Fast for 100 points
One interior angle of a triangle is 35°, and the other two angles are congruent. Choose the equation that could be used to determine the degree measure of one of the congruent angles.

2x + 35 = 180
2x − 35 = 90
x + 35 = 180
x − 35 = 90

The equation for the parabola with a focus at (-4,3) and a directrix at y=5 in terms of y is y = (-1/8)x² - x/8 + 6.

The vertex of the parabola is the midpoint between the focus and directrix, which is (−4, 4).

Since the directrix is a horizontal line, the parabola will open downward.

Using the distance formula, the distance between a point (x, y) on the parabola and the focus (-4, 3) is equal to the distance between the point and the directrix y = 5.

√((x + 4)² + (y - 3)²) = |y - 5|

Squaring both sides yields:

(x + 4)² + (y - 3)² = (y - 5)²

Expanding the squares and simplifying, we get:

x² + 8x + 16 = -8y + 64

Rearranging terms, we have:

8y = -x² - 8x + 48

Dividing by 8, we get the equation of the parabola in terms of y:

y = (-1/8)x² - x/8 + 6

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The calculated value of the distance between points A and B is 2√29 units.

We can use the distance formula to find the distance between points A and B:

d = √[(x₂ - x₁)² + (y₂ - y₁)²]

where (x₁, y₁) = A = (-2, -10) and (x₂, y₂) = B = (-6, 0).

Substituting these values into the formula, we get:

d = √[(-6 - (-2))² + (0 - (-10))²]

d = √[(-4)² + 10²]

d = √(16 + 100)

d = √116

d = 2√29

Therefore, the distance between points A and B is 2√29 units.

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Based on the given information, Mike's grandmother deposited $6,000 into the savings account.

What is simple interest?

Simple interest is a method of calculating interest on a principal amount, where the interest is calculated only on the original amount of the loan or investment, without taking into account any interest that may have been previously earned. The formula for calculating simple interest is I = P * r * t, where I is the interest earned, P is the principal amount, r is the annual interest rate as a decimal, and t is the time period in years.

We are given that the interest rate is 8% and the interest earned after 10 years is $4,800. So we can write:

4,800 = P * 0.08 * 10

Simplifying the equation, we get:

4,800 = 0.8P

Dividing both sides by 0.8, we get:

P = 6,000

Therefore, Mike's grandmother deposited $6,000 into the savings account.

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Answer:

If three dogs can eat three bones in three days, we can assume that each dog eats one bone in three days. Therefore, in one day, one dog can eat one-third of a bone.

If nine dogs were to eat in the same efficiency, we can multiply the number of dogs by the fraction of bones each can eat per day. So, nine dogs can eat 3 times more than 3 dogs in a day, which is 3 x 3 = 9 bones. In one day, each dog can eat one-third of the bone, and therefore nine dogs will eat 9 x 1/3 = 3 bones.

This means that in nine days, nine dogs can eat 9 x 3 = 27 bones.

Answer:

Step-by-step explanation:

A dilation maintains the shape of a figure but changes its size.

A reduction would mean the new figure will be a smaller version of the original.

An enlargement would mean the new figure will be a bigger version of the original.

This particular question doesn’t include a photo so depending on these definitions, one can easily identify the correct answer.

Answer:

In geometry, a dilation is a transformation that changes the size of a figure while keeping its shape the same. Imagine taking a picture of a shape and then making it bigger or smaller without changing its proportions or angles.

If a dilation makes the figure smaller than the original, we call it a reduction. This means that the new figure is a scaled-down version of the original. Conversely, if a dilation makes the figure larger, we call it an enlargement. In this case, the new figure is a scaled-up version of the original.

So, to summarize, dilations can change the size of a figure while preserving its shape, and we can describe the resulting figure as either a reduction or an enlargement depending on whether it is smaller or larger than the original.

Step-by-step explanation:

Answer:

x∈( -5; +∞)

Step-by-step explanation:

[tex]x > - 5[/tex]

[tex]x∈( - 5;+ ∞)[/tex]

Answer:

The probability of the coin landing heads up on any given flip is 1/2, and the probability of it landing tails up is also 1/2. Therefore, we can use the binomial distribution formula to calculate the probability of getting exactly 27 heads out of 90 flips: P(27 heads) = (90 choose 27) * (1/2)^27 * (1/2)^63 = 1.452 x 10^-9 So the probability of getting exactly 27 heads out of 90 flips is approximately 1.452 x 10^-9.

is would be 50 percent! you're welcome

Mrs. Smith paid R13 450.00 for a couch that originally cost R17 933.33. This means that she received a discount of R4 483.33, which is 25% of the original price.

