the area of a rectangle is 54 square units. one side has a length of 9 units. what is the other side length? explain how you know using pictures, equations, and words

The water level is rising at a rate of 1/3 ft/min.

The trough has the shape of isosceles triangles at its ends.

Height of the trough = 12 ft

Base of the isosceles triangle, b =  5 x h' = 5h' [since the width across the top of the trough is 5 ft]

Let h be the height of the isosceles triangle which is the depth of the water.

Base area of the trough = Area of the triangle

                                        = 1/2 x 5h x h

                                        = 5/2 h²sq. ft.

Volume of the trough, V = Base area x height of the trough

                                         = 5/2 h² x 12

                                         = 30h² cubic ft

Differentiating V with respect to t,

dV/dt = 30 x 2h x dh/dt = 60h dh/dt,

where dh/dt is the rate of change in the water level.

The rate of water being filled in the trough, dV/dt = 15 ft³/min.

Substituting dV/dt and when h = 9 inches = 3/4 ft,

⇒ 15 = 60 x 3/4 x dh/dt

⇒ dh/dt = 15 /(45)

⇒ dh/dt = 1/3 ft/min

So the water level is rising at a rate of 1/3  ft/min.

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According to the given conditions , the equation of the circle is \((x + 2)^2 + (y - 5)^2 = 16.\)

What is circle ?

A circle is a two-dimensional geometric shape that consists of all points in a plane that are a fixed distance, called the radius, from a given point called the center. A circle can also be defined as the set of all points that are equidistant from a central point.

The equation of a circle with center (h, k) and radius r is:

\((x - h)^2 + (y - k)^2 = r^2\)

In this case, the center of the circle is (-2, 5) and the radius is 4, so the equation of the circle is:

\((x - (-2))^2 + (y - 5)^2 = 4^2\)

Simplifying this equation gives:

\((x + 2)^2 + (y - 5)^2 = 16\)

Therefore, according to the given conditions , the equation of the circle is \((x + 2)^2 + (y - 5)^2 = 16.\)

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Answer:

f(x)=-2x+192

Step-by-step explanation:

192-184=8

8/2=4 each week there is a reduction of 4 cars.

If you substitute the week into x you will find that the equation works.

Answer:

1) -1/4

2) -1/2

3) 1/3

Step-by-step explanation:

perpendicular lines' slopes are opposite reciprocals so you flip it and change the positive or negative sign

parallel lines have the same slope

Vertically compressing the exponential parent function f(x) = 2^x by a factor of 3 means multiplying every function value by 1/3, resulting in a steeper and narrower curve closer to the x-axis.

If we vertically compress the exponential parent function f(x) = 2^x by a factor of 3, it means that every point on the graph of the function will be compressed closer to the x-axis. In other words, the function values will be multiplied by 1/3.

Let's consider a point on the original exponential function, (x, f(x)). After the vertical compression, this point will have the coordinates (x, (1/3)f(x)). For example, if f(x) = 8 for some x, after compression, the corresponding point will be (x, (1/3)(8)) = (x, 8/3).

This vertical compression affects all points on the graph uniformly, resulting in a steeper and narrower curve compared to the original exponential function.

The y-values of the compressed function will be one-third of the y-values of the original function for each x-value. Therefore, the graph will be squeezed vertically, with the y-values closer to the x-axis.

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Generally, a quotient of polynomials is decomposed into at least two partial fractions.

Any valid quotient of polynomials may be broken down into its component parts. When the degree of the numerator is lower than the degree of the denominator, a function is considered to be properly rational. Expressing a valid rational function as the sum of smaller fractions with certain denominators is the first step in breaking it down into partial fractions.

This decomposition can be helpful in a variety of mathematical situations, such as when solving equations involving rational functions or integrals. The denominator's factors determine the partial fractions' form. In particular, the rational function may be broken down into partial fractions with denominators matching to those factors if the denominator of the correct rational function can be factored into linear and/or quadratic irreducible components.

