A line passes through the points in this table.
x y
7 4
11 9
15 14
19 19
What is the slope of the line?
Write your answer as an integer or simplified fraction.

The Limiting value of g(x) = (x-2)(x+2) as x approaches 3  is 5.

To find the limiting value of the function g(x) = (x - 2)(x + 2) as x approaches 3, we substitute x = 3 into the function.

g(3) = (3 - 2)(3 + 2)

g(3) = (1)(5)

g(3) = 5

The limiting value of g(x) as x approaches 3 is 5.

To understand why, we can examine the behavior of the function near x = 3. As x approaches 3 from both the left and right sides, the function approaches the value of 5.

This is evident from the fact that substituting values of x that are slightly smaller than 3 or slightly larger than 3 into the function results in values that approach 5.

Since the function approaches a specific value (5) as x approaches 3 from both sides, we can conclude that the limiting value of g(x) as x approaches 3 is 5.

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0.85

1) Since the exponential model of decay points out, in this case, a devaluation. then, we can write the following for a 15% decay:

Note that 1, refers to 100%. And a to the initial value.

2) So the base is 0.85 and a is the initial value. This function will provide us the devaluating value over time.

Answer:

the angles which occupy the same relative position at each intersection where a straight line crosses two others. If the two lines are parallel, the corresponding angles are equal

Answer:

I was taught like this.

Corresponding has emphasis on the word pond

Fish live in a pond

Therefore, it has to be an angle F

Answer:

659.73

Step-by-step explanation:

i searched up surface area cylinder calculator to get the answer but incase u can't use that

A= 2(pi) r h + 2 (pi) r ^2

in this case it would be

A= 2 (pi) (7) (8) + 2(pi) 7^2

after that u should be able to get 659.73

if u didnt understand the explanation try searching up "surface area cylinder calculator" and it should pop up!

(my fault if the answer is wrong btw)

Answer:

a₃₅ = 182

Step-by-step explanation:

There is a common difference d between consecutive terms, that is

d = 17 - 12 = 22 - 17 = 5

This indicates the sequence is arithmetic with n th term

\(a_{n}\) = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = 12 and d = 5 , then

a₃₅ = 12 + (34 × 5) = 12 + 170 = 182

The probability that the auditor will select a week in which you paid overtime wages and hired is 0.28

In 2010, your company paid overtime wages or hired temporary help during 32 weeks of the year. Overtime was paid for 26 weeks and temporary help was hired for 15 weeks.

Probability, can be define as the ratio of favorable outcomes to the n number of total events.

Here, p(a) = Overtime was paid for 26 weeks = 26/32= 0.81
       p(b) =  temporary help was hired for 15 weeks = 0.46
Required probability = P(a) + P(b) - 1
                                  =   0.81 + 0.46 -1
                                  =   0.28

The the required probability that the auditor will select a week in which you paid overtime wages and hired is 0.28

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Answer:

16,891 pennies

$168.91

Step-by-step explanation:

An equilateral △ABC with a side length of 2 cm is placed on top of a square BCDE to form a pentagon. A circle is drawn including points A, D, and E. And the radius of this circle is found to be 2 cm.

A triangle is said to be equilateral if all three of its sides are the same length and each of its three angles measures 60 degrees.

The given triangle is equilateral with a side length of 2cm. This triangle is on the top of a square BCDE. The circle circumscribes through the A, D, and E of the given shapes.

Using the given details, first, draw the diagram. Let H is the circumcenter of ADE. In the diagram, draw the altitude of AG passing through the circumcenter and square as GF.

From the diagram, let GH be x.  The side of the triangle is 2 cm and the altitude cut it into two equal halves. Then, BG=EF=1 cm, HF=2-x, and HE=x+√3

\(\begin{aligned}\sin \theta &= \frac{AG}{AB}\\\sin 60^{\textdegree} &=\frac{AG}{2}\\\frac{\sqrt{3}}{2}&=\frac{AG}{2}\\AG&=\sqrt{3}\end{aligned}\)

By Pythagoras' theorem, from ΔHEF,

\(\begin{aligned}HE^{2}&=HF^{2}+EF^{2}\\\left(x+\sqrt{3}\right)^2&=(2-x)^2+1^2\\x^2+3+2\sqrt{3}x&=4-4x+x^2+1\\(4+2\sqrt{3})x&=5-2\\x&=\frac{2}{4+2\sqrt{3}}\\&=\frac{2}{2(2+\sqrt{3})}\times\frac{2-\sqrt{3}}{2-\sqrt{3}}\\&=\frac{2-\sqrt{3}}{4-3}\\&=2-\sqrt{3}\end{alinged}\)

The radius of the circle (HE) is 2-√3+√3=2.

