Carly bought 2 1/4 pounds of apples. she used 2/3 of the apples to make applesauce. how may pounds of apples did she have left

Answers

Answer 1

The pounds of apples that she has left is 3/4 pounds.

How many pounds of apples does she have left?

A mixed number is a number that is made up of a whole number and a proper fraction. An example of a mixed number is 1 1/4. Where 1 is the whole number and 1 /4 is the proper fraction.

The fraction of the apples used in making the applesauce = 2 1/4 x 2/3

9/4 = 3/2 = 1 1/2

Fraction of apples left = 2 1/4 - 1 1/2

[tex]2\frac{1}{4} - 1\frac{1}{2}[/tex]

[tex]1\frac{1 - 2}{4}[/tex] = [tex]\frac{3}{4}[/tex]

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Related Questions

What is the factor of the equation

Answers

Answer:

(2x - 3) (x + 3)

Step-by-step explanation:

Let's check

(2x - 3) (x + 3)

2x² + 6x - 3x - 9

2x² + 3x - 9

So, (2x - 3) (x + 3) is the correct answer.

Using the bag of marbles below, find the probability of pulling a blue marble two times in a row. After pulling the first blue marble, you do NOT replace it in the bag before pulling the second one. Each marble has an equally likely chance of being pulled. Answer as a simplified fraction.​

Answers

The probability of picking two blue marbles is 1/21.

What is the probability?

Probability is used to determine how likely it is that a random event would occur. The probability of a random event happening lies between 0 and 1. If it is certain the event would happen, the probability value is 1 and if it is certain that the event would not happen, the probability value is 0.

Probability of picking two blue marbles = (number of blue marbles / total number of marbles) x (number of blue marbles -1 / total number of marbles - 1)

Total number of marbles = 7

(2/7) x (2-1/7-1)

2/7 x 1/6 = 1/21

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A tractor dealer puts a markup of ​21% on cost on a part for which it paid ​$420. Find ​(a) the selling price as a percent of​ cost, ​(b) the selling​ price, and ​(c) the markup

Answers

the selling price as a percent of cost is 120.52%, b- the selling price is $508.20 and the markup is 20.95% of cost.

(a) To find the selling price as a percent of cost, we need to first find the selling price and then divide it by the cost and multiply by 100%.

The markup on cost is 21%, which means the dealer sells the part for:

420 + 0.21*420 = $508.20

So the selling price is $508.20 and the cost is $420.

The selling price as a percent of cost is:

508.20/420 * 100% = 120.52%

So the selling price is 120.52% of the cost.

(b) The selling price is $508.20.

(c) The markup is the difference between the selling price and the cost, expressed as a percentage of the cost:

Markup = (Selling price - Cost)/Cost * 100%

= (508.20 - 420)/420 * 100%

= 20.95%

So the markup is 20.95% of the cost.

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Find the principal.

Annual rate of interest

=

6. 5

%

=6. 5%equals, 6, point, 5, percent

Period

=

4

=4equals, 4 years

Total interest

=

1222

=1222equals, 1222 rupees

Principal

=

=equals


rupees

Answers

The principal is $467.69 rupees (rounded to two decimal places).

The concept of simple interest is a type of interest calculation based on a fixed percentage rate applied to an initial amount of money, called the principal, for a specific period of time

To find the principal, we can use the formula:

Total Interest = (Principal x Rate x Time) / 100

Where,

Rate = Annual Rate of Interest

Time = Period in years

Plugging in the given values, we get:

1222 = (Principal x 6.5 x 4) / 100

Simplifying the equation:

1222 = (26 x Principal) / 10

Multiplying both sides by 10/26:

Principal = $467.69

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Carmen's swimming pool has the shape of a rectangular prism

with a length of 20 feet, a width of 10 feet, and a depth of 5

feet. The pool will be filled with water until the water level is 1 1/2 feet from the top of the pool. Which volume of water will be filled into the pool?


