Triangle A and Triangle B are right triangles.

Triangle A has a height of 8 meters and a base of 6 meters.

Triangle B has a height that is one unit greater than triangle A and a base that is one unit less.

Part A
What is the measure of the hypotenuse of triangle A? Show your work.


Part B
Determine if the hypotenuse of triangle B has the same hypotenuse as triangle A. Justify your solution.

The limit intercepted by the given function, f'(8) is [tex]\lim_{n \to \8} \frac{\sqrt[3]{(x-8)} -8 }{x-8}[/tex]

A limit is a value toward which an expression converges as one or more variables approach certain values, a limit tells us the value of a function when its input closes to a certain value. Limits are used to define continuity, derivatives, and integrals. The limit of a product is equal to the product of the limits. The limit of a quotient is equal to the quotient of the limits. The limit of a constant function is equal to the constant.

Given that a function, f(x) = ∛x

The formula for applying the limit is :-

The first derivative is given by,

f'(x) = limx->c (f(x) - f(c))/(x-c)

Applying limit, we get,

f'(x) = [tex]\lim_{n \to \8} \frac{\sqrt[3]{(x-8)} -8 }{x-8}[/tex]

Hence, The limit intercepted by f'(8) is [tex]\lim_{n \to \8} \frac{\sqrt[3]{(x-8)} -8 }{x-8}[/tex]

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The answer is subtraction property.

Answer:

To solve this problem, we first need to find out how much time it will take for the airplane that is descending to reach the same altitude as the airplane that is ascending. To do this, we can use the formula d = r * t, where d is the distance, r is the rate, and t is the time.

In this case, the distance is the difference between the starting altitudes of the two airplanes, which is 42,000 feet for the descending airplane and 0 feet for the ascending airplane. The rate is the rate at which the descending airplane is descending, which is 3,500 feet per minute. Plugging these values into the formula, we get:

d = r * t

d = (3,500 feet/minute) * t

d = 42,000 feet

Solving for t, we get:

t = d / r

t = (42,000 feet) / (3,500 feet/minute)

t = 12 minutes

So it will take 12 minutes for the descending airplane to reach the same altitude as the ascending airplane.

To find the altitude at which the two airplanes will be at the same altitude, we can use the formula d = r * t, where d is the distance, r is the rate, and t is the time. In this case, the distance is the altitude at which the two airplanes will be at the same altitude, the rate is the rate at which the ascending airplane is ascending, which is 2,500 feet per minute, and the time is the time it will take for the descending airplane to reach the same altitude as the ascending airplane, which we calculated to be 12 minutes.

Plugging these values into the formula, we get:

d = r * t

d = (2,500 feet/minute) * (12 minutes)

d = 30,000 feet

Therefore, the altitude at which the two airplanes will be at the same altitude is 30,000 feet.

There are several other ways we could have solved this problem. For example, we could have used the formula d = r * t to find the altitude of the ascending airplane at the same time that the descending airplane reaches the same altitude, and then subtracted the starting altitude of the ascending airplane (0 feet) from this value to find the altitude at which the two airplanes will be at the same altitude.

Another way to solve this problem is to use the formula d = (v1 + v2) * t / 2, where d is the distance, v1 and v2 are the rates at which the two airplanes are moving, and t is the time. In this case, we can set d equal to the difference between the starting altitudes of the two airplanes, v1 equal to the rate at which the descending airplane is descending, v2 equal to the rate at which the ascending airplane is ascending, and t equal to the time it will take for the descending airplane to reach the same altitude as the ascending airplane.

Plugging these values into the formula, we get:

d = (v1 + v2) * t / 2

d = (3,500 feet/minute + 2,500 feet/minute) * (12 minutes) / 2

d = (6,000 feet/minute) * (12 minutes) / 2

d = (72,000 feet) / 2

d = 36,000 feet

Therefore, the altitude at which the two airplanes will be at the same altitude is 36,000 feet.

