Factor the polynomial completely. If the polynomial is prime, so state.



15y2 - 19y + 6

Answer:

B

Step-by-step explanation:

take square on both sides

7x-4 = 4x

x = 4/3

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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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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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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1. Find the vertex (turning point) of the parabola by using the formula x = -b/2a, where a = 4 and b = 8. This gives x = -1, which is the x-coordinate of the vertex. To find the y-coordinate, substitute x = -1 into the equation: y = 4(-1)² + 8(-1) + 3 = -1.

2. Plot the vertex at the point (-1, -1).

3. To find the x-intercepts, set y = 0 in the equation and solve for x. This gives x = (-8 ± √(8² - 4(4)(3)))/(2(4)) = (-8 ± √16)/8 = -1/2 or -3. Plot these points on the x-axis.

4. To find the y-intercept, set x = 0 in the equation and solve for y. This gives y = 3, so the y-intercept is at the point (0, 3).

5. Since the coefficient of x² is positive, the parabola opens upwards. Sketch the curve passing through the points found above.

6. Label the points of intersection and the turning point on the graph.

Answer:

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

[tex]\sf V_{3 Cylinders} =2.8274(in^{3} ).[/tex]

From the provided information about the ice cubes (height and diameter), it's safe to assume that they are cylinder shaped ice cubes. They could be circular cone ice cubes, but the safest assumption is cylinders. Now, to find the volume of a cylinder we use the following formula:

[tex]\sf V_{Cylinder} =\pi r^{2} h[/tex] or [tex]\dfrac{\pi d^{2} h}{4}[/tex].

For the fist equation, "r" stands for radius, and "h" for height.

On the alternate equation, "d" stands for diameter.

Since we're given the diameter and height, let's use the alternate equation:

[tex]\sf V_{Cylinder} =\dfrac{\pi (1(in))^{2} 1.2(in)}{4}=\dfrac{3}{10} \pi (in^{3} )=0.9425(in^{3} ).[/tex]

This can be done by just multiplying the volume of a single cube ([tex]\dfrac{3}{10} \pi (in^{2} )[/tex]) by 3.

[tex]\sf V_{3 Cylinders} =(3)\dfrac{3}{10} \pi (in^{3} )=\dfrac{9}{10} \pi (in^{3} )=\boxed{\sf 2.8274(in^{3} )}.[/tex]

Assuming the ice cubes have the shape of a circular cone, this is the process for calculating the volume of all 3 cubes:

[tex]\sf V_{Cone} =\dfrac{1}{3} \pi r^{2} h\\ \\\\ \\ V_{3Cones} =3*\dfrac{1}{3} \pi r^{2} h\\ \\ \\= \pi r^{2} h\\ \\ \\=\pi (\dfrac{1(in)}{2} )^{2} (1.2(in))\\ \\\\ =\dfrac{3}{10} \pi (in^{3} )=\boxed{\sf 0.9425(in^{3} )}[/tex]

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Answer:

it is the opposite way around

Step-by-step explanation:

The volume of the rectangular prism is given as follows:

V = 0.9375 cubic inches.

The volume of a rectangular prism, with dimensions length, width and height, is given by the multiplication of these dimensions, according to the equation presented as follows:

Volume = length x width x height.

The dimensions for this problem are given as follows:

Hence the volume is given as follows:

V = 1 x 1.25 x 0.75

V = 0.9375 cubic inches.

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The constant of variation that exists between the weight and the volume of the objects would be = 7/5. That is option C.

A measurement is said to vary directly with another when the increase in proportion of the object leads to a direct decrease to the other one.

That is for the given object;

Weight is directly proportional to Volume

Therefore, weight = k Volume

K = constant of variation

make k the subject of formula;

k= weight/volume

but weight = 28

volume = 20

k = 28/20

= 7/5

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[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 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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Answer:

x =  7, y = 3, z = -4

Step-by-step explanation:

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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The 99% confidence interval estimate of the population standard deviation is [12.54, 54.62] mi/h.

