the term to term rule of a sequence is divide by 2

Answer:

106

Step-by-step explanation:

For the expression \(x^64 + ax^b + 25\) to be a perfect square for all integer values of x, b must be 64, and a must be a perfect square, written as a = \(y^2.\)

To determine the values of a and b such that the expression\(x^64 + ax^b\) + 25 is a perfect square for all integer values of x, we need to analyze the properties of perfect squares.

A perfect square is an expression that can be written as the square of another expression. In this case, we want the given expression to be in the form of\((x^n)^2,\) where n is an even integer.

Let's examine the given expression: \(x^64 + ax^b\) + 25

For it to be a perfect square, the quadratic term \(ax^b\)must have the same exponent as the leading term\(x^6^4.\) This means b must be equal to 64.

So we have:\(x^64 + ax^64 + 25\)

Now, we can rewrite this as:\((x^32)^2 + 2(x^32) (\sqrt{a}) + (\sqrt{25})^2\)

By comparing this with the standard form of a perfect square, (\(x^n +\sqrt{k} )^2\), we can deduce that √a must be equal to x^32 and \(\sqrt{25}\) must be equal to \(\sqrt{k.}\)

Therefore, we have: \(\sqrt{a} = x^3^2\)and\(\sqrt{25} = \sqrt{k}\)

From the second equation, we know that k = 25.

Now, substituting the value of k back into the first equation, we have: \(\sqrt{a} = x^3^2\)

To satisfy this equation for all integer values of x, a must be a perfect square. Therefore, we can express a as a =\(y^2\), where y is an integer.

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we have that

total=226

neutral or in favor of the restructuring=64+88=152

therefore

P=152/226

simplify

Answer:

Step-by-step explanation:

At least 9 means more than 9 and includes 9

x ≥ 9     and    [9,  +∞)

At most 9 means numbers less than 9

x≤9       and  (-∞, 9]

more than 9 means bigger than 9 but not including 9

x > 9     and    (9,  +∞)

fewer than 9 means less than 9 but not including 9

x<9       and  (-∞, 9)

strictly between 7 and 9   means between 7 and 9 but not including

7<x<9      and    (7,9)       (This is the only one I'm unsure of.  Strictly, not sure if it includes or doesn't include, usually it just says include or doesn't include)

between 7 and 7 inclusive.   means it's just =7  There's no boundaries

x=7

no more than 7 means less than 7 and includes 7

x ≤ 7   and   (-∞, 7]

Answer:

u got the right answer in the picture

The linear rule for the sequence is f(n) = 7/20 + 3/20(n - 1)

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

35/100,5/10,65/100

In the above sequence, we can see that 15/100 is added to the previous term to get the new term

This means that

First term, a = 35/100

Common difference, d = 15/100

The nth term is then represented as

f(n) = a + (n - 1) * d

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

f(n) = 35/100 + 15/100(n - 1)

So, we have

f(n) = 7/20 + 3/20(n - 1)

Hence, the explicit rule is f(n) = 7/20 + 3/20(n - 1)

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Answer:

y = 1

Step-by-step explanation:

Given:

Fixed cost = $3,450

Variable cost = $12 per basketball

Selling price = $25 per basketball

Number of basketball sold = 300

To find:

Whether Rebotar did break even.

Solution:

According to the question,

Cost of 1 basketball = $12

Cost of 300 basketball = $12×300

We know that,

Total cost = Fixed cost + Variable cost

\(TC=3450+12(300)\)

\(TC=3450+3600\)

\(TC=7050\)

So, the total cost is $7050.

Now,

Selling price of a basketball = $25

Selling price of 300 basketball = $25×300

Total revenue is

\(TR=25\times 300\)

\(TR=7500\)

So, total revenue is $7500.

At break even situation the profit is zero. In other words, the total revenue is equal to total cost.

Since, \(TC\neq TR\), therefore, Rebotar did not break even.

A common denominator is a shared multiple of the denominators of the fractions involved when adding or subtracting fractions. It enables fraction comparison and addition/subtraction.

Simplification is the process of reducing a fraction to its simplest form by dividing the numerator and denominator by their greatest common divisor. This is done to represent fractions in the simplest terms viable.

