Unit 8: Right Triangles & Trigonometry Homework 2: Special Right Triangles...Please Help!

Answer:

Step-by-step explanation:

Anatomical planes are created by imaginary lines that intersect the body into parts

The end behavior of a polynomial function is as x tends to infinity, f(x) tends to negative infinity.

In this question,

The power function is f(x) =-2x^3

The end behavior of a polynomial function is the behavior of the graph of f(x) as x approaches positive infinity or negative infinity.

The degree and the leading coefficient of a polynomial function determine the end behavior of the graph.

The graph below shows the behavior of the function f(x).

The above equation has the degree of 3, which is odd and the leading coefficient has the negative coefficient.

Then the end behavior is

As x -> ∞,

\(\lim_{x \to \infty} f(x)\)

⇒ \(\lim_{x \to \infty} -2x^{3}\)

⇒ \(-2(\infty)^3\)

⇒ - ∞

Hence we can conclude that the end behavior of a polynomial function is as x tends to infinity, f(x) tends to negative infinity.

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The logarithms of prime numbers can be used to express Log4 405 and Log7 (8/81).

Log4 405:

To express Log4 405 in terms of the logarithms of prime numbers, we can use the change of base formula. This formula allows us to convert a logarithm to a different base by dividing it by the logarithm of the desired base. In this case, we want to express Log4 405 in terms of prime numbers. The prime factorization of 405 is \(3^4\) * \(5^1\), so we can rewrite Log4 405 as (Log3 405) / (Log3 4). Since 3 is a prime number, we have expressed Log4 405 in terms of the logarithm of the prime number 3.

Log7 (8/81):

To express Log7 (8/81) in terms of the logarithms of prime numbers, we can again use the change of base formula. The prime factorization of 8 is \(2^3\), and the prime factorization of 81 is \(3^4\). Using the properties of logarithms, we can rewrite Log7 (8/81) as (Log7 \(2^3\)) - (Log7 \(3^4\)). Since 2 and 3 are both prime numbers, we have expressed Log7 (8/81) in terms of the logarithms of the prime numbers 2 and 3.

Finally, we can express Log4 405 as (Log3 405) / (Log3 4) using the prime number 3, and Log7 (8/81) as (Log7 \(2^3\)) - (Log7 \(3^4\)) using the prime numbers 2 and 3.

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Answer:

21.17 to 2d.p.

Step-by-step explanation:

Using Pythagoras rearrage to find b c^2-a^2 = b^2

c= hypothenuse

32^2 = 1024 and 24^2 = 576

1024 -576 = 448

\(\sqrt{448}\) = 21.1660105

21.17 to 2d.p.

Answer:

x x 1/2=1.1

Step-by-step explanation:

The radian measure of the angle at the center of the circle is approximately 1.6623 radians.

We are given that the radius of the circle is 77.0 cm and the length of the intercepted arc is 128 cm. We need to find the radian measure of the angle at the center of the circle.

To solve this problem, we use the formula relating the angle at the center of a circle, the radius of the circle, and the arc length intercepted by the angle.

The formula is given byθ = s/rwhereθ = angle at the center of the circle in radians s = arc length intercepted by the angle r = radius of the circle Substituting the given values, we getθ = 128/77.0 = 1.6623 radians (rounded to four decimal places)

Therefore, the radian measure of the angle at the center of the circle is approximately 1.6623 radians.

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The radius of the cylinder is √((l× w)/3.14) units.

What is cylinder?

In mathematics, Cylinder is  the basic 3d shapes,  which has two parallel circular bases at a distance. The two circular bases are joined by a curved surface, at a fixed distance from the center which is called height of the cylinder.

 An orange juice company is designing cylindrical containers for their juice. The containers are going to hold the same volume and have the same height as the prism shaped container.

Let the radius of the cylinder is r units.

As height is same for both prism and cylinder.

Let us take the height of the prism= height of the cylinder = h units.

Volume of the cylinder is π × r² × h

where π= 3.14, r is the radius and h is the height.

