Calculate the perimeter for the given figure.
8 ft
8.5 14
.ft
10 11
A. 16.5 feet
B. 25.5 feet
C: 26,5 feet
D. 26.5 feet

Answer:

Statements Reasons

AB¯¯¯¯¯¯¯¯≅BC¯¯¯¯¯¯¯¯ Given

∠ADB and ∠CDB are right angles Given

ΔADB and ΔCDB are right triangles definition of right triangles

BD¯¯¯¯¯¯¯¯≅BD¯¯¯¯¯¯¯¯ reflexive property

ΔADB≅ΔCDB HL≅

AD¯¯¯¯¯¯¯¯≅DC¯¯¯¯¯¯¯¯ CPCTC (corresponding parts of congurent triangles must be congurent)

Step-by-step explanation:

Most of the geometry concepts and theorems that are learned in high school today were first discovered and proved by mathematicians such as Euclid thousands of years ago. Given that these geometry concepts and theorems have been known to be true for thousands of years, why is it important that you learn how to prove them for yourself?

Theorems and Proofs

In geometry, a postulate is a statement that is assumed to be true based on basic geometric principles. An example of a postulate is the statement “through any two points is exactly one line”. A long time ago, postulates were the ideas that were thought to be so obviously true they did not require a proof. A theorem is a mathematical statement that can and must be proven to be true. You've heard the word theorem before when you learned about the Pythagorean Theorem. Much of your future work in geometry will involve learning different theorems and proving they are true.

What does it mean to “prove” something? In the past you have often been asked to “justify your answer” or “explain your reasoning”. This is because it is important to be able to show your thinking to others so that ideally they can follow it and agree that you must be right. A proof is just a formal way of justifying your answer. In a proof your goal is to use given information and facts that everyone agrees are true to show that a new statement must also be true.

Suppose you are given the picture below and asked to prove that AD¯¯¯¯¯¯¯¯≅DC¯¯¯¯¯¯¯¯. This means that you need to give a convincing mathematical argument as to why the line segments MUST be congruent.

Here is an example of a paragraph-style proof. This is similar to a detailed explanation you might have given in the past.

AB¯¯¯¯¯¯¯¯≅BC¯¯¯¯¯¯¯¯ because it is marked in the diagram.  Also, ∠ADB and ∠CDB are both right angles because it is marked in the diagram.  This means that △ADB and △CDB are right triangles because right triangles are triangles with right angles.  Both triangles contain segment BD¯¯¯¯¯¯¯¯.  BD¯¯¯¯¯¯¯¯≅BD¯¯¯¯¯¯¯¯ because of the reflexive property that any segment is congruent to itself.  △ADB≅△CDB by HL≅ because they are right triangles with a pair of congruent legs and congruent hypotenuses.  AD¯¯¯¯¯¯¯¯≅DC¯¯¯¯¯¯¯¯ because they are corresponding segments and corresponding parts of congruent triangles must be congruent.

There are two key components of any proof -- statements and reasons.

The statements are the claims that you are making throughout your proof that lead to what you are ultimately trying to prove is true. Statements are written in red throughout the previous proof.

The reasons are the reasons you give for why the statements must be true. Reasons are written in blue throughout the previous proof. If you don't give reasons, your proof is not convincing and so is not complete.

When writing a proof, your job is to make everything as clear as possible, because you need other people to be able to understand and believe your proof. Skipping steps and using complicated words is not helpful!

There are many different styles for writing proofs. In American high schools, a style of proof called the two-column proof has traditionally been the most common (see Example 3). In college and beyond, paragraph proofs are common. An example of a style of proof that is more visual is a flow diagram proof (see Example 4). No matter what style is used, the key components of statements and reasons must be present. You should be familiar with different styles of proof, but ultimately can use whichever style you prefer.

Learning to write proofs can be difficult. One of the best ways to learn is to study examples to get a sense for what proofs look like.

Answer:

False

Step-by-step explanation:

It doesn't need to be proven in order to be used. We can just assume the postulate is true.

If attendance has climbed by 6% annually since 2015, we can estimate that 34,269 people will attend the festival in 2021.

We can use the formula for exponential growth:

\(y = a * (1 + r)^x\)

Where

Plugging in the values, we get:

\(y = 25,000 * (1 + 0.06)^x\)

Simplifying, we get:

\(y = 25,000 * 1.06^x\)

As 2021 is six years from 2015, we need to know the attendance at x = 6 in order to estimate how many people will attend the event in 2021. When we enter x = 6, we obtain:

\(y = 25,000 * 1.06^6\)

\(y =34,268.77\)

Therefore, If attendance has climbed by 6% annually since 2015, we can estimate that 34,269 people will attend the festival in 2021.

