How to factor -2(x^3 - 7x^2 + 12x -10)? Please show me the work step by step

Answer:

1/10 x 58 =5.8 if they want it in fraction its 4/5

Step-by-step explanation:

The answer would be 5 and 4/5.

Answer:

your answer is 3 liters

Step-by-step explanation:

as he brought 12 boxes and 1 box=250 ml

so 250/1000=0.25 l this is a capity of 1 box in liters so you need to multply by 12 as there is 12 box so

0.25*12=3

so 12 boxes contain 3 liters of juice

Hope it helped you if yes so please make me the brainiest

Answer:

1/720

Step-by-step explanation:

there is only one way to spell tiger but there's 720 outcomes of the other words you can make

The probability that TIGERS is spelled correctly when you hold up the posters is 0.00139 approximately or 1/720 exactly.

Suppose that there are finite elementary events in the sample space of the considered experiment, and all are equally likely.

Then, suppose we want to find the probability of an event E.

Then, its probability is given as

\(P(E) = \dfrac{\text{Number of favorable cases}}{\text{Number of total cases}} = \dfrac{n(E)}{n(S)}\)

where favorable cases are those elementary events who belong to E, and total cases are the size of the sample space.

For this case, the letters of TIGERS are given at random.

All the six letters are different and there exist 6! permutations for them. (as for n unique things, there exist n! possible arrangements of theirs).

So, the posters can be distributed in 6! = 6×5×4×3×2×1 = 720 ways.

Out of those 720 ways, there is only one correct way to spell TIGERS correctly.

Thus, we get:

P(event that correct order of posters is distributed) = \(\dfrac{1}{720} \approx 0.00139\)

Thus, the probability that TIGERS is spelled correctly when you hold up the posters is 0.00139 approximately or 1/720 exactly.

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Answer:

Graphing the points we have;

Above is the graph of the given equation showing the derived points.

Explanation:

Given the equation;

To plot the graph we need to calculate the corresponding values of x and y at each point.

Let us calculate the values of y for x = -4,-2,0,2, and 4;

Therefore, Graphing the points we have;

Above is the graph of the given equation showing the derived points.

Answer:

Step 1: Write your hypotheses and plan your research design

Step 2: Collect data from a sample

Step 3: Summarize your data with descriptive statistics

Step 4: Test hypotheses or make estimates with inferential statistics

Step 5: Interpret your results

Step-by-step explanation:

Answer:

c = 18

Step-by-step explanation:

Given

\(\frac{c}{3}\) = \(\frac{30}{5}\) = 6

Multiply both sides by 3

c = 3 × 6 = 18

(a) The sum of the series 1+2+3+4+...+392 is 77,028.

(b) The sum of the series 1+2+3+4...x is (x/2)(1 + x).

(c) The sum of the series 546 + 547 + 548 + 549 is 2,190.

To solve the exercise using Polya's four-step problem-solving strategy, we will apply the procedures presented in the lesson.

(a) For the series 1+2+3+4+...+392:

Using the arithmetic series formula Sn = (n/2)(a + l), where n is the number of terms, a is the first term, and l is the last term, we can substitute the values: Sn = (392/2)(1 + 392) = 196(393) = 77,028.

(b) For the series 1+2+3+4...x:

To find the sum of this series, we need to know the number of terms (n) based on the value of x. Since the series follows a consecutive pattern, the number of terms will be equal to x itself. Thus, the sum of the series would be Sn = (x/2)(1 + x).

(c) For the series 546 + 547 + 548 + 549:

Using the arithmetic series formula Sn = (n/2)(a + l), we can determine the number of terms (n) by subtracting 546 from 549 and then adding 1: n = 549 - 546 + 1 = 4. Substituting the values into the formula: Sn = (4/2)(546 + 549) = 2(1095) = 2,190.

The final answer for each part is:

(a) The sum of the series 1+2+3+4+...+392 is 77,028.

(b) The sum of the series 1+2+3+4...x is (x/2)(1 + x).

(c) The sum of the series 546 + 547 + 548 + 549 is 2,190.

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The exponential function sketched is defined as follows:

y = 2(0.5)^x - 6.

The standard definition of an exponential function is given as follows:

y = a(b)^x + c.

In which:

From the graph, the horizontal asymptote is of y = -6, hence the parameter c is given as follows:

c = -6.

When x = 0, y = -4, hence the parameter a is given as follows:

-4 = a - 6

a = 2.

Hence:

y = 2(b)^x - 6.

When x = -1, y = -2, hence the parameter b is given as follows:

2(b)^(-1) - 6 = -2

2/b = 4

b = 0.5.