Volume of prism = l× w× h

where l= base  length

          w= base width

        h= height

The volume is same

So

π × r² × h = l× w× h

π × r² = l × w

l × w= 3.14 × r²

Hence, the radius of the cylinder , √((l× w)/3.14) units.

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The coordinates of the given segment is (-0.5. 1).

Any of a set of numbers used in specifying the location of a point on a line, on a surface, or in space. latitude and longitude coordinates.

A set of values that show an exact position. On graphs it is usually a pair of numbers: the first number shows the distance along, and the second number shows the distance up or down. Example: the point (12,5) is 12 units along, and 5 units up.

We have given the points :

(x₁ , y₁) = A(-3, -5) and (x₂ , y₂) = B(2, 7)

The Midpoint Formula is :

[x₁ + x₂]/2, [y₁ + y₂]/2

Now, we will substitute the given points into the formula and simplify :

(-3+2)/2 , (-5+7)/2

We get, (-1/2 , 1)

As decimals we obtain,

(-0.5, 1)

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Answer:9

Step-by-step explanation:

Answer:

7.79

Step-by-step explanation:

Answer:

John had $7.79 when he got home

Step-by-step explanation:

8.43 + 0.25-0.89

Hope this helps :)

Answer:

The length is 6 in., the width is 2 in., and the height is 16 in.

Answer:

length 6in.

width 2in.

height 16in.

Step-by-step explanation:

edge 2020

The survival time of a 60kg deer without food at -20 degrees Celsius depends on various factors, including its age, sex, and physical condition. However, assuming the deer is healthy and has 5kg of fat, it could potentially survive for around 30 to 50 days without food.

The exact survival time can vary depending on several factors, such as the deer's level of physical activity, environmental conditions, and how much energy it is expending to stay warm in the cold temperature. Additionally, if the deer is able to find sources of water, this can also increase its chances of survival.

It's important to note that this is just an estimate and that the actual survival time may vary. If the deer is injured or sick, its chances of survival may be reduced, and it may not be able to survive as long without food.

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Complete Question

How many days could a 60kg deer survive without food at -20 degrees Celsius if it has 5kg of fat?

Answer:

answer is a

Step-by-step explanation:

Johnny can improve his meal in 6 different ways by choosing two condiments from his four options. Some examples of the different combinations include ketchup and salt, ketchup and pepper, salt and pepper, and so on.

To determine the number of different ways Johnny can improve his meal using condiments, we can use the concept of combinations.

Since Johnny can only make two additions to his meal, we need to find the number of combinations of condiments he can choose from his four options: ketchup, salt, pepper, and shredded cheese.

To calculate the number of combinations, we can use the formula for combinations:
nCr = n! / (r! * (n - r)!)

Where n represents the total number of items and r represents the number of items to be chosen.

In this case, n is 4 (since Johnny has four condiment options) and r is 2 (since Johnny can only make two additions).

Plugging these values into the formula, we get:

4C2 = 4! / (2! * (4 - 2)!)

Simplifying this expression:

4C2 = 4! / (2! * 2!)

The exclamation mark (!) represents the factorial operation, which means multiplying a number by all positive integers less than itself down to 1.

Calculating the factorials:
4! = 4 * 3 * 2 * 1 = 24
2! = 2 * 1 = 2

Substituting these values back into the equation:
4C2 = 24 / (2 * 2)

Simplifying further:
4C2 = 24 / 4

Finally, dividing:
4C2 = 6

Therefore, Johnny can improve his meal in 6 different ways by choosing two condiments from his four options. Some examples of the different combinations include ketchup and salt, ketchup and pepper, salt and pepper, and so on.

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Answer:

a.

\(f(t) = 21000( {.918}^{t} )\)

b.

\(f(4) = 21000( {.918}^{4}) = 14913.86\)

Answer:

Step-by-step explanation:

Question 1: the defined rules dictates that series 1 is multiples of 3 and series 2 is multiples of 9, making the ratio always 3.

