(x+3) (x-2) =2x
find the valűe of x​

Answer:  350.214

Step-by-step explanation:

The length of the Green Route in miles is 64 miles.

Miles is a unit of linear measurement. It is traditionally defined as 5,280 feet, or 1,760 yards, and is equivalent to 1.609 kilometers. Miles are commonly used to measure long distances, such as the distance between two cities. They are also used to measure the lengths of roads and other paths. Miles are one of the most commonly used units of measurement in the United States.

The length of the Green Route in miles can be calculated by subtracting the total mileage traveled on the Blue Route from the total mileage traveled on both routes.

Total miles traveled on Monday = 38 miles
Total miles traveled on Tuesday = 80 miles

Total miles traveled on the Blue Route = 5 + 11 = 16 miles

Therefore, the total miles traveled on the Green Route = 80 - 16 = 64 miles

Therefore, the length of the Green Route in miles is 64 miles.

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"There are 26C₅ = 65,780 ways the students can be chosen because the order they are chosen does not matter." is correct statement. Therefore, the answer is option C.

The problem asks us to choose 5 students out of a class of 26 to present homework problems. Since the order in which the students present the problems does not matter, we need to use the combination formula. The combination formula is used to calculate the number of ways to choose a subset of k elements from a set of n elements without regard to order, and it is denoted by nCk.

Option A, "There are 26C₅ = 65,780 ways the students can be chosen because the order they are chosen matters," is incorrect because the order in which the students are chosen does not matter.

Option B, "There are 26P₅ = 7,893,600 ways the students can be chosen because the order they are chosen matters," is incorrect because we are choosing 5 students out of 26, and the order in which they are chosen does not matter.

Option D, "There are 26P₅ = 7,893,600 ways the students can be chosen because the order they are chosen does not matter," is also incorrect because the order in which the students are chosen does not matter.

Therefore, the answer is option C.

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Complete question is:

In a class of 26 students, a teacher chooses a different student to each present five different homework problems. Which statement describes the number of ways the students can be chosen to present the problems?

A) There are 26C₅ = 65,780 ways the students can be chosen because the order they are chosen matters.

B) There are 26P₅ = 7,893,600 ways the students can be chosen because the order they are chosen matters.

C) There are 26C₅ = 65,780 ways the students can be chosen because the order they are chosen does not matter.

D) There are 26P₅ = 7,893,600 ways the students can be chosen because the order they are chosen does not matter.

Answer:

5%

Step-by-step explanation:

Percent error equation is:

(Absolute value of experimental value - actual value / actual value) * 100

Experimental Value: 315

Actual Value: 300

315 - 300 / 300 = 0.05

0.05*100 = 5

Percent error is 5%

Answer: the percent error is 5%

Step-by-step explanation:

The formula for the partial sum of a geometric sequence with first term a₁, common ratio r, and n terms is given by:

Sₙ = a₁(1 - rⁿ)/(1 - r)

A geometric sequence is a non-zero numerical sequence in which each term after the first is found by multiplying the preceding one by a fixed, non-zero quantity known as the common ratio.

In the formula, Sₙ is the sum of the first n terms of the sequence.

Alternatively, the formula can be expressed as:

Sₙ = (a₁(rⁿ - 1))/(r - 1)

Both of these formulas give the same result and can be used to calculate the partial sum of a geometric sequence.

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The sum of all the number is found to be 630 which is not given in the options.

Let the middle number be x. Then the five numbers smaller than x have an average of 44, so their sum is 544 = 220. Similarly, the five numbers larger than x have an average of 68, so their sum is 568 = 340.

The total of all the numbers is 9x since x is the median and average of all the numbers. The total of all the numbers equals 9x since we know that x is the average of all the numbers.

Therefore, we have,

9x = 220 + x + 340

Simplifying and solving for x, we get,

8x = 560

x = 70

Therefore, the sum of all the numbers is 9x = 970 = 630.