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Answer:

4.3L of the 40% solution and 5.7L of the 5% solution

Step-by-step explanation:

hope this helps

Answer:

false

Step-by-step explanation:

15²+30² =  225+900 = 1125

35² = 1225

Since Pythagoras theorem doesn't hold for this triangle, it is not a right triangle.

Answer:

y is equal to 18

Step-by-step explanation:

\(3y+20-20=5y-16-20\\3y=5y-36\\3y-5y=5y-36-5y\\-2y=-36\\\frac{-2(y)}{-2}=\frac{-36}{-2}\\(\frac{-a}{-b} = \frac{a}{yb}) =\frac{2y}{2}\\\frac{2(y)}{2}=y\\=\frac{36}{2}\\=18\\y = 18\)

Step-by-step explanation:

Aaron had 72 beads

Bessy had 60 beads

Carl had 46 beads

Dawn had 22 beads

The value of the acute angle theta is 59.99 degrees

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

tan theta equals1.73205

Express teh equation properly

So, we have the following representation

tan theta = 1.73205

Take the arc tan of both sides

theta = tan^-1(1.73205)

Evaluate

theta = 59.99

HEnce, the acute angle is 59.99

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As per the question, All four students A, B, C, and D are loss-averse over money and have the same value function as below:v(x dollars)={√x     x ≥ 0   {-2√-x  x < 0They are also loss averse over mugs and have the same value function.

v(y mugs)={3y y ≥ 0
        {4y y < 0
Now, we have to find the values of a, b, c and d as below:
- Student A owns a mug and is willing to sell it for a price of a dollars or more. i.e v(a) = v(0) + v(a-A), where A is the initial endowment of A. According to the given function, v(0) = 0, v(a-A) = 3, and v(A) = 4.
So, a ≥ A+3/2
- Student B does not own a mug and is willing to pay up to b dollars for buying it. i.e v(B-b) = v(B) - v(0), where B is the initial endowment of B. According to the given function, v(0) = 0, v(B-b) = -4, and v(B) = -3.
So, b ≤ B+1/2
- Student C does not own a mug and is indifferent between getting a mug and getting c dollars. i.e v(c) = v(0) + v(c), where C is the initial endowment of C. According to the given function, v(0) = 0, v(c) = 3.
So, c = C/2
- Student D is indifferent between losing a mug and losing d dollars. i.e v(D-d) = v(D) - v(0), where D is the initial endowment of D. According to the given function, v(0) = 0, v(D-d) = -3.
So, d = D/2
2) In this case, value function for money changes to:v(x dollars)={√x     x ≥ 0
            {-√-x   x < 0
However, the value function for mugs remains the same:v(y mugs)={3y y ≥ 0
         {4y y < 0
Therefore, values for a, b, c, and d will remain the same as calculated in part (1).
3) In this case, students are not loss-averse. Value function for money:v(x dollars)={√x     x ≥ 0
            {-√-x   x < 0
Value function for mugs:v(y mugs)={3y y ≥ 0
The reference point is the status quo, i.e initial endowment. So,
- Student A owns a mug and is willing to sell it for a price of a dollars or more. The value of mug for A is 3 initially and he would sell it for 3 or more.
So, a ≥ A+3/2
- Student B does not own a mug and is willing to pay up to b dollars for buying it. The value of mug for B is 3 initially and he would buy it for 3 or less.
So, b ≤ B+3/2
- Student C does not own a mug and is indifferent between getting a mug and getting c dollars. The value of the mug for C is 3 initially.
So, c = 3
- Student D is indifferent between losing a mug and losing d dollars. The value of the mug for D is 3 initially.
So, d = 3
4) In this case, value function for money:v(x dollars)={√x     x ≥ 0
            {-√-x   x < 0
Value function for mugs: Mug will have a value of 4 for someone who owns it and 3 for someone who does not own it.
The reference point is the status quo, i.e initial endowment. So,
- Student A owns a mug and is willing to sell it for a price of a dollars or more. The value of mug for A is 4 initially and he would sell it for 4 or more.
So, a ≥ A+2
- Student B does not own a mug and is willing to pay up to b dollars for buying it. The value of mug for B is 3 initially and he would buy it for 3 or less.
So, b ≤ B+3/2
- Student C does not own a mug and is indifferent between getting a mug and getting c dollars. The value of the mug for C is 3 initially and he would like to buy it for 3.
So, c = 3
- Student D is indifferent between losing a mug and losing d dollars. The value of the mug for D is 3 initially.
So, d = 3.

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Answer:

8

Step-by-step explanation:

y=kx where k is a constant.