We can also solve this problem using a table to track the altitude of the two airplanes over time. We can start by making a table with

The opposite of the given polynomial 4p³ + 9p - 2 is; -4p³ - 9p + 2

The opposite of a number is basically its additive inverse. This means the sum of a number and its opposite is zero. We refer to this as the property of opposites.

Thus, we can say that the opposite of −888 is 888 ; the opposite of 25 is −25 ; the opposite of 4 is −4 .

Now, we want to find the opposite of the polynomial given as;

4p³ + 9p - 2

Applying the concept of opposite numbers gives us;

-4p³ - 9p + 2

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The Population Changes table indicate the following percent of change of the three towns

Question 1: The percent of change for Centerville is about 29.6%

Question 2: The town with the greatest percent of change is Riverview

Question 3: The percent of change for Riverview is about 51%

A percent of change is the change in the value of a parameter, expressed as a percentage.

Question 1: The population Centerville in 2000 = 37,065

The population of Centerville in 2010 = 26,102

The percentage change can be found using the formula;

[tex]Percentage \ change=\dfrac{New \ value - Initial \ value}{Initial\ value} \times 100[/tex]

The percentage change for Centerville is therefore;

[tex]Percentage \ change=\dfrac{Population \ in \ 2010-Polulation \ in \ 2000}{Population \ in \ 2000} \times 100[/tex]

From which we get;

[tex]Percentage \ change \ for \ Centerville=\dfrac{26102-37065}{37065} \times 100 \approx -29.6\%[/tex]

Question 2:

The percent of change for the town of Lakeside is found as follows;

Percentage change = ((45,863 - 51,342)/(51,342)) × 100 ≈ -10.7%

The percent of change of the population of Riverview is found using the percentage change formula as follows;

Percentage change = ((63017 - 41726)/(41726)) × 100 = 51%

Therefore, the town that had the greatest percent of change is is Riverview

Question 3: The percent of change for Riverview is about 51%

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The congruent reason for the triangles is (b) HL theorem

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

Triangles = FGH and JHK

The SSS similarity theorem implies that the corresponding sides of the two triangles in question are not just similar, but they are also congruent

From the question, we can see that the following corresponding sides on the triangles:

Sides GH and HK

Sides FH and JK

These parameters are given in reasons (2) and (3) and it implies that these sides are congruent sides

For the triangle to be congruent by SSS, the following sides must also be congruent

GH must be congruent to HK

The above statement is true because point H is the midpoint of line GK

This is indicated in reason (2)

Hence, the congruent statement is SSS.

However, we can also make use of the HL theorem in (B)

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The value of θ is 60° and the the value of the equation sec 60° = 2

What are trigonometric relations?

Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles

The six trigonometric functions are sin , cos , tan , cosec , sec and cot

Let the angle be θ , such that

sin θ = opposite / hypotenuse

cos θ = adjacent / hypotenuse

tan θ = opposite / adjacent

tan θ = sin θ / cos θ

cosec θ = 1/sin θ

sec θ = 1/cos θ

cot θ = 1/tan θ

Given data ,

Let the angle be represented as θ

Now , given that the angle θ is acute

Acute angles measure less than 90 degrees

So , the value of θ < 90°

when the value of sec θ = 2

cos θ = 1/sec θ

So , cos θ = 1/2

The value of θ when cos θ is 1/2 is when the angle θ is 60°

Therefore , the value of θ is 60° and sec 60° = 2

Hence , The value of θ is 60° and the the value of the equation sec 60° = 2

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Answer: 0.6

Explanation: I am going to break them into steps, so that you can understand them more clearly.

Step 1: Find how much the amount of water is needed:

0.4(3 quarts + x quarts) = (0.6 quarts + x)

Step 2: Find how much the quarts is divided by 0.6:

1.2 + 0.4x = 0.6 + x

Step 3: each quart is equal to 1 therefore:

x = 1 quart - which is 0.6

Message: If this was helpful, let me know by giving me a thanks! :)

Answer:

0.5

Step-by-step explanation:

Answer:215.768

Step-by-step explanation:

Answer: about 216 liters

Step-by-step explanation:

Answer: Just look at how far each point is from the x=-3 line and then count to the left of the line how far away it is on the same y-cord and that is the point.

so poin U is 2 away from the x=-3 line so stay at the y line of 4 and then count to the left of the line x=-3 two and you get the point at (-5,4)

Step-by-step explanation:

Answer:

D an even or odd sum from rolling two dice

what is uniform probability with three examples?

