BC is tangent to circle A at B and to circle D at C
AB=9, BC=26, DC=8
Find AD

The value of the limit of the rational function evaluated x = - 5 is equal to - 6.

In this problem we find the limit of rational function evaluated at a given value. According to the statement, there is apparently a discontinuity at x = 5. The expression can be simplified by algebra properties:

[tex]\lim_{x \to - 5} \frac{x^{2} + 4 \cdot x - 5}{x + 5}[/tex]

[tex]\lim_{x \to -5} \frac{(x + 5)\cdot (x - 1)}{(x + 5)}[/tex]

[tex]\lim_{x \to - 5} (x - 1)[/tex]

Then, we can complete the table by means of the following expression:

f(x) = x - 1

x = - 5.01

f(- 5.01) = - 5.01 - 1

f(- 5.01) = - 6.01

x = - 5.001

f(- 5.001) = - 5.001 - 1

f(- 5.001) = - 6.001

x = - 5.0001

f(- 5.0001) = - 5.0001 - 1

f(- 5.0001) = - 6.0001

x = - 5

f(- 5) = - 5 - 1

f(- 5) = - 6

x = - 4.9999

f(- 4.9999) = - 4.9999 - 1

f(- 4.9999) = - 5.9999

x = - 4.999

f(- 4.999) = - 4.999 - 1

f(- 4.999) = - 5.999

x = - 4.99

f(- 4.99) = - 4.99 - 1

f(- 4.99) = - 5.99

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The amount of natural oil needed to make 869 liters of Petrolyn oil is given as follows:

1520.75 liters.

The necessary amount of natural oil is obtained applying the proportions in the context of this problem.

Considering the ratio given in the problem, a rule of three is established, as follows:

7 liters of natural oil - 4 liters of Petrolyn oil.

n liters of natural oil - 869 liters of Petrolyn oil.

Applying cross multiplication, the desired amount is obtained as follows:

4n = 7 x 869

n = 7 x 869/4

n = 1520.75 liters.

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Answer:

The difference in height is 8cm

Step-by-step explanation:

Volume of a cylinder=hπr²

When the bottle is full 5652:

5652=hπr²

5652=h*3.14*7.5²

5652=h*176.625

5652/176.625=h

Height=32cm

When the bottle is full by 4239:

4239=hπr²

4239=h*3.14*7.5²

4239=h*176.625

4239/176.625=h

Height=24cm

Difference in height:

32-24=8

The difference in height is 8cm

The discount on each orange is 81.3%

The discount equals the difference between the price paid for and it's par value. Discount is a kind of reduction or deduction in the cost price of a product.

A sales discount is a reduced price offered by a business on a product or service.

The total price for the oranges is;

0.75 × 7 = $5.25

She paid $ 4.30 for the oranges, this means that the discount = 5.25-4.30 = $0.95

Therefore the percentage discount on all the oranges = 0.95/5.25 × 100

= 18.1%

by discount each orange = 4.30/7 =$ 0.61

Therefore the discount on each orange = 0.61/0.75 ×100 = 81.3 %

Therefore the discount on each orange is 81.3%

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Answer:

10 minutes

Step-by-step explanation:

1/4 in 2 minutes

1 1/4 = 1/4 x 5

2 x 5 = 10

(That's REALLY good honestly)

Answer:

Step-by-step explanation:

A) In a geometric sequence, t_(1)=625 and the common ratio is r=(1)/(5). For what value of n is t_(n)=(1)/(25)?

Step 1: Write the formula for the nth term

The formula for the nth term of a geometric sequence is t_n = t_1 * r^(n-1), where t_1 is the first term and r is the common ratio.

Step 2: Substitute the given values into the formula

t_n = 625 * (1/5)^(n-1)

Step 3: Solve for n when t_n = (1/25)

(1/25) = 625 * (1/5)^(n-1)

(1/25) / 625 = (1/5)^(n-1)

(1/5)^(n-1) = (1/25) / 625

(n-1) = log base (1/5) of ((1/25) / 625)

Step 4: Solve for n

n = 1 + log base (1/5) of ((1/25) / 625)

The value of n is the number of terms that have passed when t_n = (1/25).

B) (2)/(5),(3)/(6),(4)/(7),(5)/(8),...

Step 1: Determine the type of sequence

A sequence is an arithmetic sequence if the difference between any two consecutive terms is constant. Since this sequence does not have a constant difference, it is not an arithmetic sequence.

A sequence is a geometric sequence if the ratio between any two consecutive terms is constant. We can see that the ratio between any two consecutive terms is constant, so this sequence is a geometric sequence.

Step 2: Find the common ratio

To find the common ratio, we can divide any two consecutive terms. For example, the common ratio is (3/6) / (2/5) = (3/2) / (6/5) = 5/6.

Step 3: Write the formula for the nth term

The formula for the nth term of a geometric sequence is t_n = t_1 * r^(n-1), where t_1 is the first term and r is the common ratio.

Step 4: Substitute the given values into the formula

To use this formula, we need to know the value of t_1. We are given t_1 = (2/5), so:

t_n = (2/5) * (5/6)^(n-1)

This is the formula for the nth term of the sequence (2)/(5),(3)/(6),(4)/(7),(5)/(8),...

Someone who is not a stakeholder in this business does not have any interest or concern in Biketown's decision to purchase a new automated machine.

In this scenario, stakeholders for Biketown's decision to purchase are Customers who appreciate the workmanship of Biketown's bicycles, Employees who are involved in the assembly process, Shareholders who have invested in the company, Suppliers who provide materials or components for the bicycles.

Local community members who may be impacted by the company's operations or decisions. An individual who has no knowledge of or interaction with Biketown or the bicycle industry, and therefore has no stake in the decision.

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The solution of the logarithm expression  logₐ 60 is 2.1. Therefore, the answer is D.

The logarithm expression can be solved as follows; Using the logarithm rule,

Law of multiplication of logarithm,

logₐ x + logₐ y = logₐ xy

Therefore,

logₐ 2 = 4

logₐ 3 = 5

logₐ 5 = 8

Hence, let's find logₐ 60.

logₐ 5 + logₐ 3 + logₐ 2 + logₐ 2 = logₐ (5 × 3 × 2 × 2) = logₐ 60

Hence,

0.8 + 0.5 + 0.4 + 0.4 = 2.1

Therefore,

logₐ 60 = 2.1

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The value of log a 60 is 21. The correct option is D.

Logarithms are another way of writing exponents.

Logarithm is nothing but another way of expressing exponents and can be used to solve problems that cannot be solved using the concept of exponents only.

log a 60 = log a (12 x 5)

log a 60 = log a 12 x log a 5

log a 60 = log a (4 x 3) x log a 5

log a 60 = log a 4 x log a 3 x log a 5

log a 60 = 2 log a 2 x log a 3 x log a 5

Substituting the values for the logs

log a 60 = 2 (4) + 5 + 8

log a 60 = 21

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Answer:

50 + 5x^2 + 4x.

Step-by-step explanation:

To find the sum of the expressions, we need to simplify each expression first and then add them up.

10 + 3x represents the first expression.

25 - 4x + 2x^2 represents the second expression. By simplifying this expression, we get 25 + 2x^2 - 4x.

3x^2 - 5x represents the third expression.

-x^2 + 2x + 15 represents the fourth expression.

Adding all four expressions gives us:

10 + 3x + 25 + 2x^2 - 4x + 3x^2 - 5x - x^2 + 2x + 15

By combining like terms, we get:

10 + 5x^2 + 4x + 25 + 15

The final simplified sum is:

50 + 5x^2 + 4x.

Side a will be 58cm.In mathematics, a side is a feature of a geometric shape.

The "A-side" of a record, which is the main song, is issued as a single. The "A-side" of an album is the side that this track is on. The word "side" is most frequently employed as a noun, however it can also be used as an adverb or a verb. The shapes we observe are made of points and lines (line segments) (vertices).

Finding the side, we obtain:

Given ∠A= 30°, b =100 cm .

In ΔABC,

tan A = [tex]\frac{a}{100}[/tex],

tan 30°=  [tex]\frac{a}{100}[/tex]

0.577×100=a

a=57.7≅58 cm.

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Answer:

14v-2

Step-by-step explanation:

1. distribute

2. combine like terms

see photo for more information

By subtraction we get that, Isabel has to pour 35.25 grams of salt into the container.

The operation or process of finding the difference between two numbers or quantities is known as subtraction. To subtract a number from another number is also referred to as 'taking away one number from another'.

According to the information in question:

Total salt = 90.45 grams

Amount of salt poured = 55.2 grams

Thus, the total amount of salt left with her which has to be poured will be calculated by subtraction:

Amount of salt left = 90.45 - 55.2

                               = 35.25 grams

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To answer this question, we need to use some basic trigonometry. We know that Dirk's shadow is as tall as the town hall and that Dirk is 1.40m tall. So, if we can determine the angle of elevation of the spotlight, we can calculate the height of the town hall.

Let's call the angle of elevation "α" and the distance from the spotlight to the town hall "d". To determine α, we can use the tangent function.
tan α = opposite/adjacent = (d-5)/35 = (30/35) = 0.8571

The angle of elevation is arctan(0.8571) = 53.13°.

Now, we can use the sine function to calculate the height of the town hall:
sin α = opposite/hypotenuse = 1.4/d
d = 1.4/sin 53.13° = 16.2m

Therefore, the town hall is 16.2m tall.

Answer:

Answer is in the attached photo.

Step-by-step explanation:

The solution is in the attached photo, do take note the perimeter of the rectangle is:

2 x Length + 2 x Width.

Answer:

2 x Length + 2 x Width.

Step-by-step explanation:

Their ages are 5 years, 25 years

Word problems are sentences describing a 'real-life' situation where a problem needs to be solved by way of a mathematical calculation.

Let L and Y represent the age of the older person and younger person respectively.

Using the given information, we can write:

L = 4Y + 5 --- (1)

L + Y = 30 --- (2)

From (2):

L = 30 - Y --- (3)

Put (3) in (1):

L = 4Y + 5

30 - Y = 4Y + 5

4Y + Y = 30 - 5

5Y = 25

Y = 25/5

Y = 5 years

Put Y = 5 into (3):

L = 30 - Y

L = 30 - 5

L = 25 years

Their ages are 5 years, 25 years

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Answer:

The percentage of students in Kiri's brother's class who think aliens exist is 11/25 = 44%.

Since the number of students in Kiri's class is not given, it's not possible to compare the percentage of students in Kiri's class who think aliens exist to the percentage in her brother's class. We need to know the number of students in Kiri's class and the number of students who believe in aliens in order to compare the percentages.

The probability distribution does not add up to 1.0, in other words.

The complete question is:

A researcher records the number of mistakes made during a memory skills task. He finds that the probability that participants in this study made 0 mistakes is p = .22; made 1 mistake is p = .30; made 2 mistakes is p = .16; made 3 mistakes is p = .12; and made 4 or more mistakes is p = .25. Is this probability distribution accurate?

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Answer:

It is not accurate

Step-by-step explanation:

If the complete question is:

A researcher records the number of mistakes made during a memory skills task. He finds that the probability that participants in this study made 0 mistakes is p = .22; made 1 mistake is p = .30; made 2 mistakes is p = .16; made 3 mistakes is p = .12; and made 4 or more mistakes is p = .25. Is this probability distribution accurate?

THEN:

To determine whether the probability distribution is accurate, we need to check two conditions:

The sum of the probabilities should be equal to 1.

All probabilities should be between 0 and 1.

Let's check these conditions:

Sum of probabilities:

p(0) + p(1) + p(2) + p(3) + p(4 or more) = 0.22 + 0.30 + 0.16 + 0.12 + 0.25 = 1.05

The sum of the probabilities is greater than 1, which violates the first condition. Therefore, this is not a valid probability distribution.

All probabilities should be between 0 and 1:

The probability of making 0, 1, 2, or 3 mistakes are all between 0 and 1, so they satisfy this condition.

However, the probability of making 4 or more mistakes is 0.25, which is a valid probability, but it implies that the probability of making 0, 1, 2, or 3 mistakes is negative, which is impossible. Therefore, this distribution does not satisfy this condition.

Since this probability distribution violates both conditions for a valid probability distribution, it is not accurate, and the researcher should revise their data.

Answer:

The island is 728 feet off the coast.

Step-by-step explanation:

The correct answers are given below:

(a) 1 to 55

(b) 40%

Since Mansour scores 55% of his kicks, we'd want exactly 55% of the simulated numbers to denote Mansour scoring a penalty, thus, 1 to 5 is a possible range.

To find the percentage of trials where Mansour scored exactly one penalty, we have to count the trials where one of the simulated numbers is in the range of 1 to 5 (denoting Mansour scoring the penalty) and the other is in the range of 56 to 100 (denoting Mansour missing the penalty)

Trails 1, 3, and 4, 6 are such trials. Thus, Mansour scored exactly one penalty kick in 40% of the trials.

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The average velocity, to the nearest hundredth, of a ceiling tile that fell 43 feet is 344 feet per second

Velocity is the pace and direction of an item's movement, whereas speed is the time rate at which an object is travelling along a route.

Given that the formula for the speed of a falling object is v= √64d,

where v is the speed of the object in feet per second and d is the distance the object has fallen, in feet.

And also given that d = 43 feet.

Substituting the value to the formula,

v = √64 (43)

v = 8 x 43

v = 344

Therefore, 344 feet per second is the velocity.

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Each worker would take home a net pay of $586.71.

What is the net pay?

The net pay is the amount of money that an employee takes home after all deductions have been made from their gross pay. Gross pay is the total amount of money an employee earns before taxes and other deductions are taken out.

To calculate net pay, you need to subtract all the required deductions from the employee's gross pay.

To calculate the net pay for each worker, we first need to determine their gross pay. The gross pay will depend on the number of hours they worked and whether they worked any overtime.

For the first 40 hours worked, each worker earns $15.90 per hour, so their gross pay for those hours would be:

Gross Pay for 40 hours = $15.90/hour x 40 hours = $636

For any hours worked beyond 40, the worker earns time and a half wages. This means they earn 1.5 times their regular hourly wage of $15.90, or $23.85 per hour. So, if they worked, for example, 45 hours in total, the additional 5 hours would be paid at the overtime rate, resulting in an additional gross pay of:

Gross Pay for 5 overtime hours = $23.85/hour x 1.5 x 5 hours = $178.88

Therefore, their total gross pay would be:

Total Gross Pay = Gross Pay for 40 hours + Gross Pay for 5 overtime hours = $636 + $178.88 = $814.88

Now, we need to calculate the deductions, which we are told are 28% of the gross pay. So the total deductions would be:

Total Deductions = 28% x $814.88 = $228.17

Finally, to determine the net pay, we need to subtract the total deductions from the gross pay:

Net Pay = Gross Pay - Total Deductions = $814.88 - $228.17 = $586.71

Therefore, each worker would take home a net pay of $586.71.

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Answer:

y = ( x - 4 )² - 4

Step-by-step explanation:

a² ± 2ab + b² = ( a ± b )²

~~~~~~~~~~~~

y = x² - 8x + 12

y = ( x² - 2(4)(x) + 4² ) - 4² + 12 = ( x - 4 )² - 4

y = ( x - 4 )² - 4

The slope is 2.5

The y-intercept is 5.8.

The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

Example:

The slope of the line y = 2x + 3 is 2.

The slope of a line that passes through (1, 2) and (2, 3) is 1.

We have,

y = 5.8 + 2.5x

This is in the form of y = mx + c

So,

m = 2.5

And,

The y-intercept is when x = 0.

So,

y = 5.8 + 2.5x

Substitute x = 0,

y = 5.8

Thus,

Slope is 2.5

The y-intercept is 5.8.

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The transformations taking place in the given function is a horizontal left ward shift of 9 units and 1 unit upward vertical shift.

A Transformation in Math is a process of moving an object (two-dimensional shape) from its original position to a new position.

Given that, a function f(x) undergo some transformations to become f(x+9)-1,

We know that,

Vertical Shifting:

Adding a constant to a function will shift its graph vertically (i.e. y = f (x) + c). Adding a positive constant c will shift the graph upward c units, while adding a negative constant c will shift it downward c units.

Horizontal Shifting:

Horizontal shifts are inside changes that affect the input (x-) axis values and shift the function left or right. Combining the two types of shifts will cause the graph of a function to shift up or down and right or left.

Therefore, there is transformation of a horizontal and vertical shift.

Hence, the transformations taking place in the given function is a horizontal left ward shift of 9 units and 1 unit upward vertical shift.

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The length of x is 6 in the given triangle.

The branch of Mathematics which studies relationships between side lengths and angles of triangles.

We have to find the value of x in the given triangle.

We know that tan theta is the ratio of opposite side by adjacent side.

The opposite side is x and the adjacent side has √12

tan60=x/√12

√3=x/√12

x=√12√3

x=√36

x=6

Hence, the length of x is 6.

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Answer:

the scale factor that Samir used in his drawing is 5/1.

Step-by-step explanation:

Here's a step by step explanation of how to find the scale factor of a drawing:

Identify the scale used in the drawing. In this case, the scale used in Samir's drawing is 5 inches = 1 yard.

Express the scale as a ratio between the two sizes. In this case, the ratio is 5 inches : 1 yard.

Simplify the ratio, if possible. In this case, the ratio 5 inches : 1 yard can be simplified to 5/1.

The simplified ratio, 5/1, is the scale factor of the drawing. This means that for every 5 inches on the drawing, the actual length in the real world is 1 yard.

So, the scale factor that Samir used in his drawing is 5/1.

Answer:

Step-by-step explanation:

its Reduced to 2 / 5, which is 40 percent. Maria has 40 percent of her work completed

Answer:

32/13

Step-by-step explanation:

To evaluate the expression Z₂ * Z3 / Z₁, we first need to find the complex numbers Z₂ * Z3 and Z₁.

Z₂ * Z3 = -2 + 3i * 4 + 2i = (-8 + 14i) + (-6 + 6i) = -8 + 8i

Z₁ = 3 - 2i

So, Z₂ * Z3 / Z₁ = (-8 + 8i) / (3 - 2i)

We can simplify this expression by multiplying the numerator and denominator by the complex conjugate of the denominator, which is (3 + 2i).

Z₂ * Z3 / Z₁ = (-8 + 8i) / (3 - 2i) * (3 + 2i) / (3 + 2i) = (-8 + 8i) * (3 + 2i) / (3 - 2i) * (3 + 2i)

Z₂ * Z3 / Z₁ = ((-8 * 3 + 8 * 2i) + (8 * 3 + 8 * 2i)) / (3^2 + (-2i)^2) = (16 + 16i) / 13

Therefore, Z₂ * Z3 / Z₁ = (16 + 16i) / 13.

The perimeter of the given figure is: 36 +16√5 ft ≈ 71.777 ft

The area of the figure is: 288 ft²

Supposing that there is no direct formula available for deriving the area, we can derive the area of that region by dividing it into smaller pieces, whose area can be known directly. Then summing all those pieces' area gives us the area of the main big region.

We know that the perimeter is the total length of all the sides. The length of the horizontal sides is; 8 ft + 10 ft = 18 ft.

The length of the slant sides can be found by the Pythagorean theorem.

For side length s, we have;

s^2 = 8^2 + 16^2

 s^2 = 64 +256 = 320

 s = √320 = 8√5

Then the perimeter;

 P = 2(8√5 + 18) = 36 +16√5 ≈ 71.777 . . . feet

Area,  A = bh

where b is the base and h is the height.

 A = (18 ft)(16 ft) = 288 ft²

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The interest for the first quarter would be $ 15

The value of the CD when it matures is $ 2, 030. 11

The interest is said to compound quarterly which means that the periodic interest rate per quarter is:

= 3 % / 4

= 0. 75 % per quarter

The interest in the first quarter :

= 0. 75 % x 2, 000

= $ 15

The value of the CD at maturity is:

= 2, 000 x ( 1 + 0. 75% ) ²

= $ 2, 030. 11

Note : 2 periods because 6 months is 2 quarters.

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