A. 1000 cubic feet

B. 700 cubic feet

C. 500 cubic feet

D. 300 cubic feet

Answers

[tex]1\dfrac{1}{2} = \dfrac{3}{2} = 1.5[/tex]

[tex]20 (10) (5-1.5) = 200(3.5) = 700 \ cubic \ feet[/tex]

Answer:

(B) 700 cubic feet

Step-by-step explanation:

The height of water in the pool is 5 - 1 1/2 = 3 1/2 feet.

The volume of water needed to fill the pool up to 3 1/2 feet is:

20 feet x 10 feet x 3 1/2 feet = 700 cubic feet

Therefore, the answer is (B) 700 cubic feet.

If you place 37 foot ladder against the top of a 15 foot building

Answers

I you place the 37 foot ladder against the top of the 15 foot building, it will reach a height of 52 feet.

If you place a 37 foot ladder against the top of a 15 foot building, then the ladder will reach a height of 52 feet (37+15=52). To calculate this, you can use the formula for addition, which is x + y = z, where x is the height of the building, y is the height of the ladder, and z is the total height the ladder will reach. In this case, x = 15 and y = 37, so the total height the ladder will reach will be z = 15 + 37 = 52. This means that if you place the 37 foot ladder against the top of the 15 foot building, it will reach a height of 52 feet.

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Consider the following theorem. Theorem: For any integer , is odd if and only if + 1 is even.

Construct a proof for the theorem by selecting sentences from the following scrambled list and putting them in the correct order. Note that each statement will be used at most once (or not at all).

Since 2 | 2( + 1), 2 | ( + 1).
Suppose is odd.
Therefore, + 1 is even.
Suppose + 1 is even.
Therefore, + 1 is odd.
Thus, for some integer , + 1 = 2 + 1.
Thus, for some integer , = 2.
Thus, for some integer , = 2 + 1.
Therefore, is odd.
Thus, for some integer , + 1 = 2.
Now + 1 = (2 + 1) + 1 = 2 + 2 = 2( + 1).
Now = (2 - 1) = 2( - 1) + 1 .
Proof:
(⇒)

---Select---

---Select---

---Select---

---Select---

---Select---
(⇐)

---Select---

---Select---

---Select---

---Select---

Answers

The answer of the given question based on the theorem  For any integer , is odd if and only if + 1 is even the answer is for any integer , is odd if and only if + 1 is even.

What is Theorem?

A theorem is  statement in mathematics that has been proven to be the true based on logical reasoning and the mathematical principles. In other words,  theorem is a proposition that can be demonstrated or proved to be true through  logical argument.

Proof:

(⇒) Suppose is odd.

Thus, for some integer , = 2 + 1.

Now + 1 = (2 + 1) + 1 = 2 + 2 = 2( + 1).

Therefore, + 1 is even.

(⇐) Suppose + 1 is even.

Then, for some integer , + 1 = 2.

Thus, for some integer , = 2 - 1 = 2( - 1) + 1 .

Since 2 | 2( + 1), 2 | ( + 1).

Therefore, is odd.

Thus, we have shown that for any integer , is odd if and only if + 1 is even.

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Drag each label to the correct location on the image.
Dave, Frida, Natalie, and Robbie have four adjacent seats at a baseball park. They randomly chose an order to sit in. Make a list of all the possible ways in which they can sit in the four seats. Then match the events to their correct probabilities.
the probability of Dave and
Natalie sitting together
the probability of sitting
boy, girl, boy, girl or
girl, boy, girl, boy
the probability of the two
boys sitting in the middle

the probability of Frida
and Natalie sitting
together
the probability of Robbie
sitting between the girls
the probability of Natalie
sitting between Dave
and Robbie

Answers

The probability of Natalie sitting between Dave and Robbie: 1/6

What is Probability?

