Translate the figure 1 unit left and 3 units up.
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5

Answer:

The answer is D.

Step-by-step explanation:

The function g(x) is a linear function with a y-intercept of 6 and a slope of 0, which means it is a horizontal line. Therefore, any function that is not a horizontal line will have a different end behavior than g(x). The statement that correctly compares the two functions is: "They have the same y-intercept but different end behavior." The answer is D.

Answer:

The function g(x) = 4(1) + 2 simplifies to g(x) = 6. This is a constant function that has a y-intercept of 6 and no end behavior. Therefore, it cannot be compared to another function in terms of end behavior. The correct answer is D: They have the same y-intercept but different end behavior.

The quotient is -2x - 2. Matching the expressions with their respective quotients:

(x²-3x - 18) + (x-6) → x² - 2x - 24

(x²-5x-3) + (x²+2x+1) → 2x² - 3x - 2

(x³ + 2x² - 1) / (x² + x + 1) → -2x - 2

Therefore, the expressions are matched with their respective quotients

Let's simplify each expression and match them with their corresponding quotient:

(x²-3x - 18) + (x-6)

Simplifying the expression:

x² - 3x - 18 + x - 6 = x² - 2x - 24

(x²-5x-3) + (x²+2x+1)

Simplifying the expression:

x² - 5x - 3 + x² + 2x + 1 = 2x² - 3x - 2

(x³ + 2x² - 1) / (x² + x + 1)

To divide these polynomials, we need to perform polynomial long division:

         x + 1

  ___________________

x² + x + 1 | x³ + 2x² - 1

- (x³ + x² + x)

----------------

x² - 1

- ( x² + x + 1)

----------------

-2x - 2

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Answer:

Step-by-step explanation:

First, we need to convert the dimensions of the room from feet to yards, since the price is given per square yard.

24 feet = 8 yards (since 1 yard = 3 feet)

So the dimensions of the room are 8 yards x 1 yard.

The area of the room is 8 x 1 = 8 square yards.

The cost of the carpeting per square yard is $9.97.

So, the estimated cost of the carpeting would be:

8 x $9.97 = $79.76

Rounding this to the nearest cent gives an estimated cost of $79.76.

The number of people who like Coke is 30

Since the Venn diagram visually represents the differences and the similarities between two concepts.

Given that group of 74 people, if the ratio of children who like Coke only and Pepsi only is 3:2

Also , the number of people, who like both drinks is 17 and who do not like both is 7

Total number of children who like Coke only and Pepsi only are 5x

5x = 74 - 17 - 7

5x = 50

x = 10

Thus, the number of people who like Coke  is 3x means

3 (10) = 30

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The calculated value of the circumference of the circular ring is 37.68 meters

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

Diameter, d = 12 meters

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

Circumference = π * d

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

Circumference = 12 * 3.14

Evaluate the products

Circumference = 37.68

Hence, the value of the circumference is 37.68 meters

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The measure of angle a is determined as 30 degrees.

The measure of angle a is calculated by applying the following circle theorem as follows;

If line AB is the diameter of the circle, then angle ACB will be equal to 90 degrees.

The value of a is calculated as;

a + 2a = 90 (complementary angles sum up to 90 degrees since angle ACB is equal to 90 degrees)

3a = 90

divide both sides by 3;

3a/3 = 90 / 3

a = 30

Thus, the measure of angle a is calculated by applying the following circle theorem for complementary angles.

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Answer:

The compound statement is a conjunction (AND) of two expressions, (p^q) and r. The truth value of the conjunction is true only if both expressions are true. In this case, since p is true, q is true, and r is false, the expression (p^q) is true (since both p and q are true), but the conjunction of (p^q) and r is false, because one of the expressions in the conjunction is false. Therefore, the truth value of the compound statement is False.

Answer:

a

Step-by-step explanation:

sin A = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{3}{5}[/tex]

cos A = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{4}{5}[/tex]

tan A = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{3}{4}[/tex]

then

sin A = [tex]\frac{3}{5}[/tex]

We can write k(x) as the composition of g(x) and f(x).

k(x) = g(f(x))

A composition of two functions means that we need to evaluate one function in the other one.

Here we have the functions:

f(x)=  x²

g(x) = √(x - 1)

h(x) = 2x + 3

And we know that:

k(x) = √(x² - 1)

So we have a square root, then we need to evaluate g(x), and the argument is a square, then we need to evaluate in f(x), the composition is:

k(x) = g(f(x))

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Check the picture below.

so we really have four congruent triangles with a base of hmmm 8.9 and a height of 4.4.

