This table shows values of power of 7 use the table to find the value of
A-49x2401
B-16807divided by343
C-343 raise to the power 2

Let's denote the length of the table as "x" feet. According to the problem, the width is 2 feet less than the length, so the width can be represented as "x - 2" feet. The area of the table is given as 20 square feet.

The formula for the area of a rectangle is length times width. Therefore, we can set up the equation:

Length × Width = Area

x(x - 2) = 20

Expanding the equation, we get:

x^2 - 2x = 20

Rearranging the equation in quadratic form:

x^2 - 2x - 20 = 0

To solve this quadratic equation, we can factor it or use the quadratic formula. Let's use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

For our equation, a = 1, b = -2, and c = -20. Plugging these values into the quadratic formula, we get:

x = (-(-2) ± √((-2)^2 - 4(1)(-20))) / (2(1))

Simplifying further:

x = (2 ± √(4 + 80)) / 2

x = (2 ± √84) / 2

x = (2 ± 2√21) / 2

Simplifying the expression inside the square root:

x = (1 ± √21)

So the possible values for x are 1 + √21 and 1 - √21.

Since the length cannot be negative, we take the positive value:

x = 1 + √21

Now we can find the width by substituting this value of x into the expression for width:

Width = x - 2

Width = (1 + √21) - 2

Width = -1 + √21

Therefore, the dimensions of the table are approximately 1 + √21 feet for the length and -1 + √21 feet for the width.

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Answer:

Jorge needs 1/2 apple to make the snack.

Based on the given algorithm, we can analyze the recurrence relation for the running time of the algorithm on inputs of arrays of n elements.

Let's denote the running time of the algorithm for an input of size n as t(n).

For n = 1, the algorithm computes f(g) for a single entry in the array, which costs a constant time, let's say C1. Therefore, we have:

t (1) = C1

For larger values of n, the algorithm splits the array into two subarrays of size 2n/3 each and runs recursively on each subarray. This step incurs a running time of t(2n/3) for each subarray.

Additionally, the algorithm performs the computation g(x, y) on the resulting ordered set of two integers, which costs a constant time, let's say C2.

Considering these factors, we can write the recurrence relation for the running time as:

t(n) = 2t(2n/3) + C2

Therefore, the correct option among the given recurrence relations that seems to fit the running time of the algorithm is:

c. t(1) = C, and t(n) = 2t(2n/3) + C2, for some positive constants C, C2

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Answer:

the second

Step-by-step explanation:

refers to well-founded standards of right and wrong that prescribe what humans should do, usually in terms of rights, obligations, benefits to society, justice

Answer:

14.5 - Proofs attached to answer

Step-by-step explanation:

Proofs attached to answer

Answer:1 and 3 both are 114 angle and 2 and 4 are 66

Step-by-step explanation:

so l and 3 are the same proportion which means there angle is the same and since angles add up to 360 you do 360-114-114 and you get 132 but since you still have the other 2 sides that need angles applied you divided 132/ 2 and u get 66

Answer:

angle 3 =114

angle 1= 66

angle 4 = 66

Answer: 5.57

Step-by-step explanation:

The square root of 31 is 5.56776436 and if you round that 2 decimals places you get 5.57 bc anything higher than 5 gets rounded up to the next number.

Answer:

20

Step-by-step explanation:

Evaluate for y= −5

(−5)2+(2)(−5)+5

(−5)2+(2)(−5)+5

=20

Answer:

Car A's speed is 75 miles per hour

Step-by-step explanation:

As the distance-time graph represents the straight line. Thus, the slope of any line would remain constant along the line.

We also know that in a distance-time graph, the slope of the line would be equal to the speed of the object.

Taking two points from the graph

Determining the slope

Slope = [y₂-y₁] / [x₂-x₁]

          = [100 - 25] / [1 - 0]

          = 75 / 1

           = 75 miles per hour

Therefore, Car A's speed is 75 miles per hour

Answer:

I got it right in Imagine Math

Step-by-step explanation:

The most appropriate choice for unitary method will be given by

Total cost of 200g raspberries and 200 g strawberries is £4.14

What is unitary method?

It is the method by which we find the value of single unit form the value of multiple unit and value of multiple unit from the value of single unit.

Here,

500 g of strawberries cost £4.10

1 g of strawberries cost £\(\frac{4.10}{500}\)

300 g of strawberries cost £\(\frac{4.10}{500} \times 300\)

                                           = £2.46

400 g of raspberries 300g of strawberries cost a total of £7.46

Let the cost of 400 g of raspberries be  £x

so,

x + 2.46 = 7.46

x = 7.46 - 2.46

x =  £5

cost of 400 g of raspberries =  £5

cost of 1 g of raspberries =  £\(\frac{5}{400}\)

cost of 200 g of raspberries =  £\(\frac{5}{400} \times 200\)

                                                = £2.5

cost of 300 g strawberries = £2.46

cost of 1 g strawberries = £\(\frac{2.46}{300}\)

cost of 200 g of strawberries = £\(\frac{2.46}{300} \times 200\)

                                                 = £1.64

Total cost of 200g raspberries and 200 g strawberries = £(2.5 + 1.64)

                                                                                            = £4.14

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Complete question

400 g of raspberries and 300 g of strawberries cost a total of £7.46.