To find the original price of the couch, we need to first understand what a 25% discount means.

A discount is a reduction in price from the original or regular price of an item. A discount is usually given as a percentage of the original price. For example, a 25% discount means that the price of an item has been reduced by 25% of its original price.

Let's use this information to solve the problem at hand.

Let x be the original price of the couch. The discount given is 25%, which means that the price paid by Mrs. Smith is 75% of the original price. Mathematically, we can write this as:

75% of x = R13 450.00

To solve for x, we need to isolate it on one side of the equation. We can do this by dividing both sides of the equation by 75% or 0.75 (which is the decimal equivalent of 75%).

75% of x / 0.75 = R13 450.00 / 0.75

x = R17 933.33 (rounded to the nearest cent)

Therefore, the original price of the couch was R17 933.33.

In conclusion, Mrs. Smith paid R13 450.00 for a couch that originally cost R17 933.33. This means that she received a discount of R4 483.33, which is 25% of the original price.

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We can start by finding the length of the arc \overset{\LARGE\frown}{TS} using the fact that the length of the arc \overset{\LARGE\frown}{RS} is \frac{4}{3}\pi times the radius of the circle. Since angle RQS is 120 degrees, arc \overset{\LARGE\frown}{TS} is \frac{1}{3} of the circumference of the circle:

arc \overset{\LARGE\frown}{TS} = \frac{1}{3} (2\pi R) = \frac{2}{3}\pi R

Next, we can find the length of the chord TS using the Law of Cosines:

TS^2 = TR^2 + RS^2 - 2(TR)(RS)\cos(\angle TRS)

Since \angle TRS is 120 degrees, we have:

TS^2 = R^2 + (4/3)^2R^2 - 2(R)(4/3)R(-1/2)

Simplifying this expression, we get:

TS^2 = \frac{25}{9}R^2

Taking the square root of both sides, we get:

TS = \frac{5}{3}R

Now we can find the height of the shaded region by drawing the altitude from the center of the circle to chord TS. This altitude bisects chord TS and is also perpendicular to it, so it divides TS into two segments of equal length:

Height = \frac{1}{2}(TS) = \frac{5}{6}R

Finally, we can find the area of the shaded region by subtracting the area of triangle RST from the area of sector RQS:

Area of sector RQS = (120/360)\pi R^2 = \frac{1}{3}\pi R^2

Area of triangle RST = (1/2)(RS)(height) = (1/2)(4/3)R(\frac{5}{6}R) = \frac{5}{9}R^2

Area of shaded region = Area of sector RQS - Area of triangle RST = \frac{1}{3}\pi R^2 - \frac{5}{9}R^2 = \frac{2}{9}\pi R^2

Therefore, the area shaded below is \frac{2}{9}\pi times the square of the radius R of the circle.

As per the given data, in circle QQ, the area shaded below is (1/27)π.

The circumference is the perimeter of a circle or ellipse in geometry. That is, the circumference would be the circle's arc length if it were opened up and straightened out to a line segment.

To find the area shaded below, we need to first find the area of sector RQS and then subtract the area of triangle RQS to get the shaded area.

The length of arc RS is given as 4/3π. Since the circumference of the circle is 2πr, where r is the radius, we have:

2πr = 4/3π

r = 2/3

So, the radius of the circle is 2/3.

Next, we can use the formula for the area of a sector, which is given as:

A = [tex](1/2)r^2\theta[/tex]

where r is the radius of the sector and θ is the central angle in radians.

In this case, θ is 120 degrees or 2/3π radians, so we have:

A(sector RQS) = [tex](1/2)(2/3)^2(2/3\pi)[/tex] = 4/27π

Now, we need to find the area of triangle RQS. To do this, we can use the formula for the area of a triangle, which is given as:

A = (1/2)bh

Where b is the base of the triangle and h is its height.