Probability is a branch of mathematics that looks at the likelihood of a particular event occurring. It is used to determine the chance that a certain outcome will occur, such as the probability of rolling a particular number when a six-sided die is thrown. Probability can also be applied to more complex scenarios, such as determining the likelihood of a particular stock's price increasing over a certain period of time. The probability of an event is typically expressed as a number between 0 and 1, where 0 indicates that the event will not occur and 1 indicates that the event is certain.

Dave, Frida, Natalie, Robbie:
1. Dave, Frida, Natalie, Robbie
2. Dave, Natalie, Frida, Robbie
3. Frida, Dave, Natalie, Robbie
4. Frida, Natalie, Dave, Robbie
5. Natalie, Dave, Frida, Robbie
6. Natalie, Frida, Dave, Robbie

Probabilities:
1. the probability of Dave and Natalie sitting together: 1/6
2. the probability of sitting boy, girl, boy, girl or girl, boy, girl, boy: 1/2
3. the probability of the two boys sitting in the middle: 1/6
4. the probability of Frida and Natalie sitting together: 1/6
5. the probability of Robbie sitting between the girls: 1/6
6. the probability of Natalie sitting between Dave and Robbie: 1/6

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Pls help! This is due today!

Answers

Answer:

3(a−1)

———

a+1

Step-by-step explanation:

what number is missing?

Answers

The number that is needed in the missing cell on the figure in the sequence of numbers, is 4.

How to find the missing figure ?

The pattern of the numbers on the figure is such that the number on top of two numbers is acquired by subtracting the smaller of the two numbers below the number from the larger number.

This is why 2 is placed on top which was reached with :

= 5 - 3

= 2

The number that is missing can therefore be reached by subtracting 3 from 7 :

= 7 - 3

= 4

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Given the polynomial f(x) = x^3 + 3x^2 − x − 3, which of the following is true?

(x + 3) is a factor since f(3) = 0.

(x + 3) is a factor since f(−3) = 0.

(x − 3) is a factor since f(3) = 0.

(x − 3) is a factor since f(−3) = 0.

Answers

The true statement is that (x + 3) is a factor of f(x) = x³ + 3x² - x - 3 since f(-3) = 0.

How to find the factor of a polynomial ?

A polynomial is an expression that consists of variables, terms, exponents and constants.

The factors are the polynomials which are multiplied to produce the original polynomial.

The factorisation of a polynomial is breaking the polynomial as a products.

Therefore,

f(x) = x³ + 3x² - x - 3

Hence, let's use the factor (x + 3)

Therefore,

f(-3) = (-3)³ + 3(-3)² - (-3) - 3

f(-3) = -27 + 27 + 3 - 3

f(-3) = 0

Therefore, the factor is (x + 3) since f(-3) = 0

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The Gross Domestic Product (GPD) of a country in the first quarter of 2014 was $1.1395x10^7. Rewrite the GDP in standard notation.

Answers

113,950,000,000 ([tex]1.1395x10^7[/tex] is scientific notation, so you need to move the decimal to the left 7 places and add the relevant commas to get 113,950,000,000 in standard notation).

What is notation?

Notation is a method of representing information, usually in a concise and organized way. It can be used to represent mathematical equations, algorithms, music, dance, and other concepts. Notation is often used as a shorthand for communicating ideas to others, as it allows for a more precise and efficient way of conveying information. Notation also allows for the precise and consistent representation of a concept, allowing for greater accuracy and understanding.

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For the equation y=8-2, complete the table and plot the ordered pairs on the graph.
Оо
Size
O
X
y
< Previous
-3
-2
-1
0
2
3

Answers

Step-by-step explanation:

For the equation y=8-2, complete the table and plot the ordered pairs on the graph.

