Please help me prove this identity

Answer: y = f(x) = a + bx y = f(x) = a + bx y = f(x) =

explanation: The following is the formula for a linear function. y = f(x) = a + bx y = f(x) = a + bx y = f(x) = One independent variable and one dependent variable make up a linear function.

Answer:

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Two news websites have opened their memberships to the public, and their growth rates between Day 10 and Day 20 are compared to determine which website will have more members after 50 days.

To calculate the average rate of change for each website, we need to determine the difference in the number of members between Day 10 and Day 20 and divide it by the number of days in that period. Let's say Website A had 200 members on Day 10 and 500 members on Day 20, while Website B had 300 members on Day 10 and 600 members on Day 20.

For Website A, the rate of change is (500 - 200) / 10 = 30 members per day.

For Website B, the rate of change is (600 - 300) / 10 = 30 members per day.

Both websites have the same average rate of change, indicating that they are growing at the same pace during this period. To predict the number of members after 50 days, we can assume that the average rate of change will remain constant. Thus, after 50 days, Website A would have an estimated 200 + (30 * 50) = 1,700 members, and Website B would have an estimated 300 + (30 * 50) = 1,800 members.

Based on this calculation, Website B is projected to have more members after 50 days. However, it's important to note that this analysis assumes a constant growth rate, which might not necessarily hold true in the long run. Other factors such as website popularity, marketing efforts, and user retention can also influence the final number of members.

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The derivative of the function g(x) = (x² - x + 1\()^1^0\) * (tan(x))³ is g'(x) = 10(x² - x + 1)⁹ * (2x - 1) * (tan(x))³ + 3(x² - x + 1\()^1^0\) * (tan(x))² * sec²(x).

To find the derivative of the given function g(x), we can apply the product rule and the chain rule. Let's break down the function into its constituent parts: f(x) = (x² - x + 1\()^1^0\) and h(x) = (tan(x))³.

Using the product rule, the derivative of g(x) can be calculated as g'(x) = f'(x) * h(x) + f(x) * h'(x).

First, let's find f'(x). We have f(x) = (x² - x + 1\()^1^0\), which is a composite function. Applying the chain rule, f'(x) = 10(x² - x + 1\()^9\) * (2x - 1).

Next, let's determine h'(x). We have h(x) = (tan(x))³. Applying the chain rule, h'(x) = 3(tan(x))² * sec²(x).

Now, we substitute these derivatives back into the product rule formula:

g'(x) = f'(x) * h(x) + f(x) * h'(x)

       = 10(x² - x + 1)² * (2x - 1) * (tan(x))³ + 3(x² - x + 1\()^1^0\)* (tan(x))² * sec²(x).

In summary, the derivative of the function g(x) = (x² - x + 1\()^1^0\) * (tan(x))³ is g'(x) = 10(x² - x + 1)⁹  * (2x - 1) * (tan(x))³ + 3(x² - x + 1\()^1^0\) * (tan(x))² * sec²(x).

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Step-by-step explanation:

8) 125=x+90° (exterior angle= sum of two opposite interior angle)

x= 35°

9) y=80° ( vertically opposite angle)

x= 180-50-80= 50°.

hope this helps you.

Answer: 55cm + X*4cm < Y.

Step-by-step explanation:

The initial height of the tree is 55cm

The tree will grow 4cm per month, for X months.

then the height of the tree is the initial height, plus X times 4cm

H = 55cm + X*4cm

If Y is the maximum height that this tree can grow, then we can write the inequality as:

H < Y.

55cm + X*4cm < Y.

The future value P of the investment is approximately $276,442.

To find the future value P of the amount Po invested for a time period t at an interest rate k, compounded continuously, we can use the formula:

P = Po * e^(kt)

Where:

P = future value

Po = initial investment amount

k = interest rate (as a decimal)

t = time period

Given:

Po = $200,000

t = 9 years

k = 3.6% = 0.036 (as a decimal)

Substituting these values into the formula, we have:

P = $200,000 * e^(0.036 * 9)

Using a calculator or computer software, we can evaluate the exponential term:

P ≈ $200,000 * e^(0.324)

P ≈ $200,000 * 1.382209

P ≈ $276,441.80

Therefore, the future value P of the investment is approximately $276,442.

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The correlation coefficient between the student's height and the distance they were able to jump is -1.13.

To compute the correlation coefficient (r) between the person's height and the distance they were able to jump, we need to use the given formula:

\(r = \sum (xi - \bar x)(yi -\bar y) / \sqrt{(\sum (xi - \bar x)^2 * \sum (yi -\bar y)^2)\)

Where:

In our case,

\(\bar x\) = 64.44

\(\bar y = 6.06\)

Square the differences and sum them:

\(\sum ((xi -\bar x)^2) =307.84\\\\\sum ((yi -\bar y )^2) = 2.7224\)

Calculate the correlation coefficient using the formula:

\(r = -32.63 / \sqrt{(307.84 * 2.7224)}\\\\r = -32.63 / \sqrt{838.74158}\\\\\r = -32.63 / 28.96\\\\r = -1.128\)

Therefore, the correlation coefficient (r) for the linear fit between height and jump distance is approximately -1.13.

