Find the slope of the line represented
by the data below.
x 2 4 6 8
-3 39
3
9 15
y|-3
Simplify completely.
Slope = [?
Hint: The slope of a line is the
Change in y
Change in x

The solutions to the rational equations are

The rational equations can be solved as follows

(1)

(x - 2)/(2x + 4) = 1/5

This gives

5x - 10 = 2x + 4

So, we have

3x = 14

x = 14/3

(2)

For equation (2), we have

(x + 3)/2 - x/4 = 4/3

So, we have

[2(x + 3) - x]/4 = 4/3

[x + 6]/4 = 4/3

So, we have

3x + 18 = 16

x = -2/3

(3)

For equation (3), we have

3/(x + 1) - 2/(x - 1) = 1/(x² - 1)

So, we have

3(x - 1) - 2(x + 1) = 1

This gives

3x - 3 - 2x - 2 = 1

x = 4

(4)

For equation (4), we have

18/(x² - 3x) = 2x/(x - 3) - 6/x

So, we have

18 = 2x² - 6(x - 3)

This gives

x = 0 or x = 3

(5)

For equation (5), we have

3x/(x + 2) + 6/x + 4 = 12/(x² + 2x)

Multiiply through by x² + 2x

3x² + 6(x + 2) + 4(x² + 2x) = 12

Evaluate

x = 0 or x = -2

(6)

For equation (6), we have

1/(x - 2) + 4/(x + 9) = 3/(x² + 7x - 18)

Multiiply through by (x² + 7x - 18)

x - 9 + 4x + 8 = 3

So, we have

5x = 4

Evaluate

x = 4/5

(7)

For equation (7), we have

3/5x² - 1/5 = 2/25x²

Multiiply through by 25x²

15 - 5x² = 2

So, we have

5x² = 17

Evaluate

x = √(17/5)

(8)

For equation (8), we have

9/(x + 1) = 2/(x² - 1)

Multiiply through by 25x²

9x - 9 = 2

So, we have

9x = 11

Evaluate

x = 11/9

(9)

For equation (9), we have

3/(x³ - 8) = 1/(x - 2)

Cross multiiply

(x³ - 8) = 3(x - 2)

Evaluate

x = -1 and x = 2

(10)

For equation (10), we have

x²/2 - 3x/2 + 1 = 0

Multiiply through by 2

x² - 3x + 2 = 0

Factoize

(x - 1)(x - 2) = 0

So, we have

x = 1 and x = 2

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Amy's total cost: $697.26

Mackenzie's total cost: $11904.62

Amount = P = 340

Amy's interest rate = ra = 6% = 0.06

Mackenzie's interest rate = rm = 30% = 0.3

Amount is compounded yearly.

Amount at the end of the year is calulated as

Pn= P(1+r)

We will use Excel to fill given table

Person APR 0 1 2 3 6

Amy 6% 340.00 360.40 382.02 404.95 482.30

Mackenzie 30% 340.00 442.00 574.60 746.98 1641.12

Amy has an annual rate of 6%. So Amy has a monthly rate of 6 /12 = 0.5% = 0.005

Mackenzie has an annual rate of 30%. So Mackenzie has a monthly rate of 30/12 = 2.5% = 0.025

Pn= P(1+r)

Here will be replaced by a number of months and r is relaced by monthly interest rate

We can modified this formula as

12n

Pn= P(1+)

Where n and r is same as in first part of question.

We will use excel to fill given table

Person APR 0 1 2 3 6

Amy 6% 340.00 360.97 383.23 406.87 486.90

Mackenzie 30% 340.00 457.26 614.97 827.06 2011.86

From the above two tables, it is clear that it does matter how the company charges interest. When compounded monthly, the amount will more as compared to when compounded yearly. So,

Yes it matters because the more often they calculate the interest the higher the amount goes.

If neither friend made any payments for 12 years, we can add one more column to calculate for n = 12.

Amy's total cost: $697.26

Mackenzie's total cost: $11904.62

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For the given function the value of f(x) when x = 2 is 0.5, option (d) is correct.

The given function f(x) = 2/x² represents a hyperbolic curve with a vertical asymptote at x=0 and a horizontal asymptote at y=0. As x approaches infinity or negative infinity, the value of the function approaches 0.