Conversion: The process of transferring a fraction from one form to another while retaining its equal value is known as conversion. Finding a common denominator or expressing a fraction in terms of a specified unit or fraction may be required.

Fraction Addition/Subtraction: When adding or subtracting fractions, a common denominator is required. This entails determining a common multiple of

To rewrite the expression 3 + 1/5 + 2/3 using fifteenths as the common denominator, we need to find a common denominator for 5 and 3, which is 15 (since 5 and 3 are both factors of 15).

First, let's convert the fractions 1/5 and 2/3 to fifteenths:

\((\frac{1}{5})(\frac{3}{3}) = \frac{3}{15}\)

\((\frac{2}{3})(\frac{5}{5}) = \frac{10}{15}\)

Now we can rewrite the expression using the common denominator:

\(3 + \frac{3}{15}+\frac{10}{15}\)

Matt takes 157 seconds to run 1 lap.

Ratio basically compares quantities, that means it shows value of one quantity with respect to other quantity.

If a and b are two values, their ratio will be a:b,

Given that,

Time taken to run 8 laps = 1,256 seconds

To find time taken to run 1 lap, use the ratio property,

8 laps = 1256 seconds

1 lap = 1256/8 seconds

1 lap =  157 seconds

Matt takes 157 seconds to run 1 lap.

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Answer:

Natasha can wrap 128 gifts in total

Step-by-step explanation:

Let us use the ratio method to solve the question

∵ Natasha has 240 square feet of wrapping paper

∵ Natasha can wrap 8 gifts with 15 square feet

→ By using the ratio method

→  Gift  :  square feet

→   8     :  15

→   x      :  240

→ By using cross multiplication

∵ x × 15 = 8 × 240

∴ 15x = 1920

→ Divide both sides by 15

∵ x = 128

∵ x represents the number of gifts

∴ Natasha can wrap 128 gifts in total

The measure of the length EF of the triangle is; 21

We are given the the triangle BCD and we are told that;

E is the midpoint of BD.

F is the midpoint of CD

Now, since we have those midpoints, it means that by the concept of similar triangles, that;

DF/DC = EF/BC

Since F is the midpoint of DC, then it means that;

2DF = DC

We are given;

EF = 43 - 4x, and BC = 32 - 2x

Thus, we now have;

DF/(2DF) = (43 - 4x)/(32 - 2x)

1/2 = (43 - 4x)/(32 - 2x)

Cross multiply to get;

32 - 2x = 43 - 4x

4x - 2x = 43 - 32

2x = 11

x = 11/2

x = 5.5

Thus;

EF = 43 - 4(5.5)

EF = 43 - 22

EF = 21

Thus, we conclude that the side length EF is 21.

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Answer:

12.48 is the answer

Step-by-step explanation:

have a great day

Answer:

12.48

Step-by-step explanation:

104×12=1248

1248 count to decimals

12.48

The required solution is 5+39e.

What is arithmetic?

The branch of mathematics dealing with the properties and manipulation of numbers. a science that deals with the addition, subtraction, multiplication, and division of numbers. Fractions, decimals, percentages, fractions, square root, exponents, and other arithmetic operations are used to achieve mathematical simplifications

Given :

Write down the question as an algebra problem, with the unknown as X

The unknown is a number plus 5, so we write it as (X+5). The product is four times (X+5), so we write it as 39(X+5). Set it equal to e, as per the question, 5+39e

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Answer:

The area of the shaded region between \( \\ z = 1.23\) and \( \\ z = 0.86\) is \( \\ P(0.86 < z < 1.23) = 0.08554\) or 8.554%.

Step-by-step explanation:

To solve this question, we need to find the corresponding probabilities for the standardized values (or z-scores) z = 1.23 and z = 0.86, and then subtract both to obtain the area of the shaded region between these two z-scores.

We need to having into account that a z-score is given by the following formula:

\( \\ z = \frac{x - \mu}{\sigma}\)

Where

A z-score indicates the distance of x from the mean in standard deviations units, where a positive value "tell us" that x is above \( \\ \mu\), and conversely, a negative that x is below \( \\ \mu\).

