find the areas of triangles 3 and 4.​

By using the fact that the sum of the interior angles of a triangle must be 180°, we will get:

Remember that the sum of the internal angles of a triangle is always equal to 180°, then we can write:

m∠B + m∠C + m∠D = 180°

Then:

13x - 35 + 5x - 19 + 2x + 14 =180

20x -40 = 180

20x = 180 + 40

20x = 220

x = 220/20

x = 11

Now that we know the value of x, we can find the measures of the angles.

m∠B = (13x- 35)° = (13*11 - 35)° = 108°

m∠B = (5x - 19)° = (5*11 - 19)° = 36°

m∠D = (2x + 14)° = (2*11 + 14)° = 36°

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Rounded to the nearest square inch, the area of triangle EFG is 651 in².

A triangle is a polygon with three sides and three angles. It is a simple closed figure that has three straight sides and three vertices. The sum of the angles in a triangle is always 180 degrees. Triangles can be classified based on their sides and angles. Triangles with all sides and angles equal are called equilateral triangles, triangles with two sides and two angles equal are called isosceles triangles, and triangles with no sides and no angles equal are called scalene triangles. Triangles can also be classified based on their angles, such as acute triangles (all angles less than 90 degrees), right triangles (one angle equal to 90 degrees), and obtuse triangles (one angle greater than 90 degrees). Triangles are important in mathematics, physics, and engineering, and are commonly used in construction and design.

To find the area of triangle EFG, we need to use the formula:

Area = 1/2 * base * height

where the base and height are perpendicular to each other.

Since we know the length of side EF (which is the base), we can use the Pythagorean theorem to find the height of the triangle. The Pythagorean theorem states that:

c² = a² + b²

where c is the length of the hypotenuse (in this case, EG), and a and b are the lengths of the other two sides (in this case, EF and FG).

So, we have:

EG² = EF² + FG²

52² = 30² + FG²

FG² = 52² - 30²

FG ≈ 43.27 in (rounded to the nearest hundredth)

Now that we know the base (EF) and the height (perpendicular to EF), we can calculate the area:

Area = 1/2 * EF * height

Area = 1/2 * 30 in * 43.27 in

Area ≈ 650.55 in²

Rounded to the nearest square inch, the area of triangle EFG is 651 in².

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Answer:

So the scale factor would be the length of the new rectangle divided by the length of the corresponding side for the original rectangle. So the scale factor is 1/2. Note: If you're going from a bigger shape to a smaller one, you know that the scale factor must be less than 1.

Step-by-step explanation:

The commutative property for addition just means the sum is the same no matter what order you add the terms. This property is also true for multiplication of real numbers.

If altering the operands' order has no effect on the outcome, the binary operation is commutative in mathematics. Numerous binary operations depend on it as a fundamental property, and numerous mathematical arguments.

A commutative property in mathematics states that if integer positions are switched around or combined while performing addition or multiplication operations, the result will remain the same.

According to the commutative property, the numbers we use can be moved around or swapped around without changing the solution. For addition and multiplication, the property is true, but not for division or subtraction.

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let's reword all that jumbled material some

well, we know that the derivative of any function is just an equation to get the slope of a line at a given point, so once we have the derivative equation, we simply need either just one variable value or two assuming is implicit differentiation, but in the end the value we get is the slope.

we know that f'(2) = 1/2, the hell does that mean?  well, it means the slope of a line on the curve when x = 2 is 1/2 for f(x), so we know that f(x) has a slope of m = 1/2 when x = 2.

a line at the point given, at (2 , -1) is a tangential line to the curve f(x), a normal to it, it's simply a perpendicular to it.

keeping in mind that perpendicular lines have negative reciprocal slopes,

\(\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{ \cfrac{1}{2}} ~\hfill \stackrel{reciprocal}{\cfrac{2}{1}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{2}{1} \implies -2}}\)

so when rambling on the line of the normal at (2,-1) we're really looking at the equation of a line whose slope is -2 and that it passes through (2 , -1)

\((\stackrel{x_1}{2}~,~\stackrel{y_1}{-1})\hspace{10em} \stackrel{slope}{m} ~=~ - 2 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-1)}=\stackrel{m}{- 2}(x-\stackrel{x_1}{2}) \implies y +1= -2 (x -2) \\\\\\ y+1=-2x+4\implies \boxed{y=-2x+3}\)

Hello!