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Complete question - Nine numbers are written in ascending order, the middle number is the average of all the numbers, the average of the five largest numbers is 68, and the average of the five smallest is 44. What is the sum of all the numbers? ?

a) 112

b) 504

c) 144

d) 560

d) 122

The result of the operation that we have done here is -5√3.

We know that one of the most important things that we have to do in mathematics is that we have to convert word equations into mathematical equations and this is quite critical in how we can be able to work it so as to get the equation that we are looking for.

We now have that;

5/-3 * 3 * √3

5/-1 * √3

-5* √3

-5√3

We can see that after the computation of the word problem that we have here, the result is -5√3

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In 12 days, both Eve and Jenna will work out on the same day again.

To find the number of days until Eve and Jenna work out on the same day again, we need to find the least common multiple (LCM) of 6 and 4.

One way to find the LCM is to list the multiples of each number until we find a multiple that they have in common:

Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, ...

Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, ...

From this list, we see that the least common multiple of 6 and 4 is 12.

This means that in 12 days, both Eve and Jenna will work out on the same day again.

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Answer: The graph that best represents the number of centimeters the toy car travels in x seconds would be a linear graph with a slope of 12. The equation for this graph would be y = 12x, where y represents the distance traveled in centimeters and x represents the time in seconds.

Step-by-step explanation:

On performing the given row-operation on the given augmented-matrix:

(a) multiplying row1 by -2 and adding to row2, we have [tex]\left[\begin{array}{ccc}5&-2&6\\-10&10&-15\end{array}\right][/tex],

(b) interchanging row1 and row2, we have [tex]\left[\begin{array}{ccc}0&6&-3\\5&-2&6\end{array}\right][/tex],

(c) Multiplying row1 by 2, the matrix becomes [tex]\left[\begin{array}{ccc}10&-4&12\\0&6&-3\end{array}\right][/tex].

The augmented matrix on which we have to perform the row operation is

⇒ [tex]\left[\begin{array}{ccc}5&-2&6\\0&6&-3\end{array}\right][/tex],

Part(a) : We have to multiply row1 by -2 and and add to row2,

The row-operation is performed as : [tex]\left[\begin{array}{ccc}5&-2&6\\(5\times-2)+0&(-2\times-2)+6&(6\times-2)-3\end{array}\right][/tex];

Simplifying further ,

We get,

[tex]\left[\begin{array}{ccc}5&-2&6\\-10&10&-15\end{array}\right][/tex].

Part(b) : We have to interchange the "row1" and "row2",

On interchanging,

We get,

[tex]\left[\begin{array}{ccc}0&6&-3\\5&-2&6\end{array}\right][/tex].

Part(c) : We have to multiply the elements of "row1" by 2,

So, On multiplying the "row1" by 2,

We get,

⇒ [tex]\left[\begin{array}{ccc}5\times 2&-2\times 2&6\times 2\\0&6&-3\end{array}\right][/tex]

⇒ [tex]\left[\begin{array}{ccc}10&-4&12\\0&6&-3\end{array}\right][/tex].

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The value of tan A is 0. 667. Option B

To determine the value of the identity, we need to take note of the different trigonometric identities.

these identities are;

We also have that the ratio for the tangent identity is expressed as;

tan θ= opposite/adjacent

From the information given, we have that;

The hypotenuse is 18.03, the side opposite to angle A is 10, and the side adjacent to angle A is 15

Then, for the identity, we have;

tan A = 10/15

Divide the values

tan A = 0. 667

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It is financially beneficial for Harris Fishing Tours to replace the old boat with the new fuel-efficient model, as it has a net benefit of $12,000 compared to continuing to use the old boat.

To determine whether Harris Fishing Tours should replace the old boat with the new fuel-efficient model, we need to compare the costs and benefits of each option.

Option 1: Replace the old boat with the new fuel-efficient model

If Harris replaces the old boat with the new fuel-efficient model, they will have to pay $80,000 for the new boat. They can sell the old boat for $32,000, so the net cost of the new boat will be $48,000 ($80,000 - $32,000).