Hence the function is of:

y = 2(0.5)^x - 6.

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The required equation that represent the hanger is 10 + 5x = 11 and the value of x is 1/5.

Given the diagram of the hanger which one side has 10 + 5x  and other side has 11.

To find the equation, equate the expression of one side to the numerical value of the other side. On solving the equation gives the value of x.

Thus, the equation is 10 + 5x = 11.

Consider the equation 10 + 5x = 11

On subtracting 10 from each side gives,

5x = 1

Divide each side by 5 gives,

x = 1/5.

Hence,  the required equation that represent the hanger is 10 + 5x = 11 and the value of x is 1/5.

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The amount of tax that is added to the cost of the computer is 159.72

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

Computer cost = 968

Tax percentage = 16.5%

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

Tax amount = Computer cost * Tax percentage

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

Tax amount = 968 * 16.5%

Evaluate

Tax amount = 159.72

Hence, the amount of tax that is added to the cost of the computer is 159.72

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Step-by-step explanation:

Let's solve the given questions step by step:

1. Determine the equation of f:

From the given information, we know that the turning point of f is (1, 4). The general form of a quadratic function is f(x) = ax^2 + bx + c. We are given that f(x) = a(x + p)^2 + q, so let's substitute the values:

f(x) = a(x + p)^2 + q

Since the turning point is (1, 4), we can substitute x = 1 and f(x) = 4 into the equation:

4 = a(1 + p)^2 + q

This gives us one equation involving a, p, and q.

2. Determine the equation of g:

The equation of g is given as g(x) = 0.3x + p1.

3. Determine the coordinates of the x-intercept of g:

The x-intercept is the point where the graph of g intersects the x-axis. At this point, the y-coordinate is 0.

Setting g(x) = 0, we can solve for x:

0 = 0.3x + p1

-0.3x = p1

x = -p1/0.3

Therefore, the x-intercept of g is (-p1/0.3, 0).

4. For which values of x will f(x) ≥ g(x)?

To determine the values of x where f(x) is greater than or equal to g(x), we need to compare their expressions.

f(x) = a(x + p)^2 + q

g(x) = 0.3x + p1

We need to find the values of x for which f(x) ≥ g(x):

a(x + p)^2 + q ≥ 0.3x + p1

Simplifying the equation will involve expanding the square and rearranging terms, but since the equation involves variables a, p, and q, we cannot determine the exact values without further information or constraints.

To summarize:

We have determined the equation of f in terms of a, p, and q, and the equation of g in terms of p1. We have also found the coordinates of the x-intercept of g. However, without additional information or constraints, we cannot determine the exact values of a, p, q, or p1, or the values of x for which f(x) ≥ g(x).

Answer:

16

Step-by-step explanation:

12-(-4)=12+4=16

Answer:

16

Step-by-step explanation:

12 - (-4)

when you subtract a negative, you add.

12 + 4 = 16

The simplified form of the rational expression \((7x)/(14x^6)\) is \(1/(2x^6).\)

To simplify the rational expression \((7x)/(14x^6)\), we can begin by simplifying the numerator and denominator separately.

In the numerator, 7x, we can see that both 7 and x have a common factor of 7. So, we can rewrite the numerator as 7 × x = 7x.

In the denominator, \(14x^6\), we can see that both 14 and x^6 have a common factor of \(2x^6\).

So, we can rewrite the denominator as

\(14 \times x^6 = 2 \times 7 \times x^6 = 2 \times 7x^6.\)

Now, we can simplify the rational expression by canceling out the common factors in the numerator and denominator:

\((7x)/(14x^6) = (7x)/(2 \times 7x^6) \\= (7x)/(2 \times 7 \times x^6) \\= (cross(7x))/(2 \times cross(7) \times x^6) \\= 1/(2x^6)\)

Therefore, the simplified form of the rational expression\((7x)/(14x^6)\) is \(1/(2x^6).\)

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Answer:

We determined that the 10th figure will have 45 shaded squares. That means 100 – 45 = 55 squares will be unshaded

Step-by-step explanation:

hope this helps

Answer:

7. 14

15. 30

28. 56

32. 64

18 36

x 2x

1/2y. y

2x. 4x

x+3 2x+9

Step-by-step explanation:

each out is double the in

Answer:

Step-by-step explanation:

You want to group things that can actually be factored. You dont want to group -7x^3 and -9 because that would just be a mess and wouldnt give you the right answer.

\((-7x^3+21x^2)+(3x-9)\\-7x^2(x-3)+3(x-3)\\(-7x^2+3)(x-3)\)

Answer:

8inches

Step-by-step explanation:

Length of the third side = perimeter - ( side1 + side2 )

                                       = 17 - (5+4)

                                       = 17 - 9

                                       = 8 inches

The numbers can be represented as (x - 1 ) (x - 9).