We are going to find the equation of the line that aligns with:

In order to find which equation works with our given information, we will use the approach of getting the derivative of the equation and plug in "2" to see if it equals to 1/2.

Solve:

Solve each equation by getting the derivative and plugging in "2" to "x" if applicable.

When getting the derivative of each equation, we'll use the power rule: nx^(n-1).

Also, know that the derivative of a constant is 0.

A).

y = -2x + 3

Calculate the derivative

y' = -2

We won't be able to plug in "2" since there is no "x" variable, and the derivative function doesn't equal 1/2, which makes this equation wrong in this question.

B).

y = -1/2x

Calculate the derivative

y' = -1/2

Like answer choice "A", we won't be able to plug in "2" since there is no "x" variable, and the derivative function doesn't equal 1/2, which makes this equation wrong in this question.

C).

y = -1

Calculate the derivative

y' = 0

Like our above answer choices, we won't be able to plug in "2" since there is no "x" variable, and the derivative function doesn't equal 1/2, which makes this equation wrong in this question.

D).

y = 1/2x - 2

Calculate the derivative

y' = 1/2

Even though we can't plug in "2" to "x" since it doesn't appear in the derivative function, this answer would be correct since the derivative function equals 1/2. This would be our answer.

Answer:

D). y = 1/2x - 2

Answer:

\(f^{-1}(x)=2^x+3\)

Step-by-step explanation:

Given:

\(y=\log_2(x-3)\)

To find the inverse of the given function, make x the subject.

\(\textsf{Apply log law}: \quad \log_ab=c \iff a^c=b\)

\(\implies 2^y=x-3\)

Add 3 to both sides:

\(\implies x=2^y+3\)

Swap x for \(f^{-1}(x)\) and y for x:

\(\implies f^{-1}(x)=2^x+3\)

The Edit Distance Algorithm is an important concept in computer science. The algorithm compares two strings and finds the minimum number of operations (insertions, deletions, and substitutions) that are required to transform one string into the other.

Below is the solution to the given question:

X = (B, A, N, A, N, A)      

Y = (P, A, N, D, O, R, A)

Table to compute Edit Distance:

P A N D O R A 0 1 2 3 4 5 6 B 1 1 2 3 4 5 6 A 2 1 2 3 4 5 6 N 3 2 1 2 3 4 5 A 4 3 2 3 4 5 6 N 5 4 3 2 3 4 5 A 6 5 4 3 4 5 4

The table shown above contains the minimum number of operations required to transform one string into the other. The top row represents string Y, and the left column represents string X. The table is filled using the following formula: If the characters at the current position are the same, then the value is taken from the diagonal element. (In this case, no operation is required.)

If the characters are different, then the value is taken from the minimum of the three elements to the left, above, and diagonal to the current element. (In this case, the operation that produces the minimum value is chosen.)

From the table above, the optimal solution can be found by tracing back the path that produced the minimum value. Starting from the bottom right corner, the path that produces the minimum value is:

A  -> R (Substitution)

O -> O (No operation)

D -> N (Substitution)

N -> A (Substitution)

A -> A (No operation)

P -> B (Substitution)

Therefore, the optimal solution is to substitute A with N, N with D, A with N, and P with B. So, (B, A, N, A, N, A) can be transformed into (P, A, N, D, O, R, A) using four operations.

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From the given information provided, the probability of event F given that event E has occurred is 0.5.