[tex]\stackrel{ \textit{four congruent triangles} }{4\left[\cfrac{1}{2}(\underset{b}{8.9})(\underset{h}{4.4}) \right]} ~~ \approx ~~ \text{\LARGE 78.3}~in^2[/tex]

The linear function that relates y to x is given as follows:

y = -0.5x + 57.

The slope indicates that the height decays 0.5 feet per minute. The y-intercept indicates that the descent starts at a cruising altitude of 57 feet.

The slope-intercept equation for a linear function is presented as follows:

y = mx + b

The coefficients m and b represent the slope and the intercept, respectively, and are explained as follows:

From the table, when x = 0, y = 57, hence the intercept b is given as follows:

b = 57.

When x increases by 10, y decays by 5, hence the slope m is given as follows:

m = -5/10

m = -0.5.

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For the given question x=2 gives the greatest volume and graph increasing interval is [-1,2] ∪[7,∞), While at the point of intersection, both graph has same value .

a) [tex]V(x) = x(11 - 2x)(17 - 2x)[/tex]

B(x) = 140

Side and volume cannot be negative

So, x > 0

11-2x>0 and 17-2x>0

[tex]x < \frac{11}{2}[/tex] and [tex]x < \frac{17}{2}[/tex]

Domain for V(x) =  0 < x < 11/2

b)To find the greatest Volume

[tex]\frac{dV}{dx} = 0[/tex]

[tex]V(x) = x(11 - 2x)(17 - 2x) =4x^ 3 -56x^ 2 +187x[/tex]

[tex]\frac{dV}{dx} = 12x ^ 2 - 112x + 187 = 0[/tex]

[tex]x= -b[/tex] ±[tex]\frac{ \sqrt{b^{2}-4ac } }{2a}[/tex]

[tex]x=112[/tex] ± [tex]\frac{\sqrt{112^{2} -4(12)(187) }}{2(12)}[/tex]

x = 7.155, 2.177

Consider the graph

So, Volume at 7.155 is negative

Thus x=2 gives the greatest volume

C)Consider the graph

It is increasing from -1 ≤ x ≤ 2 So, Graph Increasing Interval is [-1,2] U[7,∞)

d) At the point of Intersection both graph has the same value

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The maximum value of P is 81, and it occurs at (9,0)

Given the function P = 9x - 5t and the constraints x ≥ 0; 5x + 8y ≤ 40; 9x + 4y ≥ 36, the task is to maximize P.We will first plot the feasible region.

5x + 8y ≤ 405y ≤ 40 - 8yy ≤ (40/5) - (8/5)x or y ≤ - (8/5)x + 8This is an equation of a straight line.

To plot the line, we need to find two points on the line.We take x = 0, then y = 8. And,

taking y = 0, we get x = 5 Hence the graph of the inequality is:

Similarly, 9x + 4y ≥ 369x ≥ 36 - 4yy ≥ (36/9) - (4/9)x or y ≥ - (4/9)x + 4

This is the equation of another straight line. We take x = 0, then y = 4. And, taking y = 0,

we get x = 9Hence the graph of the inequality is:We can now graphically represent the feasible region in the following manner:

The corner points of the feasible region are A(0,0), B(5,0), C(6,3), D(9,0),

The value of P at these points is:A(0,0) ⇒ P = 0B(5,0) ⇒ P = 45C(6,3) ⇒ P = 45D(9,0) ⇒ P = 81

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The measurement of m<6 is 90 degrees or 90°

To find the measurement of angle m<6, we need to use the properties of alternate interior angles.

Let's see the given diagram of a line intersecting two parallel lines.We know that, when a transversal intersects two parallel lines, alternate interior angles are congruent.

Alternate interior angles are a pair of angles that are formed when a transversal intersects two parallel lines. They are located on opposite sides of the transversal and inside the pair of parallel lines.

If angle 6 is one of the alternate interior angles, we would also need to know which other angle it is paired with.

Once we have identified the pair of alternate interior angles, we can use the property that states that alternate interior angles are congruent. This means that their measures are equal.

So, in the above diagram, we have m<1 = m<6. Therefore, m<6 = m<1 = 90° (given). Hence, the answer is 90.