Оо

Size

O

X

y

< Previous

-3

-2

-1

0

2

3

John goes to the casino and plays a slot machine. The probability that he wins on the first spin is 2/5. For all subsequent spins, the probability of John winning will be 5/6 if John wins in the preceding round, and the probability of John winning will be 1/5 if John did not win in the preceding round.(a) John plays 3 rounds. Find the probability that he wins on the third round, given that he only won two rounds of the three. (4 marks)(b) Let X denote the number of rounds John need to play before he finally wins for the first time. Comment on the suitability of modelling X after the geometric distribution. Compute P(X = 5). (3 marks)(c) John visits the casino on 20 separate days, he played exactly 10 rounds on each day. Let Y denote the number of days (out of 20) that John does not win anything. State any necessary assumptions required in order to suitably model Y after the binomial distribution. State clearly the parameters of this binomial distribution as well. (4 marks)(d) Assume that your assumptions in Question 2(c) hold. Compute E(Y) and Var(Y ). (4 marks)

Answers

For (a), the probability that John wins on the third round given that he only won two rounds of the three is 5/6.



For (b), the suitability of modelling X after the geometric distribution is appropriate because the geometric distribution is the probability distribution of the number of Bernoulli trials needed to get one success. The probability of John winning on the fifth round is $(\frac{2}{5})^4(\frac{5}{6})=\frac{50}{648}$



For (c), any necessary assumptions required in order to suitably model Y after the binomial distribution is that the trials (i.e. rounds of play) are independent, and that the probability of success is the same for each trial. The parameters of this binomial distribution are: n = 10, p = 1/5.



For (d), assuming the assumptions in Question 2(c) hold, the expected value of Y (E(Y)) is 8 and the variance of Y (Var(Y)) is 2.4.

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A rectangular piece of carpet has dimensions of 6 feet by 8 feet. A larger rectangular piece of carpet has dimensions that are times longer. What area, in square feet, does the larger piece of carpet cover?

Answers

Answer:

45

Step-by-step explanation:

$4, 700 is invested in an account earning 6.8% interest (APR), compounded continuously. Write a function showing the value of the account after t years, wher the annual growth rate can be found from a constant in the function. Round all coefficients in the function to four decimal places. Also, determine the percentage o growth per year (APY), to the nearest hundredth of a percent.

Answers

The function for the value of the account after t years is:[tex]\rm V(t) = 4700 \times e^{(0.068t)[/tex].

The percentage growth per year (APY) is 7.03%.

What is formula for continuous compounding?

The formula for the value of an account with continuous compounding is given by:

                                              [tex]\rm V = Pe^{(rt)[/tex]

where:

V is the value of the account after t years

P is the initial principal amount invested (in this case, $4,700)

e is the mathematical constant (approximately equal to 2.71828)

r is the annual interest rate expressed as a decimal (in this case, 0.068)

t is the time period in years.

Therefore, the function for the value of the account after t years is:

[tex]\rm V(t) = 4700 \times e^{(0.068t)[/tex]

To find the annual percentage yield (APY), we use the formula:

[tex]APY = 100 \times (e^r - 1)[/tex]                        

where r is the annual interest rate expressed as a decimal (in this case, 0.068).

[tex]APY = 100 \times (e^{0.068} - 1)[/tex]

= 7.03%

Therefore, the percentage growth per year (APY) is 7.03%.

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3n-6=-21 ieuhfuewigdhfu43w

Answers

Answer:

-5

Step-by-step explanation:

3n-6=-21

    +6   +6

3n=-15 --> divide both sides by 3

n=-5

Function: f (x) = x + 2

Answers

Step-by-step explanation:

let f(x) be y

y=x+2

make x the subject of the formula

x=2-y

Answer:

Step-by-step explanation:

A population of 250 wild turkeys decreases by 2. 2% per year. At the end of 8 years, there will be approximately 209 turkeys in the population

Answers

Each year, the wild turkey population, which was once 250, drops by 2.2%. There will be around 209 turkeys left after 8 years.