The given function is:

f(x) = 2 ÷ x²

We are asked to find the value of f(x) when x = 2.

Substituting x = 2, we get:

f(2) = 2 ÷ 2²

= 2 ÷ 4

= 1/2

= 0.5

Alternatively, we can use the fact that 2² = 4 and simplify the expression as follows:

f(x) = 2 ÷ x²

= 2 ÷ 4

= 1/2

Then, substituting x = 2, we get the same result:

f(2) = 1/2

f = 0.5

Hence, option (d) is correct.

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Answer:

That number is 230 × 1.08 = 248.4.

To find this number, we calculated 8% of 230, which is 18.4 , and then added it to 230, Hence The number that is 8% larger than 230 is 248.4.

To find a number that is 8% larger than 230, we can calculate the 8% increase of 230 and add it to the original number.

Step 1: Calculate the 8% increase of 230:

8% of 230 = (8/100) * 230 = 0.08 * 230 = 18.4

Step 2: Add the 8% increase to 230:

230 + 18.4 = 248.4

Therefore, a number that is 8% larger than 230 is 248.4.

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The comparison data is shown below.

Based on the information provided, we can infer that:

Without more information about the specific data and the context of the study, it is difficult to make further comparisons or draw any conclusions about the relationship between completing homework and exam scores. However, it is interesting to note that completing homework did not seem to have an impact on the average exam score or the variability of exam scores.

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Answer:

19/20--no

32/4--yes (32/4 = 8)

74--yes

23--yes

5.95--no

Answer:

x =  7, y = 3, z = -4

Step-by-step explanation:

Answer:

congruent to each other cause their measurements are same.

congruent means if 2 shapes have same measurements they are called congruent

Answer:

it is the opposite way around

Step-by-step explanation:

Answer:

f(x) = x²-8x+15

g(x) = x -3

h(x) = f(x) ÷ g(x)

= x²-8x+15 ÷ x-3

x-3√x²- 8x +15 | x-5

x² - 3x

-5x + 15

- 5x + 15

-----------

h(x) = x-5

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 1000\\ P=\textit{original amount deposited}\\ r=rate\to 1.3\%\to \frac{1.3}{100}\dotfill &0.013\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{weekly, thus fifty two} \end{array}\dotfill &52\\ t=years\dotfill &3 \end{cases}[/tex]

[tex]1000 = P\left(1+\frac{0.013}{52}\right)^{52\cdot 3} \implies 1000=P(1.00025)^{156} \\\\\\ \cfrac{1000}{(1.00025)^{156}}=P\implies 961.76\approx P[/tex]

The mean amount of electricity generated in Texas by wind-powered turbines from 2007 to 2010 is 4,353 megawatts, to the nearest megawatt.

The data for this question can be found in the following table:

Year Electricity Generated (Megawatts)

2007 4,353

2008 7,113

2009 9,403

2010 10,089

To find the mean, we simply add up the values in the table and divide by the number of values, which is 4.

Mean = (4,353 + 7,113 + 9,403 + 10,089) / 4 = 4,353 megawatts

Therefore, the mean amount of electricity generated in Texas by wind-powered turbines from 2007 to 2010 is 4,353 megawatts, to the nearest megawatt.

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Answer:

To calculate the amount you would need to deposit in the account now, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

where A is the amount you will have after 15 years, P is the principal amount (the amount you need to deposit now), r is the annual interest rate (7%), n is the number of times the interest is compounded per year (12 for monthly compounding), and t is the time in years (15).

Plugging in the values, we get:

2000 = P(1 + 0.07/12)^(12*15)

Simplifying the right side, we get:

2000 = P(1.00583)^180

Dividing both sides by (1.00583)^180, we get:

P = 2000 / (1.00583)^180

P = $775.80 (rounded to the nearest cent)

Therefore, to have $2000 in the account in 15 years with an annual interest rate of 7% compounded monthly, you would need to deposit $775.80 now.

If a turtle lives in a garden and a hedgehog lives in the woods. The distance between the garden and the woods is 450m.