72=12k

k=72/12=6

y=6x

48=6x

x=48/6=8

Explanation.

The question asked us to write the equation of the line that passes through the points (2,8) and (-2,10)

To do this, we can use the formula:

In our case, we have

We will simply put all the values above into the formula to get the equation of the line

Simplifying further

Cross multiplying

Therefore, the equation of the line is

Answer:

Section A holds 25,000 seats, section B holds 14,500 seats and section C holds 10,500 seats.

Step-by-step explanation:

From the information given you can write the following equations:

A+B+C=50,000 (1)

28A+24B+20C=1,258,000 (2)

A=B+C (3)

A= number of seats in section A

B= number of seats in section B

C= number of seats in section C

You can replace (3) in (1) and (2) to get two equations:

B+C+B+C=50,000

2B+2C=50000

28(B+C)+24B+20C=1,258,000

28B+24B+28C+20C=1,258,000

52B+48C=1,258,000

The two equations are:

2B+2C=50000 (4)

52B+48C=1,258,000 (5)

You can isolate B in (4):

2B=50,000-2C

B=(50,000/2)-(2C/2)

B=25,000-C

Now, you can replace B in (5):

52(25,000-C)+48C=1,258,000

1,300,000-52C+48C=1,258,000

1,300,000-1,258,000=4C

42,000=4C

C=42,000/4

C=10,500

Now, you can replace the value of C in B=25,000-C:

B=25,000-10,500

B=14,500

Finally, you can replace the values of B and C in A=B+C to find A:

A=14,500+10,500

A=25,000

According to this, the answer is that section A holds 25,000 seats, section B holds 14,500 and section C holds 10,500.

28.5

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e

c

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Andrew made a mistake in Step 4 of his work. He incorrectly applied the associative property. To correct his work, Andrew should use the distributive property instead. Here's the correct step-by-step explanation:

Step 1: Start with the original problem: -4.5 + 4.2 + 5.6 - 7.3

Step 2: Apply the additive inverse to -7.3: -4.5 + 4.2 + 5.6 + (-7.3)

Step 3: Rearrange the terms using the commutative property: (-4.5 + 4.2) + 5.6 + (-7.3)

Step 4: Use the distributive property: -0.3 + 5.6 + (-7.3)

Step 5: Simplify the expression: -0.3 + 5.6 - 7.3 = -2

Andrew mistakenly used the associative property in Step 4 instead of the correct property, which is the distributive property. By correcting this mistake, the simplified expression is -2.

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The height of the mountain is 1.49 miles if in traveling across flat land you notice a mountain directly in front of you.

Given,

In the question:

Its angle of elevation (to the peak) is 3.5 degrees.

After you drove 13 miles closer, the angle of elevation is 9 degrees.

To find the approximate height of the mountain.

What is trigonometry?

Trigonometry is a branch of mathematics that deals with the relationship between the sides and angles of a right-angle triangle.

Now, According to the question:

It is given that:

In traveling across flat land you notice a mountain directly in front of you.

Applying tan ratio:

tan3.5 = h/(15+x)

Here h is the height of the mountain and x is the distance between the base of the mountain and to the second position of the car.

h = (15 + x) tan3.5

h = x tan9

(15 + x) tan3.5 = x tan9

x = 9.44

h = 9.44 tan9

h = 1.49 miles

Hence, the height of the mountain is 1.49 miles if in traveling across flat land you notice a mountain directly in front of you.

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Answer:

62.5%

Step-by-step explanation:

100% - 37.5% = 62.5%

Answer:

53%

Step-by-step explanation:

24 +23 = 47

100 - 47 =

53%

Answer:

x = -2

Step-by-step explanation:

3(3 - x) = 5(2x + 7) multiply 3 with both 3 and -x then 5 with 2x and 7

9 - 3x = 10x + 35 add like terms

9 - 35 = 10x + 3x

-26 = 13x

x = - 2

The general solution of the given recurrence equation is Qn = (-1/4)(-1)n + (1/4)n(-1)n + (1/2)(3)n.

The given recurrence equation is

Qn-1 + 5Qn-2 + 3Qn-3 = 3

Let's find the characteristic equation of the given recurrence equation:

By assuming Qn = rn,

the characteristic equation can be derived as:

r3 - r2 - 5r - 3 = 0

So, the characteristic polynomial is

(r + 1)(r - 3)2

Let α = -1 and β = 3 (repeated roots)

Now, the solution of the given recurrence equation is:

Qn = Arn + Bnαn + Cnβn

As α = -1 and β = 3 are the roots of the characteristic equation, substitute these values in the above equation.