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Let's denote the amount Jolene invested at 3 percent interest as 'x' dollars. Since she put twice as much in the lower-yielding account, the amount she invested at 9 percent interest would be '2x' dollars.

To calculate the interest earned from each account, we'll use the formula: Interest = Principal × Rate × Time.

For the 3 percent interest account:

Interest_3_percent = x × 0.03

For the 9 percent interest account:

Interest_9_percent = 2x × 0.09

We know that the total annual interest is $3120, so we can set up the equation:

Interest_3_percent + Interest_9_percent = 3120

Substituting the above equations, we have:

x × 0.03 + 2x × 0.09 = 3120

Simplifying the equation:

0.03x + 0.18x = 3120

0.21x = 3120

Dividing both sides of the equation by 0.21:

x = 3120 / 0.21

x = 14857.14

Therefore, Jolene invested approximately $14,857.14 at 3 percent interest and twice that amount, $29,714.29, at 9 percent interest.

Answer:

Step-by-step explanation:

X is the amount invested at 6%

Y is the amount invested at 9%

0.06X + 0.09Y = 4998

X = 2Y

0.06(2Y) + 0.09Y  = 4998

.12Y + 0.09Y = 4998

0.21Y = 4998

21Y = 499800

Y = 499800/21 = 23800

So X = 2*23800 = 47600

$47,600 is invested at 6% and $23800 is invested at 9%

Answer:

1.c 2.b 3.a 4.h 5.g 6.f 7.d 8.e

Step-by-step explanation:

The ones with negatives are e,f,g,h. They open downward because of the negative. The ones with bigger fractions are the widest because the bigger the denominator, the more they reach out left and right. The ones that have whole numbers are tall and skinny.

The volume of the solid generated by rotating the region bounded by the curve y = x(e^x), x = 0, x = 1, and y = 0 about the y-axis is 2π[e - e^1 + 1]   and the volume of the solid generated by rotating the region bounded by the curve y = arctan(x), x = 0, x = 1, and y = 0 about the y-axis is πtan^2(1).

1) To find the volume of the solid generated by rotating the region bounded by the curve y = x(e^x), x = 0, x = 1, and y = 0 about the y-axis, we can use the method of cylindrical shells.

First, let's express the equation in terms of x: x = ln(y)/y. Now we can set up the integral to calculate the volume. The volume can be obtained by integrating the product of the circumference of each cylindrical shell and its height over the interval [0, 1]:

V = ∫[0,1] 2πx(e^x) dx.

Using integration by parts, we can evaluate this integral as follows:

V = 2π ∫[0,1] x(e^x) dx

 = 2π [x(e^x) - ∫[0,1] e^x dx]

 = 2π [x(e^x) - e^x] | [0,1]

 = 2π[(1(e^1) - e^1) - (0(e^0) - e^0)]

 = 2π[e - e^1 + 1].

2) To find the volume of the solid generated by rotating the region bounded by the curve y = arctan(x), x = 0, x = 1, and y = 0 about the y-axis, we can again use the method of cylindrical shells.

Let's express the equation in terms of x: x = tan(y). Now we can set up the integral to calculate the volume. The volume can be obtained by integrating the product of the circumference of each cylindrical shell and its height over the interval [0, 1]:

V = ∫[0,1] 2πtan(y) dy.

Using the substitution method, we can evaluate this integral as follows:

Let u = tan(y), then du = sec^2(y) dy.

When y = 0, x = tan(0) = 0, and when y = 1, x = tan(1).

Now, the integral becomes:

V = 2π ∫[0,1] u du

 = 2π [u^2/2] | [0,1]

 = 2π[(tan(1))^2/2 - 0]

 = πtan^2(1).

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The equation of a circle that is congruent to circle C and is centered at point P is (x - 5)² + (y - 1)² = 5².

In Geometry, the standard form of the equation of a circle is modeled by this mathematical equation;

(x - h)² + (y - k)² = r²

Where:

Based on the information provided, we have the following parameters for the equation of this circle:

By substituting the given parameters, we have:

(x - h)² + (y - k)² = r²

(x - 5)² + (y - 1)² = 5²

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Answer: The standard form of a linear equation is Ax+By=C. To change an equation written in slope-intercept form (y=mx+b) to standard form, you must get the x and y on the same side of the equal sign and the constant on the other side. Use inverse operations to move terms.