Conditional probability is probability of an event A occurring with given that event B has occurred. It is denoted as P(A|B) and is calculated as follows:

P(A|B) = P(A and B) / P(B)

To find P(F/E), we use the conditional probability formula:

P(F/E) = P(E and F) / P(E)

We are given that P(E and F) = 0.1 and P(E) = 0.2. Substituting the given values in the formula, we get:

P(F/E) = 0.1 / 0.2

Simplifying this expression, we get:

P(F/E) = 0.5

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you should invest approximately $500,000 today at 9% simple interest to reach your retirement goal of $1,175,000 in 15 years.

To determine how much you should invest today at 9% simple interest to reach your retirement goal of $1,175,000 in 15 years, we can use the formula for simple interest:

A = P(1 + rt)

Where A is the future value, P is the principal (the amount you should invest today), r is the interest rate, and t is the time in years.

We can rearrange the formula to solve for P:

P = A / (1 + rt)

Plugging in the values, we have:

P = 1,175,000 / (1 + 0.09 * 15)

P = 1,175,000 / (1 + 1.35)

P = 1,175,000 / 2.35

P ≈ $500,000

Therefore, you should invest approximately $500,000 today at 9% simple interest to reach your retirement goal of $1,175,000 in 15 years.

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the answer

155

324

5/9 (87/3(1/12)= 155/324

Aggregate Demand (AD) is a macroeconomic concept that represents the total demand for goods and services in an economy. The X factor in the AD equation represents exports, which are an important part of the economy.

AD is calculated by adding up the individual components of demand, which include consumer spending (C), investment spending (I), government spending (G), and net exports (X-M). The X-M component represents the difference between exports (X) and imports (M).

The X component in the equation represents exports, which are the goods and services produced domestically and sold to foreign countries. Exports are an important part of the economy as they generate income and create jobs. The M component in the equation represents imports, which are the goods and services purchased from foreign countries and consumed domestically. Imports can have a negative impact on the economy as they represent a drain on resources and can lead to a trade deficit. The X factor in the equation is used to represent exports because it is a variable that can change over time. Factors that can affect exports include exchange rates, tariffs, and global demand for certain products. If the exchange rate between two currencies changes, it can make exports more or less expensive for foreign buyers, which can affect the level of exports. Tariffs are taxes on imports, which can make domestic products more competitive in foreign markets.

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Answer:

20% loss

Step-by-step explanation:

(32000-40000)/40000 * 100 = -20%

Answer:

Step-by-step explanation:

CP of a TV=40000

Sp of a TV=32000

here CP is greater than Sp so there is loss

loss=CP-SP

=40000-32000

=8000

loss%=loss amount/cp*100%

=8000/40000*100

=800000/40000

=20%

Explanation:

Check out the diagram below. I've marked the angles that pair up which are congruent to one another. Note the order is important. The AAS rule is different from ASA. In the diagram, the green segments are not between the red and blue angles.

Note: the blue angles are congruent by the vertical angle theorem.

Answer:

69

Step-by-step explanation:

N

i

g

g

a

Answer:

y = 7x + 36

Step-by-step explanation: Slope intercept form is y = mx + b where your slope is m, your b is the y-intercept, and x and y are your plot points. To solve this you just plug in the numbers. We already know the slope is 7 so we have our m, now we plug in the coordinate (-5, 1) with -5 as x and 1 as y. Plug them in and now you have the equation 1 = 7(-5) + b. You want to solve for b. So you end up getting b= 36. Now you have your y intercept so your final equation is y = 7x + 36. Hope this helped!!

The constraints that are suitable for the situation are x≥4y , 7.50x+4.75y≤125 , x>0 and y>0 .

In the question it is given that

"x" represent the number of yellow rosebushes.

"y" represent the number of red rosebushes.

The word "at least' means "≥".

So "at least 4 times as many yellow rosebushes as red rosebushes" means x≥4y .  (constraint 1)

The number of red or yellow rosebushes cannot be negative .

