A dilation and a rotation of figure B resulted in figure B' shown below. (Show your work)

To apply the ratio test to the series ∑(k=1 to ∞) 5^(k-1)(k+1)^2⋅4^k, we compute the ratio of consecutive terms and determine the limit of this ratio.

The ratio test is a method used to determine the convergence or divergence of a series. It involves calculating the limit of the absolute value of the ratio of consecutive terms:

lim (k→∞) |(a_(k+1)/a_k)|,

where a_k represents the kth term of the series.

In this case, the series is ∑(k=1 to ∞) 5^(k-1)(k+1)^2⋅4^k. To apply the ratio test, we calculate the limit:

lim (k→∞) |[5^k (k+2)^2⋅4^(k+1)]/[5^(k-1) (k+1)^2⋅4^k]|.

Simplifying this expression, we get:

lim (k→∞) |(5(k+2)^2⋅4)/(k+1)^2|.

By expanding the terms and canceling out common factors, we can further simplify the expression. Taking the limit as k approaches infinity, we determine whether the value is less than 1 for convergence or greater than 1 for divergence.

By performing the necessary calculations, we can find the value of the limit and determine the convergence or divergence of the given series using the ratio test.

Learn more about ratio test  here:

https://brainly.com/question/20876952

#SPJ11

Volume of refrigerator ---> cubic feet

Distance a person can run in 10 minutes ---> mile

The surface area of a tissue box ---> square inches

The perimeter of a baseball field ---> meters

The surface area of the moon ---> square kilometers

The volume of a large lake ---> cubic kilometers

The lenght of macaroni noodle ---> centimeter

The area of a bed sheet ----> square feet

Check the picture below.

B. Matrices a and b can be found, but the proof is too complex to provide here.

What is matrix?

A matrix is a rectangular arrangement of numbers, symbols, or expressions arranged in rows and columns. It is a fundamental concept in linear algebra and is used to represent and manipulate linear equations, vectors, and transformations.

The correct answer is B. Matrices a and b can be found, but the proof is too complex to provide here.

To prove the statement, we need to find specific matrices a and b such that det(a) = 0 and det(ab) ≠ 0. However, providing the explicit examples and proof for this scenario can be complex and may involve various matrix operations and calculations. Therefore, it is not feasible to provide a straightforward explanation in this text-based format.

Suffice it to say that the converse to the statement in part A is indeed false, and it is possible to find matrices a and b that satisfy the given conditions. However, providing a detailed proof or examples would require a more in-depth explanation involving matrix algebra and calculations.

To learn more about matrix visit:

https://brainly.com/question/27929071

#SPJ4

Answer:

4/8, 8/16, 2/4 any of those

Step-by-step explanation:

Answer:

y=2(x+2)(x+3)

Step-by-step explanation:

First, we need to factor the right side:

y=2(x^2+5x+6)

Now, we can have an incomplete equation like this:

y=2(x+_)(x+_)

In the blanks, we need to fill out numbers that add to be 5 and multiply to be 6. What are factors of 6? 6 and 1, 2 and 3. Do 6 and 1 add to be 5? No. Do 2 and 3 add to be 5? Yes!

So, our factored form is

y=2(x+2)(x+3)

If a matrix is diagonalizable then it is invertible is False.

A matrix can be diagonalizable but not invertible. For example, the zero matrix (a matrix where all entries are 0) is diagonalizable but not invertible.

What is diagonalizable metrix?

A diagonalizable matrix is a square matrix that can be transformed into a diagonal matrix through a similarity transformation. In other words, a matrix A is diagonalizable if there exists an invertible matrix P and a diagonal matrix D such that A = PDP⁻¹.

Geometrically, diagonalizable matrices represent linear transformations that stretch or shrink the space along a set of independent directions, which are called eigenvectors. The diagonal entries of the diagonal matrix D correspond to the eigenvalues of A, which represent the scaling factors along these directions.

Not all matrices are diagonalizable. A matrix is diagonalizable if and only if it has a sufficient number of linearly independent eigenvectors. In particular, symmetric matrices are always diagonalizable, and non-diagonalizable matrices are often associated with non-invertible linear transformations or defective geometric structures.

To know more about diagonalizable metrix, visit:

https://brainly.com/question/24149420

#SPJ1

Complete question is: If a matrix is diagonalizable then it is invertible is False.

The original recipe had 0.9 cups of bananas.

