Use the table to find the average rate of change over the interval [1,9]
Type your answer in the blank, with no spaces.

The rectangle measures 6 centimetres in width and 18 centimetres in length.

The rectangle's length is two millimetres longer than its width. As a result, the length (L) is equal to 3(W) + 2, where W is the rectangle's width. Additionally, we are aware that the rectangle (A) has a 33 square centimetre area. In order to find W, we can apply the formula A = L x W. 33 = 3W2 + 2W because it is (3(W) + 2) x W. The quadratic equation can be used to find W, which equals 6. This indicates that the rectangle has a width of 6 centimetres and a length of 3(6)+2=18 cm.

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Answer:

3x+5y = -13

Step-by-step explanation:

Since there are two variables, you must solve for one of them first. One way we can do that is through elimination.

X seems the easiest to eliminate.

We can subtract the two equations.

 x - 4y = -10
- 2x+9y = -3

If we subtract it like this, it wouldn't eliminate any variables. So, let's multiply the first equation by 2 so both equations have 2x.

 2x - 8y = -20
- 2x+9y = -3
Now, subtract the equations.

-17y = -17

We can solve for y now.

y = 1

Since we have y's value, we can solve for x. Plug y back into one of the equations.

x - 4(1) = -10

x - 4 = -10

x = -6

Now that we have both the x and y values, simply plug it into 3x+5y.

3(-6) + 5(1)

-18 + 5
-13

So the answer is -13

Answer:

The Value of R is 20%.

Step-by-step explanation:

Let R be the interest rate (in percentage) per year. The interest earned after one year would be R% of £8,500, which is (R/100) * £8,500 = £(R * 85)/100.

After paying tax, the amount Nick receives would be (R * 85)/100 * (100 - 30)/100 = £(R * 85 * 70)/10000.

Since Nick receives £166.60 after paying tax, we have:

£(R * 85 * 70)/10000 = 166.60

Solving for R, we get:

R = (10000 * 166.60) / (85 * 70) = 20.0.

Therefore, the interest rate R is 20%.

Answer:

B. A radioactive compound decays at a rate of 19% per hour.

Step-by-step explanation:

We can eliminate C. (A town's population grows at a rate of 9.2% every year.) and D. (Money invested in a savings account grows at an annual rate of 4.2%.) since both of the options show growth, not decay. That leaves us with A. and B. The problem speaks of exponential, not linear, so B. would be the answer. If they asked for the linear decline or decay, A. would be the answer.

The contexts that represents exponential decline or decay is A radioactive compound decays at a rate of 19% per hour.

Exponential Decay is a reduction or decrease in the value of the quantity compared to the value of the previous quantity. Examples of phenomena that are classified as decay are a decrease in the price of goods and the decay of radioactive substances.

Based on the question above, option C and Option D Both options increase, It shows no decrease, so it can be ruled out.

While option B: the problem is exponential rather than linear.

If ask about linear decay, the answer is A.  

A.  radioactive compound decays at a rate of 19% per hour.

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Answer:

  12/37

Step-by-step explanation:

Given right triangle ABC with sides AB=37, BC=12, and CA=35, you want the cosine of angle B.

The cosine of an angle in a right triangle is ...

  Cos = Adjacent/Hypotenuse

The leg adjacent to angle B is BC=12. The hypotenuse is AB=37.

Using these values, the cosine of B is ...

  cos(B) = BC/BA

  cos(B) = 12/37

Answer:

CD = 6.3

Step-by-step explanation:

triangles CFG and CDE are similar, so their side lengths are proportional

this means CD/CF = CE/CG

since we don't know CF, we need to first solve for CF in order to find CD

luckily, we know CD = CF + FD, and FD is given:

CD/CF = CE/CG -> (CF + FD) / (CF) = CE/CG

multiply both sides by CF to get CF + FD = CE * CF / CG

move the terms with CF to one side, and the constants to the other side:

CF - CF(CE/CG) = -FD

solve for CF:

CF(1-(CE/CG)) = -FD, CF = FD / ((CE/CG) - 1) = (1.8)/(((2.4+6)/(6)) - 1) = 4.5

Since CD = CF+FD, CD = 4.5 + 1.8 = 6.3

Answer:

The minimum value of C is 14

Step-by-step explanation:

Sketch the graph of the constraints using

2x + y = 20

with intercepts (0, 20) and (10, 0)

2x + 3y = 36

with intercepts (0, 12) and (18, 0)

The solution to both are above the lines

Solve 2x + y = 20 and 2x + 3y = 36 to find the point of intersection at (6, 8)

Then the coordinates of the vertices of the region formed are

(0, 20), (6, 8) and (18, 0)

Evaluate the objective function at each vertex to determine minimum value

C = 0 + 20 = 20

C = 6 + 8 = 14

C = 18 + 0 = 18

Thus the minimum value of C is 14 when x = 6 and y = 8

Hope this helped to get you answer!