Wild turkey populations are declining at a 2.2% annual pace. The initial population of 250 turkeys is anticipated to drop to around 209 turkeys after 8 years. Using the exponential decay formula, we can determine the rate of decline annually: P is the population at a certain moment, P0 is the starting population, r is the rate of reduction expressed as a decimal, and t is the time in years. P = P0 (1 - r)t. The answer to the r equation is r = (1 - (P/P0)(1/t)) = 0.022. As a result, the population is declining by 2.2% annually.

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O RATIONAL EXPRESSIONS Multiplication and division of 3 rational expressions Simplify. (x^(2)+9x+14)/(2x)*(x^(2)-4x)/(x^(2)-49)-:(x-4)/(x-7)

Answers

The expression (x² + 9x + 14)/(2x) * (x² - 4x)/(x² - 49) ÷ (x-4)/(x-7) when simplified is 2x + 4

How to simplify the expression

Given that

(x² + 9x + 14)/(2x) * (x² - 4x)/(x² - 49) ÷ (x-4)/(x-7)

To start with, we factorize the factors of the expression

The factored expressions are

(x² + 9x + 14)/(2x) * (x² - 4x)/(x² - 49) ÷ (x-4)/(x-7) = (x + 2)(x + 7)/(2x) * x(x - 4)/(x - 7)(x + 7) ÷ (x-4)/(x-7)

Cancel out the common factors to reduce the expression

So, we have

(x² + 9x + 14)/(2x) * (x² - 4x)/(x² - 49) ÷ (x-4)/(x-7) = (x + 2)/(2) * (x - 4)/(x - 7) ÷ (x-4)/(x-7)

Express division as product

(x² + 9x + 14)/(2x) * (x² - 4x)/(x² - 49) ÷ (x-4)/(x-7) = (x + 2)/(2) * (x - 4)/(x - 7) * (x - 7)/(x - 4)

Evaluate the quotient

(x² + 9x + 14)/(2x) * (x² - 4x)/(x² - 49) ÷ (x-4)/(x-7) = (x + 2)/(2)

So, we have

(x² + 9x + 14)/(2x) * (x² - 4x)/(x² - 49) ÷ (x-4)/(x-7) = 2x + 4

Hence, the solution is 2x + 4

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Suppose that 20% of all copies of grade 7 Science text book fail a certain binding strength test. Let X denote the number among 15 randomly selected copies that fail the test.
b. What is the probability that at least 8 fail the test?

Answers

binomial distribution

Question: Suppose that 20% of all copies of grade 7 Science textbook fail a certain binding strength test. Let X denote the number among 15 randomly selected copies that fail the test.b. What is the probability that at least 8 fail the test?To find the probability that at least 8 fail the test, we will use the binomial probability formula.The binomial distribution is a statistical distribution that describes the probability of success or failure in an experiment or survey with two possible outcomes.Suppose a trial consists of n independent experiments, each of which has two possible outcomes: either success with probability p or failure with probability q = 1 – p. If X is the number of successes in n trials, then X is said to follow a binomial distribution with parameters n and p. The probability that X = x is given by;P(X = x) = nCxpx(1-p)n-xwhere nCx = n! / x! (n-x)! is the binomial coefficient which counts the number of ways that x successes can be chosen from n trials.Using the formula, we have;P(X >= 8) = P(X = 8) + P(X = 9) + P(X = 10) + P(X = 11) + P(X = 12) + P(X = 13) + P(X = 14) + P(X = 15)Here n = 15, p = 0.2 and q = 0.8P(X >= 8) = P(X = 8) + P(X = 9) + P(X = 10) + P(X = 11) + P(X = 12) + P(X = 13) + P(X = 14) + P(X = 15)= 15C8 (0.2)^8 (0.8)^7 + 15C9 (0.2)^9 (0.8)^6 + 15C10 (0.2)^10 (0.8)^5 + 15C11 (0.2)^11 (0.8)^4 + 15C12 (0.2)^12 (0.8)^3 + 15C13 (0.2)^13 (0.8)^2 + 15C14 (0.2)^14 (0.8)^1 + 15C15 (0.2)^15 (0.8)^0= 0.0094 + 0.0267 + 0.0524 + 0.0864 + 0.1174 + 0.1312 + 0.1184 + 0.0352= 0.5771Therefore the probability that at least 8 fail the test is 0.5771 (rounded to four decimal places).Answer: 0.5771

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A dilation has center (0,0). Find the image of the point L(-4,3) for the scale
factor 3.