500 g of strawberries cost £4.10.

Work out the total cost of 200 g of raspberries and 200 g of strawberries.

Step-by-step explanation:

(f+g)(x) means we just add the 2 functions, so we have

(x-3) + 2x² = 2x² + x - 3

(f-g)(x) means we subtract g(x) from f(x), so we have

(x-3) - (2x²) = -2x²+x-3

Assuming that the dot signifies a multiplication sign and not a composition  sign, we have

(f*g)(x) = f(x) * g(x)

= (x-3) * 2x²

= 2x³ - 6x²

Plugging -2 in, we get

2(-2)³-6(-2)² = -16 -24 = -40

Thus, the range of set X is {2, 3, 7, 11, 17, 19}, with the prime number K being 2.

To find the range of set X, we need to determine the possible values for the unknown prime number K that satisfy the given conditions.

We know that set X consists of prime numbers {3, 11, 7, K, 17, 19}.

The product of all the elements in set X, represented by Y, can be calculated as:

Y = 3 * 11 * 7 * K * 17 * 19

We are given that 11Y is an even number. To make 11Y even, Y must be divisible by 2.

Since Y is the product of all the prime numbers in set X, it must already be an odd number because it includes only odd prime numbers.

For Y to be divisible by 2, we need to include a factor of 2 in the product. However, the set X only consists of prime numbers, and 2 is the only even prime number.

Therefore, the prime number K must be equal to 2 to make the product Y even.

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Answer:

D

Step-by-step explanation:

f(x) =x(x-9)

X(x-9)=0

X2-9x=0

X2-9x+0=0

(X2-9X)

x(x-9)=0

X-9=0

X=9

X+0=0

X=0

Answer:

Measure of angle B is 70 degrees

Step-by-step explanation:

If they are both supplementary, it means that add up to be 180 degrees

Thus;

5x + 25 + 3x + 19 = 180

8x + 44 = 180

8x = 136

x = 136/8

x = 17

Measure of angle B will be;

3(17) + 19

= 51 + 19 = 70 degrees

a) We have the function given by; y = 8x + 3We need to find the arclength of the curve between the limits of x = 2 and x = 8.The arclength L of the curve is given by; L = ∫(2,8) sqrt(1 + f'(x)²)dx Here, f(x) = 8x + 3 Differentiate f(x) with respect to x;f'(x) = 8Now, substitute f'(x) in the above equation; L = ∫(2,8) sqrt(1 + 8²)dx L = ∫(2,8) sqrt(65)dxL = sqrt(65)∫(2,8)dxL = sqrt(65) [x]₂⁸L = sqrt(65) [8 - 2]L = 6sqrt(65)Therefore, the arclength L of this curve is 6sqrt(65).

b) We are given the function y = 8x + 3We need to rotate this curve by 2π radians about the x-axis to get the required surface of revolution. The formula for the surface area of the surface of revolution generated by revolving the curve y = f(x) between x = a and x = b about the x-axis is given by;A = ∫(a,b) 2πf(x) sqrt(1 + f'(x)²)dx Here, f(x) = 8x + 3f'(x) = 8We know that the limits of integration are from x = 2 to x = 8.

Substitute the values in the above equation; A = ∫(2,8) 2π(8x + 3) sqrt(1 + 8²)dxA = 16π ∫(2,8) (8x + 3) sqrt(65)dxA = 16π [∫(2,8) (8x sqrt(65))dx + ∫(2,8) (3 sqrt(65))dx]A = 16π [2/3(8sqrt(65))² - 2/3(2sqrt(65))² + 3sqrt(65)(8 - 2)]A = 16π [2/3(8sqrt(65))² - 2/3(2sqrt(65))² + 3sqrt(65)(6)]A = 192πsqrt(65)

Therefore, the area of the surface of revolution, A that is obtained when the curve is rotated by 2π radians about the x-axis is 192πsqrt(65) square units.

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Answer:

length 10 breadth 4

Step-by-step explanation:

First see the multiples of 40. see how we can get 40 by multiplying two numbers. Then I get 10 into 4 equals 40

Now find the perimeter 10 plus 10 plus 4 plus 4 It equals 28.

Accoding to the calculations , the correct answer is:

A) Depreciation charge 16,000; revaluation surplus £20,000

According to IAS 16 Property, Plant and Equipment, the depreciation charge for an asset should be based on its carrying amount, useful life, and residual value.

In this case, the buildings were purchased for £400,000 (£480,000 - £80,000) and had a useful life of 25 years. Since there is no residual value, the depreciable amount is equal to the initial cost of the buildings (£400,000).

