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The length of AC in given in the diagram is 10 cm.

Pythagoras' theorem states that “In a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the two shorter sides.”

By Pythagoras' theorem,

c² = a² + b²

Given that DE = EB

DB = 6 cm

So, DE = 3 cm

We take the triangle DCE

DC = 4 cm

DE = 3 cm

CE =?

DC² = DE² + CE²

4² = 3² + CE²

CE² = √16 - 9

CE = √7

CE = 2.64

Now triangle 2 is ∠ADE

By Pythagoras' theorem,

AD² = DE² + EA²

8² = 3² + EA²

EA² = 64 - 9

EA = √55

EA = 7.41

Now, CE + EA

2.64 + 7.41 = 10.05

Thus, the length of AC is 10 cm.

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Answer:

x = 21

Step-by-step explanation:

Since SR = ST then the triangle is isosceles with 2 base angles being congruent, so

∠ STR = 5x - 30

∠ STR and ∠ STU are adjacent angles on a straight line and sum to 180° , that is

5x - 30 + 5x = 180

10x - 30 = 180 ( add 30 to both sides )

10x = 210 ( divide both sides by 10 )

x = 21

Answer:

3√2 or 4.242641 units

Step-by-step explanation:

distance formula

The predicted graphs for large circles (diameter > 20 cm) and small circles (diameter < 20 cm) would show positive linear relationships between circumference and diameter, with the graph of large circles being steeper.

Predicted Graphs:

The graph for large circles would have a steeper slope compared to the graph for small circles, indicating a greater increase in circumference for larger changes in diameter. Both graphs would start at the origin and show a positive linear relationship, but the rate of increase in circumference would be more pronounced for the large circles.

Steeper Graph:

The decision that the graph of large circles would be steeper is based on the understanding that the circumference of a circle is directly proportional to its diameter. Since the large circles have diameters greater than 20 cm, their corresponding circumferences would increase at a faster rate compared to the small circles with smaller diameters. Therefore, the graph for the large circles would have a steeper slope, reflecting a greater change in circumference per unit change in diameter.

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The following ordered pair is given as {(1, -1), (2,0), (3,1)} for the given data of movement of arrow.

A set comprises elements or members that can be mathematical objects of any sort, including numbers, symbols, points in space, lines, other geometric forms, variables, or even other sets. A set is the mathematical model for a collection of various things.

An ordered pair consists of two items. The order of the objects in the pair matters because, unless a = b, the ordered pair differs from the ordered pair. Ordered pairs are also known as 2-tuples, or 2-length sequences.

An ordered pair is made up of the ordinate and the abscissa of the x coordinate, with two values given in parenthesis in a certain sequence. In order to understand a point visually, it might be helpful to position it on the Cartesian plane. An ordered pair's numerical values may be fractions or integers.

The following ordered pair is given as {(1, -1), (2,0), (3,1)} for the given data of movement of arrow.

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Answer:

D

Step-by-step explanation:

5 more than a number is greater or equal to 27

The "number" can be represented as x.

\(\boxed{x+5\geq 27}\)

Answer:

2/5, 4/7, 5/2

Step-by-step explanation:

5/2=2.5     2/5=.40    4/7= .59 that's aproximately  for 4/7

The derivative of f(x) = 35x^2 ln(x) is given by f'(x) = 70x ln(x) + 35x. Therefore, option (e) 70x is the correct answer.

To find the derivative of f(x) = 35x^2 ln(x), we can apply the product rule and the chain rule of differentiation. The product rule states that the derivative of the product of two functions u(x) and v(x) is given by u'(x)v(x) + u(x)v'(x). In this case, u(x) = 35x^2 and v(x) = ln(x).

Differentiating u(x), we obtain u'(x) = 2 * 35x^(2-1) = 70x. For differentiating v(x), we use the chain rule, which states that if y = f(u(x)), then dy/dx = f'(u(x)) * u'(x). In our case, f(u) = ln(u) and u(x) = x. Differentiating v(x), we have v'(x) = 1/x.

Applying the product rule, we get:

f'(x) = u'(x)v(x) + u(x)v'(x) = 70x ln(x) + 35x.

Therefore, the correct answer is option (e) 70x, which matches the derivative expression obtained. This derivative represents the rate of change of the function f(x) with respect to x and provides information about the slope and behavior of the original function.

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The NPV is positive, it is worth taking the Investment.