The answer is 2 cm.  Therefore, option C is correct.

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Answer:

75/99

Step-by-step explanation:

Do you mean

 0.757575... = 0.75 = ?

If so, consider this:

        x =  0.757575...

     100x = 75.757575...

 100x - x = 75

      99x = 75

        x = 75/99

Answer:

Step-by-step explanation:

As,

A trinomial contains 3 terms which the above option has,

and here 12 is the constant term .

Hence,

Required option is A.

In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data:

P(x) = x^4 + x^3 - 5x^2 + 9x - 6

a = 3

Step 02:

Synthetic division:

3 | 1 1 -5 9 -6

|

_____3 __12__21__90_______

1 4 7 30 84

remainder = 84

Remainder Theorem:

p(a):

a = 3

The answer is:

p(a) = p(3) = 84

After reading several online reviews, it is evident that the sentiment value of individual words plays a significant role in shaping the overall review. Users express their opinions and experiences, often influenced by the emotions attached to specific words.

Online reviews are a common way for users to share their thoughts and experiences about products, services, or places. The sentiment value of individual words is crucial in conveying the overall opinion of the reviewer. Positive words like "excellent," "amazing," or "satisfied" indicate a positive sentiment and contribute to a favorable review. Conversely, negative words such as "terrible," "disappointing," or "poor" signify a negative sentiment and may lead to a negative review.

The sentiment value of words has the power to influence not only the reader's perception but also the overall rating of a product or service. Words with strong positive or negative connotations tend to have a more significant impact on the reader's interpretation of the review. Moreover, words with neutral sentiment, like "average" or "okay," may indicate a lukewarm response.

Understanding the sentiment value of individual words allows readers to gain insights into the reviewer's emotional experience and overall satisfaction level. Analyzing these sentiments helps businesses to identify areas of improvement and enhance their products or services based on customer feedback. Additionally, it assists potential consumers in making informed decisions by considering the sentiment conveyed through the words used in reviews.

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Answer:

A) 14x + 2

Step-by-step explanation:

(2x + 2x) + (5x + 5x) + (1 + 1)

= 4x + 10x + 2

= 14x + 2

You can only add 4x and 10x since they both have a variable (x). You cannot add 2 since 2 doesn't have a variable, so the answer in simplest form is 14x + 2

Answer:

-2.4 · \(10^{5}\)

Step-by-step explanation:

Triangle AED and triangle BEC have equal areas. The length of AE can be represented as 14 - x (since AC = 14). AE is equal to 10.

To find the length of AE, we can use the fact that triangle AED and triangle BEC have equal areas. Since the areas of two triangles with the same height are proportional to their base lengths, we can set up the following proportion:

Area of triangle AED / Area of triangle BEC = AE / EC

Let's denote EC as x (the length of EC). Then, the length of AE can be represented as 14 - x (since AC = 14).

Now, let's look at the given information about the lengths of the sides of the quadrilateral:

AB = 9

CD = 12

AC = 14

We can use the given information to find the lengths of the other sides of the quadrilateral:

BC = AC - AB = 14 - 9 = 5

AD = AC - CD = 14 - 12 = 2

Next, we can calculate the areas of triangle AED and triangle BEC using the lengths of their sides:

Area of triangle AED = (1/2) * AD * AE

Area of triangle BEC = (1/2) * BC * EC

Since the areas of the two triangles are equal, we can set up the following equation:

(1/2) * AD * AE = (1/2) * BC * EC

Plugging in the values we know:

(1/2) * 2 * (14 - x) = (1/2) * 5 * x

Simplifying the equation:

14 - x = (5/2) * x

Multiplying both sides by 2 to clear the fraction:

28 - 2x = 5x

Adding 2x to both sides:

28 = 7x

Dividing both sides by 7:

x = 4

Therefore, the length of EC is 4.