Answer:

126

Step-by-step explanation:

a=9

b=3

we have

15b+a^2

just substitute the value

15*3+9*9

45+81

126

Answer:

126 is your answer!

Step-by-step explanation:

15 x 3=45

9^2=81

45+81=126

The equivalent expression 36x + 12 is the same as 24x - 48. Because the statement is identical to itself, the label 24x - 48 fits it.

This equation denotes the result of multiplying 24 by x and then subtracting 48.

The phrase is referred to as "36x + 12" since it is a duplicate of itself. This formula denotes the result of multiplying 36 by x and then adding 12.

The formulations in the two scenarios cannot be compared since they use different coefficients for x and different constant terms. The word "neither" does not apply to either phrase because they are both equal to one another.

Therefore, 36x + 12 is equal to the formula 24x - 48.

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Hi there, here's your answer:

Geometric mean between 2 numbers a and b: [tex]\sqrt{ab}[/tex]

Therefore, the geometric mean between 16 and 64 will be

[tex]\sqrt{16*64}[/tex] = [tex]\sqrt{1024}[/tex] = 32.

Hope it helps!

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Answer: How can you tell whether X and Y are proportional?

Step-by-step explanation: How can you tell whether X and Y are proportional?

To know if a relationship is proportional, you should look at the ratios between the two variables. If the ratio is always the same, the relationship is proportional. If the ratio changes, the relationship is not proportional. please select brainiest if right

The system is inconsistent.

The two lines are parallel and never intersect.

====================================================

Work Shown:

Solving the 1st equation for y.

3x-y=18

-y=18-3x

y = -(18-3x)

y = -18+3x

y = 3x-18

Plugging that into the other equation to solve for x.

-2y=-6x-120

-2(y)=-6x-120

-2(3x-18)=-6x-120

-6x+36=-6x-120

-6x+6x=-120-36

0x = -156

0 = -156

We arrive at a false statement.

Therefore, this system has no solutions

The system is inconsistent.

If you were to use a graphing tool like Desmos or GeoGebra, then you'll see the two lines are parallel. They never intersect to form a solution.

The number of bagels when you buy for $50 will be 120 bagels.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

A shop sells bagels for $5 per dozen.

Let 'x' be the number of bagels and 'y' be the total cost. Then the equation is given as,

y / x = 5 / 12

12y = 5x

The number of bagels when you buy for $50 will be given as,

12(50) = 5x

600 = 5x

5x = 600

x = 120

The number of bagels when you buy for $50 will be 120 bagels.

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A polynomial regression model is a good choice for this data, as it can fit the trend of increasing population growth over time.

A function is a mathematical concept that assigns a unique output value for each input value.

In mathematical notation, a function is usually expressed as "f(x)" where "x" is the input and "f(x)" is the corresponding output. For example, a function could be defined as f(x) = x^2, which means that for any value of x, the function will calculate and return the square of that value.

To model the world population data, we can use a mathematical function to fit the data points. A polynomial regression model is a good choice for this data, as it can fit the trend of increasing population growth over time.

To find the expected world population in 2017, we would need to estimate the polynomial regression model using the data points provided and then evaluate the model at the year 2017.

Research shows that the actual world population in 2017 was approximately 7.5 billion, which is higher than our estimated value based on the limited data points provided. This highlights the importance of considering additional factors and data when making predictions about the world population.

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The complete question is

The equation that represents the whole scenario is 3.80 + 2.25(x) = 33.05  and the number of miles is 13.

Here we will use the linear equation concept to solve the problem. Since we don't know the number of miles represent it with a variable 'x' and form a Linear equation according to the given condition in the problem. Now solve the resultant equation for the value of variable 'x'  

Here we have  

The taxi company charged a pick-up fee of $3.80 plus $2.25 per mile. the total fare was $33.05, not including the tip.    

Let 'x' be the number of miles in the taxi ride

Total cost to travel 'x' mile = 3.80 + 2.25(x)  

From the given data, the total fare was $33.05

=> 3.80 + 2.25(x) = 33.05

=> 2.25x = 33.05 - 3.80

=> 2.25x = 29.25

=> x = 29.25/2.25

=> x = 13

Therefore,

The equation that represents the whole scenario is 3.80 + 2.25(x) = 33.05  and the number of miles is 13.