Uniform probability is a type of probability distribution in which all outcomes have the same probability of occurring. This means that all outcomes have an equal chance of being selected, and no one outcome is more likely to occur than any other. For example, if you were to roll a die, each of the six outcomes (1, 2, 3, 4, 5, 6) would have an equal probability of occurring. Here are three examples of uniform probability:

1. Tossing a coin: When a coin is tossed, the probability of it landing on either heads or tails is 50%. This is because both outcomes have an equal chance of occurring, making it a uniform probability.

2. Rolling a dice: When a dice is rolled, the probability of it landing on any of the six numbers (1, 2, 3, 4, 5, 6) is equal, at 16.67%. This is because all outcomes have an equal chance of occurring, making it a uniform probability.

3. Drawing a card from a deck: When a card is drawn from a deck, the probability of it being any of the 52 cards (13 of each suit) is equal, at 1.92%. This is because all outcomes have an equal chance of occurring, making it a uniform probability.

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The number in the middle is 15.

A ratio is a way to show a relationship or compare two numbers of the same kind. We use ratios to compare things of the same type.

Given that, The ratio of three numbers 2:3:4. The greatest number is 10 more than the least number.

Let the numbers be 2x, 3x and 4x,

Since, the difference in greatest and smallest numbers is 10, then,

4x-2x = 10

2x = 10

x = 5

Therefore, the middle number is 3x5 = 15

Hence, The number in the middle is 15.

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Answer:

-2x² - 10xy + 2y²

Step-by-step explanation:

4x² - 9xy - 4y² - 6x² - xy + 6y² =

= 4x² - 6x² - 9xy - xy - 4y² + 6y²

= -2x² - 10xy + 2y²

By using remainder theorem , value of P(1) = (-1)

P(1) = 1 + 3 + 4 - 9

P(1) = (-1)

Remainder Theorem is an approach of Euclidean division of polynomials. According to this theorem, if we divide a polynomial P(x) by a factor ( x – a); that isn’t essentially an element of the polynomial; you will find a smaller polynomial along with a remainder. This remainder that has been obtained is actually a value of P(x) at x = a, specifically P(a)

For finding the value of P(1) we have to put the value of 1 on the place of x, then we can get  P(1) = (-1)

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By solving a linear equation, it can be calculated that-

799 participants were successful

At first it is important to know about linear equation

Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.

A one degree equation is known as linear equation.

Here, a linear equation needs to be solved.

Number of men = 1945

Number of women = 2849

Total number of participants = 1945 + 2849 = 4794

Let the number of participants who were successful be x

Number of men who were not successful = 5x

Total number of participants = 5x + x = 6x

By the problem,

The linear equation is

6x = 4794

x = [tex]\frac{4794}{6}[/tex]

x = 799

799 participants were successful

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Answer:

true

Step-by-step explanation:

Answer:

true.

Step-by-step explanation:

5 miles is the distance a cyclist travels in 20 minutes, then 0.25 miles does the cyclist travel in 1 minutes.

A mile was equivalent to 1,000 Roman strides, with a stride being equal to two paces. The term "mile" is derived from the Latin "mille passus," which means "one thousand paces." The English Parliament established the Mile at eight furlongs (one furlong is 660 feet) in 1592. 5,280 feet, 1,760 yards, or around 1,609 meters make up a mile. On July 1, 1959, an international agreement established the mile's precise measurement at 1609.344 metres. Currently, the mile is the only unit of measurement used in the US and UK.

So, a mile is one of many different distance units.

Given that,

In 20 minutes a cyclist travels distance of 5 miles

So, in 1 minutes cyclist travels distance of [(5/20) × 1] miles

                                                                     = 0.25 miles

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4

divide 16 by 4, which equals 4

Answer:

4 goes into 16 4 times

Step-by-step explanation:

4 x 4=16

Hope this helps!