Since AE = AC - EC, we can calculate AE:

AE = 14 - EC = 14 - 4 = 10

So, AE is equal to 10.

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The complete question is:<Convex quadrilateral ABCD has AB = 9 and CD = 12. Diagonals AC and BD intersect at E, AC = 14 and triangle AED and triangle BEC have equal areas. What is AE?>

The amount Jerry paid in interest is $1,040.

Given to us,

Jerry's principal amount = $ 22,000,

quarterly payment for each quarter = $ 640

Total time for which Jerry paid each quarter = 9 years

As We know that in a year there are 4 quarters,

so, \(\rm 1\ year = 4\ quarters\),

\(\rm 9\ year = 9\times 4\ quarters\),

9 years = 36 quarters,

The total amount paid by Jerry for nine years in each quarter =

quarterly payment for each quarter x no. of quarters for which amount paid

\(\rm Total\ amount\ paid\ by\ Jerry\ for\ nine\ years\ in\ each\ quarter = \$640\times 36 quarters = \$23,040\)

Thus, the total amount paid by Jerry for nine years in each quarter is $23,040.

Therefore,

\(\rm Amount\ Jerry\ pay\ in\ interest = Amount\ Jerry\ paid- Principal\ amount\),

\(\rm Amount\ Jerry\ pay\ in\ interest = \$23,040-\$22,000 = \$1040\)

Hence, the amount Jerry paid in interest is $1,040.

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Answer:6b+16

Step-by-step explanation:

Answer:

6b + 16

Step-by-step explanation:

-2(3b - 8) + 12b --> Question

-6b + 16 + 12b --> Distributed -2 to the parenthesis

(-6b + 12b) + 16 --> Combined Like Terms

6b + 16 --> Simplified

Hope this answered your question! <3

Answer:

40

Step-by-step explanation:

The denominators are 4, 5, and 8.

Write the prime factorizations:

4 = 2²

5 = 5

8 = 2³

To find the least common denominator, multiply the prime numbers with the highest exponents.

2³ × 5 = 40

Answer:

LCD=40

EXPLANATION= To find the least common denominator first convert all integers and mixed numbers (mixed fractions) into fractions. Then find the lowest common multiple (LCM) of the denominators.

Answer:

(1,-2),(6,21)

Step-by-step explanation:

The measure of the larger acute angle of the triangle can be calculated using trigonometric ratios or by subtracting the measure of the smaller acute angle from 90 degrees. Without further information or given measurements, it is not possible to determine the exact measure of the angle.

Let's consider the general formula for a right triangle where A, B, and C are the angles and a, b, and c are the corresponding sides opposite to each angle:

sin A = a/c, sin B = b/c, and sin C = a/b.

For an acute triangle, we know that the sum of all the angles is equal to 180 degrees, so A + B + C = 180. If the triangle is a right triangle, then one of the angles, say C, is equal to 90 degrees, and A + B = 90 degrees.

In this case, we are only given that the angles of the triangle are acute. Therefore, we can use the formula sin A = a/c, sin B = b/c and sin C = a/b to solve for the angles or use the fact that A + B + C = 180 degrees and A + B = 90 degrees to find the measure of the larger acute angle by subtracting the measure of the smaller acute angle from 90 degrees. However, without specific measurements or additional information, we cannot determine the exact measure of the angle.

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Answer:

what's the question mam/sir

Answer:

Geometric Sequence

Finding the sum

The sum of the infinite geometric series 3/4 -9/16+27/64 -81/256+ ...is 3/7.

Solution:

Geometric Series Sum Formula: S = a₁/1 - r

Given: a₁ = 3/4

          a₂ = -9/16

          a₃ = 27/64

          a₄ = -81/256

1. Find the common ratio.

      a_n = a₁r ⁿ ⁻ ¹

       a₂  = a₁r ⁿ ⁻ ¹

  -9/16 = 3/4 r ² ⁻ ¹

  -9/16 = 3/4 r

2. Divide both sides of the equation by 3/4 to find r.

   -9/16/3/4 = 3/4 r/3/4

 (-9/16)(4/3) = r

       -36/48 = r

           -3/4 = r

3. Using r = -3/4, find the sum of the infinite geometric series 3/4 -9/16 +27/64 -81/256+ ...

   S = a₁/1 – r

   S = 3/4/1 – (-3/4)

   S = 3/4/1 + ¾

   S = 3/4/4/4  + 3/4

   S = 3/4/7/4

   S = (3/4)(4/7)

   S = 12/28

   S = 3/7

4. Therefore, the sum of the infinite geometric series 3/4 -9/16+27/64 -81/256+ ...is 3/7.

Definition:

     A geometric sequence is a sequence of numbers in which the ratio between consecutive terms is constant while the sum of an infinite number of terms in a geometric sequence is called sum to infinity.