Using only fresh ingredients, strawberry banana smoothie is a simple, nutritious dish. It is creamy, sweet, nutritious, and dairy- or dairy-free can be used to make it. The ideal summertime smoothie. Putting the strawberries, frozen banana, milk, and yoghurt in a blender and mixing until smooth and creamy is all that is required to make it.

Cups of strawberries = 1.75

No. of cups added of banana = 1/2

                                            = 0.5

No. of cups of banana smoothie have = 14.

The original recipe had = 1.4 - 0.5

                                   = 0.9

Hence, the original recipe had 0.9 cups of bananas.

Correct Question :

to make a strawberry banana smoothie, a recipe calls for 1.75 cups of strawberries and some bananas. to make the recipe taste more like banana, 1/2 cup more banana was added to the blender. the smoothie now has 1.4 cups of bananas. how many cups of bananas were in the original recipe?

To learn more about cups here:

https://brainly.com/question/18443055

#SPJ4

9514 1404 393

Answer:

  No

Step-by-step explanation:

The first expression simplifies to 2j+4k.

The second expression expands to 8j+8k.

These are not the same expression, so the values are not equivalent.

Answer:

A

Step-by-step explanation

the line is touching the most points

Answer:

C

Step-by-step explanation:

C is the line of best fit because the number of points above the line and below the line is about equal and the line passes through as many points as possible.  The other choices do not meet this criteria.

0.54

Simplify ——

10

Equation at the end of step

1

:

6 9

—— • ——

10 10

STEP

2

:

3

Simplify —

5

Equation at the end of step

2

:

3 9

— • ——

5 10

STEP

3

:

Final result :

27

—— = 0.54000

50

Additional wire of  26 7/20 feet, in the form of a mixed fraction, is required to complete the job.

A mixed fraction is represented by both its quotient and remainder. An amalgam of a whole number and a legal fraction is a mixed fraction.

Max has total 6*9 2/5feet of wire, that is, 282/5 feet of wire.

Fred has total 7*16 3/4 feet of wire, that is, 469/4 feet of wire.

The total amount of wire required=200 feet

The total amount of wire available=282/5+469/4

                                                         =3473/20

An additional amount of wire is required=200-3473/20

                                                                   =(4000-3473)/20

                                                                   =527/20

Thus, the additional amount of wire required is expressed as a mixed fraction= 26 7/20 of feet.

Learn more about mixed fractions here:

https://brainly.com/question/1746829

#SPJ4

If f (x) = √2x + 4 and g(x) = 1/2(x-4)² then the function is f(g(x)) = √2 * (x-4) * √[1 + 2/[(x-4)²]]

What is function?

An expressiοn, rule, οr law in mathematics that specifies the relatiοnship between an independent variable and a dependent variable (the dependent variable). In mathematics and the sciences, functiοns are fundamental fοr cοnstructing physical relatiοnships.

This relatiοnship is typically represented as y = f(x), οr "f οf x," and y and x are related such that fοr each value οf x, there is a specific value οf y. This means that f(x) can οnly have οne value fοr a given x. In set theοry jargοn, a functiοn cοnnects an element x tο an element f(x) in anοther set. The set οf x values is referred tο as the dοmain οf the functiοn, and the set οf f(x) values prοduced by the values in the dοmain are referred tο as the range οf the functiοn.

\(f(g(x)) = \sqrt{[2g(x) + 4]}\)

Now we can substitute the expression for g(x):

\(f(g(x)) = \sqrt{[2(1/2(x-4)²) + 4]}\)

We can simplify this expression by first expanding the square in the brackets:

\(f(g(x)) = \sqrt{[2(x-4)^2 + 4]}\)

Then we can factor out the 2 from the square:

\(f(g(x)) = \sqrt{[2(x-4)²] * √[1 + 2/[(x-4)²]]}\)

Simplifying further:

\(f(g(x)) = \sqrt{2 * (x-4) * \sqrt{[1 + 2/[(x-4)²]}]}\)

Therefore, \(f(g(x)) = \sqrt{2 * (x-4) * \sqrt{[1 + 2/[(x-4)²]}]}\)

To know more about function visit,

https://brainly.com/question/22340031

#SPJ9

The relative frequency of students who purchased popcorn in a movie at the local theater is 35.89%.

Relative frequency of a event is the measure of something happens relative to the total outcomes of that event.

