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Since both terms are perfect squares, factor using the difference of squares formula,  a ^2 − b^ 2 = ( a + b ) ( a − b )  where  a = a ^2  and  b = 4 . ( a ^2 + 4 ) ( a + 2 ) ( a − 2 )

Answer:

the second one on the top right

Step-by-step explanation:

Answer:

The answer is C

Step-by-step explanation:

You can tell by where the line crosses the y-intercept as a positive, and the direction in which the line is going tells you it has a negative slope

Answer:

Area = base x height

Step-by-step explanation:

8X11=88sq

Answer:

88 units^2

Step-by-step explanation:

The area of a parallelogram can be found using he following formula:

a=b*h

where b is the base and h is the height.

We know that 11 units is the base and 8 units is the height (forms a right angle with one of the bases).

b= 11 units

h= 8 units

Substitute these values into the formula.

a= 11 units * 8 units

Multiply

a= 88 units^2

The area of the parallelogram is 88 square units.

You would need to wait approximately 51.33 years from now to grow your initial investment of $39,000 to $174,000 at an interest rate of 10% per year.

To calculate the number of periods (years) required to grow an initial investment to a desired future value, we can use the formula for compound interest:

FV = PV * \((1 + r)^n\)

Where:

FV is the future value

PV is the present value (initial investment)

r is the interest rate per period

n is the number of periods

In this case:

PV = $39,000

FV = $174,000

r = 10% per year

Let's calculate the number of periods (years):

FV = PV * \((1 + r)^n\)

174,000 = 39,000 * \((1 + 0.10)^n\)

Divide both sides by 39,000:

4.4615 = \((1.10)^n\)

Take the logarithm of both sides to solve for n:

log(4.4615) = n * log(1.10)

n ≈ log(4.4615) / log(1.10)

n ≈ 2.1270 / 0.0414

n ≈ 51.33 (rounded to two decimal places)

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Answer:

7.833 yards²

Step-by-step explanation:

I can't take a pic but heres a link that does the math for you and explains. The top of the rectangular prism btw is called the surface area

https://www.omnicalculator.com/math/surface-area-rectangular-prism

Answer: 1.42

Step-by-step explanation:

Answer:

Right, 6 cm is the height. 5 cm is the base

Step-by-step explanation:

Answer:

24/30 this is the anwser

To measure the width of the river, the surveyor uses trigonometry. With an angle of 35° at point B, a 90° turn at C, and a 150 ft distance, the width of the river is approximately 76 meters.



To find the width of the river, we can use trigonometry. Let's assume the width of the river is represented by the letter 'x'.

Given that the surveyor turned 90 degrees at point C, we can conclude that angle A is also 90 degrees. Using the given angle at point B (35 degrees), we can calculate angle C as 180 - 90 - 35 = 55 degrees.Now, we have a right-angled triangle with angle C as 55 degrees, side BC as 150 feet, and we want to find side AC (which represents the width of the river).

Using the trigonometric ratio tangent, we can write the equation:

tan(55 degrees) = AC / BC

Solving for AC:

AC = tan(55 degrees) * BC

    = tan(55 degrees) * 150 ft

Now, we can convert the distance from feet to meters. Assuming 1 foot is approximately 0.3048 meters, we have:

AC = tan(55 degrees) * 150 ft * 0.3048 m/ft

    ≈ 75.69 m

Rounded to the nearest meter, the width of the river is approximately 76 meters.

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Answer:

log_4(256)=4

log_4(1/1024)=-5

log_4(16)=2

log_4(1/256)=-4

Step-by-step explanation:

We want to write a number, x, such that

Log_4(y)=x.

In exponential form that is 4^x=y.

So first number is x=4.

4^4=256 which means log_4(256) is 4 as a logarithm with base 4.

The second number is x=-5.

4^-5=1/4^5=1/1024 which means log_4(1/1024) is -5 as a logarithm with base 4.

The third number is x=2.

4^2=16 so log_4(16) is 2 as a logarithm with base 4.

The fourth number is x=-4.