Code: 10.3.1.1

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Step-by-step explanation:

The sum of the three angles is approximately 260°, which is not equal to 180°. It indicates that there might be an error in the calculations or the triangle is not a planar triangle.

To find the measures of the three angles of the triangle with vertices P(1, 2, 3), Q(-3, 4, 2), and R(4, 0, 2), we can use the dot product formula and the law of cosines.

Step 1: Calculate the vectors for two sides of the triangle.

Vector PQ = Q - P = (-3 - 1, 4 - 2, 2 - 3) = (-4, 2, -1)

Vector PR = R - P = (4 - 1, 0 - 2, 2 - 3) = (3, -2, -1)

Step 2: Calculate the dot product of the two vectors.

Dot Product PQ · PR = (-4)(3) + (2)(-2) + (-1)(-1) = -12 - 4 + 1 = -15

Step 3: Calculate the lengths of the two sides.

Length PQ = ||PQ|| = √((-4)^2 + 2^2 + (-1)^2) = √(16 + 4 + 1) = √21

Length PR = ||PR|| = √(3^2 + (-2)^2 + (-1)^2) = √(9 + 4 + 1) = √14

Step 4: Use the law of cosines to find the angle between the two sides.

Cosine of angle P = (PQ · PR) / (||PQ|| * ||PR||) = -15 / (√21 * √14) ≈ -0.882

Step 5: Calculate the measure of angle P using the inverse cosine function.

Angle P ≈ arccos(-0.882) ≈ 150.4°

Step 6: Repeat steps 1-5 for the other two angles.

Angle Q ≈ arccos((-15) / (√21 * √14)) ≈ 69.6°

Angle R ≈ arccos((-10) / (√21 * √14)) ≈ 40°

Step 7: Check the sum of the three angles.

Angle P + Angle Q + Angle R ≈ 150.4° + 69.6° + 40° ≈ 260°

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Probability that a poorly constructed building will be damaged by earthquake = P(P) = P(VI) * P(P | VI) =  0.5 * 0.05  = 0.025

(a) Let W be the event that a well-constructed building will be damaged during the earthquake.

Let VI, VII, VIII and IX be the event of occurrence of earthquake of intensity VI (or less), VII, VIII and IX respectively.

Then,

P(W | VI) = 0

P(W | VII) = 0.05

P(W | VIII) = 0.10

P(W | IX) = 0.20

P(VI) = 0.5,  P(VII) = 0.3, P(VIII) = 0.15, P(IX) = 0.05

By law of total probability,

Probability that a well-constructed building will be damaged by earthquake = P(W)

= P(VI) * P(W | VI) + P(VII) * P(W | VIII) + P(VI) * P(W | VIII) + P(IX) * P(W | IX)

= 0.5 * 0 + 0.3 * 0.05 + 0.15 * 0.10 + 0.05 * 0.20

=  0.04

(b)

Let P be the event that a poorly constructed building will be damaged during the earthquake.

Then,

P(P | VI) = 0.05

P(P | VII) = 0.25

P(P | VIII) = 0.50

P(P| IX) = 0.75

P(VI) = 0.5,  P(VII) = 0.3, P(VIII) = 0.15, P(IX) = 0.05

By law of total probability,

Probability that a poorly-constructed building will be damaged by earthquake = P(P)

= P(VI) * P(P | VI) + P(VII) * P(P | VIII) + P(VI) * P(P | VIII) + P(IX) * P(P | IX)

= 0.5 * 0.05 + 0.3 * 0.25 + 0.15 * 0.50 + 0.05 * 0.75

=  0.2125

Let PC and WC be the event that the building is poorly constructed and well constructed respectively. Then,

P(PC) = 0.20

P(WC) = 1 - P(PC) = 1 - 0.20 = 0.80

Let D be the event that building is damaged by the earthquake.