Let d represent the distance between the turtle's garden and the hedgehog's wood

Let h represent the  speed of the hedgehog

Let the  turtle's speed = h-10

Le the time it takes for the hedgehog to walk from the woods to the meeting point= t

Set up two equations

d = (h-10)(t+4.5) + ht (Equation 1)

d - 150 = ht (Equation 2)

Solve for d by substituting equation 2 into equation 1:

ht + (h-10)(t+4.5) = ht + 150

(h-10)t + 45h = 150

t = (150 - 45h) / (h-10)

Substitute t into equation 2:

d = ht + 150 - (h-10)(t+4.5)

d = h(150 - 45h)/(h-10) + 150 - (h-10)(45h/(h-10) + 4.5)

d = 2250/(h-10) (distance between the garden and the woods)

Since the turtle and hedgehog meet in 5 hours

Thus,

d = ( h-10 ) (5) + h( 5- 4.5 )

d = 5h - 25

Substitute

5h - 25 = 2250/(h-10)

Multiplying both sides by h-10

5h² - 75h + 250 = 0

Dividing both sides by 5

h²- 15h + 50 = 0

Using the quadratic formula

h = (15 ± sqrt(15^2 - 4(1)(50))) / (2*1)

h = (15 ± 5) / 2

So,

h = 10 or h = 5

Distance between the garden and the woods :

d = 2250/(h-10)

d= 2250/(5-10)

= 450 meters

Therefore the distance is 450m.

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Answer:

It is 50x or 50*x or 50(x).

Answer: 9

Step-by-step explanation:

Range = maximum number - minimum number (in a data set)

50-41 = 9 minutes

if a student scored a 69 on his first test, predict that his score on the second test will be approximately 64.57.

Students’ test scores on the first two tests in an introductory calculus class.

To make a prediction for the student's score on the second test based on their score of 69 on the first test, we need to find the regression equation for the data set.

The regression equation for these data is

y = 0.6443x + 19.943

Where y is the predicted score on the second test and x is the actual score on the first test.

Substituting x = 69 into this equation, we get

y = 0.6443(69) + 19.943 ≈ 64.57

Therefore, if a student scored a 69 on his first test, we predict that his score on the second test will be approximately 64.57.

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The given total area including the frame is y = (8+2x)(10+2x).

As per the question the thickness of the frame is x.

The area of a rectangle is given by A=L*B

For a picture with frame it will be A=(L+2t)*(B+2t)

1. Comparing the above equation with the given equation it can be concluded that the Length is 10 and the width is 8.

2. The given equation is 100=(8+2x)(10+2x)

Upon solving it simplifies to [tex]x^2+9x-5=0[/tex]

x=0.525.

Thus the thickness x=0.525.

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A)  The continuous rate of growth of this bacterium population = 0.35

B) The initial population of the culture = 920

C) The number of bacteria at time t=5 are 5294

Here, the function [tex]n(t)=920\times e^{(0.35\times t)}[/tex] represents the number of bacteria in a culture at time t

A) We know that in exponential function f(x) = [tex]ae^{kx}[/tex], k is the rate of growth

Here, in this function n(t) = [tex]920\times e^{(0.35\times t)}[/tex],  the continuous rate of growth is 0.35

B) To find the initial population of the culture

Substitute t = 0, in n(t)

n(0) = [tex]920\times e^{(0.35 \times 0 )}[/tex]

n(0) = 920 × e⁰

n(0) = 920

This is the initial population.

C) Now we find the number of bacteria at time t=5

[tex]n(t)=920\times e^{(0.35\times t)}[/tex]

Substitute t = 5 in above equation.

n(5) =[tex]920 \times e^{(0.35 \times 5)}[/tex]

n(5) = 5294.23

n(5) ≈ 5294

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The number of bacteria in a culture is given by the function

n(t) =920e^0.35t Where t is measured in hours

A) what is the continuous rate of growth of this bacterium population? Your answer is __ percent

B) what is the initial population of the culture (at t=0) your answer is __

C) how many bacteria will the culture contain at time t=5 ? Your answer is __ Round to the nearest bacteria

Answer:

8 = 2m + 4

2m = 4, so m = 2

So the equation of this line is y = 2x + 4.

D is the correct answer.

Answer:

its 112.7

Step-by-step explanation:

x+2x=3x. 3x = 338

divide 3x and 338 by 3 three is cancelled and x equals to 112.7

[tex]\sf x=13.[/tex]

Assuming that the canvas has a standard rectangle shape, the area should be given by: [tex]\sf A= bh[/tex], where "b" is the base length of the rectangle, and "h" its heignt.