The new boat is expected to be extremely fuel efficient, which means that the fuel costs will be $15,000 per year lower than the old boat. Over the remaining four years of the old boat's useful life, this represents a total savings of $60,000 ($15,000 x 4).

Therefore, the total cost of replacing the old boat with the new fuel-efficient model is $48,000 - $60,000 = -$12,000, which means that this option has a net benefit of $12,000.

Option 2: Continue to use the old boat until it wears out

If Harris decides to continue using the old boat until it wears out, they will not incur the $80,000 cost of purchasing the new boat.

However, they will continue to pay $15,000 per year more in fuel costs than they would with the new boat. Over the remaining four years of the old boat's useful life, this represents a total cost of $60,000 ($15,000 x 4).

In addition, at the end of the four years, the old boat will have no salvage value since it will have reached the end of its useful life.

Therefore, the total cost of continuing to use the old boat until it wears out is $60,000, which means that this option has a net cost of $60,000.

Conclusion

Based on the analysis above, it is more financially beneficial for Harris Fishing Tours to replace the old boat with the new fuel-efficient model. This option has a net benefit of $12,000, while continuing to use the old boat until it wears out has a net cost of $60,000.

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The wrong formula was used. The correct method is: area of sector = 115/360 * 255 ≈ 81.46 square feet.

The area of a sector is calculated by using the formula:

Area of sector = ∅/360 * πr², where:

r is the radius of the circle

∅ is the central angle measure.

The error made was that a wrong method/formula was used in finding the area of sector.

Given the following:

Area of circle = 255 square feet (πr²)

∅ = 115°

Note that πr² represents the area of a circle, therefore, substituting the values into the formula, we have:

Area of sector = 115/360 * 255

Area of sector ≈ 81.46 square feet

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There are 29 degrees of freedom for this repeated-measures t-test.

The degrees of freedom (df) for a repeated-measures t-test is calculated as (n-1), where n is the number of paired observations.

In this case, each hamster's activity was measured during both summer and winter, resulting in a paired sample design. Therefore, the number of paired observations is equal to the number of hamsters, which is n = 30.

Hence, the degrees of freedom for this repeated-measures t-test is:

df = n - 1 = 30 - 1 = 29

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Jordan's account balance at the end of the month would be $143.85.

What is the basic arithmetic operations?

The four basic mathematical operations are Addition, subtraction, multiplication, and division.

To determine Jordan's account balance at the end of the month, we need to add up the deposits and withdrawals to the initial balance.

Initial balance: $92.66

Deposits: $7.72 + $70.42 + $107.46 = $185.60 (sum of positive amounts)

Withdrawals: -$84.26 + (-$50.15) = -$134.41 (sum of negative amounts)

To calculate the account balance at the end of the month, we can add the deposits and withdrawals to the initial balance:

Account balance at the end of the month = Initial balance + Deposits - Withdrawals

= $92.66 + $185.60 - $134.41

= $143.85

Hence, Jordan's account balance at the end of the month would be $143.85.

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The expression can be simplified to get:

2.7^(1)*3.8^(5)

The correct option is C.

Remember that if we have the product of two powers with the same base, we only need to add the exponents.

Then we will get:

2.7^(-3) * 3.8^(2) * 2.7^(4) * 3.8^(3)

= (2.7^(-3)*2.7^(4)*3.8^(2)*3.8^(3))

= (2.7^(-3 + 4)*3.8^(2 + 3))

= 2.7^(1)*3.8^(5)

That is the expression simplified, we can see that the correct option is C.

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The calculated value of the probability that the experiment results in exactly 1 success is 0.08719

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

n = 7

x = 1

p = 0.45

The probability is then calculated as

P(x = x) = nCr * p^x * (1 - p)^(n - x)

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

P(x = 1) = 7C1 * (0.45)^1 * (1 - 0.45)^(7-1)

Evaluate the expression

So, we have

P(x = 1) = 0.08719

Hence, the probability is 0.08719

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The percentage of the powdered lemon mix in Dianelys's mix indicates that Dianelys's mix is more lemony.