A confidence interval is the mean of your estimate plus and minus the variation in that estimate. This is the range of values you expect your estimate to fall between if you redo your test.

x = [64, 60, 56, 60, 52, 59, 58, 59, 70, 68]

s = 5.963

n = 10

CI = [(n-1)*s²/chi2_upper, (n-1)*s²/chi2 lower]

CI = [(9*5.963^m²)/19.022, (9*5.963²)/2.700]

CI = [12.54, 54.62]

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The solutions of the equation tan(3) + 1 = sec(3) in the interval [0, 2) are approximately:

3 ≈ 0.523599 radians or 30 degrees (in the first quadrant)

3 + π ≈ 3.66444 radians or 210 degrees (in the third quadrant)

The equation tan(3) + 1 = sec(3) can be rewritten as:

tan(3) + 1 = 1/cos(3)

Multiplying both sides by cos(3), we get:

sin(3) cos(3) + cos(3) = 1

Using the identity sin(2x) = 2sin(x)cos(x), we can rewrite the left-hand side as:

sin(2*3) + cos(3) = 1

Simplifying this expression, we get:

2sin(3)cos(3) + cos(3) = 1

Factorizing out cos(3), we get:

cos(3)(2sin(3) + 1) = 1

Dividing both sides by 2sin(3) + 1, we get:

cos(3) = 1/(2sin(3) + 1)

We know that sin^2(3) + cos^2(3) = 1, so we can substitute cos^2(3) = 1 - sin^2(3) into the above equation and simplify:

1/(2sin(3) + 1) = cos(3) = sqrt(1 - sin^2(3))

Squaring both sides and simplifying, we get:

(2sin(3) + 1)^2 = 1 - sin^2(3)

Expanding the left-hand side and simplifying, we get:

4sin^3(3) - 3sin^2(3) - 3sin(3) + 1 = 0

This is a cubic equation in sin(3), which can be solved using various methods, such as Cardano's formula or numerical methods. However, the solutions are quite complicated and involve complex numbers.

In the interval [0, 2), we can use a numerical method, such as Newton's method, to find an approximate solution. Starting with an initial guess of sin(3) = 0.5, we can iteratively apply the formula:

sin(3)_n+1 = sin(3)_n - f(sin(3)_n)/f'(sin(3)_n)

where f(sin(3)) = 4sin^3(3) - 3sin^2(3) - 3sin(3) + 1 and f'(sin(3)) = 12sin^2(3) - 6sin(3) - 3.

After several iterations, we find that sin(3) ≈ 0.464758. Substituting this into the equation cos(3) = 1/(2sin(3) + 1), we get cos(3) ≈ 0.885005.

Therefore, the solutions of the equation tan(3) + 1 = sec(3) in the interval [0, 2) are approximately:

3 ≈ 0.523599 radians or 30 degrees (in the first quadrant)

3 + π ≈ 3.66444 radians or 210 degrees (in the third quadrant)

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Answer:

[tex]100( {1.05}^{5} ) = 127.63[/tex]

[tex]127.63 - 100 = 27.63[/tex]

The closest answer here is B. $25

Answer:

B is the answer of the given above question

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 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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Answer:

8 = 2m + 4

2m = 4, so m = 2

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

D is the correct answer.

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 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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Answer:

| only

Step-by-step explanation:

The equation in standard form of the eclipse is expressed as:

D. x²/9 + y²/8 = 1.

The standard form equation for an ellipse with center at the origin, a vertex at (a, 0), and a focus at (c, 0) is:

x²/a² + y²/b² = 1, where c² = a² - b².

In this case, the center is at the origin, a vertex is at (3, 0), and a focus is at (1, 0).

Since the center is at the origin, we know that a vertex is located a distance of a units to the right and left of the center, so a = 3.

Since the focus is located a distance of c units to the right and left of the center, we know that c = 1.

Using c² = a² - b², we can solve for b²:

1² = 3² - b²

b² = 8

So the equation in standard form is:

x²/9 + y²/8 = 1.

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An equation that models the position of the object at time t is:

s(t) = -2cos(2πt/5).

The general form for the equation that will model a wave is:

±a (sin/cos) (2π(x - p)/T)

where:

a is the amplitude

p is the phase shift

T is the period.

The ± will become +ve provided that the graph starts in the positive direction, and the will become -ve provided it starts in the negative direction.

The (sin/cos) will become sine provided the graph starts at 0 before it is being shifted. Then, it becomes cosine provided that the graph starts at the amplitude.

In this case, our graph begins at negative, and the at the amplitude that has no phase shift, the ±ve will become -ve, (sin/cos) will now become cos, and p will become zero. Plugging in the values that were given in the problem, we see that a = 2 and T = 5.

Thus, this equation is: s(t) = -2cos(2πt/5).

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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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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