A rectangular patio has a length of (1 + 2x) yards and a width of (2 - 3x) yards. Which correctly describes the area and perimeter of the patio?

Answer:

Step-by-step explanation:

To solve for f, we can cross-multiply the equation:

f/40 = 10/f

Multiplying both sides by 40f gives:

f^2 = 400

Taking the square root of both sides yields:

f = ±20

Therefore, the solutions for f are f = 20 and f = -20. However, since f represents a physical quantity (presumably a frequency), we take only the positive value:

f = 20

The accrued value of the account in 14 years is $4967.89

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

Using the above as a guide, we have the following:

Amount = P * (1 + 0.25r)ᵗ

Where

P = Principal = 4200

r = Rate = 5.2% = 0.052

t = time = 13

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

Amount = 4200 * (1 + 0.25 * 0.052)¹³

Evaluate

Amount = 4967.89

Hence, the amount is 4967.89

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The three statements that are true about the function and its graph are:

The graph of the function is a parabola.

The graph opens downwards, since the coefficient of x² is positive.

The graph contains the point (0, 12), which can be obtained by substituting x=0 in the function.

To check the other statements:

To find f(-10), we substitute x=-10 in the function:

f(-10) = 1/5*(-10)² - 5*(-10) + 12 = 82. So the statement "The value of f(–10) = 82" is true.

To check if the graph contains the point (20,-8), we substitute x=20 in the function:

f(20) = 1/5*(20)² - 5*(20) + 12 = -68. This means the point (20,-8) does not lie on the graph of the function.

To check if the graph contains the point (0,0), we substitute x=0 in the function:

f(0) = 1/5*(0)² - 5*(0) + 12 = 12. This means the point (0,0) does not lie on the graph of the function.

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Answer:

No

Step-by-step explanation:

to determine if (- 5, 3 ) is a solution substitute the x- coordinate into both equations and if the value of y is equal to the y- coordinate then the point is a solution to the system.

y = x - 6 = - 5 - 6 = - 11 ≠ 3

y = - 2x - 7 = - 2(- 5) - 7 = 10 - 7 = 3

since both equations are not satisfied , then

(- 5, 3 ) is not a solution to the system

The missing values of h(x) to show it is a linear function are:

X=1, h(x)=3

X=3, h(x)=17

X=5, h(X)=31

So, the correct answer is (c)

A linear function is a mathematical relationship between two variables that produces a straight line when plotted on a graph, with a constant rate of change between them.

A function is a mathematical rule that assigns each input value to a unique output value. It can be represented graphically, algebraically, or with a table of values.

According to the given information:

To prove that h(x) is a linear function, we need to show that the difference in h(x) values between any two points is proportional to the difference in their corresponding x values.

Using the given values in the table, we can calculate the differences in h(x) values and x values:

Δh(x) = h(x) - h(x-1)

Δx = x - (x-1) = 1

Δh(x=1) = h(x=1) - h(x=0) = ? - (-4) = ?

Δh(x=3) = h(x=3) - h(x=2) = ? - 10 = ?

Δh(x=5) = h(x=5) - h(x=4) = ? - 24 = ?

If h(x) is a linear function, then the ratio of Δh(x) to Δx should be the same for all pairs of consecutive x values. We can use the given values of Δh(x=2) and Δx=1 to calculate this ratio:

Δh(x=2)/Δx = (10 - (-4))/2 = 7

We can now use this ratio to find the missing values of h(x):

Δh(x=1)/Δx = ?/1 = 7

Δh(x=3)/Δx = ?/1 = 7

Δh(x=5)/Δx = ?/1 = 7

?/1 = 7  =>  ? = 7

Therefore, the missing values of h(x) are:

X=1, h(x)=3

X=3, h(x)=17

X=5, h(X)=31

So, the correct answer is (c)

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(a) As a percentage, 105 grams is 1.04% of 10 kilograms.

(b) As a percentage 1 kilometer is approximately 99.21% of 8 meters.

(a) To express the second quantity, 105 grams, as a percentage of the first quantity, 10 kilograms, we first need to convert both quantities to the same unit.