A percentage is an expression of a ratio of two quantities as a fraction of 100.

The number of cups of water Zachary mixes with 5 cups of powdered lemon mix = 11 cups of water
Number of cups of water Dianelys mixes with 4 cups of powdered lemon mix = 7 cups of water

Zachary's percentage of powdered lemon mix = (5/(11 + 5)) × 100 = 31.25%

Dianelys's percentage of powdered lemon mix = (4/(7 + 4)) × 100 = 36.[tex]\overline{36}[/tex]%

The percentage of powdered lemon mix for Dianelys which is more than the percentage in Zachary's powdered lemon mix indicates that Danialys mix is more lemony.

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The bottom end of the pendulum travels 18,115.2 meters/day, which is approximately 18.12 kilometers/day (since 1 kilometer = 1000 meters).

The motion of the pendulum is a simple harmonic motion and the period of oscillation can be calculated as follows:

T = 2π√(l/g)

where l is the length of the pendulum and g is the acceleration due to gravity (approx. 9.81 m/s²).

Substituting l = 1 m, we get

T = 2π√(1/9.81)

T ≈ 2.006 s.

In one day, there are

24 hours x 60 minutes/hour x 60 seconds/minute

= 86,400 seconds.

The pendulum makes half a period (i.e., one back-and-forth swing) in 2/2 = 1 second. Therefore, it makes

86,400/2

= 43,200 back-and-forth swings in one day.

The distance traveled by the bottom end of the pendulum in one complete swing is equal to the length of the pendulum times twice the maximum angle it makes with the vertical, which is

2 x 12 degrees

= 24 degrees

= 0.419 radians.

Therefore, the distance traveled by the bottom end of the pendulum in one complete swing is

1 meter x 0.419

= 0.419 meters.

Multiplying by the number of swings in one day, we get:

0.419 meters/swing x 43,200 swings/day

= 18,115.2 meters/day.

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1) Line AB

2) Ray AB

3) Line segment AB

4)Ray BA

The first drawing is a line AB because a line passing through two different points A and B

The second drawing is ray AB because it started at A

The third drawing is a line segment AB because it is part of a straight line that is bounded by two distinct end points, and contains every point on the line that is between its endpoints

The fourth drawing is ray BA

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Answer:

it's 4 cm

Step-by-step explanation:

A. Square = 50 cm²

A. Square = s × s

50 = s²

s = √50

SP = hypotenuse (c) = s

c = s = √50

b = √34

a = PT = ...?

use Pythagorean theorem to find PT

a² + b² = c²

a² + (√34)² = (√50)²

a² + 34 = 50

a² = 50 - 34

a² = 16

a = √16

a = 4 cm

Note that the perimeter of the parallelogram is 42

recall that opposite sides of a parallelogram are congruent always

We have to to find the distance between the  points Q(6, 6 ) and R(1, -6) using the distance formula which is

d = √[(x2 - x1) ² + (y2 - y 1)²]

where d is the distance between two points with paris   (x1 , y1)

and (x2, y2).

PS = QR = √(6-1)²  + (6+6)²

    = √5² + 12²
= √(25+144

= √(169)

= 13

PQ = SR = 8

Perimeter  = 13 + 13 + 8 + 8
Perimeter = 42.

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Full Question:

Although part of your question is missing, you might be referring to this full question:

See attached image.

Answer:

Step-by-step explanation:

When x_1 =7 then you can figure out by given condition say X_n+1= 2X_n-3

then X_2= 11 by substituting the value of X_1 as 7 similarly you can find out the value of X_3 by substituting X_2 as 11 so X_3 =19.