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The value of x, given the parallel lines and the angles involved, can be found to be 12. 3 .

The angles on the parallel lines are drawn such that 11 x and 45 degrees are supplementary angles .

This means that they add up to 180 degrees .

The value of x can therefore be found to be :

11 x + 45 = 180

11 x = 180 - 45

11 x = 135

x = 135 / 11

x = 12. 3

In conclusion, the value of x is 12. 3 .

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Answer:

Step-by-step explanation:

Since ∠S and ∠Y are complementary, we have:

∠S + ∠Y = 90°

We also know that:

m∠S = 2(m∠Y) − 30°

Substituting the second equation into the first equation, we get:

2(m∠Y) − 30° + ∠Y = 90°

Combining like terms:

3(m∠Y) = 120°

Dividing both sides by 3:

m∠Y = 40°

Therefore, m∠Y is 40 degrees.

Answer:

(x - 2) is not a factor of f(x)

Step-by-step explanation:

We can use the Remainder Theorem to check if (x - 2) is a factor of f(x) = x^3 - 2x^2 + 2x + 3.

The Remainder Theorem states that if we evaluate a polynomial at a specific value and the result is zero, then that value must be a root of the polynomial and therefore the polynomial can be divided by the corresponding linear factor.

So, if we plug in x = 2 into f(x), we get:

f(2) = 2^3 - 2 * 2^2 + 2 * 2 + 3

= 8 - 8 + 4 + 3

= 7

Since f(2) is not equal to zero, it follows that (x - 2) is not a factor of f(x).

Alternatively, we could use the Factor Theorem, which states that a polynomial is divisible by (x - a) if and only if f(a) = 0. Since f(2) is not equal to zero, (x - 2) is not a factor of f(x).

The solution of c(r) in 3D spherical coordinates behaves differently  because in 3D, there are radial and angular dimensions.

3D coordinates refers to the system of three-dimensional spatial representation of an object, where each point in 3D space is represented by a set of three values, also known as coordinates. These coordinates are typically written in the form (x, y, z), where x, y, and z represent the values along the three axes of a three-dimensional coordinate system.

3D coordinates are commonly used in computer graphics, engineering, and mathematics to describe the positions and orientations of objects in 3D space. In computer graphics, for example, objects are often represented using 3D coordinates to specify their position, orientation, and size in the virtual world. In engineering and mathematics, 3D coordinates are used to describe the positions of points in three-dimensional space and to perform transformations, such as rotations and translations, on these points.

The 3D coordinate system is a fundamental tool for visualizing, analyzing, and manipulating objects in three-dimensional space, and it provides a powerful way to describe complex 3D shapes, geometric relationships, and physical interactions.

The solution of c(r) in 3D spherical coordinates behaves differently than the solution of c(x) in 1D coordinates because in 3D, there are radial and angular dimensions to consider, which can affect the overall behavior of the solution. Additionally, the spherical coordinates take into account the spherical symmetry of the problem, while the 1D coordinates do not.

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Alex will not be able to complete his job. According to the measurement given for the coil, the electrician will not be able to complete the job.

The circumference of the coil of wiring can be calculated with

C= 2πr

where r is the radius and π= 3.14

The radius can be calculated by dividing the diameter by 2. Then:

r= 18 inches ÷ 2

r= 9 inches

Convert 9 inches to yards (1 yard= 36 inches)

(9 inches)(1 yard ÷ 36 inches) = 0.25 yard

Substitute this radius into the formula:

C= 2(3.14)(0.25 Yard)

C= 1.57 Yard

Since there are 21 circles of wire, we need to multiply C= 1.57 yards by 21

C = (1.57 Yard)(21) = 32.97 Yard

The coil has 32.97 yards of wire and Alex needs 34 yards, therefore, this coil will not be enough to complete the job.

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The total kilotons of carbon dioxide would the country emits over the course of the 11-year period will be 2.23 x 10 ⁻¹⁵ kilotons.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that a small country emits 115,000 kilotons of carbon dioxide per year. in a recent global agreement, the country agreed to cut its carbon emissions by 1.6% per year for the next 11 years.

The total kilotons of carbon dioxide would the country emits over the course of the 11-year period will be calculated as:-

Amount = 115000 x ( 0.016)¹¹

Amount = 2.23 x 10 ⁻¹⁵ kilotons.