So , x>0 (constraint 2)

y>0   (constraint 3)

Also ,

the cost of each yellow rosebushes = $7.50

number of yellow rosebushes = x

total cost of yellow rosebushes =7.50x

the cost of each red rosebushes = $4.75

number of yellow rosebushes = y

total cost of yellow rosebushes =4.75y

According to the question ,

she can spend no more than $125  , that means

7.50x+4.75y≤125  ( constraint 4)

Therefore , the constraints that are suitable for the situation are x≥4y , 7.50x+4.75y≤125 , x>0 and y>0 .

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Answer:

Human rights include the right to life and liberty, freedom from slavery and torture, freedom of opinion and expression, the right to work and education, and many more. Everyone is entitled to these rights, without discrimination.

Step-by-step explanation:

these are the 5 basic rights, most of them were taken for george floyd

hope this helped

Answer:

-31.5

Step-by-step explanation:

36(0.25)+ 42(-1)-18(0.25)+6
9-42-4.5+6

=-31.5

a. The expected value is 14 days, the variance is 196 days^2, and the standard deviation is 14 days.

b. The probability that the number of days ahead a traveler will purchase an airline ticket is between 10 and 16 days is approximately 0.345 or 34.5%.

c. The probability that the number of days the traveler purchases the ticket is more than 9 days is approximately 0.591 or 59.1%.

Since the square root of variance is regarded as the standard deviation for the specified data set, variance and standard deviation have a relationship in statistics. The terms variance and standard deviation are defined here.

(a) To find the expected value, variance, and standard deviation of the number of days ahead of time a traveler will purchase an airline ticket, given that it follows an exponential distribution with λ = 1/14, we can use the following formulas:

Expected value (mean): E(X) = 1/λ

Variance: Var(X) = 1/λ²

Standard deviation: SD(X) = √Var(X)

Given λ = 1/14, we can calculate:

Expected value: E(X) = 1 / (1/14) = 14 days

Variance: Var(X) = 1 / (1/14)² = 196 days²

Standard deviation: SD(X) = √Var(X) = √196 = 14 days

Therefore, the expected value is 14 days, the variance is 196 days^2, and the standard deviation is 14 days.

(b) To find the probability that the number of days ahead a traveler will purchase an airline ticket is between 10 and 16 days, we can use the cumulative distribution function (CDF) of the exponential distribution.

P(10 ≤ X ≤ 16) = F(16) - F(10)

where F(x) is the CDF of the exponential distribution.

Using the formula for the CDF of the exponential distribution, we can calculate:

P(10 ≤ X ≤ 16) = \(e^{(-10/14)\) - \(e^{(-16/14)\) ≈ 0.345

Therefore, the probability that the number of days ahead a traveler will purchase an airline ticket is between 10 and 16 days is approximately 0.345 or 34.5%.

(c) Given that the number of days ahead of time a traveler will purchase an airline ticket is more than 7 days, we need to find the probability that the number of days the traveler purchases the ticket is more than 9 days.

Using conditional probability notation, we want to find P(X > 9 | X > 7).

P(X > 9 | X > 7) = P(X > 9 and X > 7) / P(X > 7)

Since X follows an exponential distribution, the exponential distribution is memoryless, meaning that P(X > a + b | X > a) = P(X > b) for any a, b > 0.

Therefore, P(X > 9 | X > 7) = P(X > 9) / P(X > 7)

Using the formula for the survival function (1 - CDF) of the exponential distribution, we can calculate:

P(X > 9) = 1 - F(9) = \(e^{(-9/14)\)

P(X > 7) = 1 - F(7) = \(e^{(-7/14)\)

So, P(X > 9 | X > 7) = \((e^{(-9/14))\) / \((e^{(-7/14)\)) ≈ 0.591

Therefore, given that the number of days ahead of time a traveler will purchase an airline ticket is more than 7 days, the probability that the number of days the traveler purchases the ticket is more than 9 days is approximately 0.591 or 59.1%.

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If the price paid for a certain item is $40 and the consumer surplus is $4, then the maximum buying price for that item is $44 .