10 kilograms is equal to 10,000 grams (since 1 kilogram = 1000 grams), so:

10,000 grams + 105 grams = 10,105 grams

105 grams / 10,105 grams * 100% = 1.04%

Therefore, 105 grams is 1.04% of 10 kilograms.

(b) To express the second quantity, 1 kilometer, as a percentage of the first quantity, 8 meters, we first need to convert both quantities to the same unit.

1 kilometer is equal to 1000 meters (since 1 kilometer = 1000 meters), so:

8 meters + 1000 meters = 1008 meters

1000 meters / 1008 meters * 100% = 99.21%

Therefore, 1 kilometer is approximately 99.21% of 8 meters.

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Answer: 13 units

Step-by-step explanation:

If you look at the corresponding side on the other triangle, it is also 13, and in the question it say the side on the other triangle has the same length as the one you are finding.

The answer of the given question based on the circle and rectangle is , the perimeter of the shape is approximately 83.8 feet, and its area is approximately 148.4 feet².

Perimeter is a measurement of the distance around the edge of a two-dimensional shape. It is the sum of the lengths of all the sides of the shape. The perimeter is often measured in units of length, such as centimeters, meters, or feet.

To find the perimeter and area of the composite shape formed by a rectangle and two semicircles, we can break it down into its individual components and then add them up.

First, let's find the perimeter. The shape consists of two semicircles, each with a diameter of 15 feet, and a rectangle with a width of 4 feet and a length equal to the diameter of the semicircles, which is 15 feet. The perimeter can be calculated as:

Perimeter = 2 × (semicircle circumference) + rectangle perimeter

The circumference of circle is by the formula 2πr, where r is the radius. Since each semicircle has a diameter of 15 feet, its radius is 7.5 feet. Therefore, the circumference of each semicircle is:

C = 2πr = 2π(7.5) = 15π feet

The perimeter of the rectangle is simply the sum of its four sides, which is:

P = 2(length + width) = 2(15 + 4) = 38 feet

Putting it all together, we have:

Perimeter = 2 × 15π + 38 ≈ 83.8 feet

Now let's find the area. The shape consists of two semicircles, each with a diameter of 15 feet, and a rectangle with a width of 4 feet and a length equal to the diameter of the semicircles, which is 15 feet. The area can be calculated as:

Area = (semicircle area) + rectangle area

The area of a circle is given by the formula πr². Since each semicircle has a diameter of 15 feet, its radius is 7.5 feet. Therefore, the area of each semicircle is:

A = (1/2)πr² = (1/2)π(7.5)² = 44.18 feet²

The area of the rectangle is simply its length multiplied by its width, which is:

A = length × width = 15 × 4 = 60 feet²

Putting it all together, we have:

Area = 2 × 44.18 + 60 = 148.4feet²

Therefore, the perimeter of the shape is approximately 83.8 feet, and its area is approximately 148.4 feet².

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Part A: The maximum velocity occurs at t = 0. We can plug this value into the velocity function to find the maximum velocity:

v_max = 0² = 0

Part B: The time at which the vehicle comes to rest is T = 0.

What is function?

In mathematics, a function is a relationship between two sets of elements, called the domain and the range.

The first step is to integrate the acceleration function to obtain the velocity function. Then, we can integrate the velocity function to obtain the position function.

Let's assume that the acceleration function is given by:

a(t) = 2t, where t is time in seconds.

Part A:

To find the velocity function, we integrate the acceleration function with respect to time:

v(t) = ∫a(t)dt = ∫2tdt = t² + C

where C is the constant of integration. We can find C by using the initial condition v(0) = 0.

v(0) = C = 0

Therefore, the velocity function is given by:

v(t) = t²

To find the maximum velocity, we can take the derivative of the velocity function and set it equal to zero:

dv/dt = 2t = 0

t = 0

Therefore, the maximum velocity occurs at t = 0. We can plug this value into the velocity function to find the maximum velocity:

v_max = 0² = 0

So, the maximum velocity is 0 m/s.