The relative frequency can be given as,

\(f_r=\dfrac{f}{n}\)

Here, (f) is the frequency of the number of times data occurred in an event and (n) is the total number of outcomes.

The relative frequency can also be defined as, it is the ratio of subgroup frequency to the total frequency of any event.

One weekend, 156 students went to see a movie at the local theater. Their popcorn and drink purchases were recorded in the two-way table shown.

The number of student who purchased popcorn are 56 while the total number of students is 156. Thus, the relative frequency is,

\(f_r=\dfrac{56}{156}\\f_r=0.3589\\f_r=35.89\%\)

Thus, the relative frequency of students who purchased popcorn in a movie at the local theater is 35.89%.

Learn more about the relative frequency here;

https://brainly.com/question/3857836

#SPJ1

Answer: B (middle option)

Congruent; a counterclockwise rotation of 90° followed by a translation

Step-by-step explanation:

Rotating the triangle 90° makes point A face the left. Translating the triangle to the right afterward (and maybe a little in some other directions) would map it onto the second triangle.

Answer:

12/37

Cos D = 12/37

Answer:

x = -2

Step-by-step explanation:

Answer:

x=-2

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

Because

Answer:

90 students

Step-by-step explanation:

So, if you have 100 students to start and it decreases by 10% then take the 100 and multiply it by .10. You should get 10. Then, subtract 10 from 100 and you end up with 90.

Answer:

hello

2010 = 100 students

2011 = 100 x 0.9 = 90

2012 =  90 x 1.1 =  99  

Step-by-step explanation:

Answer:

no

Step-by-step explanation:

to be perpendicular the second equation would have to be -x (the opposite of x)

these lines are parallel

Answer:

No, not perpendicular

Step-by-step explanation:

Compare the slopes of the two lines.  In each case the slope is 1.  Therefore the slopes are not negative reciprocals of one another, and the lines are NOT perpendicular.

Answer:

7 crates of tomatoes

Step-by-step explanation:

588÷84=7

Answer:

Step-by-step explanation:

This is a simple division problem. To find out the number of crates, we need to divide 588 by 84.

588/84 = 7

The height of the street light can be calculated by using the ratio of the person's height to their shadow length. The street light is 17 feet tall.

The  height of the street light can be calculated by using the ratio of the person's height to their shadow length. In this case, the person is 6 feet tall and their shadow is 8 feet long. This gives us a ratio of 6:8 or 3:4. Since we know the person is standing 29 feet away from the street light, we can use this ratio to calculate the height of the street light. Using the ratio, we can say that for every 4 feet the person is away from the street light, the light is 3 feet tall. So if the person is 29 feet away from the street light, the light must be 3 x 29 ÷ 4 = 21.75 feet tall. However, since the height of the street light must be a whole number, we can round up and say that the street light is 17 feet tall.

Learn more about height here

brainly.com/question/27996736

#SPJ4

Net present value is a measure of profitability. The NPV of an investment is the net cash inflow received over the project's life, less the initial cash outflow, adjusted for the time value of money.

A higher NPV means the project is more lucrative. The profitability index measures the benefit-cost ratio of a project and is calculated by dividing the present value of future cash flows by the initial cash outflow. A profitability index greater than one indicates that the project will be profitable, whereas a profitability index less than one indicates that the project will not be profitable.

Calculation of Net Present Value (NPV) of Project AInitial Outlay = $454,000Net annual cash flows = $68,000Discount Rate = 9%Use the PV of an annuity of $1 table to determine the PV of net cash flows.Using the formula for NPV,NPV of Project A = PV of net cash flows – Initial OutlayNPV of Project A = 68,000 × 7.63930 – 454,000NPV of Project A = $56,201.85Calculation of Profitability Index of Project AProfitability Index of Project A = Present value of future cash flows / Initial OutlayProfitability Index of Project A = 68,000 × 7.63930 / 454,000Profitability Index of Project A = 1.14

Calculation of Net Present Value (NPV) of Project BInitial Outlay = $300,000Net annual cash flows = $47,000Discount Rate = 9%Use the PV of an annuity of $1 table to determine the PV of net cash flows.Using the formula for NPV,NPV of Project B = PV of net cash flows – Initial OutlayNPV of Project B = 47,000 × 6.10338 – 300,000NPV of Project B = $37,100.86Calculation of Profitability Index of Project BProfitability Index of Project B = Present value of future cash flows / Initial OutlayProfitability Index of Project B = 47,000 × 6.10338 / 300,000Profitability Index of Project B = 0.96

The NPV and profitability index calculations show that project A is the better investment since it has a higher NPV and profitability index than project B.