Since 4^4=256 then 4^-4=1/256 which means -4 as a logarithm with base 4 is log_4(1/256).

The logarithmic expressions are: \(\log_4(256) = 4\), \(\log_4({4^{-5}}) = -5\), \(\log_4({16) = 2\) and \(\log_4({4^{-4}) = -4\)

A number x written in logarithm form is represented as:

\(\log_b(y)=x.\)

Where:

\(b^x=y\)

Given that the base is 4, the equations become:

\(\log_4(y) = x\)

\(4^x = y\)

For number 4, we have:

\(y = 4^4\)

\(y = 256\)

This gives

\(\log_4(256) = 4\)

For number -5, we have:

\(y = 4^{-5}\)

This gives

\(\log_4({4^{-5}}) = -5\)

For number 2, we have:

\(y = 4^{2}\)

\(y =16\)

This gives

\(\log_4({16) = 2\)

For number -4, we have:

\(y = 4^{-4}\)

This gives

\(\log_4({4^{-4}) = -4\)

Hence, the logarithmic expressions are: \(\log_4(256) = 4\), \(\log_4({4^{-5}}) = -5\), \(\log_4({16) = 2\) and \(\log_4({4^{-4}) = -4\)

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By the definition of lunar month, it can be inferred that-

If the moon were farther from earth than it is now, then lunar month will be more than 28 days.

What is lunar month?

Time taken by the moon to make one complete revolution around the earth is called lunar month.

If the moon were farther from earth than it is now, then the moon will have to travel a greater distance to make one complete revolution around the moon. So time taken by the moon to make one complete  revolution around the earth will increase. So lunar month will be more than 28 days.

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If the combination r = 5% and Y = $100 billion is on the Fed rule line, and the combination r = 7% and Y = $100 billion is considered, it would represent a movement up the Fed rule.

The Fed rule represents the relationship between the interest rate (r) and the level of real GDP (Y). As the interest rate increases from 5% to 7% while keeping the level of real GDP constant at $100 billion, it indicates a movement along the Fed rule line in an upward direction.

This implies that as the interest rate increases, the recommended level of real GDP decreases, based on the Fed rule. Therefore, the combination r = 7% and Y = $100 billion represents a movement up the Fed rule.

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Answer:

= 4.4591 × 1010

(scientific notation)

= 4.4591^10

= 44.591 × 109

Its actually pretty hard, so I don't really want to show my explanations with words, but there is a number explanation. Sorry if this is wrong. It is pretty hard, since you asked lots of times, I tried to give it a go.

6 X 10^-5 is 2*10^3 times the value of 3 X 10^-8.

6 X 10^-5 is how many times the value of 3 X 10^-8 is to be determined.

Fraction is defined as the number of compositions that constitute the whole.

Let 6 X 10^-5 is x  times the value of 3 X 10^-8.

\(6 * 10^{-5}= x 3 * 10^{-8}\\\\x = \frac{6 * 10^{-5}}{3 * 10^{-8}} \\\\x = 2 *10^3\)

Thus, 6 X 10^-5 is 2*10^3  times the value of 3 X 10^-8.

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Answer:

5. x+4=86

6. An equation can be used to predict values from a pattern by merely substituting any value to determine the equivalent value. An example is the geometric series which has a standard equation of an = a1 * r^(n-1) and is used to predict the nth term of the series

Step-by-step explanation:

Using linear function to solve this problem, for every 1 gallon of gas, Francisco travelled 27.9 miles

A linear function is a function that represents a straight line on the coordinate plane. For example, y = 3x - 2 represents a straight line on a coordinate plane and hence it represents a linear function. Since y can be replaced with f(x), this function can be written as f(x) = 3x - 2. A linear function is of the form f(x) = mx + b where 'm' and 'b' are real numbers. Isn't it looking like the slope-intercept form of a line which is expressed as y = mx + b? Yes, this is because a linear function represents a line, i.e., its graph is a line. where m is slope of the line and b is the y - intercept

We can use the data given in writing out our equation

390.6 = 14x

If 14 gallons = 390.6 miles

 1 gallon = x miles

x = 390.6 / 14

x = 27.9 miles

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In the context of Range Safety and Risk Mitigation, the ability to detect, assess, and respond to potential hazards is essential.