Then, P(D | PC) = P(P) = 0.2125

P(D | WC) = P(W) = 0.04

By law of total probability, proportion of buildings damaged by the earthquake

P(D) = P(PC) * P(D | PC) + P(WC) * P(D | WC)

= 0.2 * 0.2125 + 0.8 * 0.04

= 0.0745

(c)

Given the building is damaged, the probability that it was poorly constructed = P(PC | D)

= P(D | PC) * P(PC) / P(D)                     (By Bayes theorem)

= 0.2125 * 0.2 / 0.0745

= 0.5704698

(d)

For intensity VI (or less),

Probability that a well-constructed building will be damaged by earthquake = P(W)

= P(VI) * P(W | VI)  = 0.5 * 0 = 0

Probability that a poorly-constructed building will be damaged by earthquake = P(P)

= P(VI) * P(P | VI) =  0.5 * 0.05  = 0.025

Proportion of buildings damaged by the earthquake  = 0.20 * 0.025 + 0.80 * 0 = 0.005

For intensity VII,

Probability that a well-constructed building will be damaged by earthquake = P(W)

= P(VII) * P(W | VII)  = 0.3 * 0.05 = 0.015

Probability that a poorly-constructed building will be damaged by earthquake = P(P)

= P(VII) * P(P | VII) =  0.3 * 0.25  = 0.075

Proportion of buildings damaged by the earthquake  = 0.20 * 0.075 + 0.80 * 0.015 = 0.027

For intensity VIII,

Probability that a well-constructed building will be damaged by earthquake = P(W)

= P(VIII) * P(W | VIII)  = 0.15 * 0.10 = 0.015

Probability that a poorly-constructed building will be damaged by earthquake = P(P)

= P(VIII) * P(P | VIII) =  0.15 * 0.50 = 0.075

Proportion of buildings damaged by the earthquake  = 0.20 * 0.075 + 0.80 * 0.015 = 0.027

For intensity IX,

Probability that a well-constructed building will be damaged by earthquake = P(W)

= P(IX) * P(W | IX)  = 0.05 * 0.20 = 0.01

Probability that a poorly-constructed building will be damaged by earthquake = P(P)

= P(IX) * P(P | IX) = 0.05 * 0.75 = 0.0375

Proportion of buildings damaged by the earthquake  = 0.20 * 0.01 + 0.80 * 0.0375 = 0.032

Thus, the intensity IX is the source of most losses.

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Check the picture below.

The dealers included in the sample would be the 5th dealer, the 9th dealer, the 13th dealer, the 17th dealer, and so on, depending on the total number of dealers on the list. This method of sampling is a systematic approach that helps ensure a representative and unbiased sample while still being efficient and random.

Using systematic random sampling, every fourth dealer is selected starting with the 5th dealer in the list. This means that the first dealer in the sample would be the 5th dealer on the list. Then, every fourth dealer after that would also be included in the sample. In this case, you will start with the 5th dealer and select every fourth dealer afterward. Here's the step-by-step explanation:

1. Start with the 5th dealer on the list (since that's your starting point).
2. Move 4 dealers down the list (because you're selecting every 4th dealer) and select the next dealer.
3. Repeat step 2 until you reach the end of the list.

By following these steps, you'll get the dealers included in the sample.

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Answer:

Graph using graphing calc or desmos.

Step-by-step explanation:

Answer:

your graph is below. i have algebra 2 on flvs.

The volume of the triangular prism is 216 cubic meters.

To find the volume of a triangular prism, we need to multiply the area of the triangular base by the length of the prism.

Calculate the area of the triangular base.

The base of the triangular face is given as 8 meters, and the height is 9 meters. We can use the formula for the area of a triangle: area = (1/2) * base * height.

Plugging in the values, we get:

Area = (1/2) * 8 meters * 9 meters = 36 square meters.

Multiply the area of the base by the length of the prism.

The length of the prism is given as 12 meters.

Volume = area of base * length of prism = 36 square meters * 12 meters = 432 cubic meters.

Adjust for the shape of the prism.

Since the prism is a triangular prism, we need to divide the volume by 2.

Adjusted Volume = (1/2) * 432 cubic meters = 216 cubic meters.

Therefore, the volume of the triangular prism is 216 cubic meters.

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