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To evaluate the function f(x) = 3x + 8 for a specific value of x, we can substitute the value into the function and perform the necessary calculations. In this case, when evaluating f(-4), we substitute -4 into the function to find the corresponding output. The result is f(-4) = 3(-4) + 8 = -12 + 8 = -4.



The function f(x) = 3x + 8 represents a linear equation in the form of y = mx + b, where m is the coefficient of x (in this case, 3) and b is the y-intercept (in this case, 8). To evaluate f(-4), we substitute -4 for x in the function and calculate the result.

Replacing x with -4 in the function, we have f(-4) = 3(-4) + 8. First, we multiply -4 by 3, which gives us -12. Then, we add 8 to -12 to get the final result of -4. Therefore, f(-4) = -4. This means that when x is -4, the function f(x) evaluates to -4.

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Answer:

46.5

Step-by-step explanation:

Of all straight angles have 180 degrees in them.

So, to find x we need to form this equation:

x + 65 + x - 22 = 180

2x + 43 = 180

2x = 180-43

2x = 137

68.5 degrees = x

68.5-22 = 46.5 degrees.

m<CBD = 46.5 degrees.

m<GBF = also 46.5 degrees because it is a vertical angle to <46.5 degrees.

Answer:

−6b+29

Step-by-step explanation:

Let's simplify step-by-step.

8−3(2b−7)

Distribute:

=8+(−3)(2b)+(−3)(−7)

=8+−6b+21

Combine Like Terms:

=8+−6b+21

=(−6b)+(8+21)

=−6b+29

have a great day <3

Answer: -6b + 29

Step-by-step explanation:

8 -6b + 21

-6b + 29

Answer:

I'm pretty sure it's c like 80% sure not certain though, the x value should shift left 7 so more then likely C

Answer:

its c

Step-by-step explanation:

The critical points for this system are: (0, y), (1, y), (x, 0), and (x, -1/2).

What is the system of equations?

A system of equations is a collection of one or more equations that are considered together. The system can consist of linear or nonlinear equations and may have one or more variables. The solution to a system of equations is the set of values that satisfy all of the equations in the system simultaneously.

To find the critical points (equilibrium solutions) of the given systems of differential equations, we need to set both derivatives equal to zero and solve for x and y.

dx/dt = x - xy, dy/dt = y + 2xy

Setting dx/dt = 0, we have:

x - xy = 0

x(1 - y) = 0

This gives us two critical points: (0, y) and (1, y), where y can take any value.

Setting dy/dt = 0, we have:

y + 2xy = 0

y(1 + 2x) = 0

This gives us two critical points: (x, 0) and (x, -1/2), where x can take any value.

Therefore, the critical points for this system are: (0, y), (1, y), (x, 0), and (x, -1/2).

Regarding the stability and classification of each critical point, we need to analyze the eigenvalues of the Jacobian matrix at each point. The stability of a critical point is determined by the sign of the real parts of the eigenvalues.

To describe the basin of attraction for each asymptotically stable critical point, we would need to perform further analysis of the system's behavior near each critical point.

Hence, the critical points for this system are: (0, y), (1, y), (x, 0), and (x, -1/2).

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Answer:72 minutes

Step-by-step explanation:

30/25=  1.2 * 60= 72

The interval of I₁ or I₂ or I₄ is  (2.5 ,10].

The interval of I₁ and I₂ is  [3 , 5.5] .

The interval of I₁ and I₃ is  [5.5]

The interval of I₁ and I₄ is (5.6 , 7]

(a) because the all 3 intervals square measure connected by or which suggests they're going to all embrace the quantity lying from interval one to three and is given by (2.5 ,10].

(b) because the interval square measure connected by and which suggests the common numbers lying in interval one and a couple of and is given by [3 , 5.5] .

(c) because the interval square measure connected by and which suggests the common numbers lying in interval one and three and is given by [5.5]

(d)As the interval square measure connected by and which suggests the common numbers lying in interval one and four and is given by (5.6 , 7] .