Part B:

To find the position function, we integrate the velocity function with respect to time:

x(t) = ∫v(t)dt = ∫t²dt = (1/3)t³ + C

where C is the constant of integration. We can find C by using the initial condition x(0) = 0.

x(0) = C = 0

Therefore, the position function is given by:

x(t) = (1/3)t³

To find the total distance traveled, we can find the area under the velocity graph. Since the velocity is always positive, the total distance traveled is the same as the total displacement. Therefore, we can find the displacement by finding the area under the velocity graph from t = 0 to t = T, where T is the time at which the vehicle comes to rest.

v(T) = 0

T² = 0

T = 0

Therefore, the time at which the vehicle comes to rest is T = 0.

The displacement is given by:

x_displacement = ∫v(t)dt from t=0 to t=T = ∫0 dt = 0

Therefore, the total distance traveled is 0 meters.

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The Simplification of the algebraic expression gives:

a. -2/3x² - (4/15)xy +  (11/4)y²

b. -(12/7)x³ + (20/9)y

Simplification of an algebraic expression is the process of writing an expression in the most efficient and compact form without affecting the value of the original expression

a. (1/3)x² - (2/5)xy + 2y² + (2/15)xy - 3x² + (3/4)y²

To simplify this, add or subtract like terms. That is:

(1/3)x² - (2/5)xy + 2y² + (2/15)xy - 3x² + (3/4)y²

     = (1/3)x² - 3x² - (2/5)xy + (2/15)xy + 2y²  + (3/4)y²

     = -2/3x² - (4/15)xy +  (11/4)y²

b. (2/7)x³ - (1/3)y + 2y - 2x³ + (5/9)y

To simplify this, add or subtract like terms. That is:

(2/7)x³ - (1/3)y + 2y - 2x³ + (5/9)y = (2/7)x³- 2x³ - (1/3)y + 2y + (5/9)y

                                                    = -(12/7)x³ + (20/9)y

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As a result, angle B has a 24 degree measure as the total of the two angles, which are along a straight line, is 180 degrees.

Thus according their size or measurement, angles can be categorised. An oblique angle is larger than 90 degrees but far less than 180 degrees, a straight angle is exactly 90 degree, a right angle is turned 90 degrees, and an acute angle is less than 90 degrees. Reflex angles are angles that are higher than 180o but a little less than 360 degrees, and complete angles are angles that measure exactly 360 degrees. Geometry, trigonometry, physics, engineering, and many other branches of mathematics and science all make use of angles.

given

The total of the two angles, which are along a straight line, is 180 degrees. Let's refer to the angle B's measurement as x.

The information provided in the problem can then be used to create an equation as follows:

m∠A = 5(m∠B + 7.2°)

Due to the fact that the two angles are perpendicular to one another, we may replace mA with 180 - mB:

180 - m∠B = 5(m∠B + 7.2°)

The right side is being widened:

180 - m∠B = 5m∠B + 36

Simplifying and putting all the mB words to one side:

6m∠B = 144

m∠B = 24

As a result, angle B has a 24 degree measure as the total of the two angles, which are along a straight line, is 180 degrees.

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Answer:

30 minutes

Step-by-step explanation:

1/45 m + 1/90 m = 1

2/9 m + 1/90 m = 1

3/90 m = 1   Multiply both sides by 90/3

90/3 x 3/90 m = 1 x 90/3

m = 90/3

m = 30

Helping in the name of Jesus.

If prices are rising, I would choose to use the FIFO (first-in, first-out) cost flow assumption. This is because under FIFO, the earliest inventory items purchased are assumed to be sold first, leaving the more recently purchased, and therefore higher-priced, items in inventory. As a result, the cost of goods sold (COGS) will be based on the lower, earlier purchase prices, resulting in higher net income and, therefore, a higher year-end bonus.

Hope this helps :)

Answer:

5 [tex]\frac{1}{3}[/tex]

Step-by-step explanation:

[tex]\frac{4}{1}[/tex] x [tex]\frac{4}{3}[/tex] = [tex]\frac{16}{3}[/tex]

You can re-write [tex]\frac{16}{3}[/tex] as

[tex]\frac{3}{3}[/tex] + [tex]\frac{3}{3}[/tex] + [tex]\frac{3}{3}[/tex] + [tex]\frac{3}{3}[/tex] + [tex]\frac{3}{3}[/tex] + [tex]\frac{1}{3}[/tex]  I wrote it like this because every [tex]\frac{3}{3}[/tex] is equal to 1.