The standard normal distribution is a normal distribution with \( \\ \mu = 0\) and \( \\ \sigma = 1\), and has probabilities for standardized values obtained using [1]. All these probabilities are tabulated in the standard normal table (available in any Statistical book or on the Internet).

Using the cumulative standard normal table, for \( \\ z = 1.23\), the corresponding cumulative probability is:

\( \\ P(z<1.23) = 0.89065\)

The steps are as follows:

Following the same procedure, the cumulative probability for \( \\ z = 0.86\) is:

\( \\ P(z<0.86) = 0.80511\)

Subtracting both probabilities (because we need to know the area between these two values) we finally obtain the corresponding area between them (two z-scores):

\( \\ P(0.86 < z < 1.23) = 0.89065 - 0.80511\)

\( \\ P(0.86 < z < 1.23) = 0.08554\)

Therefore, the area of the shaded region between \( \\ z = 1.23\) and \( \\ z = 0.86\) is \( \\ P(0.86 < z < 1.23) = 0.08554\) or 8.554%.

We can see this resulting area (red shaded area) in the graph below for a standard normal distribution, \( \\ N(0, 1)\), and  \( \\ z = 0.86\) and \( \\ z = 1.23\).

A. The solution of  linear equation is (x, y) = (-3, 8).

B. The solution is (x, y) = (3/4, -1).

C. The solution is (x, y) = (-31/8, 3/8).

D. The solution is (x, y) = (55/7, -117/14).

A. 3x - y = -11 --- (1)

-x + y = 5 --- (2)

From equation (2), we can write y = x + 5, and substitute it in equation (1):

3x - (x + 5) = -11

2x = -6

x = -3

Substituting x in equation (2):

-y = -8

y = 8

Therefore, the solution of the system is (x, y) = (-3, 8).

To check the solution, we substitute the values of x and y in the original equations:

3(-3) - 8 = -11 (True)

-(-3) + 8 = 5 (True)

So, the solution is correct.

B. -2y + 3 = 4x + 2 --- (1)

6x + 4y = 1 --- (2)

From equation (1), we can write 4x + 2 = -2y + 3, and substitute it in equation (2):

6x + 4y = 1

6x - 4y = 8 (rearranging)

12x = 9

x = 3/4

Substituting x in equation (1):

-2y + 3 = 4(3/4) + 2

-2y + 3 = 5

-2y = 2

y = -1

Therefore, the solution of the system is (x, y) = (3/4, -1).

To check the solution, we substitute the values of x and y in the original equations:

-2(-1) + 3 = 4(3/4) + 2 (True)

6(3/4) + 4(-1) = 1 (True)

So, the solution is correct.

C. 32y - x = -25 --- (1)

5x = 100 + x - 8y --- (2)

From equation (2), we can write 4x = 100 - 8y, and substitute it in equation (1):

32y - x = -25

32y - (100 - 8y) = -25

40y = 75

y = 3/8

Substituting y in equation (1):

32(3/8) - x = -25

x = -31/8.

Therefore, the solution of the system is (x, y) = (-31/8, 3/8).

To check the solution, we substitute the values of x and y in the original equations:

32(3/8) - (-31/8) = -25 (True)

5(-31/8) = 100 + (-31/8) - 8(3/8) (True)

So, the solution is correct.

D. To solve the system of equations:

2y + 3x = 6 --- (1)

4x + 5y + 20 = 0 --- (2)

We can rearrange equation (2) to isolate one of the variables:

4x + 5y = -20 (subtracting 20 from both sides)

5y = -4x - 20 (subtracting 4x from both sides)

y = (-4/5)x - 4 (dividing both sides by 5)

Substituting this value of y in equation (1):

2((-4/5)x - 4) + 3x = 6

(-8/5)x - 8 + 3x = 6

(-8/5)x + 3x = 14

(-8/5 + 3)x = 14

(-8/5 + 15/5)x = 14

(7/5)x = 14

x = 10

Substituting this value of x in the equation for y:

y = (-4/5)(10) - 4

y = -12.

Therefore, the solution of the system is (x, y) = (10, -12).

To check the solution, we substitute the values of x and y in the original equations:

2(-12) + 3(10) = 6 (True)

4(10) + 5(-12) + 20 = 0 (True)

So, the solution is correct.