Range safety and risk mitigation involve identifying and minimizing potential hazards associated with range operations, such as the launch or test of rockets, missiles, or unmanned aerial vehicles. To ensure safety, it is critical to have the ability to detect and assess potential hazards, such as debris, vehicle or equipment malfunctions, and human error. Once hazards have been identified and assessed, the next step is to develop and implement appropriate safety measures to mitigate the risk associated with those hazards. These measures may include the use of safety protocols, engineering controls, or administrative procedures to ensure that all personnel and equipment are protected. In summary, the ability to detect, assess, and respond to potential hazards is critical for effective range safety and risk mitigation. By implementing appropriate safety measures and protocols, the risks associated with range operations can be minimized, ensuring the safety of personnel and equipment.

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The greatest common factor (GCF) is the largest positive integer that divides evenly into two or more numbers. It represents the highest common divisor of the given numbers.

To find the GCF, you need to determine the factors of each number and identify the largest factor that they have in common. The GCF is considered to be the greatest because it represents the largest number that can divide all the given numbers without leaving a remainder.

When finding the GCF, you start by listing the factors of each number. Factors are the numbers that divide evenly into a given number without leaving a remainder.

Once you have listed the factors of each number, you compare them to identify the largest common factor. This is done by finding the factors that appear in the factor lists of all the given numbers and selecting the highest one. The GCF represents the largest number that can divide all the given numbers without leaving a remainder, making it the greatest common factor.

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Answer:

HI

Step-by-step explanation:

The equation of this circle in standard form is x² + y² - 8x  - 16y + 73.75 = 0

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

Endpoints of the longest chord on a circle are (4, 5.5) and (4, 10.5)

These endpoints represent endpoints of the diameter

So, we have the diameter to be

diameter = √[(x₂ - x₁)² + (y₂ - y₁)²]

Substitute the known values in the above equation, so, we have the following representation

diameter = √[(4 - 4)² + (5.5 - 10.5)²]

Evaluate

diameter = 5

So, we have

radius, r = 5/2

The midpoint is

(a, b)= 1/2[(4 + 4, 5.5 + 10.5)]

So, we have

(a, b)= (4, 8)

The circle equation is calculated as

(x - a)² +(y - b)² = r²

Substitute the known values in the above equation, so, we have the following representation

(x - 4)² +(y - 8)² = 2.5²

This gives

x² - 8x + 16 + y² - 16y + 64 = 6.25

Evaluate the like terms

x² + y² - 8x  - 16y + 73.75 = 0

Hence, the equation is x² + y² - 8x  - 16y + 73.75 = 0

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By using the permutation, there are 14 rose trees in the garden.

The total number of ways that 1 shrub and 1 rose can be chosen = 252 ways.

Number of shrubs = 18

So, the number of ways of selecting a shrub will also be = 18

Now, let the number of roses be x.

Now, we will use the concept of permutation.

So, we get that:

18 × x = 252

x = 252 / 18

x = 14 roses

Therefore, we get that, by using the permutation, there are 14 rose trees in the garden.

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The shortest possible height of the aquarium is given as follows:

18 inches.

The volume of a rectangular prism, with dimensions length, width and height, is given by the multiplication of these dimensions, according to the equation presented as follows:

Volume = length x width x height.

The dimensions for this problem are given as follows:

h = w + 4, w and 49 - w.

Hence the equation for the volume is given as follows:

w(w + 4)(49 - w) = 8820

w³ - 45w² - 196w + 8820 = 0.

Inserting the equation into a cubic equation calculator, the smallest value of w is:

w = 14.

Hence the smallest height is of:

w + 4 = 18 inches.

The aquarium is given by the image presented at the end of the answer.

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Step-by-step explanation:

step 1. 286,000,000(.149) = 42,614,000 bytes

step 2. this can also be written as 42.6 megabytes.