A quadratic equation is a second-order polynomial equation in a single variable x, ax²+bx+c=0. with a ≠ 0

The condition can be well represented as quadratic equation.

This is because the middle term of the quadratic equation represent the addition/ subtraction of two numbers and last term represent the product of the same numbers.

So, we can write x² - 10x + 9 = 0

So,  factor the quadratic equation above is:

(x - 1 ) (x - 9)

Hence, the b can be represented as (x - 1 ) (x - 9).

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There is evidence to suggest that the percentage of mathematics research published by U.S. authors is no longer 40%.

To test the claim that the percentage of research in mathematics published by U.S. authors is no longer 40%, we can use a hypothesis test with a 0.05 level of significance.

Let p be the true proportion of mathematics research published by U.S. authors.

The null hypothesis is that p = 0.4, and the alternative hypothesis is that p ≠ 0.4 (two-tailed test).

sample proportion, x/n = 62/130 = 0.477

The test statistic for a two-tailed test is given by:

z = (0.477 - 0.4) / √(0.4 * 0.6 / 130)

= 2.41

Using a z-table, we find that the p-value for a two-tailed test with z = 2.41 is approximately 0.016.

Since  0.016 < 0.05

, we reject the null hypothesis and conclude that there is evidence to suggest that the percentage of mathematics research published by U.S. authors is no longer 40%.

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a) The step in which McKenna made her first mistake is given as follows: Step 4.

b) The correct simplified expression in standard form is given as follows: -15a - 15.

The expression in this problem is defined as follows:

3 − 5(3a + 6)

On the third step, the expression is given as follows:

3 + (−5)(3a + 6)

And on the fourth step, the expression is given as follows:

−2(3a + 6).

This is where the mistake happened, as the multiplication takes precedence over the subtraction.

Then to obtain the correct expression the first step is applying the distributive property, as follows:

3 − 5(3a + 6) = 3 - 15a - 18.

Then the like terms 3 and -18 are combined to obtain the correct simplified expression, as follows:

3 - 15a - 18 = -15a - 15.

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The expression to represent the area of the flag as a sum of areas of each section is 2*x + 2(\(1\frac{1}{2}\) ) + 3*(x + \(1\frac{1}{2}\) )  .

In the question ,

a flag is given that have three colors ,

we have to find an expression for the area of the flag .

For the Green Part ;

the length is 2 units ,

and the width is x units .

So ,the area of the green part is = 2*x .

For the Orange Part ;

the length is 2 units ,

and the width of the orange part is = \(1\frac{1}{2}\) units ,

So , the area of the orange part is = 2(\(1\frac{1}{2}\) ) units .

For the Purple part ;

the length is = 3 units ,

and the width is = (x + \(1\frac{1}{2}\) ) units .

So , the area of the purple part is = 3*(x + \(1\frac{1}{2}\) ) units .

So the area of the flag is = area of ( Green part + Orange Part + Purple Part) .

Substituting the values ,

we get ,

Area = 2*x + 2(\(1\frac{1}{2}\) ) + 3*(x + \(1\frac{1}{2}\) ) .

Therefore , the expression for the area is 2*x + 2(\(1\frac{1}{2}\) ) + 3*(x + \(1\frac{1}{2}\) )  .

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Answer:

I do not have access to Annexure A and Annexure B, so I cannot collect the data, draw the frequency table or pie chart, or answer the last question. However, I can provide a general explanation of how to calculate the mean, mode, median, and range from a set of data.

To find the mean (average) of a set of data, add up all the values in the set and divide by the number of values. For example, if the maximum temperatures of the 30 days are:

25, 28, 29, 27, 26, 30, 31, 32, 29, 27, 26, 24, 23, 25, 28, 30, 32, 33, 34, 31, 29, 28, 27, 26, 25, 24, 23, 21, 20, 22

The sum of the values is:

25 + 28 + 29 + 27 + 26 + 30 + 31 + 32 + 29 + 27 + 26 + 24 + 23 + 25 + 28 + 30 + 32 + 33 + 34 + 31 + 29 + 28 + 27 + 26 + 25 + 24 + 23 + 21 + 20 + 22 = 813

Dividing by the number of values (30), we get:

Mean = 813/30 = 27.1

To find the mode of a set of data, identify the value that occurs most frequently. In this example, there are two values that occur most frequently, 27 and 29, so the data has two modes.