Net Present Value (NPV) is an assessment method that determines the attractiveness of an investment. It is a technique that determines whether an investment has a positive or negative present value.

This method involves determining the future cash inflows and outflows and adjusting them to their present value. This helps determine the profitability of the investment, taking into account the time value of money and inflation.The formula for calculating NPV is:

NPV = Σ [CFt / (1 + r)t] – CIWhere CFt = the expected cash flow in period t, r = the discount rate, and CI = the initial investment.

The given problem can be solved by using the following steps:

Calculate the present value (PV) of the expected cash inflows:

Year 1: $28,000 / (1 + 0.08)¹ = $25,925.93Year 2: $28,000 / (1 + 0.08)² = $24,009.11Year 3: $28,000 / (1 + 0.08)³ = $22,173.78Total PV = $72,108.82

Calculate the PV of the initial investment: CI = $7,000 / (1 + 0.08)¹ + $35,000 / (1 + 0.08)²CI = $37,287.43Calculate the NPV by subtracting the initial investment from the total PV: NPV = $72,108.82 – $37,287.43 = $34,821.39

Since the NPV is positive, it is worth taking the investment.

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Answer:

1.12x14=208

Step-by-step explanation:

base X height

To determine the number of people who went to the Harlem Globetrotters game, we divide the total amount spent ($137.50) by the cost per ticket ($27.50). The result indicates that five people went to the game.

If the tickets for the Harlem Globetrotters game cost $27.50 per person, and you spent a total of $137.50, we can calculate the number of people who attended the game by dividing the total amount spent by the cost per ticket.
Dividing $137.50 by $27.50 gives us 5. Therefore, the answer is that five people went to the Harlem Globetrotters game.
This calculation works because we are essentially finding the number of times $27.50 can be divided into $137.50. Since each person requires one ticket, the number of people who attended the game corresponds to the number of times the ticket price can be evenly divided into the total amount spent.

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B(3,-1)

Explanation

Step 1

Point 1

(-2,0)

replace

Point 2

(8,0)

c) c= c, so

Step 2

when the function is in the form

the vertex is given by

so,replace

therefore, the component of the vertex is 3

let's check the options

A. (3,0)

B. (3,-1)

we can see that y component of option A is zero , it means (3,0 ) is a zero of the function, but we had already the zeros, therefore, we can discard this options,

in other words,

the answer is

B(3,-1)

I hope this helps you

If I were to hypothesize that communication students will have a higher average score on the oral communication measures,

I would have a research hypothesis. A research hypothesis is a statement that is used to explain a relationship between two or more variables,

in this case, the relationship between being a communication student and having a higher score on oral communication measures.

The hypothesis can then be tested through research and analysis of data to determine if there is a significant correlation between the two variables. In order to fully test this hypothesis,

it would be necessary to gather data on both communication students and non-communication students and compare their scores on oral communication measures.

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Answer:

Okey I answer it clearly

What is StartFraction 8 Over 9, EndFraction divided by two-thirds?

\(1 \frac{1}{3} \)

Step-by-step explanation:

If it's wrong, my apologies

Answer:

I think its B. 2 1/9

Step-by-step explanation:

The sentence "The airplane takes off smoothly" can be interpreted in terms of the function f, its derivative f', and its second derivative f". In this interpretation, f represents the altitude of the plane, which is a function of time.

The sentence implies that the function f is continuous and differentiable, indicating a smooth takeoff.

The derivative f' of the function f represents the rate of change of the altitude, or the velocity of the airplane. If the airplane takes off smoothly, it suggests that the derivative f' is positive and increasing, indicating that the altitude is increasing steadily.

The second derivative f" of the function f represents the rate of change of the velocity, or the acceleration of the airplane. If the airplane takes off smoothly, it implies that the second derivative f" is either positive or close to zero, indicating a gradual or smooth change in velocity. A positive second derivative suggests an increasing acceleration, while a value close to zero suggests a constant or negligible acceleration during takeoff.

Overall, the interpretation of the sentence in terms of f, f', and f" indicates a continuous, differentiable function with a positive and increasing derivative and a relatively constant or slowly changing second derivative, representing a smooth takeoff of the airplane.