We're told that the canvas is "x" inches wide, and that the length of it is "twice as long as the width", thus it is "2x". Now, let's take width as the base, and length as the height.

Since the formula for area is just a product between width and length, and those values are "x" and "2x", respectively, the formula for the area of this canvas is:

[tex]\sf (x)(2x)=338(in^{2} )[/tex]

a) Solve the product.

[tex]\sf (x)(2x)=338(in^{2} )\\ \\\sf 2x^{2} =338(in^{2} )[/tex]

b) Divide by "2" on both sides of the equation.

[tex]\sf \dfrac{2x^{2}}{2} =\dfrac{338(in^{2} )}{2} \\ \\x^{2} =169[/tex]

c) Take the square root of both sides.

[tex]\sf \sqrt{x^{2}} =\sqrt{169} \\ \\x=13[/tex]

[tex]\sf x=13.[/tex]

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The function that is even is f(x) = 6x² - 8.

option C.

An even function is a function that satisfies the condition f(-x) = f(x) for all values of x in its domain. In other words, an even function is symmetric with respect to the y-axis.

The function that is even is calculated as follows;

f(x) = 5x² - x

f(-x) = 5(-x)² - (-x)

f(-x) = 5x² + x

f(x) ≠ f(-x)

f(x) = 3x³ + x

f(-x) = 3(-x)³ + (-x)

f(-x) = -3x³ - x

f(x) ≠ f(-x)

f(x) = 6x² - 8

f(-x) = 6(-x)² - 8

f(-x) = 6x² - 8

so f(x) = f(-x), this function is even.

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The most common point total scored was 10 with a frequency of 9 or 25% of the total frequency.

To create the score frequency distribution, we have to list the unique values in the data set and count how many times each value appears.

1                                   1                       1/24 =  0.042 = 4.2%

3                                  2                      2/24 = 0.083  = 8.3%

4                                  1                       1/24 = 0.042  = 4.2%

5                                  1                       1/24 = 0.042  = 4.2%

6                                  1                       1/24 = 0.042 = 4.2%

7                                  2                      2/24 = 0.083 = 8.3%

8                                  1                       1/24 = 0.042   = 4.2%

9                                  2                      2/24 = 0.083  = 8.3%

10                                 6                      6/24 = 0.25   = 25%

11                                  1                       1/24 = 0.042 = 4.2%

12                                 2                      2/24 = 0.083 = 8.3%

13                                 2                      2/24 = 0.083 = 8.3%

14                                 2                      2/24 = 0.083  = 8.3 %

                                 ----------                                  

                                    24                                    

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a)There is higher variability of Y with larger values of X.

b) There is non linear relation between X and Y.

a) Based on the given figure, we can make the following observations:

Therefore, the correct statement is There is higher variability of Y with larger values of X.

b) Based on the features, it is likely that a linear model may not be suitable for these data, and a non-linear model or other regression techniques may be more appropriate to capture the relationship between X and Y accurately.

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The equation is not a quadratic equation. Statement is false.

A second-order polynomial equation with just one variable, x, is referred to as a quadratic equation. with a ≠ 0 . The fundamental theorem of algebra guarantees that it has at least one solution since it is a second-order polynomial equation. The arrangement might be genuine or complex.

This is a linear equation in the form y = mx + b, where m is the slope and b is the y-intercept. In this case, the slope is 5 and the y-intercept is 2. A quadratic equation is an equation in the form y = ax^2 + bx + c, where a, b, and c are constants and x is the variable.

Thus, given equation is not a quadratic equation. Statement is false.

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The total charge if 138 guests attend the conference is $5450

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

Using the above as a guide, we have the following:

Total = ballroom + food * number of guests

Substitute the known values in the above equation, so, we have the following representation

Total = 620 + 35 * 138

Evaluate

Total = 5450

Hence, the total charges is $5450

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The equation is true based on the model is B) (-3) + 5 = 2.

If we consider the circles on the left as negative units and the circles on the right as positive units.

Then we can see that there are 5 positive units and 3 negative units, so the sum is

= 5 - 3

= 2.

Therefore, the correct equation is: B) (-3) + 5 = 2.

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