Similarly you can find out b)

a) over the interval of 0 - 10 hours, the average rate of change of the temperature is 17,088°C/hr.

b) the average temperature of the water in the system is 1527.

c) over the interval of 10 - 20 hours, the total change in the temperature of the water in the solar steam power system is -14,351°C.

a) g'(x) = 2 + [tex]\int\limits^x_0[/tex] ƒ'(t) dt

g'(-3) = -2

b) The absolute maximum value of g on the closed interval [-5, 5]=

10 + 2√7.

c) The x-coordinates of the points of inflection of the graph of g are -1, 0 and 2.

What is right Riemann sum formula?

The right Riemann sum formula uses the right-most value of each interval as the value of the function over that interval.

a) g(5) = 2(5) + [tex]\int\limits^5_0[/tex] ƒ(t) dt

= 10 + 2√7

g'(x) = 2 + [tex]\int\limits^x_0[/tex] ƒ'(t) dt

g'(-3) = 2 + [tex]\int\limits^3_0[/tex]ƒ'(t) dt

= 2 - (4 + 0)

= -2

b) The absolute maximum value of g on the closed interval [-5, 5]=

10 + 2√7.

This is because the highest value of ƒ(t) dt on the interval= 4√7, which occurs at x = 2.

The highest value of g is thus given by 10 + 2√7.

c) The x-coordinates of the points of inflection of the graph of g are -1, 0 and 2.

This is because ƒ'(t) dt is undefined at these points, so the second derivative of g is also undefined.

a) To evaluate the  S'(t) dt, we need to calculate the area under the curve of the temperature data given in the table. To do this, we use the trapezoidal rule. This gives us the following:

[tex]\int\limits^10_0[/tex] S'(t) dt = [(142 + 210 + 254 + 280 + 274 + 268)/2] × 8

= 17,088

This means that over the interval of 0 - 10 hours, the average rate of change of the temperature is 17,088°C/hr.

This can be interpreted in the context of the problem as the average rate at which the temperature of the water in the solar steam power system is changing over the given time interval.

b) To approximate the average temperature of the water in the system using a right Riemann approximation, we need to calculate the area under the curve of the temperature data given in the table. We can do this using the right Riemann sum formula, which gives us the following:

Right Riemann Approximation = [(210 + 254 + 280 + 274)/4] × 6 = 1527

In this case, the right-most value of each interval is lower than the true average over that interval, so the approximation will be lower than the true average.

c) To determine the total change in the temperature of the system for the interval 10≤t≤20, we need to calculate the area under the curve of the equation S'(t)=-√2xe (√x²-100)/x.

This can be done using the definite integral of the equation, which gives us the following:

Total Change = ∫1020-√2xe (√x²-100)/x dx

= -14,351

This means that over the interval of 10 - 20 hours, the total change in the temperature of the water in the solar steam power system is -14,351°C.

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Answer:

75%

Step-by-step explanation:

To determine the total percentage of athletes who enjoy cycling, we need to consider the percentages given in the problem.

According to the information provided:

55% of the team does not like to run.

Of those who do not like to run, 70% enjoy cycling.

Of those who enjoy running, 80% also enjoy cycling.

To calculate the total percentage of athletes who enjoy cycling, we need to consider the percentages from both branches of the tree diagram.

Percentage of athletes who do not like to run and enjoy cycling:

= (Percentage of athletes who do not like to run) * (Percentage of those who enjoy cycling within that group)

= 55% * 70% = 38.5%

Percentage of athletes who enjoy running and enjoy cycling:

= (Percentage of athletes who enjoy running) * (Percentage of those who enjoy cycling within that group)

= (100% - 55%) * 80% = 45% * 80% = 36%

Total percentage of athletes who enjoy cycling:

= Percentage of athletes who do not like to run and enjoy cycling + Percentage of athletes who enjoy running and enjoy cycling

= 38.5% + 36% = 74.5%

Therefore, the correct answer is:

74.5%

Note that the scatter plot (attached) for the given data is described below.

The scatter plot for the given data set shows a moderately strong negative linear relationship between x and y. The data points appear to form a somewhat linear pattern, indicating that there is a linear association between the variables.

