Find an explicit rule for the nth term of a geometric sequence where the second and fifth terms are -6 and 162, respectively.

A; an = 2 • 3n - 1
B; an = 2 • (-3)n - 1
C; an = 2 • 3n
D; an = 2 • (-3)n + 1

Answer:

-1

Step-by-step explanation:

Direct substitution is just filling in the limit for x then solving. So in this case the limit is 0.

x^2-1

0^2-1

-1

A trapezoid is a quadrilateral having one set of opposing sides that are parallel to each other.  The perimeter of the trapezoid is equal to 32 inches.

A trapezoid is a quadrilateral having one set of opposing sides that are parallel to each other. It can have right angles (a right trapezoid) and congruent sides (isosceles), but neither is necessary.

As is mentioned that the area of the trapezoid is 69.6 in², while its altitude is 8.7 inches. Therefore, the sum of the bases of the trapezoid can be written as,

[tex]\rm \text{Area of trapezoid} = \dfrac{1}{2} \times (Base_1 + Base_2) \times Altitude[/tex]

[tex]69.6 = \dfrac{1}{2} \times (b_1 + b_2) \times 8.7\\\\(b_1 +b_2) = 16\rm\ inches[/tex]

Now, it is mentioned that the sum of the legs of the trapezoid is equal to the sum of its bases. Therefore, the perimeter of the trapezoid is,

[tex]\text{Perimeter of Trapezoid} = (\text{Sum of its bases}) +(\text{Sum of its legs})\\\\\text{Perimeter of Trapezoid} = 16+16 = 32\rm\ inches[/tex]

Hence, the perimeter of the trapezoid is equal to 32 inches.

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Final answer:

When both teams work together, they can wrap the gifts with a combined rate of 12/35 of the work per hour. It would take them 35/12 hours, which is approximately 2.92 hours. Rounded to the nearest half-hour, both teams will take about 3 hours to wrap all of the gifts.

Explanation:

To determine the time it would take for both teams of interns to wrap the gifts when working together, we need to add their work rates. Team A can wrap the gifts in 7 hours, which means their rate is 1/7 of the work per hour. Team B can wrap the gifts in 5 hours, giving them a rate of 1/5 of the work per hour.

When combined, the rate at which they can wrap the gifts together is the sum of their individual rates:

Team A's rate: 1/7
Team B's rate: 1/5
Combined rate: 1/7 + 1/5 = 5/35 + 7/35 = 12/35 of the work per hour.

To find out how many hours it will take them to wrap all of the gifts together, we divide the entire job (1) by their combined rate (12/35):

1 / (12/35) = 35/12 hours = 2.9166... hours.

Rounded to the nearest half hour, they would take approximately 3 hours to wrap all of the gifts.

Final answer:

To determine how much the 34-pound dog should eat, set up a proportion based on the 15-pound dog's food intake. After setting up the proportion 15 pounds / 2 1/8 cups = 34 pounds / x cups and solving it, we find that the 34-pound dog should eat approximately 4.82 cups per day.

Explanation:

The question deals with proportional relationships and mathematics, specifically in finding out how much dog food to feed a dog based on its weight. To solve this problem, we need to establish a ratio or proportion from the information provided and then use it to find out how much food the 34-pound dog should eat.

A 15-pound dog eats 2 1/8 cups of dog food per day. We convert 2 1/8 cups to an improper fraction which is 17/8 cups. Now, we set up the proportion:

15 pounds / (17/8 cups) = 34 pounds / x cups

By cross-multiplying we have:

15 * x = 34 * (17/8)

x = (34 * 17) / (8 * 15)

x = (578) / (120)

After simplifying the fraction, we obtain x = 4.8166 which we can round to 4.82 cups per day for a 34-pound dog.

The rule that describes the composition of transformations that maps figure ABCDE to figure A"B"C'D"E" is the transformation composition rule. This involves applying a translation followed by a reflection in a specific order.

The rule that describes the composition of transformations that maps figure ABCDE to figure A"B"C'D"E" is the transformation composition rule.

Transformation composition involves applying multiple transformations in a specific order. In this case, we need to determine the sequence of transformations that would result in the mapped figure.

By applying these transformations in the given order, we can map figure ABCDE to figure A"B"C'D"E".

The rule that describes the composition of transformations that maps figure ABCDE to figure A"B"C'D"E" could involve a sequence of translations, reflections, rotations, or dilations, applied in a specific order. The specific transformations and their order would depend on the given figures and the desired outcome.

The rule that describes the composition of transformations that maps figure ABCDE to figure A"B"C'D"E" is called a sequence of transformations.

A sequence of transformations involves applying multiple transformations in a specific order to transform one figure into another. In this case, the figure ABCDE is transformed into A"B"C'D"E".

Let's break down the possible transformations that could be involved in this sequence:

1. Translation: A translation moves a figure without changing its size or shape. It involves sliding the figure in a specific direction. For example, if figure ABCDE is translated 3 units to the right and 2 units up, it would result in figure A"B"C'D"E".