Answer:

B

Step-by-step explanation:

the line crosses the x-axis at -1 and crosses the y at 0.5.

The cost of one plate is $4.30 and the cost of one cup is $2.00.

Let's assume the cost of one plate is p dollars and the cost of one cup is c dollars.

From the given information, we can set up two equations based on the total costs:

Equation 1: 5p + 4c = 26.30 (since 5 plates and 4 cups cost $26.30)

Equation 2: 6p + 5c = 32.00 (since 6 plates and 5 cups cost $32.00)

We have a system of two equations with two unknowns. We can solve this system of equations using various methods, such as substitution or elimination. Let's use the elimination method.

Multiply Equation 1 by 5 and Equation 2 by 4 to eliminate the variable "c" when we add the equations together:

25p + 20c = 131.50 (5 times Equation 1)

24p + 20c = 128.00 (4 times Equation 2)

Subtract Equation 2 from Equation 1:

25p - 24p = 131.50 - 128.00

p = 3.50

Now, substitute the value of p into Equation 1 to find the value of c:

5(3.50) + 4c = 26.30

17.50 + 4c = 26.30

4c = 26.30 - 17.50

4c = 8.80

c = 2.20

Therefore, the cost of one plate is $3.50 and the cost of one cup is $2.20.

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The vertices of polygon A'B'C'D' are approximately:

A'(-2.4, 3.6), B'(-1.2, 1.2), C'(2.4, -1.2), D'(2.4, 2.4).

To dilate a polygon, you need to multiply the coordinates of each vertex by the scale factor and the center of dilation, which in this case is the origin (0, 0).

The scale factor is 3/5, so you'll multiply each coordinate by 3/5. Let's calculate the new coordinates of each vertex:

For vertex A(-4, 6):

x-coordinate: -4 * 3/5 = -12/5 ≈ -2.4

y-coordinate: 6 * 3/5 = 18/5 ≈ 3.6

So, A' is approximately (-2.4, 3.6).

For vertex B(-2, 2):

x-coordinate: -2 * 3/5 = -6/5 ≈ -1.2

y-coordinate: 2 * 3/5 = 6/5 ≈ 1.2

So, B' is approximately (-1.2, 1.2).

For vertex C(4, -2):

x-coordinate: 4 * 3/5 = 12/5 ≈ 2.4

y-coordinate: -2 * 3/5 = -6/5 ≈ -1.2

So, C' is approximately (2.4, -1.2).

For vertex D(4, 4):

x-coordinate: 4 * 3/5 = 12/5 ≈ 2.4

y-coordinate: 4 * 3/5 = 12/5 ≈ 2.4

So, D' is approximately (2.4, 2.4).

Therefore, the vertices of polygon A'B'C'D' are approximately:

A'(-2.4, 3.6), B'(-1.2, 1.2), C'(2.4, -1.2), D'(2.4, 2.4).

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The best estimate of the residual value is (d) -0.25

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

The scatter plot

From the scatter plot, we have

(x, y) = (2, 2) and (6.5, 4)

A linear equation is represented as

y = mx + c

So, we have

2m + c = 2

6.5m + c = 4

So, we have

4.5m = 2

Evaluate

m = 4/9

Next, we have

2 * 4/9 + c = 2

So, we have

c = 10/9

So, the equation is

y = 4/9x + 10/9

When x = 5. we have

Predicted = 3.33

Actual = 3

So, we have

residual = actual - predicted

This gives

residual = 3 - 3.33

Evaluate

residual = -0.33

The closest to this is -0.25

Hence, the best estimate of the residual value is (d) -0.25

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Answer: A box plot

Step-by-step explanation:

A box plot (also called a box-and-whisker plot) is an appropriate graph to represent the interquartile range. The box plot displays the five-number summary of a dataset: the minimum value, the first quartile (Q1), the median (Q2), the third quartile (Q3), and the maximum value. The box in the middle of the plot represents the interquartile range (IQR), which is the difference between the third and first quartiles. The whiskers extend from the box to the smallest and largest values that are not outliers.

Box plots are useful for comparing the distribution of multiple datasets and identifying any outliers. They provide a visual summary of the central tendency, variability, and skewness of a dataset.

Por lo tanto, the final temperature of the iron will be approximately 38.70 °C if 1300 calories are supplied.