Question 2: You must pay attention to the values of the coins based on how many going from 0 to 3 so the nickels are 0, 5, 10, 15 and the values of dimes is 0, 10, 20, 10. Looking only at the values one could easily jump to answer A because the values initially double for each, but breaks down at 3 coins.

The circulation of the field f = x i y j around the curve r(t) = [cos(t)] i [sin(t)] j is    2π ∫₀ (cos t sin t - sin t cos tj)dt = 0

Integration is described as blending matters or human beings collectively that have been formerly separated. An example of integration is while the schools have been desegregated and there have been now not separate public faculties for African individuals.

The method of finding integrals is referred to as integration. at the side of differentiation, integration is a fundamental, crucial operation of calculus, and serves as a device to solve troubles in mathematics and physics regarding the location of an arbitrary form, the length of a curve, and the extent of a solid, among others.

r (t) = cost i + sin t j = dr( sin ti + cos t)dt

F =  -xi -yj = -costi - sin tj

Flux = F .dr = \(\int\limit2n^0_b {-costi - sin tj} \, dx\)j)-( sin ti + cos t)dt

           \(\int\limit2n^0_b {-costi - sin tj} \, dx\) -( sin ti + cos t)dt

     2π ∫₀ (cos t sin t - sin t cos tj)dt = 0

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the chance that the weight of a product is between 115 LB and 118 LB is approximately 0.1207, or 12.07%.

To find the probability that the weight of a product is between 115 LB and 118 LB, we can use the properties of the normal distribution.

Given that the weight of products follows a normal distribution with a mean (µ) of 120 LB and a standard deviation (σ) of 30 LB, we can standardize the values of 115 LB and 118 LB using the z-score formula:

z = (x - µ) / σ

For 115 LB:

z1 = (115 - 120) / 30 = -0.1667

For 118 LB:

z2 = (118 - 120) / 30 = -0.0667

Next, we can use a standard normal distribution table or a calculator to find the corresponding probabilities for these z-values.

Using a standard normal distribution table, the probability of having a z-value between -0.1667 and -0.0667 is approximately 0.1207.

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Answer:

Type 2

Step-by-step explanation:

Equation of the line is:

y=2

slope is 0

Markov analysis is used for analyzing the performance and reliability of complex systems, while replacement charts are used for optimizing the replacement timing of deteriorating assets.

Markov Analysis:

Markov analysis is a probabilistic model that is used to predict the future state of a system based on its current state.

It involves the use of Markov chains to model the transitions between different states of a system over time.

Markov analysis is commonly used when the equipment or system under consideration can be in multiple states with varying probabilities of transition.

It is suitable for analyzing systems that have a continuous or non-repairable nature, such as complex machinery, infrastructure, or systems with multiple failure modes.

The primary objective of Markov analysis is to assess the reliability, availability, and performance of the system and make decisions regarding maintenance, replacement, or repair strategies.

Replacement Chart:

A replacement chart, also known as a replacement model or replacement policy, is a decision-making tool used to determine the optimal time to replace a piece of equipment or system.

It involves comparing the costs associated with continuing to use the existing equipment (including maintenance and repair costs) with the costs of replacing it.

The replacement chart provides a visual representation of the costs over time and helps identify the point at which replacement becomes more cost-effective than continued use.

Replacement charts are commonly used for assets that are subject to wear and tear, aging, or deterioration over time, such as vehicles, machinery, or equipment with a defined lifespan.

The primary objective of a replacement chart is to minimize costs associated with the asset's life cycle by optimizing the replacement timing.

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1. The angles measures are larger than the original angle measures is a false statement.

2. If two sides parallel in the original figure, then those sides are parallel in the final figure is true statement.

3. The final angle measure are the same as the original angle measure is false statement.

4. The original figure and the final figure may not be congruent is true statement.

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Step-by-step explanation:

y= x^2+5x-7

the vertex is -2.5 , -13.25

solutions ( -6.14 , 0) and (1.14 , 0 )

..........

y= -x^2+3x+8

vertex(1.5 ,10.25)

solutions ( -1.7 , 0) and (4.7 ,0 )

In solving a system of equations, we look for a point where the two lines intersect. The point of intersection will be a point that is a solution to both equations in the system. We can solve a system of equations by several methods, but one of the most common methods is using substitution or elimination.