1 + 1 + 1 + 1 + 1 + [tex]\frac{1}{3}[/tex] = 5[tex]\frac{1}{3}[/tex]

Helping in the name of Jesus.

The given input-output relation is a nonlinear function of the input signal x(t), since it involves squaring the signal at every point in time. A linear system must satisfy the property of superposition, which states that the output to a linear combination of inputs must be the same as the linear combination of the outputs to each individual input.

To determine whether the system is time-invariant, we need to check if a time shift in the input signal produces the same time shift in the output signal. That is, if: [tex]y(t) = T{x(t)}[/tex] for all values of t. Then we want to check [tex]y(t - τ) = T{x(t - τ)}[/tex] for all values of [tex]τ[/tex] and [tex]t[/tex].

We shall the consider the case where [tex]τ > 0[/tex], then we have:

[tex]y(t - τ) = (x(t - τ))^2[/tex]

[tex]T{x(t - τ)} = (x(t - τ))^2[/tex]

Since [tex]y(t - τ) = T{x(t - τ)}[/tex], we can conclude that the given system is time-invariant.

Therefore, the given system is nonlinear but time-invariant.

Answer: The two lists that are in order from least to greatest are:

C) 0.005, 0.045, 0.102, 0.63

and

E) 7.045, 7.452, 7.599, 7.604

Step-by-step explanation:

To determine which lists are in order from least to greatest, we need to compare the values and arrange them accordingly. Here is the explanation for the two correct answers:

C) 0.005, 0.045, 0.102, 0.63

This list is already in order from least to greatest. Starting from the smallest value of 0.005, each subsequent value increases until we reach the largest value of 0.63.

E) 7.045, 7.452, 7.599, 7.604

This list is also in order from least to greatest. Starting from the smallest value of 7.045, each subsequent value increases until we reach the largest value of 7.604.

For the other options:

A) 117.51, 17.382, 17.38, 17.23 - This list is not in order from least to greatest.

B) 452.8, 45.18, 452.28, 453.71 - This list is not in order from least to greatest.

D) 2.452, 2.749, 2.981, 2.994 - This list is not in order from least to greatest.

Therefore, the two lists that are in order from least to greatest are C (0.005, 0.045, 0.102, 0.63) and E (7.045, 7.452, 7.599, 7.604).

(10) The value that will make the equation a perfect square is 25.

(11) The value that will make the equation a perfect square is 64.

(12) The value that will make the equation a perfect square is 400.

(13) The value that will make the equation a perfect square is 6.25.

To make a perfect square trinomial of the form x² + bx + c, we need to add (b/2)² to both sides.

the perfect square is calculated as;

x² + 10x + __

b = 10,

(b/2)² = 25

the perfect square is calculated as;

x² - 16x + __

b = -16

(b/2)² = 64

the perfect square is calculated as;

x² + 40x + __

b = 40

(b/2)² = 400

the perfect square is calculated as;

x² + 5x + __

b = 5

(b/2)² = 6.25

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The complete table is

Time (mins)              0     1      2     3     4      5     6     7     8     9     10  

Amount of air (ft³)   40   36   32   28   24    20   16   12    8      4     0

The rate of change refers to the speed at which a quantity is changing with respect to time or some other variable.

It is a measure of how quickly or slowly a quantity is increasing or decreasing, and it is often represented as the slope of a graph or function. To fill the table we need to know the rate of change per minute in the air. Using the rate of change we can fill the table as follows  

Here we have

A scuba tank started with 40 cubic feet of air and was empty after a 10-minute dive.

To complete the table, calculate the rate of change of the amount of air in the scuba tank.

We know that the scuba tank started with 40 cubic feet of air and was empty after a 10-minute dive, so we can use this information to find the rate of change:

Rate of change = (final amount - initial amount) / time

Rate of change = (0 - 40) / 10 = -4 ft³/min

The negative sign indicates that the amount of air in the scuba tank is decreasing over time, which makes sense since the diver is using up the air during the dive.