To resolve this problem, we need to use the formula for the amount of heat transferred:

Q = m * c * ΔT

Donde:

Q es la quantity de calor transferido

m es la masa del material (in grams)

c es la capacidad calorífica specifica del material (en cal/g°C)

ΔT is the change in temperature (in °C)

First, we must determine the specific calorific capacity of iron. For iron, the specific calorific capacity is approximately 0.11 cal/g°C.

Now, we can calculate the change in temperature (ΔT) using the formula:

ΔT = Q / (m * c)

Substituyendo los valores conocidos:

ΔT = 1300 cal / (600 g * 0.11 cal/g°C)

ΔT = 1300 cal / 66 cal/°C

ΔT ≈ 19.70 °C

Finally, we can calculate the final temperature by adding the change in temperature (ΔT) to the initial temperature:

Temperature final = Temperature initial + ΔT

Final temperature = 19 °C + 19.70 °C

Final temperature ≈ 38.70 °C

Por lo tanto, the final temperature of the iron will be approximately 38.70 °C if 1300 calories are supplied.

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There are 60 triangles in the figure.

Since, We know that;

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

We have to given that;

There are so many triangle are shown in image.

Now, We have to know the number of triangles in the figure.

Since, The rule for number of triangles in first row,

⇒ 5 + 4 + 3 + 2 + 1

(Since, There are 5 small triangles.)

⇒ 15

Hence, Total number of triangles in the figure are,

⇒ 15 x 4

⇒ 60

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The number 405273 can be written in expanded form as:

400,000 + 5,000 + 200 + 70 + 3

We have,

In expanded form, we break down the number into its place values.

Each digit represents a specific place value, such as ones, tens, hundreds, thousands, etc. By multiplying each digit with its corresponding place value and then adding them together, we can express the number in expanded form.

In the case of 405273, we have:

4 in the hundred thousands place (4 * 100,000 = 400,000)

0 in the ten thousands place (0 * 10,000 = 0)

5 in the thousands place (5 * 1,000 = 5,000)

2 in the hundreds place (2 * 100 = 200)

7 in the tens place (7 * 10 = 70)

3 in the ones place (3 * 1 = 3)

Adding these values together.

400,000 + 5,000 + 200 + 70 + 3 = 405,273

Thus,

The number 405273 in the expanded form is 400,000 + 5,000 + 200 + 70 + 3.

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Answer:

1)  The functions are not inverses.

[tex]\textsf{2)} \quad g^{-1}(n)=&\dfrac{3}{8}n-\dfrac{7}{8}[/tex]

[tex]\textsf{3)} \quad g^{-1}(x)&=\sqrt[3]{\dfrac{1}{2}-\dfrac{1}{2}x}[/tex]

Step-by-step explanation:

The inverse composition rule states that if two functions are inverses of each other, then their compositions result in the identity function.

Given functions:

[tex]g(x) = 4 + \dfrac{7}{2}x \qquad \qquad f(x) = 5 - \dfrac{4}{5}x[/tex]

Find g(f(x)) and f(g(x)):

[tex]\begin{aligned} g(f(x))&=4+\dfrac{7}{2}f(x)\\\\&=4+\dfrac{7}{2}\left(5 - \dfrac{4}{5}x\right)\\\\&=4+\dfrac{35}{2}-\dfrac{14}{5}x\\\\&=\dfrac{43}{2}-\dfrac{14}{5}x\\\\\end{aligned}[/tex]                 [tex]\begin{aligned} f(g(x))&=5 - \dfrac{4}{5}g(x)\\\\&=5 - \dfrac{4}{5}\left(4 + \dfrac{7}{2}x \right)\\\\&=5-\dfrac{16}{5}-\dfrac{14}{5}x\\\\&=\dfrac{9}{5}-\dfrac{14}{5}x\end{aligned}[/tex]

As g(f(x)) or f(g(x)) is not equal to x, then f and g cannot be inverses.

[tex]\hrulefill[/tex]

To find the inverse of a function, swap the dependent and independent variables, and solve for the new dependent variable.