Answers

Answer: To find the image of point L(-4,3) after a dilation with a scale factor of 3 and center at the origin, we need to multiply the coordinates of point L by the scale factor.

The formula for dilation is:

(x', y') = (kx, ky)

where (x, y) are the original coordinates, (x', y') are the coordinates of the image, and k is the scale factor.

In this case, k = 3 and the coordinates of point L are (-4, 3).

So,

x' = kx = 3(-4) = -12

y' = ky = 3(3) = 9

Therefore, the image of point L(-4, 3) after the dilation with a scale factor of 3 and center at the origin is (-12, 9).

Step-by-step explanation:

The cubic function has three roots. Verify
that x=2 is one of them and find the other two.

Answers

a)  Verified

b)  4 + √7 and 4 - √7

Given a cubic function with three roots, one of the roots is given as x = 2. The other two roots can be found by using the factor theorem. Using factor theorem, we have(f(x) = x³ - 10x² + 27x - 18)(x - 2) is a factor of f(x)if and only if f(2) = 0.So, we have f(2) = 2³ - 10(2²) + 27(2) - 18 = 0. Therefore, (x - 2) is a factor of f(x) and we can find the other two roots by factorizing the cubic function. Using long division method, we get f(x) = (x - 2)(x² - 8x + 9) Now, to find the other two roots, we solve the quadratic equation x² - 8x + 9 = 0 using the quadratic formula. x = (-b ± √(b² - 4ac))/2a. We have a = 1, b = -8 and c = 9. Substituting the given values in the above formula, we get x = (8 ± √(8² - 4(1)(9)))/2= (8 ± √28)/2= 4 ± √7. Therefore, the three roots of the cubic function are 2, 4 + √7 and 4 - √7.

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Help me right one gets brainiest

Answers

Answer:

7x = 7

with solution of x = 1

This is the first choice

Step-by-step explanation:

Choice 1
7x = 7 => x = 7/7 = 1

Choice 2
7x = 7x provides no additional info and therefore there are an infinite number of solutions; any value of  will satisfy

Choice 3
x + 1 = x + 1; infinite solutions for reasons cited under choice 2

Choice 4
x + 1 = x + 2
Eliminating x from both sides gives 1 = 2
Such an equation will have no solution; no value of x can satisfy the equation

Correct answer: Choice 1: 7x = 7

Need urgently!! Fast asap

Answers

Answer:

1a) x=40°

2a) x=30°

Step-by-step explanation:

Use the fact that the sum of the angles of a triangle is always 180°.

So for 1a), x + x+40 + x+20 = 180

Simplify to

3x + 60 = 180

3x = 120

x = 40

apply the same logic to all the others.

For circles, the sum of the angles is 360°, so for 2b)

5x+3x+4x = 360 =>

12x = 360

x = 30°

suppose that a new employee starts working at $7.22 per hour and receives a 4% raise each year. After time t, in years, his hourly wage is given by the equation y=$7.03(1.03)^t. find the amount of time after which he will be earning $10.00 per hour.

Answers

After approximately 9.95 years, the employee will be earning $10.00 per hour.

What is property of logarithms?

The properties of logarithms are a set of rules that can be used to manipulate logarithmic expressions, including the product, quotient, power, and change of base properties.