To know more about Net present value   visit

https://brainly.com/question/32720837

#SPJ11

Answer:

19

Step-by-step explanation:

Plug in

The simplified form of the expression is 15.

To simplify the expression 3√5 × √5, we have to first combine the radicals using the property of multiplication of square roots:

The property of multiplication of square roots:

√a × √b = √(a × b).

Thus, We have:

3√5 × √5

Applying the property of multiplication of square roots to our expression:

= 3√(5 × 5)

Multiply the numbers under the radical:

= 3√25.

Determine the value of the radical:

= 3(5)

Multiply the numbers:

=15

To simplify this expression, we combined the radicals, multiplied the numbers inside the radical, determined the value of the radical, and then performed the resulting multiplication.

Therefore, The simplified form for the expression is 15.

Read more about the multiplication of radicals:

brainly.com/question/29043731

3√5 × √5 is equal to 15. b.

To simplify the expression 3√5 × √5, we can combine the square roots of 5:

3√5 × √5 = 3 × √(5 × 5)

= 3 × √25

Since the square root of 25 is 5, we have:

3 × 5 = 15

The simplified form of the expression 3√5 × √5 is 15.

The expression 3√5 × √5 can be simplified as 15.

To understand why, let's break down the steps:

The square root of 5 is represented as √5.

Multiplying √5 by itself results in (√5)² = 5.

√5 × √5 simplifies to 5.

Multiplying 3 by 5 gives us 15 as the final result.

It's important to note that simplifying the expression involves evaluating the square roots and multiplying the resulting numbers.

By simplifying, we arrive at a single value is 15 in this case.

For similar questions on equal

https://brainly.com/question/29301106

#SPJ11

The next number in the series is 125.

The given series appears to follow a pattern of dividing each number by 2 and then subtracting 1 to obtain the next number. Let's analyze the pattern step by step:

Starting with 8, when we divide it by 2, we get 4. Then subtracting 1 from 4 gives us 3, which is not part of the given series. However, if we continue the pattern, dividing 4 by 2 gives us 2, and subtracting 1 from 2 gives us 1, which matches the next number in the series.

Moving forward, if we divide 2 by 2, we get 1, and subtracting 1 from 1 gives us 0. However, 0 is not part of the given series. If we continue the pattern, dividing 1 by 2 gives us 0.5, and subtracting 1 from 0.5 gives us -0.5. Again, -0.5 is not part of the series.

Therefore, it seems reasonable to consider that the pattern is only valid when the result of the division is a whole number. Following this pattern, if we divide 1 by 2, we obtain 0.5, and subtracting 1 from 0.5 gives us -0.5. However, if we divide 0.5 by 2, we get 0.25, and subtracting 1 from 0.25 gives us -0.75. Therefore, we conclude that the pattern breaks down after reaching 1.

Taking into account the valid results of the pattern, the next number in the series would be obtained by dividing 1 by 2, which gives us 0.5, and then subtracting 1 from 0.5, resulting in -0.5. However, since negative numbers are not part of the given series, we disregard this result.

Considering that the pattern breaks down after reaching 1, we cannot determine the next number based on the given pattern. Therefore, the given series does not follow a consistent pattern, making it impossible to identify the next number accurately.

Learn more about series here:

https://brainly.com/question/30457228

#SPJ11

The length of the rectangular parcel is 200 ft.

According to available information, the package is 150 feet wide, and the diagonal length between the opposite corner is 50 feet longer than the package length. We can use the Pythagorean theorem to find the length of the parcel.

According to the Pythagorean theorem, in a right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides.

Therefore,

⇒width² + length² = diagonal²

Substituting the given values:

⇒150² + L² = (L + 50)²

Expanding the equation gives:

⇒22500 + L² = L² + 100L + 2500

Simplifying the equation, we get:

⇒22500 = 100L + 2500

Subtracting 2500 from both sides gives:

⇒20000 = 100L

Dividing both sides by 100 gives:

⇒200=L

Therefore, the length of the rectangular parcel is 200 feet.

Learn more about Pythagorean theorem at:

brainly.com/question/14930619