To calculate the annual depreciation charge, we divide the depreciable amount by the useful life:

£400,000 / 25 = £16,000

Therefore, the depreciation charge for the year ended 30 September 2021 is £16,000.

Now, let's calculate the balance on the revaluation surplus as at that date.

The revaluation surplus is the difference between the fair value of the property and its carrying amount. On 1 October 2020, the property was revalued to £500,000, and the carrying amount was £480,000 (£400,000 for buildings + £80,000 for land).

Revaluation surplus = Fair value - Carrying amount

Revaluation surplus = £500,000 - £480,000

Revaluation surplus = £20,000

Therefore, the balance on the revaluation surplus as at 30 September 2021 is £20,000.

Based on the calculations above, the correct answer is:

A) Depreciation charge £16,000; revaluation surplus £20,000

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Answer:

A, D, E

Step-by-step explanation:

GOT IT RIGHT ON EDGE

The true statement about the histogram are

The dataset is given as:

5.5, 6, 7, 10, 7.5, 8, 9.5, 9, 8.5, 8, 7, 7.5, 6, 6.5, 5.5

Using a statistical calculator, we have the following summary:

Mean = 7.43

Median = 7.5

Notice that the median and the mean are approximately equal

i.e. 7.43 ≈ 7.5

When the mean and the median are equal, the histogram would have an approximately normal curve

Also, when the dataset is sorted, we have:

5.5, 5.5, 6, 6, 6.5, 7, 7, 7.5, 7.5, 8, 8, 8.5, 9, 9.5, 10

Notice that there are more data elements between 6 and 9.

Hence, the true statement about the histogram are (a), (d) and (e)

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Aggregate Demand (AD) is a macroeconomic concept that represents the total demand for goods and services in an economy. The X factor in the AD equation represents exports, which are an important part of the economy.

AD is calculated by adding up the individual components of demand, which include consumer spending (C), investment spending (I), government spending (G), and net exports (X-M). The X-M component represents the difference between exports (X) and imports (M).

The X component in the equation represents exports, which are the goods and services produced domestically and sold to foreign countries. Exports are an important part of the economy as they generate income and create jobs. The M component in the equation represents imports, which are the goods and services purchased from foreign countries and consumed domestically. Imports can have a negative impact on the economy as they represent a drain on resources and can lead to a trade deficit. The X factor in the equation is used to represent exports because it is a variable that can change over time. Factors that can affect exports include exchange rates, tariffs, and global demand for certain products. If the exchange rate between two currencies changes, it can make exports more or less expensive for foreign buyers, which can affect the level of exports. Tariffs are taxes on imports, which can make domestic products more competitive in foreign markets.

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Answer:

Correct Answer: Option D

Step-by-step explanation:

9 1/3

hope that helps

Answer: 21

Step-by-step explanation:

24 times 16 equals 384

21 times 90 equals 1890

5 . 3

6 I 3 1 . 8

- 3 0

1 8

- 1 8

0

Therefore, the answer is 5.3

Step-by-step explanation:

please give me brainlest to me please

Answer:Angle B is 44 Degrees

Step-by-step explanation: Angle C intersects the circle at the endpoints of a diameter, it intercepts an arc of 180 degrees

The measure of an inscribed angle is half the measure of its intercepted arc, so we know that the measure of angle C is 90 degrees

The angles of triangle ABC must add up to 180 degrees

m∠A+m∠B+m∠C=180

46+m∠B+90=180

m∠B+136=180

m∠B=44

The measure of Angle B in the given diagram is 44 Degrees

Angle C intersects the circle at the endpoints of a diameter, it intercepts an arc of 180 degrees

The measure of an inscribed angle is half the measure of its intercepted arc, so we know that the measure of angle C is 90 degrees

The angles of triangle ABC must add up to 180 degrees.

The total sum of the angle in triangles is180 degrees.

m∠A+m∠B+m∠C=180

46+m∠B+90=180

m∠B+136=180

m∠B=44

Therefore, The measure of Angle B in the given diagram is 44 Degrees.

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Answer:

the multiplacative inverse of ⅔ is 3/2 because when we multiply them both it returns 1

2/3 x 3/2 = 1

ANSWER:

No solution in real numbers

STEP-BY-STEP EXPLANATION:

We have the following equation:

We solve for x as follows:

Since the absolute value is always positive, the equation loses its meaning since it is equal to -5, which is not possible.

Which means that there is no solution for x in the real numbers.

p(x) = 30 + x

4. p(2) = 30+2 = 32

(f + p)(2) = f(2) + p(2) = 4 + 32 = 36

5. f(1) = 0

p(f(1)) = p(0) = 30

6. f(4) = 11

p(f(4)) = 30 + 11 = 41

7. f(x) = 0 then based on the table x = 1

Answer:

Step-by-step explanation:

p(x)=30x

4.p(2)=f(2)+p(2)=4+32=36

5.f(1)=0

6.f(4)=11

p(f(1))=36+11=41

7.f(x)=o then based on the table x=1