2. Reflection: A reflection involves flipping a figure over a line called the line of reflection. The line of reflection acts as a mirror, with each point on the figure reflecting across the line. If figure ABCDE is reflected over a line, it would result in figure A"B"C'D"E".

3. Rotation: A rotation involves turning a figure around a fixed point called the center of rotation. The figure is rotated by a specific angle in a clockwise or counterclockwise direction. If figure ABCDE is rotated 90 degrees counterclockwise around a given point, it would result in figure A"B"C'D"E".

4. Dilation: A dilation involves changing the size of a figure while maintaining its shape. The figure is either enlarged or reduced by a scale factor. If figure ABCDE is dilated with a scale factor of 2 centered at a specific point, it would result in figure A"B"C'D"E".

Answer : C

the roots of the polynomial equation x^3-10x=-3x^2+24

We use a graphing calculator

Graph the left hand side expression using graphing calculator

We graph [tex]y=x^3 - 10x[/tex]

Then we graph the right hand side expression using graphing calculator

[tex]y=-3x^2+24[/tex]

so we got two system of equations

The intersection of two graphs is our solution

The graph is attached below

We can see that the graph intersects at 3 points

(-4, -24)  (-2,12) and (3,-3)

So the roots are -4, -2 , 3

Answer:

a(8) = -12

Step-by-step explanation:

The 8th term in the sequence is when n = 8. Substitute x = 8 into the rule An=-2x+4.

a(8) = -2(8) + 4

a(8) = -16 + 4

a(8) = -12

Answer:  The required slope is 2.

Step-by-step explanation:  We are given to find the slope between the points where x = 3 and x = 7 from the following table :

x      3       4      7

y      1        6      9

We know that

the slope of a line between the points (a, b) and (c, d) is given by

[tex]m=\dfrac{d-b}{c-a}.[/tex]

At x = 3, y = 1  and  at x = 7, y = 9.

Therefore, the slope between the points (3, 1) and (7, 9) is given by

[tex]m=\dfrac{9-1}{7-3}=\dfrac{8}{4}=2.[/tex]

Thus, the required slope is 2.

Amount of fluid recommended by Harry's fitness trainer =8 fluid ounces of water 8 times a day = 8x8=64 fluid ounces.

Amount of fluid Harry water bottle holds= [tex] 1\frac{1}{4}=1.25 pints [/tex]

Amount of fluid Harry drinks when he fills the bottle 3 times = 1.25x3=3.75 pints.

1 pint = 16 fluid ounce

3.75 pint =16x3.75 =60 fluid ounces.

Harry drank only 60 fluid ounce compared to 64 fluid ounce his trainer recommended.

Harry claims that he drank the total amount of water recommended by his fitness trainer is not true.

Solution:

we have been asked to find

Which of the given number words represents the numeral 4,056?

Its about the counting.

On unit place we have 6.

on Tenth place we have 5.

on hundredth place we have 0.

On Thousand place we have 4.

so in our number word representation there will be no "Hundreds".

So it will make

Hence the given number words representing the numeral 4,056 is Four thousands and fifty six

Answer: 1/4

Step-by-step explanation:

Number at Second Show               100             100 ➗100

—————————————-    =      ————   =    — — ———-   = 1/4

Number at First show                     400              400➗100

Hoped it help.

Answer:358

Step-by-step explanation:just because it is

To compute for the minimum amount of wrapping paper Dylan will need to completely cover the box, you have to compute the surface area of the box. The formula in getting the surface area of a rectangle is:

A = 2WL + 2LH + 2HW

Substituting the given measurements to the formula:

A = 2(5)(6) + 2(6)(3) + 2(3)(5)

A = 60 + 36 + 30

A = 126 square inches

Therefore, Dylan needs to purchase at least 126 square inches of wrapping paper to completely cover the box.

Answer:

Dividend is the number which we divide. Divisor is the number by which we divide. Quotient is the quantity produced by the division of two numbers. Remainder is an amount left over after division.

Step-by-step explanation:

The fraction of 1 foot is 3 inches is, 1/ 4

And, The fraction of 1 yard is 3 inches is, 1 / 12

A measurement unit is a standard quality used to express a physical quantity. Also it refers to the comparison between the unknown quantity with the known quantity.

Given that;

To find the fraction of 1 foot is 3 inches.

And, The fraction of 1 yard is 3 inches.

We know that;

As shown on the number line,

⇒ 1 foot = 12 inches.

Hence, To find fraction of a foot 3 inches is,

we have to compare 3 inches to 12 inches as;

3 / 12

1 / 4

Thus, The fraction of 1 foot is 3 inches is, 1/ 4

And, We know that;

1 yard = 36 inches

Hence, We get;

The fraction of 1 yard is 3 inches is,

⇒ 3 / 36

⇒ 1 / 12

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