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Answer:

Step-by-step explanation:

-3≤ x = graph 6

-3 > x = graph 3

x≥ 3 = graph 2

x ≤ 3 = graph 4

3 > x = graph 1

x > 3 = graph 5

the closed circles means greater/less than or equal to

the open circle means greater/less than

the direction of the arrow tells you if the number is greater than x or less than x

Consider the standard form of each of the following options given, and note the hyperbola properties through that derivation -

\(Standard Form - \frac{\left(x-5\right)^2}{\left(\sqrt{7}\right)^2}-\frac{\left(y-\left(-5\right)\right)^2}{3^2}=1,\\Properties - \left(h,\:k\right)=\left(5,\:-5\right),\:a=\sqrt{7},\:b=3\\\)

Similarly we can note the properties of each of the other hyperbolas. They are all similar to one another, but only option C is correct. Almost all options are present with a conjugate axis of length 6, but only option c is broad enough to include the point ( 1, - 5 ) and ( 9, - 5 ) in a given radius.

Solution = Option C!

Answer:

I think the ans is option 'a'

Final Answer:

Corresponding Angles Theorum; ∠AGF and ∠EHD are congruent

Answer:

x = 8

Step-by-step explanation:

3/4x + 5 = 11

3/4x = 6

12/4 = 3x = 24

3x = 24

x = 8

Answer:

x = 8

Step-by-step explanation:

\(\frac{3}{4}\) x + 5 = 11

\(\frac{3}{4}\) x = 6

x = \(\frac{4}{3}\) (6)

x = 8

-2

Step-by-step explanation:

The difference between second term and first term or third term and second term in an AP series is called common difference.

Hence, in the given sequence −2,−4,−6,......, the common difference is −4−(−2)=

The percent error of the estimate is -2.14%

In this question, the figures are given as

Estimate = 5.5 cm

Actual = 5.62 cm

The percentage of the error is then calculated using the following equation

Error percentage = (Estimate - Actual)/Actual * 100%

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

Error percentage = (5.5 - 5.62)/5.62 * 100%

Evaluate

Error percentage = -2.14%

Hence, the error percentage is -2.14%

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Answer: The answer is 4.63✨

Step-by-step explanation: You have to round to 4.625 to the nearest hundredth consider the thousandths’ value of 4.625, which is 5 and equal or more than 5. Therefore, the hundredths value of 4.625 increases by 1 to 3.

4.625 rounded to the nearest hundredth = 4.63

Answer:

25

Step-by-step explanation:

10÷1/4=25

Answer:

Javier reads 90 pages in 2.25 hours.

Step-by-step explanation:

# of pages read every hour: 40 pages.

# of hours in total: 2.25 hours.

Multiply the number of pages he can reads every hour (40 pages) by the number of hours in total.

40 x 2.25 = ?

The Product is your answer;

? = 90

Hope this helps :)

Solving a system of equations we can see that:

We can use the variables:

x = mass of the 60% solution.

y = mass of the 85% solution.

We can write a system of equations.

x + y = 70

x*0.6 + y*0.85 = 70*0.8

We can isolate x on the first equation to get:

x = 70 - y

Replace that in the other one:

(70 - y)*0.6 + y*0.85 = 70*0.8

Now we can solve this for y.

y*0.25 = 70*0.8 - 70*0.6

y = 14/0.25 = 56

Then he needs to use 56 ounces of the 85% solution, and 14 ounces of the 60% solution.

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\( \large \bf \implies{ {x}^{2} + 3x - 10}\)

\((x + 5)(x - 2)\)

Step 1) : Using the identity

\( \bf \longrightarrow{(x+a)(x+b) = x² + (a+b)x + ab}\)

Step 2) : Simplify it with using the identity told earlier in step 1) .

\( \bf \longrightarrow(x + 5)(x - 2) \\ \\ \bf \longrightarrow{x}^{2} + (5 + ( - 2))x + (5)( - 2) \\ \\\bf \longrightarrow {x}^{2} + (5 - 2)x + ( - 10) \\ \\\bf \longrightarrow {x}^{2} +3x - 10\)

Step 3) : We have got the answer in step 2) .

\( \large\bf \longrightarrow { {x}^{2} + 3x - 10}\)