction of 1/3 of the whole amount.

What is fraction?

In mathematics, a fraction is used to denote a portion or component of the whole. It stands for the proportionate pieces of the whole. Numerator and denominator are the two components that make up a fraction. The numerator is the number at the top, and the denominator is the number at the bottom.

The number of people are = 3

The amount of money to be shred equally is = $36

Let the amount of money each person gets be = x

Then for 3 people the amount will be = 3x.

The formula to find the value of x is -

3x = 36

x = 36/3

x = 12

Therefore, each person get $12.

The fraction that represents the amount will be -

share of each person / total amount

Substitute the value into the expression -

12/36 = 1/3

Therefore, each person shares 1/3 of the money.

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The only two possible results of the expression num % 2 if the variable num contains a positive integer is 0 and 1.

Variables include effects like height, age, income, fiefdom of birth, academy grades, and kind of dwelling. There are two introductory types of variables order and numeric. also, each order is divided into two subcategories separate or nonstop for numeric variables, and nominal or ordinal for categorical variables. In this section, these orders are compactly described.

A quantifiable property with numerical values is known as a numeric variable( also known as a quantitative variable)( except figures which are canons standing up for orders). Both nonstop and separate numerical variables are possible.

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The n will be 12.175074 for which (5/6)^n is less than 0.00001.

We start by converting the target number to scientific notation: 0.00001 = 1 x 10^-5

Next, we take the logarithm base (5/6) of both sides:

n = log base (5/6) of (1 x 10^-5)

Using logarithm rules, we can simplify this to:

n = log base (5/6) of 1 - log base (5/6) of 10^-5

Using logarithm tables or a calculator, we find that:

log base (5/6) of 1 = 0

log base (5/6) of 10^-5 = -12.175074

So,

n = 0 - (-12.175074) = 12.175074

Therefore, n = 12.175074.

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f(x)= x+2  a function if the input value is 5 then the output should be 5,7,9,11,13

g is a transformation f the function f.

We have to figure out the transformation and write the equation of g with respect to f.

g is (with respect to the function f):

• reflected upside down [reflected about x-axis]

• translated 3 units left

Reflection with respect to x-axis makes the function negative, so:

f(x) would be -f(x)

Then,

Translation "a" units to the left, makes a function f(x) into f(x+a), thus:

f(x) would be -f(x+3)

hence f(x)= x+2  a function if the input value is 5 then the output should be 5,7,9,11,13

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Answer:

3 and 4 or {3,4}

Step-by-step explanation:

3 and 4 are the only numbers greater than 2, but less than 5.

Answer:

C

Step-by-step explanation:

7(x + 3) = 2x + 1 ← distribute parenthesis on left side by 7

7x + 21 = 2x + 1 ( subtract 2x from both sides )

5x + 21 = 1 ( subtract 21 from both sides )

5x = - 20 ( divide both sides by 5 )

x = - 4

Answer:

x=-4

Step-by-step explanation:

7(x+3)=2x+1

distribute 7

7x+21=2x+1

subtract 1 from both sides

7x+20=2x

subtract 7x from both sides

20=-5x

divide both sides by -5

x=-4

When the empirical probability that a CD drive would fail is 0.016%, there are four possible failures.

The probability that a happening will occur or a claim will be true is measured by probability theory, a branch of mathematics. The probability of an occurrence is a value between 0 and 1 and 1, where about 0 represents how likely something event is always to occur and 1 represents certainty. A probabilities is a numerical illustration of the possibility that a specific occurrence will take place. Probabilities can also be expressed as percentages ranging from 0% to 100percentage or from 0 to 1. the ratio of the number of outcomes to the proportion of occurrences in a whole set of fairly probable options that lead to a specific occurrence.

given

Let n = number of operations and P = error.

P = .016

n = 250

Increase P and n.

.016 (250) = 4

When the empirical probability that a CD drive would fail is 0.016%, there are four possible failures.

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One ounce of food contains average  about 28 grams of carbs.

One of the three macronutrients that the body needs for energy, carbohydrates can be found in a wide variety of foods. Sugar, starch, and fiber are the three elements that make up carbohydrates. Weight is measured in ounces, which weigh 28.35 grams. As a result, one ounce of food contains about 28 grams of carbs. Carbohydrates are crucial for supplying the body with the 4 calories per gram of energy it needs to function, fuel physical activity, and help with digestion. Foods like fruits, vegetables, grains, nuts, and dairy products all naturally include ounces of carbs. It is crucial to remember that there are several kinds of carbs, some of which are healthier than others.

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The complete question is

How many grams of carbs in an ounce of food ?

The equation can be factorized as (x + 4/3) (x + 3/2).

The expression 2x² + bx - 9 will be prime for the the values of b = 18, 12, and -1.

Quadratic expressions are polynomial expressions of second degree.

The general form of a quadratic expression is ax² + b x + c.

18. The zeroes of the expression ax² + b x + c can be found by,

x = [-b ± √(b² - 4ac)] / 2a

The given expression is 6x² + 17x + 12.

We have to factorize the expression.

x = [-17 ± √(17² - 4×6×12)] / [2 × 6]

  = [-17 ± √(289 - 288)] / 12

  = (-17 ± 1) / 12

x = -16/12 = -4/3 and x = -18/12 = -3/2

The expression can be factorized as (x + 4/3) (x + 3/2).

19. The expression is non factorable if the value of the discriminant is neither zero nor a positive perfect square.

For ax² + b x + c, Discriminant = b² - 4ac

The expression given is 2x² + bx - 9.

Discriminant = b² - (4 × 2 × -9) = b² + 72

When b = 18, b² + 72 = 396, not a perfect square root

When b = 3, b² + 72 = 81, a perfect square root

When b = 12, b² + 72 = 216, not a perfect square root

When b = -3, b² + 72 = 81, a perfect square root

When b = -7, b² + 72 = 121, a perfect square root

When b = -1, b² + 72 = 73, not a perfect square root

When b = 17, b² + 72 = 361, a perfect square root

So when b = 3, -3, -7 and 17, the expression is factorable.

When b = 18, 12, and -1, the expression is prime.

Hence the expression 2x² + bx - 9 is prime when the values of b are  18, 12, and -1.

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