Since RQ is the base of triangle RQS and is also a radius of the circle, its length is 2/3. To find the height of the triangle, we can draw a perpendicular from point S to line QR and call the point of intersection T.

Since angle RQS is 120 degrees, angle RQT is 30 degrees (since the sum of the angles in a triangle is 180 degrees), and we have:

sin 30 = h/2/3

h = 1/3

So, the area of triangle RQS is:

A(triangle RQS) = (1/2)(2/3)(1/3) = 1/9

Finally, we can find the shaded area by subtracting the area of triangle RQS from the area of sector RQS:

A(shaded) = A(sector RQS) - A(triangle RQS) = (4/27π) - (1/9) = (1/27)π

Therefore, the area shaded below is (1/27)π.

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The nurse is responsible for giving Medication G in a quantity of 30 mL, which is approximately equivalent to 1.014 fluid ounces.

First, we need to convert 0.6 g to mg:

0.6 g = 600 mg

Next, we need to calculate how many mL are needed to deliver 600 mg of Medication G. From the label, we know that there are 100 mg of Medication G in 5 mL, so we can set up a proportion:

100 mg / 5 mL = 600 mg / x mL

Cross-multiplying, we get:

100x = 5 * 600

Simplifying, we get:

x = 30 mL

Finally, we can convert 30 mL to fluid ounces. There are 29.5735 mL in one fluid ounce, so:

30 mL / 29.5735 mL/oz ≈ 1.014 fl oz

Therefore, the nurse should administer 30 mL (or approximately 1.014 fluid ounces) of Medication G.

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The difference between t-distribution T0 and t0 is nothing, They are the same thing option B.

The central limit theorem explains the connection between the original population and the sampling distribution of means. Keep in mind that we must first determine the variance of the original population if we are to determine the variance of the sampling distribution.

A point estimate of the mean may be calculated without knowing the variance of the sampling distribution, but other, more complex estimation methods demand that you either know or estimate the variance of the population.

If you stop and think for a second, you'll see that it seems bizarre to know the population's variance when you don't know the mean. As the population variance and standard deviation must be calculated, it is necessary to know the population mean.

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Answer:

a=671000

Step-by-step explanation:

woah

The formula for the number of internet host computers as an exponential function of t is: n(t) = 35.3 × e^((1/7) × ln(n(7) / 35.3) × t) and the values of a and k in the model are k = (1/7) × ln(n(7) / n(0)) and a = n(0) = 35.3 million

a. To find the values of a and k, we can use the information given in the question. Let n(0) be the number of host computers in July 1998, which is 35.3 million. Let n(7) be the number of host computers in July 2005, which is 352.1 million. We can use these values to solve for a and k.

n(0) = a × e^(k0) = a

n(7) = a × e^(k7)

Dividing the second equation by the first equation, we get:

n(7) / n(0) = e^(k×7)

Taking the natural logarithm of both sides, we get:

ln(n(7) / n(0)) = k×7

Therefore, k = (1/7) × ln(n(7) / n(0)) and a = n(0) = 35.3 million.

Therefore, the formula for the number of internet host computers as an exponential function of t is:

n(t) = 35.3 × e^((1/7) × ln(n(7) / 35.3) × t)

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Answer:

14

Step-by-step explanation:

A = length x width

l = length

w = 3l + 2

A = l(3l + 2) = 56

3l² + 2l - 56 = 0

Now you have a polynomial you can solve by factoring or using the quadratic equation to find the 2 roots of l:

using the quadratic equation with a = 3, b = 2, c = -56

l = 4, -14/3

Disregarding the negative root,

l = 4

Therefore, w = 3(4) + 2 = 14

The mathematical function model for Bailey's income is: Regular earning +overtime pay=total earnings

A relation between a collection of inputs and outputs is known as a function.

A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output.

So, we've said the:

12$ =1hours

initial forty hours a week

Then after a week, 18 dollars per hour.

We must ascertain the function that represents Bailey's income.

Then, the formula for regular earnings:

regular hour × regular rate=regular eaning

40(12)=480$

overtime hours × overtime rate=overtime pay

Regular earning +overtime pay=total earnings

The overtime hours in this case are unknown.

Because of this, we are unable to determine total earnings.

Therefore, the mathematical function model for Bailey's income is: Regular earning +overtime pay=total earnings

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Correct question:
Each week, Bailey earns $12 per hour for the first 40 hours she works, and $18 for each hour of work after 40 hours. Her weekly earnings are a function of the amount of time she works.

Which function models the amount of money that Bailey earns?

Answer:

Step-by-step explanation:

Step 1: Substitute d for 75

|500-50t| - 75 = 0

Step 2: Move the constant to one side

|500-50t| = 75

Step 3: Separate the equation into two possible cases

500−50t=75

500−50t=−75​

Step 4: Solve the equation for t

t = 17/2 = 8.5

t = 23/2 = 11.5

Solution:

D: 8.5 seconds and 11.5 seconds

If your dependent variable is measured on a ratio scale, you should use statistical procedure of parametric test. The correct answer is D).

Parametric tests are statistical tests that assume a normal distribution of data and require interval or ratio scale measurements. Examples of parametric tests include t-tests, ANOVA, and linear regression. Non-parametric tests, on the other hand, do not assume a normal distribution of data and can be used for nominal, ordinal, interval, or ratio scale measurements.

Examples of non-parametric tests include the chi-square test for goodness of fit and the chi-square test for independence. However, these tests are not appropriate for ratio scale measurements, so you should use a parametric test. So, the correct option is D).

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--The given question is incomplete, the complete question is given

"what type of statistical procedure should you use if your dependent variable is measured on a ratio scale? select one:

A) chi-square test for goodness of fit

B) chi-square test for independence

C) non-parametric test

D) parametric test"--

We predict that Dylan will sell 114.79 hot cocoas if the day's high temperature is 25°F on the basis of the line of best fit.

Intercept is the point on the graph where the line crosses the x-axis or the y-axis. This point is calculated by solving the equation of the line for the given axis. It is used to determine the relationship between two variables.

To predict the number of hot cocoas to be sold at 25° Fahrenheit, we need to use the line of best fit equation.

The equation of the line of best fit can be determined by calculating the slope and y-intercept of the line and then using the point-slope form of a line.

The slope of the line can be calculated using the formula

m = (y₂-y₁) / (x₂-x₁)

For this graph, the slope can be calculated as

m = (104-94) / (12-0)

= 10/12

= 0.83

The y-intercept of the line can be calculated using the formula y = mx + b, where m is the slope and b is the y-intercept.

For this graph, the y-intercept can be calculated as

b = 104 - 0.83(12)

= 94.04

Therefore, the equation of the line of best fit is y = 0.83x + 94.04

Substituting the given temperature, 25°F into the equation, we get

y = 0.83(25) + 94.04

= 114.79 hot cocoas

Hence, based on the line of best fit, we predict that Dylan will sell 114.79 hot cocoas if the day's high temperature is 25 degree Fahrenheit.

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Answer:

To find the value of a5, we need to know the formula for the nth term of the sequence. We know that a1 = 2, so we can start by finding the common difference (d) between consecutive terms. an-1 + 5 = a1 + (n-2)d + 5 Simplifying this equation, we get: an-1 = a1 + (n-2)d Substituting a1 = 2, we get: an-1 = 2 + (n-2)d We also know that a5 is the 5th term of the sequence, so n = 5. Substituting n = 5, we get: a4 = 2 + (5-2)d a4 = 2 + 3d We don't have enough information

Finally, using the first term a1 = 2500 and the common ratio r = 0.6, we can formulate the explicit rule for the sequence as follows: a = 2500 × 0.6^(n-1) (n-1)

Equation: A declaration that two expressions with variables or integers are equal. In essence, equations are questions and attempts to systematically identify the solutions to these questions have been the driving forces behind the creation of mathematics.

Given :

We can use the fact that each word is produced by multiplying the previous term by the common ratio r to determine the value of r. Thus:

1500/2500 = 0.6 = r

We can keep adding r to the preceding term to find the next two terms:

900 × 0.6 = 540

540 × 0.6 = 324

540 and 324 are the next two terms as a result.

Finally, using the first term a1 = 2500 and the common ratio r = 0.6, we can formulate the explicit rule for the sequence as follows:

a = a1 × r^(n-1) (n-1)

The clear rule is as follows: a = 2500 × 0.6^(n-1) (n-1).

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a. To test whether the population mean daily number of texts for one age group differs from the population mean daily number of texts for another age group, we should use the following alternative hypothesis:
H1: μ1 ≠ μ2

b. To compute the p-value, we need to perform the following steps:
1. State the null hypothesis: H0: μ1 = μ2
2. Calculate the test statistic:
  t = (sample mean - hypothesized mean difference) / (population standard deviation / √n)
  Assuming the hypothesized mean difference is 0, and plugging in the given values:
  t = (sample mean - 0) / (population standard deviation / √30)
3. Find the p-value using a t-distribution table or calculator, and round to four decimal places.
c. If the p-value is less than the level of significance (α), we reject the null hypothesis and conclude that there is a significant difference in the population mean daily texts between the two age groups.

If the p-value is greater than or equal to α, we do not reject the null hypothesis and cannot conclude that there is a significant difference.
d. For the critical value approach, we compare the test statistic (t) with the critical value (±1.96).

If the test statistic falls in the rejection region (outside of ±1.96), we reject the null hypothesis and conclude that the population mean differs.

If the test statistic falls within the acceptance region (inside ±1.96), we do not reject the null hypothesis and cannot conclude that the population mean differs.

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Answer: (c) 0

Step-by-step explanation:There is no variable x involved, so we can say that this polynomial is of degree 0.

Polynomial as having a constant term of 5 and no other terms involving x.

If p(x)=x^5 then degree of polynomial is 5

degree of polynomial = highest degree of x

Answer:

The correct answer is D. Enough to feel rested.

Answer: We can start by factoring the given expression for the area of the rectangle:

Area = 144x^2 - 81

Area = (12x)^2 - (9)^2

Area = (12x + 9)(12x - 9)

We can see that the area is expressed as the product of two binomials (12x + 9) and (12x - 9), which represent the length and width of the rectangle, respectively. Therefore:

Length = 12x + 9

Width = 12x - 9

Note that we can check that the product of the length and width indeed equals the area:

Length x Width = (12x + 9)(12x - 9) = 144x^2 - 81 = Area

So, the expressions for the dimensions of the rectangle are:

Length = 12x + 9

Width = 12x - 9

Step-by-step explanation:

The discriminant shows that the volume will reach 2750 shares in 24.6 weeks, but will never reach 4000 shares in a week.

What is the volume of a company's stock and will it ever reach certain values using the given equation and discriminant?

To determine if the volume will ever reach a certain value, we need to solve the equation V = 250t - 5t^2 for t and see if there are any real solutions for t that satisfy the condition.

a) For V = 2750, we have:

2750 = 250t - 5t^2

Rearranging and simplifying, we get:

5t^2 - 250t + 2750 = 0

Using the quadratic formula, we can find the solutions for t:

t = (-(-250) ± sqrt((-250)^2 - 4(5)(2750))) / (2(5))

t = (250 ± sqrt(62500 - 55000)) / 10

t = (250 ± sqrt(7500)) / 10

t ≈ 24.6 or t ≈ 5.4

Since one solution is positive and the other is negative, the only solution that makes sense in this context is t ≈ 24.6 weeks. Therefore, the volume will reach 2750 shares in 24.6 weeks.

b) For V = 4000, we have:

4000 = 250t - 5t^2

Rearranging and simplifying, we get:

5t^2 - 250t + 4000 = 0

Using the discriminant, which is b^2 - 4ac in the quadratic formula, we have:

b^2 - 4ac = (-250)^2 - 4(5)(4000) = 2500

Because the discriminant is positive, there are only two possible solutions for t. Therefore, the volume will reach 4000 shares in a week at some point. However, we need to solve the equation to find the exact solutions:

t = (-(-250) ± sqrt((-250)^2 - 4(5)(4000))) / (2(5))

t = (250 ± sqrt(62500 - 80000)) / 10

t = (250 ± sqrt(-17500)) / 10

There are no real solutions for t that satisfy the condition because the square root of a negative number is not a real number. Therefore, the volume will never reach 4000 shares in a week.

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the area of section A, which has side lengths of 7 inches each.

To determine the area, we will use the following terms:

Area = Side length × Side length

Area = 7 inches × 7 inches

7 inches × 7 inches = 49 square inches

So, the area of section A is 49 square inches (OA).

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The value of x is 45° for the Newton bounces a ball off of a wall to Descartes as shown in figure.

An angle that is exactly 90 degrees, or a quarter turn, is called a right angle. It is made up of two lines that are perpendicular to one another or line segments that cross at a point, forming four equal angles.



If we consider the figure below we can find some angles and AD is a Straight line;    (Refer the below figure 2)

⇒ ∠AOB + ∠BOC+ ∠DOC = 180°

⇒ x° + 90° + x° = 180°

⇒ 2x° = 180° - 90°

⇒ x° = 90°/ 2

⇒ x° = 45°

Therefore, the value of x is 45°

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Complete question-

According to the figure, x is 45° when Newton bounces a ball off of a wall and Descartes.

Right angles are angles that are exactly 90 degrees, or a quarter turn. It is composed of two parallel lines or line segments that cross at a place to produce four equal angles. It is referred to as a right angle if the angle formed by two rays exactly equals 90 degrees, or π/2.

If we look at the graphic below, we can see that AD is a straight line and there are certain angles;

∠AOB + ∠BOC+ ∠DOC = 180°

x° + 90° + x° = 180°

2x° = 180° - 90°

x° = 90°/ 2

x° = 45°

Therefore, the value of x is 45°

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The complete question is attached below,

Therefore, the sphere described here cannot hold all of the water from the cylinder.

Diameter is a straight line passing through the center of a circle or a sphere, and connecting two points on its circumference. It is the longest distance between any two points on a circle or a sphere, and it is equal to twice the radius. In other words, if you know the diameter of a circle or a sphere, you can find its radius by dividing the diameter by 2, and vice versa, if you know the radius, you can find the diameter by multiplying the radius by 2.

The volume of the cylinder can be calculated as follows:

Radius of cylinder = Diameter[tex]/2 = 3/2 = 1.5 cm[/tex]

Volume of cylinder[tex]= \pi r^2h = \pi (1.5)^2(8) = 56.55 cm^3[/tex]

To determine if a sphere with a radius of 2 cm can hold all of the water from the cylinder, we can calculate its volume as follows:

Volume of sphere [tex]= 4/3\pi r^3 = 4/3\pi (2)^3 = 33.51 cm^3[/tex]

Since the volume of the cylinder is greater than the volume of the sphere, the sphere cannot hold all of the water from the cylinder. Therefore, the sphere described here cannot hold all of the water from the cylinder.

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The provided arithmetic expression's explicit and recursive formulas are as follows:

Recursive formula = [tex]a_{n+1}=a_{n-7}[/tex]

Explicit formular is Tn = 22 - 7n

An explicit formula can be used to determine the value of any phrase in a sequence. The natural numbers 1, 2, 3, 4, and so on make up the integers. If you have a recursive formula for the sequence and know the value of the (n-1)th term in the series, you can use it to calculate the value of the nth term. While explicit formulae provide the value of a specific term depending on the location, recursive formulas supply the value of a specific phrase based on the preceding term. This is the primary difference among recursive and explicit formulations.

Given:

[tex]a_1[/tex] = 15

[tex]a_2[/tex] = 22 = 15 - 7 = [tex]a_1[/tex] - 7

Recursive formular = [tex]a_{n+1}=a_{n-7}[/tex]

a = 15, d = -7

Fn = a + (n - 1)d = 15 + (n - 1)-7 = 15 - 7n + 7 = 22 - 7n

Explicit formular is Tn = 22 - 7n

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Graph attached below,

To find the length of the hypotenuse of a right triangle, we need to use the Pythagorean Theorem, which states that the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b):

c^2 = a^2 + b^2

In this case, we have two sides with lengths given by the expressions 5x + 7 and 3x. When x = 14, we can substitute this value into the expressions to find the lengths of the sides:

a = 5x + 7 = 5(14) + 7 = 77

b = 3x = 3(14) = 42

Now we can use the Pythagorean Theorem to find the length of the hypotenuse:

c^2 = a^2 + b^2 = 77^2 + 42^2 = 5929 + 1764 = 7693

Taking the square root of both sides, we get:

c = sqrt(7693) ≈ 87.7

Therefore, when x = 14, the length of the hypotenuse of the triangle is approximately 87.7 units. I