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Answer:

\(Q1 . (11x + 9) - (5x +1) = 11x + 9 -5x - 1 = 6x + 8\)

option 1

\(Q2. \ \ 6(2x -3)+4=16-(-18)\\\)

         \(12x - 18 + 4 =16 +18\\12 x -14 = 34\\12x = 34 + 14 \\12x = 48\\x = 4\)

option 4

\(Q3 .f(x) = 2x, \ g(x) = -2x^3 +2x\\\)

        \(f(x) + g(x) = -2x^3 +4x\)

option 3

\(Q4. \ \sqrt{18x^3y5^}\) \(= \sqrt{2*3^2*x^3*y^5} = 3*x*y^2\sqrt{2*x*y} = 3xy^2\sqrt{2xy}\)

option  2

Answer:

i think megan

Step-by-step explanation:

Answer:

Im pretty sure Nora has a better ratio of candy

Answer:

Month 5

Step-by-step explanation:

According to the question, the four consecutive numbers can be written as :

First = \(x\); Second = \(x+2\);  Third = \(x+4\); Fourth = \(x+6\)

As per the question, the final expression is :

\(2((x+2)+(x+4)) = 3(x)+32\)

\(4x+12 = 3x+32\)

\(x = 20\)

Therefore, the four values can be calculated by substituting the above value:

\(x=20; x+2=22; x+4=24; x+6=26\)

The four consecutive numbers are: \(20,22,24,26\)

Substitute the calculated values in the final expression, to check whether the answer is correct or not.

\(2(22+24) = 3(20)+32\)

\(92=92\)

Therefore, the calculated values are correct.

What are consecutive terms?

Consecutive terms are those terms which follow one sequential order.

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Answer:

6/7

Step-by-step explanation:

We want the numerical ratio

   green apple trees          18

  ------------------------------ = --------    which reduces to 6/7 (answer)

     red apple trees             21

The positive value of x is 6

An index, or power, is the small floating number that appears after a number or letter.

For example, x⁵ is an exponent expression. 5 is the index or power and x is the base. There are some rules that guides Indices.

25^(2x) = 5^(x²-12)

= 5^(4x) = 5^(x²-12

4x = x²-12

x²-4x -12 = 0

x² -6x +2x -12 = 0

(x²-6x) (2x-12) = 0

x( x-6) 2( x-6) = 0

(x+2)(x-6) = 0

x+2 = 0 or x-6 = 0

x = -2 or +6

therefore the positive value of x is 6

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The pressure of the dry gas is 91.7 kPa.

Given that a gas is bubbled through water at a temperature of 30 °C and an atmospheric pressure of 95.9 kPa.

The pressure of the dry gas needs to be calculated. This can be done using the Dalton's law of partial pressures.

According to Dalton's Law of Partial Pressures, The total pressure (P) of a gas mixture is equivalent to the sum of the partial pressures of the gases in the mixture.

Therefore, P = P₁ + P₂ + P₃ + ...where P₁, P₂, P₃, etc. are the partial pressures of the individual gases in the mixture.

The pressure of the dry gas can be calculated as follows:

Given, atmospheric pressure = 95.9 kPa Temperature of the gas = 30 ° C

The pressure of the water vapor = pressure exerted by the water vapor at 30 ° C = 4.2 kPa

Total pressure = atmospheric pressure - pressure of water vapor = 95.9 kPa - 4.2 kPa = 91.7 kPa

Therefore, the pressure of the dry gas is 91.7 kPa.

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Answer:

91%

Step-by-step explanation:

182/200 = .91

.91 = 91%

Hope that helps!

The percentage of questions Xin answered correctly on the final exam is 91% if he answered the number of 182 questions correctly on her multiple choice.

It is defined as the ratio of two numbers expressed in the fraction of 100 parts. It is the measure to compare two data, the % sign is used to express the percentage.

We have:

Total number of problems = 200

Total number of Xin answered correctly = 182

Then the percentage of questions XIn answers correctly:

\(= \frac{182}{200} \times100\)

= 0.91×100

= 91 %

Thus, the percentage of questions Xin answered correctly on the final exam is 91% if he answered the number of 182 questions correctly on her multiple choice.

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Answer:

Complementary angles are two angles that add up to 90° in total measurement.

Example:

Angle 1 is 34°. It's complement would be 56°.

\(90 -34=56\)

Brainilest Appreciated.

Answer:

A. 7

Step-by-step explanation:

If you were to solve for c by using d as 7 you would get:

c+7=40

c would then equal 33, which is greater than 30

Table of values

4 0

5 1

6 2

7 3