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The complete question is given below :

Given the intervals I₁ = (2.5, 5.5], I₂ =[3, 6], I₃=[5.5, 7] and I₄ = (5.5, 10]. Find

(a) I₁ or I₂ or I₄

(b) I₁ and I₂

(c) I₁ and I₃

(d) I₁ and I₄

The area of rectangular region r is = 12.

Given:

each diagonal of r has length 5. the perimeter of r is 14.

Let l and b be the length and breadth of a rectangle.

we know that

perimeter of rectangle = 2 ( l + b )

2 ( l + b ) = 14

divide by 2 on both sides

( l + b ) = 14/2

l + b = 7

l = 7 - b

l^2 + b^2 = d^2

( 7 - b )^2 + b^2 = 5^2

7^2 + b^2 - 2 * 7 * b  + b^2 = 25

49 + 2b^2 - 14b = 25

2b^2 - 14b + 24 = 0

on solving b = 4,3

Take any one value

b = 4

l = 7 - 4

l = 3

Area of rectangle = l * b

= 4 * 3

= 12

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The frequently used charts together to monitor and control quality are the p-chart and the R-chart. These charts help track nonconforming items and variation within a sample, respectively, in Statistical Process Control (SPC).

In quality management and control, the p-chart and R-chart are commonly used together as part of Statistical Process Control (SPC) methodologies. The p-chart, short for proportion chart, is used to monitor the proportion of nonconforming items or defects in a sample. It helps identify if a process is stable or if there are changes in the defect rate over time.On the other hand, the R-chart, short for range chart, is used to monitor the range or variation within a sample. It helps detect shifts in process variability and assess the consistency of the process output.

By utilizing both charts, organizations can gain a comprehensive understanding of the quality of their processes. The p-chart helps identify if the process is producing within acceptable defect levels, while the R-chart helps assess the consistency and stability of the process. Together, these charts provide valuable insights to monitor and control the quality of products or services, enabling organizations to take corrective actions and continuously improve their processes.

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The area of the parking lot is  2,025 .81 meter2.

In essence, it is equal to 1/2 of the height times the base, or A = 1/2 b h. Therefore, we need to know the triangular polygon's base (b) and height (h) in order to calculate its area.

A triangular parking lot has sides measuring 90 meters, 54 meters, and 128 meters.

Triangle Height Determination Using Area

Now that you are aware of the triangle's area, you may use the triangle formula A=1/2bh to get the triangle's height.

s   = a + b+ c /2

90 + 54 + 128 / 2 = 136

A = \(\sqrt{s (s-a) (s-b) (s-c)}\)

A = \(\sqrt{136(136-90)(136-54)(136-128}\))

A = 2,025 .81

The area of the parking lot is  2,025 .81 meter2.

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a) It would take Anya approximately 4 years to accumulate $40,000 with an annual interest rate of 12%. b) Anya must earn an annual rate of return of approximately 12.6% to save $40,000 in 3 years.

a) To calculate the number of years it would take Anya to accumulate $40,000, we can use the future value formula for compound interest:

Future Value = Present Value * (1 + interest rate)ⁿ

Where:

Future Value = $40,000

Present Value = $25,000

Interest rate = 12% = 0.12

n = number of years

Substituting the given values into the formula, we have:

$40,000 = $25,000 * (1 + 0.12)ⁿ

Dividing both sides of the equation by $25,000, we get:

(1 + 0.12)ⁿ = 40,000 / 25,000

(1.12)ⁿ = 1.6

To solve for n, we can take the logarithm of both sides of the equation:

n * log(1.12) = log(1.6)

Using a calculator, we find that log(1.12) ≈ 0.0492 and log(1.6) ≈ 0.2041. Therefore:

n * 0.0492 = 0.2041

n = 0.2041 / 0.0492 ≈ 4.15

b) To calculate the required rate of return for Anya to save $40,000 in just 3 years, we can rearrange the future value formula:

Future Value = Present Value * (1 + interest rate)ⁿ

$40,000 = $25,000 * (1 + interest rate)³

Dividing both sides of the equation by $25,000, we have:

(1 + interest rate)³ = 40,000 / 25,000

(1 + interest rate)³ = 1.6

Taking the cube root of both sides of the equation:

1 + interest rate = ∛1.6

Subtracting 1 from both sides, we get:

interest rate = ∛1.6 - 1

Using a calculator, we find that ∛1.6 ≈ 1.126. Therefore:

interest rate = 1.126 - 1 ≈ 0.126

To express the interest rate as a percentage, we multiply by 100:

interest rate = 0.126 * 100 = 12.6%

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A sequence is characterised as one that adheres to a predetermined pattern. The following term is created by increasing or decreasing the previous word by a certain amount.

On occasion, an expression is followed by every term in the series. The general formula for an AP is T n = a + (n - 1) d.

Understanding the underlying pattern or rule that creates the sequence is necessary for formulating the general term an of the sequence. Finding a formula for the overall term of a series can be done in a number of ways, including:

1) Finding a pattern: In some cases, a pattern can be found by examining the terms of the sequence and looking for a common ratio or difference. For instance, the formula for the general term can be written as a = a1 + (n - 1)d, where a1 is the first term and d is the common difference, assuming the terms of a sequence are rising by a constant amount.

2) Recurrence relations are used to characterise some sequences. These relations define the nth term in terms of the phrases that came before it. If the recurrence relation, for instance, is a = an-1 + an-2, then the general term's formula can be discovered by resolving the recurrence relation.

3) Making use of generating functions: Sequences can be represented mathematically using generating functions. A formula for the general term of a sequence can be discovered by fiddling with the generating function.

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The types of roots in math are known as real roots , imaginary roots or repeated roots.

roots > 0  imaginary

roots < 0  real

roots = 0  repeated

When the roots are bigger than zero, they are referred to as real roots. When the value of the obtained roots is less than zero, the obtained roots are referred to be not real or imaginary roots.

When the sum of the obtained roots equals zero, we conclude that the roots are repeated.

In order to find the roots of a equation we can plot them on a graph and the solve them or we can factorize the given equation. We can also use the formula to calculate graph using determinant method.

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Answer:

The answer is option D - 1120°

1120° is the sum of the sixed marked angle in the picture. Therefore, the correct option is option D.

An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.

The angle formed by the rays lying perpendicular to the two crossing curves at the point of junction is another property of intersecting curves. Angle can also refer to the size of such an angle or a rotational angle. The width of a circular path divided by its radius is the traditional definition of this metric, which may also be signed. 1120° is the sum of the sixed marked angle in the picture.

Therefore, the correct option is option D.

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Answer:

your answer is 1/343 in decimal form it is 0.00291545

Answer:

1990.98

Step-by-step explanation:

:)

The rewritten form of the given expression such that it is without absolute value notation is; 2b.

It follows from the task content that the rewritten form of the given expression; | 2b | is to be determined.

On this note, since it is given that the variable b is less than zero; i.e b < 0.

It follows that the expression evaluation of 2b yields a negative number.

However, the rewritten form of the expression without the absolute value notation since the value of b is unknown still remains; 2b.

Therefore, the required rewritten form is; 2b.

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The length of the shorter part is 12 inches.

The ratio shows how many times one value is contained in another value.

Example:

There are 3 apples and 2 oranges in a basket.

The ratio of apples to oranges is 3:2 or 3/2.

We have,

Length of the line segment = 30 inches.

The ratio of two parts of the line segment = 2 : 3

Now,

2x + 3x = 30 inches

5x = 30

x = 6 inches

Now,

2x = 2 x 6 = 12 inches

3x = 3 x 6 = 18 inches

Thus,

The length of the shorter part is 12 inches.

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Answer:

False

Step-by-step explanation:

It's actually C=πd d is diameter or C=πr^2

Answer:

True

Step-by-step explanation: Calculate circumference from area

We are given the area, and by substitution we know that 13π = πr2. We divide out the π and are left with 13 = r2. We take the square root of r to find that r = √13. We find the circumference of the circle with the formula C = 2πr.