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Answer: I got 13x^2+4x+7, I hope this helps

The students who has the method that is most representative of the school’s population is Amir.

Population refers to the group of people being studied in an experiment or the group from which a sample is drawn.

Amir has the method that is most representative of the school’s population because the method includes all students in the school studying different subjects but picked at random (every tenth students)

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Answer:

Height of the tree is 78.11 feet.

Step-by-step explanation:

By applying the tangent rule in the right triangle formed,

Since, tanθ = \(\frac{\text{Opposite side}}{\text{Adjacent side}}\)

tan(32)° = \(\frac{h}{125}\)

h = 125(tan32°)

h = 125(0.62487)

h = 78.109

  ≈ 78.11 ft

Height of the tree will be 78.11 feet.

Step-by-step explanation:

5x + 2 = -28

5x = -28 - 2

5x = -30

x = -6.

Answer:

x= -6

Step-by-step explanation:

The restriction on the variable is that x ≠ -1. If x = 1, this will make the denominator 0 and form the indeterminate form, which is not possible to solve.

A two-function expression where limit cannot be inferred purely as from limits of a individual functions is said to have an indeterminate form.

The given equation is:

= 4(x + 9)/ (x + 1)

If x = -1

= 4(-1 + 9)/ (-1 + 1)

= 32/ 0

= ∞

Thus,  If x = 1, this will make the denominator 0 and form the indeterminate form, which is not possible to solve.

So, the restriction on variable is that x ≠ -1.

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Using the t-distribution, as we have the standard deviation for the sample, it is found that the test statistic is given by:

A. -4.47

At the null hypothesis, it is tested if they spend 7 hours a week answering their email, that is:

H₀: µ = 7

At the alternative hypothesis, it is tested if they spend less than 7 hours, that is:

H₁:  µ < 7

The test statistic is given by:

t = x -  µ/s/√n

The parameters are:

x is the sample mean.

µ is the value tested at the null hypothesis.

s is the standard deviation of the sample.

n is the sample size.

In this problem, the parameters are given as follows:

x = 6.02 ,  µ = 7, s =7.8, n=1264

Hence the test statistic is:

t =  x -  µ/s/√n

t = 6.02-7/7.8/√1264

t = -4.47

Thus the test elastic is -4.47.

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Answer:

2,359,000,000

Step-by-step explanation:

Answer:

2,359,000,000 would be the standard form

Step-by-step explanation:

The statement that shows equivalent measurements is "52 meters = 520 decimeters." Option C.

To determine the equivalent measurements, we need to understand the relationship between different metric units.

In the metric system, each unit is related to others by factors of 10, where prefixes indicate the magnitude. For example, "deci-" represents one-tenth (1/10), "centi-" represents one-hundredth (1/100), and "kilo-" represents one thousand (1,000).

Let's analyze each statement:

5.2 meters = 0.52 centimeters: This statement is incorrect. One meter is equal to 100 centimeters, so 5.2 meters would be equal to 520 centimeters, not 0.52 centimeters.

5.2 meters = 52 decameters: This statement is incorrect. "Deca-" represents ten, so 52 decameters would be equal to 520 meters, not 5.2 meters.

52 meters = 520 decimeters: This statement is correct. "Deci-" represents one-tenth, so 520 decimeters is equal to 52 meters.

5.2 meters = 5,200 kilometers: This statement is incorrect. "Kilo-" represents one thousand, so 5.2 kilometers would be equal to 5,200 meters, not 5.2 meters.

Based on the analysis, the statement "52 meters = 520 decimeters" shows equivalent measurements. So Option C is correct.

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Note the correct and the complete question is

Select the statement that shows equivalent measurements.

A.) 5.2 meters = 0.52 centimeters

B.) 5.2 meters = 52 decameters

C.) 52 meters = 520 decimeters

D.) 5.2 meters = 5,200 kilometers

The circumference of a circle with a diameter of 21 centimeters can be calculated using the formula C = πd, where C represents the circumference and d represents the diameter. Using the value of π as 22/7, the correct answer is 66 centimeters.

The formula for the circumference of a circle is C = πd, where C is the circumference and d is the diameter. In this case, the diameter is given as 21 centimeters. To calculate the circumference, we can substitute the value of π as 22/7 and the diameter as 21 into the formula:
C = (22/7) * 21
C = 22 * 3
C = 66
Therefore, the circumference of the circle is 66 centimeters. Among the given options, the correct answer is 66 centimeters, which represents the distance around the circle.

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The statement is true for any sets A and B.

The statement "A = A - B" is true if and only if every element of A is not an element of B.

The set A - B represents the elements that are in A but not in B. Therefore, A = A - B means that A contains no elements that are in B. In other words, A and B have no elements in common. This is equivalent to saying that every element of A is not an element of B.