The scatter plot suggests that as the x values increase, the corresponding y values decrease.

An appropriate sale for this data set would be a linear regression, which can provide a mathematical model for predicting y values based on x values.

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Answer:

(x-3)(x+4)

Step-by-step explanation:

This way is how it s done in Greece. If u don't understand don't read the explanation Δ=β2-4αγ=81-32=49

χ1,2=-1+-7^2=3

=-4

The values of the composite functions are (g o f)(x) = [tex]\frac{9x^2-18x+4}{4}-5[/tex], (j o g)(x) = 3x² - 15x + 1, (g o h)(x) = [tex]\frac{\left(2x-1\right)^2}{1089}-\frac{5\left(2x-1\right)}{33}[/tex] and (g o g)(-2) = 126

Given that we have the function definitions

The composite functions are calculated below

(g o f)(x) = g(f(x))

(g o f)(x) = (f(x))² - 5f(x)

So, we have

(g o f)(x) = (3/2x + 1)² - 5(3/2x + 1)

Evaluate

(g o f)(x) = [tex]\frac{9x^2-18x+4}{4}-5[/tex]

Next, we have

(j o g)(x) = j(g(x))

(j o g)(x) = 3g(x) + 1

So, we have

(j o g)(x) = 3(x² - 5x) + 1

(j o g)(x) = 3x² - 15x + 1

Next, we have

(g o h)(x) = g(h(x))

(g o h)(x) = (h(x))² - 5h(x)

So, we have

(g o h)(x) = ((2x - 1)/33)² - 5((2x - 1)/33)

Evaluate

(g o h)(x) = [tex]\frac{\left(2x-1\right)^2}{1089}-\frac{5\left(2x-1\right)}{33}[/tex]

Lastly, we have

(g o g)(-2) = g(g(-2))

(g o g)(-2) = (g(-2))² - 5g(-2)

So, we have

(g o g)(-2) = ((-2)² - 5(-2))² - 5((-2)² - 5(-2))

(g o g)(-2) = 126

Hence, the values are (g o f)(x) = [tex]\frac{9x^2-18x+4}{4}-5[/tex], (j o g)(x) = 3x² - 15x + 1, (g o h)(x) = [tex]\frac{\left(2x-1\right)^2}{1089}-\frac{5\left(2x-1\right)}{33}[/tex] and (g o g)(-2) = 126

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Answer:

Starting with the equation:

-2x + 6 = -x^2

First, we can rearrange it to put it in standard quadratic form:

x^2 - 2x - 6 = 0

To complete the square, we need to add and subtract a constant term that will make the left-hand side of the equation a perfect square. The constant we need to add is (b/2)^2, where b is the coefficient of x. In this case, b = -2, so:

x^2 - 2x + 1 - 1 - 6 = 0

The first three terms can be written as a perfect square:

(x - 1)^2 - 7 = 0

Add 7 to both sides:

(x - 1)^2 = 7

Now we can take the square root of both sides:

x - 1 = ±√7

Add 1 to both sides:

x = 1 ± √7

So the solutions to the equation are:

x = 1 + √7 or x = 1 - √7

mark me brilliant

Therefore , the solution of the given problem of fraction comes out to be 3/4 cups of yoghurt to the blender.

Any configuration of identically sized parts can be combined to represent the total. In Standard English, quantity is defined as "a portion" within a specific measurement. 8, 3/4. Wholes also include fractions. These serve as the divisor of the ratio, which in mathematical terms would be a pair of numbers. Here are a few illustrations of how to convert simple halves into whole numbers.

Here,

A visual fraction model can be used to illustrate the various fractions in a cup of yoghurt that you want to add in portions to a blender.

For instance, you may divide the cup into four equal parts and use one of those parts to represent 1/4 cup of yoghurt in the blender.

You can divide the cup into two equal parts and display two of those parts to symbolise the addition of 1/2 cup of yoghurt.

You would have added

=> 1/4 + 1/2 = 3/4 cups of yoghurt to the blender.

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