Answer:

:)))))

Step-by-step explanation:

╰(*°▽°*)╯༼ つ ◕_◕ ༽つ^3^:-3(✿◡‿◡)（*＾-＾*）(´▽`ʃ♡ƪ)(●ˇ∀ˇ●)(❁´◡`❁)♪(^∇^*)( *︾▽︾)o((>ω< ))o

Answer:

Step-by-step explanation:

formula 0.5 x base x height

Answer:

Remember the formula a^2+b^2=c^2

Step-by-step explanation:

This can be used on right triangles. Now your a and b represent the legs of a triangle and the c represents the hypotenuse(the longest side). If you had a leg that was 2 inches and a second leg that was 4 inches you would plug it into the equation so...

2^2+4^2=c^2

Now evaluate

2^2=4

4^4=16

so

4+16=c

20=c

Now take the square root of 20 which is approximately 4.47 or leave it as square root of 20

If you had one leg and a hypotenuse then plug in and solve like any other equation.

Hope this helps!

Answer:

x = 5348/45

Step-by-step explanation:

It appears that the system dynamics can be manipulated through the control input u to minimize the time required for convergence to the origin (0,0).

Here, we have,

given that,

min t_i

x₁ = x₂-u

x₂ = u

-1 ≤ u ≤ 1, (x₁, x₂) are arbitrary starting point.

and origin  (0,0) be the begging of the coordinate.

also given that, (x₁, x₂)→ (0,0)

so, min t_i at origin (0,0) = t

Therefore, the generality condition of the situation does not met.

so, we get,

The given system can be represented by the following equations:

x₁' = x₂ - u

x₂' = u

To analyze the behavior of the system, we can examine the dynamics of each variable separately.

For x₁:

x₁' = x₂ - u

The equation implies that the rate of change of x₁ is dependent on x₂ and the input u. The term (-u) acts as a control input that can affect the dynamics of x₁. If we choose an appropriate control input u, we can manipulate the rate of change of x₁ and potentially minimize the time required to reach the origin.

For x₂:

x₂' = u

The equation for x₂ indicates that the rate of change of x₂ is solely determined by the input u. The variable x₂ can be directly controlled by the input u, allowing us to influence its behavior and potentially expedite convergence.

Based on the given equations, it appears that the system dynamics can be manipulated through the control input u to minimize the time required for convergence to the origin (0,0).

By carefully selecting the control input, it is possible to achieve the shortest time to reach the origin from any arbitrary starting point (x₁, x₂).

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Answer:

.899

Step-by-step explanation:

The equation of the altitude from vertex A of the triangle is y = (3/2)x + 3/2.

To write an equation for the altitude from vertex A of the triangle where point A is (-1,0), point B is (8,-5), and point C is (2,-3), we need to use the slope-intercept form of an equation for the line that contains the side opposite vertex A. Here are the steps:

1. Find the slope of the line containing side BC using the slope formula: m = (yb - yc)/(xb - xc) = (-5 - (-3))/(8 - 2) = -2/3.

2. Find the equation of the line containing side BC using point-slope form: y - yb = m(x - xb). Using point B, we get: y + 5 = (-2/3)(x - 8). Simplifying, we get y = (-2/3)x + 19/3.

3. The altitude from vertex A of the triangle is perpendicular to side BC. Therefore, its slope is the negative reciprocal of the slope of side BC, which is 3/2.

4. We can find the equation of the altitude by using point-slope form again, this time using point A: y - ya = m(x - xa). Using point A and the slope 3/2, we get: y - 0 = (3/2)(x + 1). Simplifying, we get: y = (3/2)x + 3/2.

Summary: To find the equation of the altitude from vertex A of the given triangle, we first found the slope of the line containing the side opposite vertex A, which is BC. Then, we found the equation of this line using point-slope form. Next, we used the fact that the altitude is perpendicular to side BC and found its slope, which is the negative reciprocal of the slope of side BC. Finally, we used the point-slope form again to find the equation of the altitude using point A and its slope. The equation we obtained is y = (3/2)x + 3/2.

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Find nodes

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Find x intercepts

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