We have

A(-1)n + Bn(-1)n + Cn(3)n ... (1)

As we are going to find the general solution of Qn, the constants A, B, and C need to be determined.

Let's solve for A, B, and C by considering the first few terms of the given recurrence equation.

Suppose n = 3 in the recurrence equation Qn-1 + 5Qn-2 + 3Qn-3 = 3, we have

Q2 + 5Q1 + 3Q0 = 3 ... (2)

Now, substitute n = 2 in the general solution (1), we have

Q2 = A(-1)2 + B2(-1)2 + C23 ... (3)

Now, substitute n = 1 in the general solution (1), we have

Q1 = A(-1)1 + B1(-1)1 + C31 ... (4)

Now, substitute n = 0 in the general solution (1), we have

Q0 = A(-1)0 + B0(-1)0 + C30 ... (5)

Now, let's solve for A, B, and C using equations (2), (3), (4), and (5).

Q2 + 5Q1 + 3Q0 = 3:

2A + 5B + 3C = 3A(-1)2 + B2(-1)2 + C23:

A - B + 9C = 3A(-1)1 + B1(-1)1 + C31:

-A - B + 3C = 1A(-1)0 + B0(-1)0 + C30:

A + B + C = 1

On solving the above equations,

we get A = -1/4, B = 1/4, and C = 1/2

So, the general solution of the given recurrence equation is  

Qn = (-1/4)(-1)n + (1/4)n(-1)n + (1/2)(3)n

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Answer:

see explanation

Step-by-step explanation:

the equation of a line in gradient- intercept form is

y = mx + c ( m is the gradient and c the y- intercept )

given

2x - 3y = 5 ( subtract 2x from both sides )

- 3y = - 2x + 5 ( divide through by - 3 )

y = \(\frac{2}{3}\) x - \(\frac{5}{3}\) ← in gradient- intercept form

with gradient m = \(\frac{2}{3}\)

Answer:

180 sq ft

Step-by-step explanation:

12 x 15 = 180

The total amount of carpet Mrs. Ownes bought for her rectangular room of 12 ft by 15 ft is 180 sq ft.

Area of a rectangle is the product of the length of the rectangle and the width of the rectangle. It can be given as,

A=a\times b

Here, (a)is the length of the rectangle and (b) is the width of the rectangle

Mrs. Owens laid carpet in a rectangular room, 12 ft by 15 ft. Here, the length of the rectangular carpet for the room should be 15 ft and width should be 12 ft.

Thus, the area of the carpet is,

\(A=15\times12\\A=180\rm\; ft^2\)

Thus, the total amount of carpet Mrs. Ownes bought for her rectangular room of 12 ft by 15 ft is 180 sq ft.

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You have the following operation:

958 ÷ 10

To determine what is the missing number, calculate the given division:

95

10 | 958

- 90

58

-50

8

as you can notice, the missing number is 58 in the given procedure of the division 958 ÷ 10.

Hence, the asnwer is C. 58

Answer:

the answer is 5

Step-by-step explanation:

Answer:

0.27272727272 is the reciproval of 3 2/3

The ratio is 98 games won: 64 games lost and is a part-to-part ratio.

According to the question,

During the 2015 regular season, the Pittsburgh Pirates won 98 baseball games, 53 of which were won in their home stadium.

∴ the team won 98 games and played 162 total games,

then they lost =162−98 = 64 games. (using the subtraction method)

The ratio of the number of games won to the number of games lost is then 98 games won: 64 games lost. Since the number of games won and lost are both parts, then this ratio is a part-to-part ratio.

The ratio is 98 games won: 64 games lost and is a part-to-part ratio.

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A spurious correlation is the implied causal relationships between events that are statistically  linked.

Spurious correlation;

A spurious correlation (or spuriousness) in statistics is an apparent causal relationship between two variables. Any reported dependencies between variables are solely the result of chance or are both a result of an unidentified confounder when there is misleading correlation.

When the price of higher education and the cost of living both rise, for instance, this doesn't necessarily indicate a causal link between the two factors because higher education tuition isn't always the result of rising living costs.

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Answer:
Josh's percentage profit would be 52.5%.

Step-by-step explanation:

Total cost:

Josh buys 120 books for £4 each, so the total cost is:

Total cost = 120 books * £4/book = £480

Total revenue:

Josh sells half of the books for £5 each, which means he sells (1/2) * 120 = 60 books at £5 each. So, the revenue from this sale is:

Revenue = 60 books * £5/book = £300

Josh also sells 40% of the books for £7 each, which means he sells 0.4 * 120 = 48 books at £7 each. So, the revenue from this sale is:

Revenue = 48 books * £7/book = £336

The remaining books that Josh sells at £8 each are (1 - 0.5 - 0.4) = 0.1 or 10% of the total books. Therefore, the revenue from this sale is:

Revenue = 10% * 120 books * £8/book = £96

Total revenue = £300 + £336 + £96 = £732

Profit:

Profit = Total revenue - Total cost = £732 - £480 = £252

Percentage profit:

Percentage profit = (Profit / Total cost) * 100%

Percentage profit = (£252 / £480) * 100% ≈ 52.5%

Therefore, Josh's percentage profit is approximately 52.5%.

The probability that at least 22 families out of 90 chosen at random is equal to 0%

Sample size = 90

To calculate the probability that at least 22 out of 90 families will have a phone,

Use the binomial probability formula.

The probability of success (p) is the proportion of families that have a landline phone, which is 1/5 = 0.2.

The number of trials (n) is 90.

Calculate the probability of getting 22, 23, 24,..., up to 90 successes.

To simplify the calculation,

Calculate the probability of the complement event the probability that fewer than 22 families have a phone and subtract it from 1.

Using a binomial probability calculator

find the probability of fewer than 22 successes,

P(X < 22)

= \(\sum_{0}^{21}\)of C(n, k) × \(p^k\) × \((1 - p)^{(n - k)\)

The notation (n choose k) represents the binomial coefficient,

which calculates the number of ways to choose k successes out of n trials.

The sum calculates the cumulative probability of getting fewer than 22 successes.

Calculating this probability, we find,

P(X < 22) ≈ 0.99974

To find the probability of at least 22 successes, we subtract this value from 1:,

P(X >= 22) = 1 - P(X < 22)

≈ 1 - 0.99974

≈ 0.000..26

Rounding this probability to the nearest whole percent, we get 0%.

Therefore, the probability that at least 22 out of 90 families will have a phone is extremely close to 0%.

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Answer:

<S = 151 degrees

<DCE = 52 degrees

Step-by-step explanation:

The sum of interior angle of pentagon is 540 degrees

5x+2+7x-11+13x-31+8x-19+10x-3 = 540

43x - 62= 540

43x = 540+62

43x =602

x = 602/43

x =  14

get <S

<S = 13x-31

<S  = 13(14)-31

<S = 182-31

<S = 151 degrees

2) The sum of interior angle is the exterior

180-7x+2+180-4x-33 = 9x-31

360-11x-31 = 9x - 31

360 = 9x+11x

360 = 20x

x = 360/20

x = 18

<DCE = 180 - 7x - 2

<DCE = 180-7(18)-2

<DCE = 180-126-2

<DCE =  180-128

<DCE = 52 degrees

Answer:

4x+y-4=0

Step-by-step explanation: For an equation to be parallel to another all it needs is the same slope but a different y-intercept. So you can really other equations like 4x+y-3=0, 4x+y-5=0, 4x+y-6=0, etc. can be the answer to your problem.

The amount closest to the combined value of the two accounts at the end of 3 years is approximately $599.85.

To find the combined value of the two accounts at the end of 3 years, we'll calculate the value of each account separately and then add them together.

Account I:

Principal (P) = $350

Interest rate (r) = 3% = 0.03

Time (t) = 3 years

Simple interest formula: A = P * (1 + r * t)

A = 350 * (1 + 0.03 * 3)

A = 350 * (1 + 0.09)

A = 350 * 1.09

A ≈ $381.50

Account II:

Principal (P) = $200

Interest rate (r) = 2.75% = 0.0275

Time (t) = 3 years

Compound interest formula: A = P * (1 + r)^t

A = 200 * (1 + 0.0275)^3

A = 200 * (1.0275)^3

A ≈ $218.35

Combined value:

Combined value = Account I value + Account II value

Combined value ≈ $381.50 + $218.35

Combined value ≈ $599.85

Therefore, the amount closest to the combined value of the two accounts at the end of 3 years is approximately $599.85.

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The value of the equation x² - x + 3 is 37/9.

We have,

We can start by multiplying both sides of the equation by x:

2x - 3/x = x + 1

2x - 3 = x^2 + x

Rearranging and simplifying, we get:

x^2 - x + 3 = (2x - 3) + x^2

x^2 - x + 3 = x^2 + 2x - 3

-x + 3 = 2x - 3

5 = 3x

x = 5/3

Now we can substitute x into the equation x^2 - x + 3:

x^2 - x + 3 = (5/3)^2 - 5/3 + 3

x^2 - x + 3 = 25/9 - 15/9 + 27/9

x^2 - x + 3 = 37/9

Therefore,

The value of x² - x + 3 is 37/9.

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