Using this rate of change, we can complete the table as follows:

For 1 min  = 40 ft³ - 4 ft³ = 36 ft³

For 2 min = 36 ft³ - 4 ft³ = 32 ft³

For 3 min = 32 ft³ - 4 ft³ = 28  ft³

Similarly, we can fill the table as given below

Therefore

The complete table is

Time (mins)              0     1      2     3     4      5     6     7     8     9     10  

Amount of air (ft³)   40   36   32   28   24    20   16   12    8      4     0

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The missing value in the table include the following: B. 4 1/2 in.

In Mathematics and Geometry, the volume of a rectangular prism can be calculated by using the following formula:

Volume of a rectangular prism = L × W × H

Where:

By substituting the given dimensions (parameters) into the formula for the volume of a rectangular prism, we have;

50 5/8 = 5 × W × 2 1/4

Width, W = 4 1/2 inches.

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Complete Question:

The volume of a rectangular prism is 50 5/8 cubic inches.

The dimensions are given below.

What is the missing value in the table?

Length Width Height

5 in. 214 in.

A. 79in.

B. 412in.

C. 134in.

D. 1018in.

The interest that have been earned after two years is $25.

A type of interest known as compound interest is computed using both the original sum and any accrued interest from earlier periods. The interest that is earned on interest is, in other terms, interest.

We know that by the compound interest formula;

A = P(1 + r/n)^nt

A = amount

P = principal

r = rate

n = Number of times compounded

t = time

Thus;

A = 1100(1 + 0.0114/365)^365* 2

A = $ 1125

Thus the interest after two years is;

$ 1125 - $1100

= $25

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If over what interval does f(x) = 2x increase faster than g (X): A. 1

To determine over what interval f(x) = 2x increases faster than g(x) = x^2, we need to compare their derivatives. The derivative of f(x) is 2, which is a constant, and the derivative of g(x) is 2x. Therefore, f(x) increases at a constant rate of 2, while g(x) increases at a rate that depends on x.

To find the interval where f(x) increases faster than g(x), we need to find where the derivative of g(x) is less than 2. Setting 2x < 2 and solving for x, we get x < 1.

So, over the interval x < 1, f(x) = 2x increases faster than g(x) = x^2.

Therefore, the answer is A. 1.

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The features of function g if g(x) = -f(x)-1 include the following:

B. domain of (0, ∞).

C. vertical asymptote of x = 0.

D. x-intercept at (1/2, 0).

In Mathematics and Geometry, a domain is the set of all real numbers for which a particular function is defined.

Additionally, the vertical extent of any graph of a function represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.

By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following key features:

Domain = (0, ∞)

Range = (-∞, ∞).

vertical asymptote, x = 0.

x-intercept = (1/2, 0).

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The true statements are (a) A sphere with half the radius has 1/8 of the volume and (c) A sphere with 3 times the radius has 27 times the volume

Given that the radius of the sphere is represented as

Radius, r = 4 inches

The formula of the volume of the sphere is represented as

V = 4/3πr³

For the transformed volume, we have

V₂ = 4/3πR³

Where

R = kr and k is the scale factor

So, we have

V₂ = 4/3π(kr)³

V₂ = 4/3πr³k³

This gives

V₂ = Vk³

Testing the statements, we have

(a) A sphere with half the radius has 1/8 of the volume

V₂ = V(1/2)³

Evaluate

V₂ = 1/8V

So, the statement is true

(b) A sphere with twice the radius has 6 times the volume

V₂ = V(2)³

Evaluate

V₂ = 8V

So, the statement is false

(c) A sphere with 3 times the radius has 27 times the volume

V₂ = V(3)³

Evaluate

V₂ = 27V

So, the statement is true

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Complete question

A sphere has a radius of 4 inches.

Choose True or False for each statement.

(a) A sphere with half the radius has 1/8 of the volume

(b) A sphere with twice the radius has 6 times the volume

(c) A sphere with 3 times the radius has 27 times the volume

Answer:

9 : 7

Step-by-step explanation:

4.5 : 3.5 are decimals so we can multiply them both by 2 to get whole numbers. 4.5 doubled is 9 and 3.5 doubles is 7. Therefore the ratio becomes 9:7