To solve a system of equations using substitution, we have to solve one of the equations for one of the variables, and then substitute the result into the other equation. This process eliminates one variable and makes the system easier to solve. Therefore, the best choice that describes a possible first step in solving the system of equations is to solve for y in the second equation. Here is the step-by-step solution:2x - 7y = -14-2x + y = -10Solve for y in the second equation.-2x + y = -10y = 2x - 10Now substitute 2x - 10 for y in the first equation.2x - 7(2x - 10) = -14Simplify:2x - 14x + 70 = -14-12x + 70 = -14-12x = -14 - 70-12x = -84x = -84/-12x = 7Substitute x = 7 into either equation. Let's use the second equation.-2(7) + y = -10-14 + y = -10y = -10 + 14y = 4Therefore, the solution to the system of equations is (x, y) = (7, 4).

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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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Using the Fundamental Counting Theorem, it is found that 6 different possible outcomes are there.

What is the fundamental principle of counting?

The total number of times an event can occur is m n if there are m possible ways for one event to happen and n various ways for another. A rule used to determine the total number of potential outcomes in a circumstance is known as the fundamental counting principle.

                        It states that there are n m times m n times m methods to do both of these activities if there are n ways to perform one action and m ways to perform another action after that.

For the coin, there are two outcomes, hence . n₁ = 2

For the spinner, there are three outcomes, hence n₂ = 3

Then, the number of outcomes is given by:

N = 2 x 3 = 6.

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The number of fliers that she has still not broadcasted will be 48 fliers.

Algebra is the study of ideational characters, while logic is the manipulation of all those opinions.

Linda had 90 fliers to post around town. Last week, she posted 1/5 of them. Then the number of fliers staying is given as,

⇒ (1 - 1/5) x 90

⇒ (4/5) x 90

⇒ 72 fliers

This week, she posted 1/3 of the remaining fliers. Then the number of fliers that she has still not broadcasted is given as,

⇒ (1 - 1/3) x 72

⇒ (2/3) x 72

⇒ 48 fliers

The number of fliers that she has still not broadcasted will be 48 fliers.

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After answering the provided question, we can conclude that Therefore, equation the only zero of the function (x-8)³ is x = 8.

An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the statement "2x + 3" equals the value "9". The goal of equation helping to solve is to determine the value or virtues of the variable in the model) that will allow the equation to be true. Equations can be simple or complex, regular or nonlinear, and include one or more factors. In the equation "x2 + 2x - 3 = 0," for example, the variable x is raised to the second power. Lines are used in many different areas of mathematics, such as algebra, calculus, and geometry.

To find the zeros of the function (x-8)³.

(x-8)³ = 0

∛(x-8)³ = ∛0

x - 8 = 0

x = 8

Therefore, the only zero of the function (x-8)³ is x = 8.

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Step-by-step explanation:

So 2 pints = 1 quart

She need 3 quart

so 2 pints × 3 = 1 quart × 3

6 pints = 3 quart

...

The she need 6 pints which is

2 cups = 1 pint

She need 6, so mutiply with 6

2 cups × 6 = 1 pint × 6

12 cups = 6 pints

Then this is the answer, you got

12 cups = 6 pints = 3 quart

She need 12 cups of water to make fruit punch

Answer:

C) \(3\cdot10^{-6}\)

Step-by-step explanation:

Divide the two numbers:

\(\displaystyle \frac{6\cdot10^{-2}}{2\cdot10^{-8}}=\frac{6}{2}*\frac{10^{-2}}{10^{-8}}=3\cdot10^{-2-(-8)}=3\cdot10^{-2+8}=3\cdot10^{6}\)

Thus, C is the correct choice.

Answer:

is A

Step-by-step explanation: