solve the following question

Answer:

x = - 5 , x = 2

Step-by-step explanation:

f(x) = x² + 3x - 10

to find the zeros let f(x) = 0 , that is

x² + 3x - 10 = 0

consider the factors of the constant term (- 10) which sum to give the coefficient of the x- term (+ 3)

the factors are + 5 and - 2 , since

5 × - 2 = - 10 and 5 - 2 = + 3 , then

(x + 5)(x - 2) = 0 ← in factored form

equate each factor to zero and solve for x

x + 5 = 0 ( subtract 5 from both sides )

x = - 5

x - 2 = 0 ( add 2 to both sides )

x = 2

the zeros are x = - 5 , x = 2

His total expenditure is $100. After that, he sold the CD player for $125. As a result, he earned $25.

Al initially bought a CD player for $100 and then sold it for $125. After that, he bought it back for $150 and later sold it for $175. The question is whether Al made money, lost money, or broke even.

Let's examine the transactions in more detail to determine the answer.

Initially, Al bought the CD player for $100.

Now his total income is $25 and his expenditure remains at $100. Next, he purchased the same CD player again for $150. This adds to his expenditure, which is now $250.

Later, he sold the CD player for $175, which means he earned another $25, bringing his total income to $50 (i.e., $25 from the first sale and $25 from the second sale).

Since Al's total expenditure was $250 and his total income was $50, he lost money. He spent more than he earned.

He sold the CD player twice and earned a total of $50, which is less than what he spent on the CD player, which was $250. Al had a net loss of $200 ($250 - $50). Therefore, he lost money.

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Answer:

$6240

Step-by-step explanation:

given likelihoods:

sunny day = 14% = 0.14

cloudy day = 26% = 0.26

rainy day = 60% = 0.60

profits:

profit on a sunny day = $40,000

profit on a cloudy day = $14,000

Loss on a rainy day = -$5,000

expected profit = (probability of sunny day * profit on sunny day) + (probability of cloudy day * profit on cloudy day) + (probability of rainy day * loss on rainy)

expected profit = (0.14 * $40,000) + (0.26 * $14,000) + (0.60 * -$5,000)

=6240

The exact circumferences of the inscribed and circumscribed circles for the given polygons are 8π cm and 15π cm, respectively.

To find the exact circumference of a circle inscribed or circumscribed by a polygon, we can use the Pythagorean theorem to determine the diameter of the circle.

In the case of an inscribed polygon, the diameter of the circle is equal to the diagonal of the polygon. Let's consider the polygon with a diagonal of 8 cm. If we draw a line connecting two non-adjacent vertices of the polygon, we get a diagonal that represents the diameter of the inscribed circle.

Using the Pythagorean theorem, we can find the length of this diagonal. Let's assume the sides of the polygon are a and b. Then the diagonal can be found using the equation: diagonal^2 = a^2 + b^2. Substituting the given values, we have 8^2 = a^2 + b^2. Solving this equation, we find that a^2 + b^2 = 64.

For the circumscribed polygon with a diagonal of 15 cm, the diameter of the circle is equal to the longest side of the polygon. Let's assume the longest side of the polygon is c. Therefore, the diameter of the circumscribed circle is 15 cm.

Once we have determined the diameter of the circle, we can calculate its circumference using the formula C = πd, where C is the circumference and d is the diameter.

For the inscribed circle, the circumference would be C = π(8) = 8π cm.

For the circumscribed circle, the circumference would be C = π(15) = 15π cm.

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(a) The average cost in 2010 is $2088.82.

(b) A graph of the function g for the period 2006 to 2015 is: D. graph D.

(c) Assuming that the graph remains accurate, its shape suggest that: B. the average cost increases at a slower rate as time goes on.

Based on the information provided, we can logically deduce that the average annual cost (in dollars) for health insurance in this country can be approximately represented by the following function:

g(x) = -1736.7 + 1661.4lnx

where:

x = 6 corresponds to the year 2006.

For the year 2011, the average cost (in dollars) is given by;

x = (2010 - 2006) + 6

x = 4 + 6

x = 10 years.

Next, we would substitute 10 for x in the function:

g(10) = -1736.7 + 1661.4ln(10)

g(10) = $2088.82

Part b.

In order to plot the graph of this function, we would make use of an online graphing tool. Additionally, the years would be plotted on the x-axis while the average annual cost would be plotted on the x-axis of the cartesian coordinate as shown below.

Part c.

Assuming the graph remains accurate, the shape of the graph suggest that the average cost of health insurance increases at a slower rate as time goes on.

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Answer:

2(M - 14) = 64

M - 14 = 32

M = 46

The simplified form of the expression for 4( x + 2 ) + ( 8 + 2x ) is 6x + 16.

Given the expresion in the equestion:

4( x + 2 ) + ( 8 + 2x )

To simplify the expression 4( x + 2 ) + ( 8 + 2x ), first, apply distributive property by distributing 4 to the terms ( x + 2 ):

4( x + 2 ) + ( 8 + 2x )

4 × x + 4 × 2 + 8 + 2x

4x + 8 + 8 + 2x

Collect and add like terms:

4x + 2x + 8 + 8

Add 4x and 2x

6x + 8 + 8

Add the constants 8 + 8

6x + 16

Therefore, the simplified form is 6x + 16.

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Answer:

try gauth. math! Take a photo of each question and upload the photo to see if it works

Answer:

PO = 12

Step-by-step explanation:

given a tangent and a secant from an external point to the circle then

the product of the measures of the secant's external part and the entire secant is equal to the square of the measure of the tangent , that is

OP × OQ = NO²

OP × 27 = 18² = 324 ( divide both sides by 27 )

OP = 12

Answer:

8/15

Step-by-step explanation:

1/15(4 + 1/20(4)

4/15 + 4/20  I can reduce 4/20 to 1/5

4/15 + 1/5

4/15 + 3/15 = 7/15

Together they can get 7/15 of the job done.  15/15 - 7/15 is 8/15.

That means that they have 8/15 left to do.

Helping in the name of Jesus.

From the Table display of scores and students on a recent exam, The mean of the scores to the nearest 10th is  83.7.

To find the mean of the scores, we need to calculate the sum of the products of each score and its corresponding number of students, and then divide it by the total number of students.

Here's the calculation:

(70 * 6) + (75 * 3) + (80 * 9) + (85 * 5) + (90 * 7) + (95 * 8) = 420 + 225 + 720 + 425 + 630 + 760 = 3180

Total number of students = 6 + 3 + 9 + 5 + 7 + 8 = 38

Mean = Sum of products / Total number of students = 3180 / 38 ≈ 83.7 (rounded to the nearest tenth)

Therefore, the mean of the scores is approximately 83.7.

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In mathematics, a set is a well-defined collection of distinct objects, called elements or members of the set. These objects can be anything: numbers, letters, people, or even other sets.

he concept of sets is fundamental in various branches of mathematics, including set theory, algebra, and statistics.There are different kinds of sets based on their properties:

Finite set: A set with a specific number of elements, which can be counted.Infinite set: A set with an endless number of elements.Empty set: A set with no elements. It is denoted by the symbol Ø or {}.

Singleton set: A set with only one element.Subset: A set whose elements are all contained within another set.Universal set: A set that includes all the possible elements of interest in a particular context.Operations on sets involve various ways of combining or manipulating sets:

Union: The union of two sets A and B is the set that contains all the elements from both sets. It is denoted by A ∪ B.Intersection: The intersection of two sets A and B is the set of elements that are common to both sets. It is denoted by A ∩ B.

Complement: The complement of a set A, denoted by A', is the set of all elements that are not in A but are in the universal set.Difference: The difference between two sets A and B is the set of elements that are in A but not in B. It is denoted by A - B.

Cartesian Product: The Cartesian product of two sets A and B is the set of all possible ordered pairs, where the first element is from set A and the second element is from set B. It is denoted by A × B.

For teaching the concept of the union of sets, you can use the following activity:

Activity: Venn Diagrams

Draw two overlapping circles on the board or use physical cut-out circles.Label one circle as Set A and the other as Set B.

Ask the students to suggest elements for each set and write them inside the circles.Discuss the elements that are common to both sets and write them in the overlapping region.Explain that the union of sets A and B represents all the elements in both sets.

Combine the elements from sets A and B, including the elements in the overlapping region, and write them in a new circle labeled as A ∪ B.Emphasize that the union includes all the distinct elements from both sets without repetition.

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Answer:

(-13, -9) and (-5, -9)

Step-by-step explanation:

The given equation of the hyperbola is:

[tex]\dfrac{(y+9)^2}{25}-\dfrac{(x+9)^2}{16}=1[/tex]

As the y²-term of the given equation is positive, the transverse axis is vertical, and so the hyperbola is vertical (opens up and down).

The standard equation for a vertical hyperbola is:

[tex]\boxed{\dfrac{(y-k)^2}{a^2}-\dfrac{(x-h)^2}{b^2}=1}[/tex]

where:

Compare the given equation with the standard equation to find the values of h, k, a and b:

The formula for the co-vertices of a vertical hyperbola is (h±b, k).

Substitute the values of b, h and k into the formula:

[tex]\begin{aligned}\textsf{Co-vertices}&=(h\pm b,k)\\&=(-9\pm 4, -9)\\&=(-13,-9)\;\;\textsf{and}\;\;(-5, -9)\end{aligned}[/tex]

Therefore, the co-vertices of the given hyperbola are:

The co-vertices of the hyperbola are (-4, -9) and (-14, -9).

To find the co-vertices of the hyperbola defined by the equation:

[(y + 9)² / 25] - [(x + 9)² / 16] = 1

We can compare the equation to the standard form of a hyperbola:

[(y - h)² / a²] - [(x - k)² / b²] = 1

In this case, we have h = -9 and k = -9.

The co-vertices of a hyperbola lie on the transverse axis, which is the line passing through the center of the hyperbola. The center of the hyperbola is given by (h, k), which in this case is (-9, -9).

For a hyperbola with the equation in this form, the co-vertices are located a units to the right and left of the center. In this case, since the equation is [(y + 9)² / 25] - [(x + 9)² / 16] = 1, we have a = 5.

Therefore, the co-vertices are located at (-9 ± a, -9), which gives us:

(-9 + 5, -9) = (-4, -9)

(-9 - 5, -9) = (-14, -9)

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Answer:

So we have $11.64 in American dollars and £5 in British pound coin

Step-by-step explanation:

To solve this problem, we can use a system of equations. Let x be the number of American dollars and y be the number of British pound coins. Then we have:

x + y/1.65 = 20.25 (since each British pound coin is worth 1.65 American dollars)

x = 17 - y (since there are 17 items altogether)

Substituting the second equation into the first, we get:

(17 - y) + y/1.65 = 20.25

Multiplying both sides by 1.65, we get:

28.05 - y + y = 33.4125

y = 33.4125 - 28.05

y = 5.3625

Therefore, we have 5 British pound coins and:

x = 17 - y = 17 - 5.3625 = 11.6375

The point A divides the line segment AB into the ratio 3:1, while the point B divides it into the ratio 1:3.

1. To find the ratio in which each point divides AB, we need to calculate the distances from each endpoint to the dividing point.

2. Let's calculate the distance from point A to the dividing point. The x-coordinate of point A is -7, and the y-coordinate is -14. Similarly, the x-coordinate of point B is 5, and the y-coordinate is 10.

3. We'll use the distance formula, which states that the distance between two points (x1, y1) and (x2, y2) is given by:

  distance = sqrt((x2 - [tex]x1)^2 + (y2 - y1)^2)[/tex]

4. Applying the distance formula, we find the distance from point A to the dividing point:

[tex]distance_A[/tex] = sqrt((5 -[tex](-7))^2 + (10 - (-14))^2)[/tex]

             = sqrt((5 + [tex]7)^2 + (10 + 14)^2)[/tex]

             = sqrt([tex]12^2[/tex] + [tex]24^2[/tex])

             = sqrt(144 + 576)

             = sqrt(720)

             = 12√5

5. Similarly, let's calculate the distance from point B to the dividing point:

[tex]distance_B[/tex] = sqrt((-7 - [tex]5)^2 + (-14 - 10)^2)[/tex]

             = sqrt((-[tex]12)^2 + (-24)^2)[/tex]

             = sqrt(144 + 576)

             = sqrt(720)

             = 12√5

6. The dividing ratio can be determined by comparing the distances from each endpoint to the dividing point. Since distance_A:distance_B = 3:1, we conclude that point A divides the line segment AB into the ratio 3:1, and point B divides it into the ratio 1:3.

Thus, the endpoints A and B divide the line segment AB into the ratios 3:1 and 1:3, respectively.

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Answer:

the ratio for point C is 1 : 2.

the ratio for point D is 3 : 1.

the ratio for point E is 2 : 1.

Step-by-step explanation:

I just got it right on the test

The cubic function with the desired properties is:

f(x) = (-3/4)x³ - (9/4)x² - (113/4)x + 63/4

To find the values of a, b, c, and d, we can use the given information about the relative maximum, relative minimum, and point of inflection.

Relative Maximum:

The point (-7, 163) is a relative maximum. At this point, the derivative of the cubic function is equal to zero. Taking the derivative of the cubic function, we have:

f'(x) = 3ax² + 2bx + c

Setting x = -7 and f'(-7) = 0, we get:

49a - 14b + c = 0

Relative Minimum:

The point (5, -125) is a relative minimum. At this point, the derivative of the cubic function is equal to zero. Taking the derivative of the cubic function, we have:

f'(x) = 3ax² + 2bx + c

Setting x = 5 and f'(5) = 0, we get:

75a + 10b + c = 0

Point of Inflection:

The point (-1, 19) is a point of inflection. At this point, the second derivative of the cubic function changes sign. Taking the second derivative of the cubic function, we have:

f''(x) = 6ax + 2b

Setting x = -1, we get:

-6a + 2b = 0

Solving the system of equations formed by the above three equations, we can find the values of a, b, c, and d.

49a - 14b + c = 0

75a + 10b + c = 0

-6a + 2b = 0

Solving these equations, we find:

a = -3/4

b = -9/4

c = -113/4

d = 63/4

Therefore, the cubic function with the desired properties is:

f(x) = (-3/4)x³ - (9/4)x² - (113/4)x + 63/4

Hello!

Volume

= (18cm * 15cm * 6cm) + ((13cm - 6cm) * 15cm * 6cm)

= 1,620cm³ + 630cm³

= 2,250cm³

Answer:

8

Step-by-step explanation:

let x be the number,

according to the question,

-29 + 28 = -7 + x

1 + 7 = x

thus, x = 8

The possible roots for the function are given as follows:

C. ± 1, ±2, ±4, ±5, ±10, ±20.

The parameters for this function are given as follows:

The factors are given as follows:

Hence, by the Rational Zero Theorem, the possible roots are given as follows:

C. ± 1, ±2, ±4, ±5, ±10, ±20.

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The limit of the trigonometric expression is equal to 0.

In this problem we find the case of a trigonometric expression, whose limit must be found. This can be done by means of algebra properties, trigonometric formula and known limits. First, write the entire expression below:

[tex]\lim_{\Delta x \to 0} \frac{\cos (\pi + \Delta x) + 1}{\Delta x}[/tex]

Second, use the trigonometric formula cos (π + Δx) = - cos Δx to simplify the resulting formula:

[tex]\lim_{\Delta x \to 0} \frac{1 - \cos \Delta x}{\Delta x}[/tex]

Third, use known limits to determine the result:

0

The limit of the trigonometric function [cos (π + Δx) + 1] / Δx evaluated at Δx → 0 is equal to 0.

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The length of the segment AD found using the triangle proportionality theorem is the option (B)

(B) = 4 1/2

The triangle proportionality theorem states that if a line drawn parallel to a side of a triangle, intersecting the other two points at two distinct point, then it will divide the two sides intersected in the same ratio.

The arrow markings indicates that the segment DE and ACV are parallel, therefore, according to the triangle proportionality theorem, we get;

8/12 = 3/AD

AD/3 = 12/8

AD = 3 × (12/8) = 4.5

AD = 4 1/2

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Answer:

(- 4, - 4 )

Step-by-step explanation:

x - 5y = 16 → (1)

4x - 2y = - 8 → (2)

multiplying (1) by - 4 and adding to (2) will eliminate x

- 4x + 20y = - 64 → (3)

add (2) and (3) term by term to eliminate x

(4x - 4x) + (- 2y + 20y) = - 8 - 64

0 + 18y = - 72

18y = - 72 ( divide both sides by 18 )

y = - 4

substitute y = - 4 into either of the 2 equations and solve for x

substituting into (1)

x - 5(- 4) = 16

x + 20 = 16 ( subtract 20 from both sides )

x = - 4

solution is (- 4, - 4 )

The sentence that best describes the paragraph is: "The pirates didn't believe Caesar would kill them because he was their prisoner." So, the correct option is c) Pirates didn’t believe Caesar will kill them because he was their prisoner.

The paragraph recounts the events of Caesar's kidnapping by pirates while crossing the Aegean Sea. Despite being held captive, Caesar maintained an attitude of superiority. The pirates demanded a ransom of 20 talents of silver, but Caesar insisted they ask for 50. This indicates that Caesar saw himself as more valuable than the initial ransom amount suggested by the pirates.

After the ransom was paid, Caesar did not forget the pirates' actions. He raised a fleet, pursued the pirates, and captured them. The sentence implies that the pirates didn't believe Caesar would actually kill them because he was their prisoner and they likely saw his promises as mere jest.

However, Caesar, true to his word, had the pirates crucified on his own authority.

This sequence of events highlights Caesar's determination, strategic thinking, and his ability to command respect even in dire circumstances. Despite being initially taken prisoner, he managed to turn the tables on the pirates, assert his authority, and exact his revenge. So, the correct option is c) Pirates didn’t believe Caesar will kill them because he was their prisoner.

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To find the area of a rectangle, we need to know its length and width. Let's solve the problem step by step:

Let's assume that the width of the rectangle is represented by "w" (in feet).

According to the given information, the length of the rectangle is 4 feet longer than its width, which means the length can be represented as "w + 4" (in feet).

The perimeter of a rectangle is calculated by adding up all the sides. In this case, the perimeter is given as 32 feet.

Since a rectangle has two pairs of equal sides (length and width), we can express the perimeter equation as the following:

2(length + width) = perimeter

Substituting the values into the equation, we get:

2(w + (w + 4)) = 32

Simplifying the equation, we have:

2(2w + 4) = 32

4w + 8 = 32

4w = 24

w = 6

Now we know that the width of the rectangle is 6 feet. To find the length, we can substitute this value back into the equation for the length:

Length = w + 4 = 6 + 4 = 10 feet

The width is 6 feet, and the length is 10 feet. Now we can calculate the area of the rectangle:

Area = Length × Width = 10 × 6 = 60 square feet

Answer: The area of the rectangle is 60 square feet.

The amount of tax owed is $13,420

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

Single with a taxable income of ​$61,000

Using the table of marginal tax, we have

Tax = 22%

So, we have

Tax = 22% * 61000

Evaluate

Tax = 13420

Hence, the amount of tax owed is $13,420

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Ki Tae used 54 meters of fencing to construct a 6-sided outdoor dog pen. Two of the sides are each 15 meters long, while the remaining four sides are each 6 meters long.

Let's solve the problem step by step. We know that Ki Tae used a total of 54 meters of fencing to construct a 6-sided outdoor dog pen. Two of the sides have a length of 15 meters each.

Let's denote the length of the remaining four sides as "x."

Since the dog pen has six sides, we can set up an equation based on the total length of the fencing:

15 + 15 + x + x + x + x = 54

Simplifying the equation, we have:

30 + 4x = 54

Subtracting 30 from both sides, we get:

4x = 24

Dividing both sides by 4, we find:

x = 6

Therefore, each of the remaining four sides has a length of 6 meters.

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Answer:

Step-by-step explanation:

When the equation is in the slope intercept form of y = mx + b, you know that the m is the slope and the b is the y-intercept (0, b)

By looking at the equation  y=2x + 2, you can determine that the y-intercept will be at the point (0, 2)  and the slope is 2.

To graph, start with the point of (0, 2) then go up 2 units and to the right 1 unit.  So the next point will be at (1, 4)

You can also, substitute and number in for the x and calculate the y value.   For example, if x is 3, then  y=2(3)+2; y = 8 so the point (3, 8) is on the line.

Answer:

x=50

Step-by-step explanation:

Make this equal to 180.

x+3x-35+x-35 = 180

5x = 180 + 70

5x=250

x=50