We are given that the employee's hourly wage after t years is given by the equation [tex]y=7.03(1.03)^t[/tex]. We need to find the amount of time t after which he will be earning $10.00 per hour. So we set y = $10.00 and solve for t as follows:

$10.00 = $[tex]7.03(1.03)^t[/tex]

Divide both sides by $7.03:

1.4246 = [tex]1.03^t[/tex]

Take the natural logarithm of both sides:

ln(1.4246) = ln([tex]1.03^t[/tex])

Using the property of logarithms that ln([tex]a^b[/tex]) = b * ln(a), we can simplify the right-hand side:

ln(1.4246) = t * ln(1.03)

Solve for t:

t ≈ 9.95 years

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To find the area of the blue parallelogram, you can move the red triangle to the green triangle to make a rectangle. After doing this, what can you conclude about the formula for the area of a parallelogram?

Answers

The area of a parallelogram can be obtained from the formula for a rectangle by using the same base and height, leading to the formula Area of parallelogram = base x height.

By moving the red triangle to the green triangle, we create a rectangle with the same base and height as the original parallelogram. Therefore, the area of the original parallelogram is equal to the area of the rectangle, which is given by the formula:

Area of rectangle = base x height

We can conclude that the formula for the area of a parallelogram is also given by:

Area of parallelogram = base x height

This is because a parallelogram can be divided into two congruent triangles, and the area of each triangle is half the area of the parallelogram. Therefore, the area of a parallelogram is equal to the base times the height, which is the same as the formula for the area of a rectangle.

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What I still need to know is, what's Jonothan FLAW

Answers

As portrayed in the show, his biggest flaw is not knowing how to be a man. He had spent his life avoiding her responsibility, but she came anyway. He unnecessarily bows to Daenerys after she agrees to fight the Night King.

Perhaps Jon's biggest lingering flaw can be seen in book five: he's not a very good communicator. He struggled to sell his long-term ideas to his subordinates, and he also struggled to balance being overly friendly with them and alienating them, and he chose the latter. Other characters portray him as gruff, hard to read, and lacking in articulation, which isn't great when you're trying to bring about sweeping social reform. This is especially serious when you are dealing with people who are ready to kill you to prevent the implementation of the aforementioned social reforms.

I always say that Robb and Jon have the opposite problem: Robb is very good at selling himself, selling his ideas and thinking short term.

Jon is better at long-term strategic thinking and big-picture thinking, but lacks Robb's ability to really bring people to him.

Then of course, perhaps paradoxically, you have the underlying temper that he sometimes explodes (think of him heaving Thorne's throat with one hand, strangling Iron Emmett, etc.). He also felt very self-pity and defensive about his half-blood identity, both before and after joining the Night's Watch, while considering himself socially and militarily superior to his brothers in the Night guard. He needs someone to line him up (Donal Nye in the book, Tyrion in the show).

Then you have his flaws, which others might interpret as strengths. Lots of people criticized Jon for getting too involved in politics, like helping Stannis, throwing Creeker Stark in an ice prison, and getting Aryskar Stark to marry Saigon. Effective and ruthless efficiency, in the eyes of some, could on the other hand be described as a senseless (insidious?) intervention, the Pink Letter is Jon's intervention, which catches up with him. I also don't think the fictional character Harry Potter is that exciting.

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5. Explain the properties of logarithms that you
would need to use to solve the following:
log₂2x + log₂4 = 5

Answers

Answer:

x = 4

Step-by-step explanation:

log a + log b = log ab

log(base b) x = y, then b^y = x

log₂2x + log₂4 = 5

log₂ (2x × 4) = 5

log₂ 8x = 5

8x = 2^5

8x = 32

x = 4

1. Explain what Marc did in steps 4 and 5.

2. Why did he do this?

3. Create your own radical equation and explain how to solve it.

4. Is there an extraneous solution to your equation?

Answers

1. In step 4 he created a cube root and separated out out 5^4. In step 5 since it was a cube root in order to take out a number you need 3 of the same number. He took out a single 5 because there was only one set of three fives.
2.He did this in order to simplify the cube root of five to the fourth
3. Sqrt 16
4. There are no extraneous solutions
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