The Consumer's Surplus is defined as the difference between the maximum price a consumer is willing to pay for an item and the actual price paid for the item.

If the price paid for the item is $40 and the consumer's surplus is $4, then the maximum buying price for that item can be calculated as :

⇒ Maximum buying price = Price paid + Consumer's surplus

Substituting the values of Price paid and consumer surplus ,

we get ;

⇒ $40 + $4

⇒ $44

Therefore , the maximum buying price for that item is $44 .

The given question is incomplete , the complete question is

If the price paid for a certain item is $40 and the consumer surplus is $4, then what is the maximum buying price for that item ?

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Answer:

Step-by-step explanation:

The vertex form of  the equation of the parabola with vertex (h, k)   is:

y = a(x - h)² + k  

So  the equation of the parabola with vertex (3, 4):

y = a(x - 3)² + 4

The parabola passes through point (2, -2) so if x=2 then y=-2

- 2 = a(2 - 3)² + 4

- 2 -4 = a(-1)² + 4 -4

- 6 = a

So, the equation written in vertex form of a parabola with a vertex of (5, 7) that passes through (2, -2):

                                       y = - 6(x - 3)² + 4  

Answer:She incorrectly factored out the value of a.

Step-by-step explanation:

In solving a quadratic equation by completing the square method, the value a is not factored out. Rather, the steps involved are:

Divide through all the terms by a

Move the term c/a to the right had side

Complete the square on both sides using the value of b/2

Obtain the values of x

Answer: B. She subtracted the wrong value to maintain balance after completing the square.

The required value of p would be 54 units which is determined by the similar triangles property.

Triangle is defined as a basic polygonal shape of a triangle that has three sides and three interior angles.

Triangles ΔABC has:

Side AC = 30 units

Side AB = 35 units

Side BC = 10 units

Triangles ΔFGH has:

Side FG = p

Side GH = 6 units

Side HF = 18 units

Triangles ΔABC and ΔFGH are similar triangles that are given in the question.

As per the similar triangles property,

Side AC / Side FG = Side BC / Side HF

30 / p = 10 / 18

Apply the cross-multiplication operation,

10p = 30 × 18

p = (30 × 18) / 10

p = 54

The required value of p would be 54 units.

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Answer:

p=54

Step-by-step explanation:

Answer:

30.1 ft²

Step-by-step explanation:

The area of a triangle with an included angle and two sides cam be found using the formula, A = ½*ab*sin(C)

a = 7 ft

b = 9 ft

C = 73°

Plug in the values

Area = ½*7*9*sin(73)

Area = 30.1235998 ≈ 30.1 ft² (nearest tenth)

Answer:

11 years old

Step-by-step explanation:

33+11=44 (four times of Jerry's age)

44÷4=11 (Jerry's age)

Hope this helps! Thanks.

Jamal would need approximately 7.9 gallons of gas to travel 296.25 miles.

We can use the concept of direct variation to solve this problem. Direct variation means that two quantities are related by a constant ratio. In this case, the number of miles driven is directly proportional to the number of gallons used.

To find the constant of proportionality, we can use the given data. From the table, we can see that when Jamal used 14 gallons, he drove 525 miles. So we can write:

14/525 = k

where k is the constant of proportionality.

Solving for k, we get:

k = 14/525

Now we can use this value of k to find how many gallons Jamal would need to travel 296.25 miles. Let x be the number of gallons he would need. Then we can write:

x/296.25 = k

Substituting the value of k, we get:

x/296.25 = 14/525

Solving for x, we get:

x = (296.25 × 14) / 525

x ≈ 7.9

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i think its 4x and I'm sure

Answer:

c option 4x because it is multiplied

Answer:

A  The data is proportional and the unit rate per package is $8   This is because y= 8x

Step-by-step explanation:

/y relationship is no of packages = 1                                                                          x/ = total cost to ship = 8    = 8/1  = 16/2 = 24/3 = 32/4 means they are all proportional to 8/1 = 8    y = 8x  see graph attached