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Answer:

Second choice:

[tex]\mbox{\large y = \sqrt{wz}}[/tex]

Step-by-step explanation:

Consider the right triangle ABC

By the Pythagorean theorem,

AB² = BC² + AC²

BC = x, AC = (w + x) and AB = v

Plug in above values
(w + z)² = v² + x²    (1)

In right triangle BCD,
BC² = BD² + CD²

Plugging in values we get
x² = w² + y²  (2)

In right triangle ABD
AB² = BD² + AD²
v² = y² + z²  (3)

Plug in values of x² from eq (2) and v² from eq 3 into equation (1) to get

(w + z)² = y² + z²  +w² + y²  

Left side (w + z)² = w² + 2wz + z²

==>  w² + 2wz + z² = y² + z²  +w² + y²  

w² and z² cancel out since they are on both sides of the equation with same sign

=> 2wz = y²+y²

2wz = 2y²

Divide by 2:

wz = y²

Switch sides:

y² = wz

[tex]\mbox{\large y = \sqrt{wz}}[/tex]

The mean (expected value) of X is 3.48, and the standard deviation of X is 1.27.

The mean or expected value of X, representing the number of games the team might win, can be calculated using the formula:

E(X) = n * p

where:

n = number of games (6)

p = probability of winning each game (0.58)

So, E(X) = 6 * 0.58 = 3.48

The standard deviation of X, representing the spread of the distribution, can be calculated using the formula:

SD(X) = √(n * p * (1 - p))

where:

n = number of games (6)

p = probability of winning each game (0.58)

So, SD(X) = √(6 * 0.58 * (1 - 0.58)) = 1.27

Therefore, the mean of X is 3.48, and the standard deviation of X is 1.27.

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The exponential function of the family f(x) = 2^x with a vertical shrink and a translation down 5 units is given as follows:

A. f(x) = 0.5(2)^x - 5.

The parent function is defined as follows:

f(x) = 2^x.

For the vertical shrink, the function is multiplied by a constant that has an absolute value less than one, hence:

f(x) = 0.5(2)^x.

For the translation down 5 units, the number 5 is subtracted from the definition of the function, hence:

A. f(x) = 0.5(2)^x - 5.

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Answer:

(-1,1)

Step-by-step explanation:

1.  Rearrange either equation to isolate one of the variables.   Lets use 6x - y = -7 :

6x - y = -7

-y = -7 - 6x

y = 7+6x

2.  Now use this definition of x in the second equation:

5x + y = -4

5x + (7+6x) = -4

11x  = -11

 x = -1

3.  Now use x = -1 in either equation to find y:

   6x - y = -7

  6 (-1) - y = -7

-y = -1

y = 1

The solution is  (-1,1)

See the attached graph.

The infinite series ax/a+x can be expressed as a geometric series with the sum being a/a-x.

The infinite series for ax/a+x can be represented as a geometric series. The first five terms can be expressed as:

[tex]Term 1: ax/(a+x)\\Term 2: (ax)^2/(a+x)^2\\Term 3: (ax)^3/(a+x)^3\\Term 4: (ax)^4/(a+x)^4\\Term 5: (ax)^5/(a+x)^5[/tex]

The infinite series can be expressed using summation notation as:

[tex]∑_(n=1)^∞ (ax)^n / (a+x)^n[/tex]

Using the formula for a geometric series, the sum of the infinite series can be calculated as:

[tex]S = ax/(a+x) * 1/(1-ax/(a+x)) \\ = ax/(a+x) * (a+x)/(a-ax) \\ = ax/(a-ax) \\ = a/a-x[/tex]

Therefore, the infinite series ax/a+x can be expressed as a geometric series with the sum being a/a-x.

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Step-by-step explanation:

The difference in elevation between the bottom of the canyon and the bird's nest is 504 1/2 - (-62 2/5) = 504 1/2 + 62 2/5 = 566 5/5 = 566 feet

Answer:

Step-by-step explanation:

Say sea level is 0.

Bottom of the canyon is -62.4ft and bird's nest is 504.5ft

Subtract.

504.5 - 62.4 = 442.1ft

Based on the given time; the number the second hand points at are;

There are a total of 12 numbers on a clock starting from 1 and ending at 12

There are 60 strokes or lines with equal spaces on a clock

Each stroke or line represents a second

60 seconds = 1 minutes

1. 15 seconds after 1:00.

= The seconds hand points at 3

2. 30 seconds after 1:00.

The seconds hand points at 6

3. 1 minute after 1:00.

1 minutes = 60 seconds

The seconds hand points at 12

4. 5 minutes after 1:00

5 minutes = 300 seconds

The seconds hand points at 12

Therefore, the seconds hand of the given time points at 3, 6, 12 and 12 respectively.

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