Now, since A and B have no elements in common, it follows that B is a subset of A (i.e., B ⊂ A). This is because if an element is in B, it cannot be in A (as A contains no elements of B), and if an element is not in B, it must be in A. Similarly, since A contains no elements of B, it follows that 0 ≤ B ⊆ A. Moreover, since every element of A is not an element of B, it follows that 0 ≤ A ⊆ Bᶜ (the complement of B). Finally, since every set is a subset of itself, it follows that 0 ≤ ⊆ A.

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To calculate the weighted mean of student 40's exam scores with exam 1 weighted twice that of the other 3 exams, you will need to use the weights provided in the spreadsheet. First, locate student 40's scores for all four exams on the second sheet of the spreadsheet. Then, apply the weights provided to each exam score.

To weight exam 1 twice that of the other 3 exams, you will need to multiply the exam 1 score by 2 and leave the other three scores as they are. Once you have adjusted the weights accordingly, you can calculate the weighted mean using the formula:

weighted mean = (weight1 * score1 + weight2 * score2 + weight3 * score3 + weight4 * score4) / (weight1 + weight2 + weight3 + weight4)

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.

Answer:

If angle A and angle B are supplementary then angle A is 79*

Step-by-step explanation:

180 - 121 = 79

Answer:

(x - 10)² + (y + 4)² = 121

Step-by-step explanation:

the equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k ) are the coordinates of the centre and r is the radius

here (h, k ) = (10, - 4 ) and r = 11 , then

(x - 10)² + (y - (- 4) )² = 11² , that is

(x - 10)² + (y + 4)² = 121

Answer: y=3x+1

Step-by-step explanation:

3x+y-1=0

3x+y-1+1=0+1

3x+y=1

3x-3x+y=1-3x

y=3x-1

When lines are parallel they have the same slope.

y=3x+b

4=3(1)+b

4=3+b

4-3=3-3+b

1=b

The formula is y=3x+1

The  values of x will f(x) > 0 for x < 0, and f(x) < 0 for -6 < x < 0 and x > -6.

To determine the values of x for which f(x) > 0, we need to find the intervals where the function is positive. Let's analyze the function f(x) = x*-x³-6x².

First, let's factor out an x from the expression to simplify it: f(x) = x(-x² - 6x).

Now, we can observe that if x = 0, the entire expression becomes 0, so f(x) = 0.

Next, we analyze the signs of the factors:

1. For x < 0, both x and (-x² - 6x) are negative, resulting in a positive product. Hence, f(x) > 0 in this range.

2. For -6 < x < 0, x is negative, but (-x² - 6x) is positive, resulting in a negative product. Therefore, f(x) < 0 in this range.

3. For x > -6, both x and (-x² - 6x) are positive, resulting in a negative product. Thus, f(x) < 0 in this range.  

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If 100 students participate in the fundraiser, each student needs to raise $137.50.If 25 students participate in the fundraiser, each student needs to raise amount $550.

Amount = (Total Amount Needed) ÷ (Number of Students)

For 60 students:

Amount = $275 ÷ 60 = $4.58

For 75 students:

Amount = $275 ÷ 75 = $3.67

For 40 students:

Amount = $275 ÷ 40 = $6.88

To solve this problem, we need to use a simple equation: Amount = (Total Amount Needed) ÷ (Number of Students). We can then plug in the given information to calculate the amount each student needs to raise. For example, if 50 students participate in the fundraiser, we can calculate that each student needs to raise $275 ÷ 50 = $5.50. We can then use this equation to calculate the amount that each student needs to raise if there are different numbers of students participating in the fundraiser. For example, if there are 100 students participating in the fundraiser, each student needs to raise $275 ÷ 100 = $2.75. Similarly, if there are 25 students participating in the fundraiser, each student needs to raise $275 ÷ 25 = $11.00.

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Answer:

b

Step-by-step explanation:

Using trigonometric ratio and the angle of elevation given, the height of the antenna is 4.5m

Using trigonometric ratio;

tan(41°) = height of building / 16 meters

height of building = 16 meters * tan(41°)

height of building =13.91 m

We also know that the angle of elevation from Kayden's eyes to the top of the antenna is 49°. This means that the tangent of 49° is equal to the height of the antenna plus the height of the building divided by 16 meters. We can use this to find the height of the antenna:

tan(49°) = (height of antenna + height of building) / 16 meters

height of antenna + height of building = 16 meters * tan(49°)

`

height of antenna + 13.91 meters = 16 meters * tan(49°)

height of antenna = 16 meters * tan(49°) - 13.91 meters

height of antenna = 4.5 meters

The height of the antenna = 5m

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Answer:

it alrdy is

Step-by-step explanation:

Answer:

4/5 is simplest form

Step-by-step explanation:

hope this helps

Answer:

Step-by-step explanation: if 5/2:2/5 then 4/5 of a pint= 10/2 and you now only need 1/5 of a pint so you have to divid 5/2 by 2. that will give you 1.25 and 1.25 as a fraction is 5/4. now you need to change the fraction 10/2 so that you can add them. Equation for that is 10/2 times 2/2 that gives you 20/4 and 20/4+ 5/4=25/4 or 6 1/4(six and one fourth) of a cup