Calculate the inverse of g(n):

[tex]\begin{aligned}y &= \dfrac{8}{3}n + \dfrac{7}{3}\\\\n &= \dfrac{8}{3}y + \dfrac{7}{3}\\\\3n &= 8y + 7\\\\3n-7 &= 8y\\\\y&=\dfrac{3}{8}n-\dfrac{7}{8}\\\\g^{-1}(n)&=\dfrac{3}{8}n-\dfrac{7}{8}\end{aligned}[/tex]

Calculate the inverse of g(x):

[tex]\begin{aligned}y &= 1-2x^3\\\\x &= 1-2y^3\\\\x -1&=-2y^3\\\\2y^3&=1-x\\\\y^3&=\dfrac{1}{2}-\dfrac{1}{2}x\\\\y&=\sqrt[3]{\dfrac{1}{2}-\dfrac{1}{2}x}\\\\g^{-1}(x)&=\sqrt[3]{\dfrac{1}{2}-\dfrac{1}{2}x}\\\\\end{aligned}[/tex]

Answer:

1.

If the composition of two functions is the identity function, then the two functions are inverses. In other words, if f(g(x)) = x and g(f(x)) = x, then f and g are inverses.

For[tex]\bold{g(x) = 4 + \frac{7}{2}x\: and \:f(x) = 5 -\frac{4}{5}x}[/tex], we have:

[tex]f(g(x)) = 5 - \frac{4}{5}(4 + \frac{7}{2}x)\\ =5 - \frac{4}{5}(\frac{8+7x}{2})\\=5 - \frac{2}{5}(8+7x)\\=\frac{25-16-14x}{5}\\=\frac{9-14x}{5}[/tex]

[tex]g(f(x)) = 4 + (\frac{7}{5})(5 - \frac{4}{5}x) \\=4 + (\frac{7}{5})(\frac{25-4x}{5})\\=4+ \frac{175-28x}{25}\\=\frac{100+175-28x}{25}\\=\frac{175-28x}{25}[/tex]

As you can see, f(g(x)) does not equal x, and g(f(x)) does not equal x. Therefore, g(x) and f(x) are not inverses.

Sure, here are the inverses of the functions you provided:

2. g(n) = (8/3)n + 7/3

we can swap the roles of x and y and solve for y to find the inverse of g(n). In other words, we can write the equation as y = (8/3)n + 7/3 and solve for n.

y = (8/3)n + 7/3

n =3/8*( y-7/3)

Therefore, the inverse of g(n) is:

[tex]g^{-1}(n) = \frac{3}{8}(n - \frac{7}{3})=\frac{3}{8}*\frac{3n-7}{3}=\boxed{\frac{3n-7}{8}}[/tex]

3. g(x) = 1 - 2x^3

We can use the method of substitution to find the inverse of g(x). We can substitute y for g(x) and solve for x.

[tex]y = 1 - 2x^3\\2x^3 = 1 - y\\x = \sqrt[3]{\frac{1 - y}{2}}[/tex]

Therefore, the inverse of g(x) is:

[tex]g^{-1}(x) =\boxed{ \sqrt[3]{\frac{1 - x}{2}}}[/tex]

hello

the answer to the question is:

x³ - 3x² + 3x - 1 > (3/2)x(x - 1)² ---->

(x - 1)³ > (3/2)x(x - 1)² ----> x - 1 > (3/2)x ---->

(1/2)x < - 1 ----> x < 2

The amount of wrapping paper needed, without overlapping, is 112 square inches.

The correct answer is not listed among the options provided.

To calculate the amount of wrapping paper needed for the rock-shaped rectangular pyramid, we need to find the total surface area of the pyramid.

The rectangular pyramid consists of one rectangular base and four triangular faces.

The area of the rectangular base can be calculated by multiplying the length and width:

Area of rectangular base = 5 inches * 4 inches = 20 square inches

The area of each triangular face can be calculated using the formula for the area of a triangle:

Area of triangular face = (base * height) / 2

For the large triangular face, the base is 4 inches and the height is 5 inches:

Area of large triangular face = (4 inches * 5 inches) / 2 = 10 square inches

For the small triangular face, the base is 5 inches and the height is 5.2 inches:

Area of small triangular face = (5 inches * 5.2 inches) / 2 = 13 square inches

Now, we can find the total surface area by summing up the areas of all the faces:

Total surface area = Area of rectangular base + 4 * (Area of triangular face)

                      = 20 square inches + 4 * (10 square inches + 13 square inches)

                      = 20 square inches + 4 * 23 square inches

                      = 20 square inches + 92 square inches

                      = 112 square inches

Therefore, the amount of wrapping paper needed, without overlapping, is 112 square inches.

The correct answer is not listed among the options provided.

For more such questions on wrapping paper, click on:

https://brainly.com/question/16613694

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