To find the median of a set of data, arrange the values in order from smallest to largest and find the middle value. If there are an even number of values, take the mean of the two middle values. In this example, the values in ascending order are:

20, 21, 22, 23, 23, 24, 24, 25, 25, 26, 26, 27, 27, 27, 28, 28, 29, 29, 29, 30, 30, 31, 31, 32, 32, 33, 34

There are 30 values, so the median is the 15th value, which is 28.

To find the range of a set of data, subtract the smallest value from the largest value. In this example, the smallest value is 20 and the largest value is 34, so the range is:

Range = 34 - 20 = 14

To create a frequency table for the maximum temperature data, we need to group the data into intervals and count the number of values that fall into each interval. For example, we could use the following intervals:

20-24, 25-29, 30-34

The frequency table would look like this:

Interval | Frequency

20-24 | 4

25-29 | 18

30-34 | 8

To calculate the size of the angles for the pie chart, we need to find the total frequency (30) and divide 360° by the total frequency to get the proportion of each interval in degrees. For example, for the interval 25-29:

Proportion = Frequency/Total frequency = 18/30 = 0.6

Angle = Proportion * 360° = 0.6 * 360° = 216°

We can repeat this calculation for each interval to obtain the angles for the pie chart.

In terms of the last question, it is not clear what is meant by "which data collection best describe the maximum and why?". If you could provide more context or clarification, I would be happy to try to help.

The correct answer is C) 9.9 lbs as it is above the upper boundary 6.4865, it is the outlier in this dataset.

An outlier is an observation that is much higher or lower than the other observations in a dataset.

In this case, the weights of the catfish range from 2.7 to 4.8 lbs, with one observation that is much higher at 9.9 lbs.

Therefore, 9.9 lbs is the outlier in this dataset.

To find the outlier in this dataset, we can calculate the interquartile range (IQR).

This is done by first calculating the first quartile (Q1) and third quartile (Q3).

The Q1 for this dataset =3.75

and the Q3= 4.675.

IQR= Q3 - Q1

= 0.925.

We then calculate the lower boundary as Q1 - (1.5 x IQR) = 2.3625.

The upper boundary is Q3 + (1.5 x IQR)= 6.4865.

Since 9.9 lbs is above this upper boundary, it is the outlier in this dataset.

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I. The solution to the system of equations using Gaussian elimination is x = 1, y = -1, and z = 2.

II. For the LU-decomposition method, we need to have a square coefficient matrix, which is not the case in the given system. Therefore, we cannot directly apply the LU-decomposition method.

III. For this method to converge, the coefficient matrix must be diagonally dominant, which is not the case in the given system. Therefore, the Gauss-Jacobi method cannot be directly applied either.

IV. It requires the coefficient matrix to be diagonally dominant, which is not satisfied in the given system. Hence, the Gauss-Seidel method cannot be directly used.

I. Gaussian Elimination Method:

To solve the system of linear equations using Gaussian elimination, we perform row operations to reduce the system into upper triangular form. The augmented matrix for the given system is:

| 6 2 -1 | 4 |

| 1 5 1 | 3 |

| 2 1 4 |27 |

We can start by eliminating the coefficients below the first element in the first column. To do this, we multiply the first row by a suitable factor and subtract it from the second and third rows to eliminate the x coefficient below the first row. Then, we proceed to eliminate the x coefficient below the second row, and so on.

After performing the necessary row operations, we obtain the following reduced row-echelon form:

| 6 2 -1 | 4 |

| 0 4 2 | -1 |

| 0 0 3 | 6 |

From this form, we can easily back-substitute to find the values of x, y, and z. We have z = 2, y = -1, and x = 1.

II. LU-Decomposition Method:

LU-decomposition is a method that decomposes a square matrix into a product of two matrices, L and U, where L is lower triangular and U is upper triangular.

III. Gauss-Jacobi Method:

The Gauss-Jacobi method is an iterative numerical method to solve systems of linear equations.

IV. Gauss-Seidel Method:

Similar to the Gauss-Jacobi method, the Gauss-Seidel method is an iterative method for solving linear systems.

Therefore, out of the four methods mentioned, only the Gaussian elimination method can be used to solve the given system of linear equations.

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The sum of the angles of the triangle expressed in two ways are x + 1/2x + 3/2x and 2x + x + 3x/2

It is important to note that the sum of the angles of a triangle is equal or equivalent to 180 degrees.

We have the angle measurements as;

Substitute the values

x + 1/2 x + 3/2x = 180

Find the lowest common multiple

2x + x + 3x /2 = 180

Add the numerators

6x/2 = 180

cross multiply

6x = 360

x = 60

Hence, the expression is x + 1/2x + 3/2x and 2x + x + 3x/2

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