Answer:

Below

Step-by-step explanation:

angle = x

complement = 90 - x

  complement also is given as   2x-18

      2x-18 = 90 - x

       3x = 108

         x = 36°       then complement = 90-x = 54°

I asked you if you typed it correctly, and you said that it was typed correctly.

x^2 - 4x + 3 = 0

This is not the equation of a graph, it is vertical lines with infinite slope.

But, if it were a regular function

x^2 - 4x + 3 = y

a        b      c

To find the vertex, use the vertex formula

-b/2a

-(-4)/2(1)=4/2 = 2.  

The vertex is at x = 2

4-8+3=y

y = -1

Coordinates of vertex is (2,-1)

It is a minimum because the coefficient a is a positive number

Hope this helps :)

-Jeron

Answer: D

Step-by-step explanation: I had this same question before

Answer:

Step-by-step explanation: the answer is probably 50 because the bottom line is the same length as the other 50.

Answer: 45

(Read the explanation to make sure it is correct)

Step-by-step explanation:

Let's start with what we know. Since the sum of all angles in a triangle add up to 180, we can use that logic to find the last angle in the triangle. So far, we have:

85 + 50 + x = 180

We subtract 135 from both sides to get:

x = 45!

Answer:7 meter

Step-by-step explanation:8 meter and 5meter are both sides and perimeter is all side added together so 8+5 is 13 meter and u must have 20 so take the 13 m and subtract it 20m-13m=7m

and there you get answer

The function f(x) after translation by 4 units left is g(x) = y = 3x + 2.

Given is the function as -

f(x) = 3x - 10.

We have the function -

y = 3x - 10

We can write the function f(x) after translation by 4 units left as -

y = 3(x + 4) - 10

y = 3x + 12 - 10

y = 3x + 2

Therefore, the function g(x) can be written as y = 3x + 2

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The algebraic expression known as a trinomial contains three terms then the trinomials exists 3y + 5y² + y and [tex]$$x^4[/tex] + x² + 1.

Three non-zero terms make up a trinomial, which is an algebraic expression. The algebraic expression known as a trinomial contains three terms. An mathematical equation called a trinomial has three terms with on-zero coefficients, each separated by a + or - sign. It is a trinomial if three monomials are divided by addition or subtraction.

When a polynomial has three terms, it is referred to as a trinomial. Its general expression is ax² + bx + c, where a and b are coefficients and c is a constant. In order to factor trinomials, you must follow these three easy steps: Calculate the values of b (middle term) and c. (last term).

A. 8x  

Not a trinomial because, it contains only one term.

B. 3y +5y² + y

A trinomial because, it contains three terms.

C. 6x²

Not a trinomial because, it contains only one term.

D. [tex]x^{4}[/tex] + x² +1

A trinomial because, it contains three terms.

E. x² + 3

Not a trinomial because, it contains two terms only.

F. x¹¹

Not a trinomial because, it contains only one term.

Therefore, the correct answer is

B. 3y + 5y² + y and D. [tex]$$x^4[/tex] + x² + 1

The complete question is:

Which of the following are trinomials?

A. 8x

B. 3y + 5y² + y

C. 6x²

D. [tex]$$x^4[/tex] + x² + 1

E. x² + 3

F. [tex]$$x^{11[/tex]

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The total cost of the new outfits for all the members is $264. So, the correct answer is option A.

A total is a whole or complete amount, and "to total" is to add numbers or to destroy something. In math, you total numbers by adding them: the result is the total.

Given that, the shirts are $21, the pants are $26, the hats are $6 and the canes are $13.

Here, the cost of outfits for a person is

(21+26+6+13)=66

The cost of outfits for the four members is

66×4=$264

Therefore, option A is the correct answer.

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Answer:

-1/4

Step-by-step explanation:

y=mx+b

m-slope

b-  y-intercept

here, m = -1/4. Slope =-1/4