7.3. If the entries of both A and A-1 are integers, is it possible that det A = 3? Hint: what is det(A) det(A-1)?

Answer:

Step-by-step explanation:

The terms will be multiplied in order to get the simplified polynomials.

a. 6(x + 7)(x + 2)

\(6(x + 7)(x + 2)\\=6[x(x+2)+7(x+2)]\\=6(x^2+2x+7x+14)\\=6(x^2+9x+14)\\=6x^2+54x+84\)

The simplified form of 6(x + 7)(x + 2) is \(6x^2+54x+84\)

b. (2y – 5)^2

Using the formula: \((a-b)^2 = a^2+b^2-2ab\)

\(=(2y)^2+(5)^2-2(2y)(5)\\=4y^2+25-20y\)

The simplified form is: \(4y^2-20y+25\)

c. (5x + 4y)(2x - y)

\(=5x(2x-y)+4y(2x-y)\\=10x^2-5xy+8xy-4y^2\\=10x^2+3xy-4y^2\)

The simplified form of (5x + 4y)(2x - y) is \(10x^2+3xy-4y^2\)

d. (3x + 7)(3x – 7)

Using the formula: \((a+b)(a-b) = a^2-b^2\)

\(= (3x)^2-(7)^2\\= 9x^2-49\)

The simplified form of (3x + 7)(3x – 7) is \(9x^2-49\)

e. (t + 2) – (4t +9) – t

\(=t+2-4t-9-t\\=t-4t-t+2-9\\= -4t-7\)

The simplified form of (t + 2) – (4t +9) – t is \(-4t-7\)

Hence,

a. The simplified form of 6(x + 7)(x + 2) is \(6x^2+54x+84\)

b. The simplified form is: \(4y^2-20y+25\)

c. The simplified form of (5x + 4y)(2x - y) is \(10x^2+3xy-4y^2\)

d. The simplified form of (3x + 7)(3x – 7) is \(9x^2-49\)

e. The simplified form of (t + 2) – (4t +9) – t is \(-4t-7\)

Answer:

20×2=40bnmcsshjvghjpiutewqadgjlmbcz

Answer: all real numbers

Step-by-step explanation:

Answer:

-Max has $10.00. He earns $25.75 for every lawn that he mows.

-Sasha sells a scarf for $10.00 and x jackets for $25.75 each.

Step-by-step explanation:

Answer:

I believe the answer should be C

Answer:

<

Step-by-step explanation:

because 4/6/7 is less than 0

Answer:

2/21 < 4

Step-by-step explanation:

Lets break this up

4/6=2/3

2/3 / 7 = 2/3 * 1/7

2/21

Answer:

18064

Step-by-step explanation:

these equations are always in this order:

Parentheses

Exponents

Multiplication

Division

Addition

Subtraction

To remember this, my teacher told us the phrase; "Please Excuse My Dear Aunt Sally".

To solve the equation 15 + 2x = 36, we can start by subtracting 15 from both sides of the equation to get 2x = 21. Then, we can divide both sides by 2 to get x = 10.5. Rounded to the nearest ten-thousandth, the solution is x = 10.5000.

In this triangle, the product of tan A and tan C is `(BC)^2/(AB)^2`.

The given triangle ABC has angle A measuring 45 degrees, angle B measuring 90 degrees, and angle C measuring 45 degrees , Answer: `(BC)^2/(AB)^2`.

We have to find the product of tan A and tan C.

In triangle ABC, tan A and tan C are equal as the opposite and adjacent sides of angles A and C are the same.

So, we have, tan A = tan C

Therefore, the product of tan A and tan C will be equal to (tan A)^2 or (tan C)^2.

Using the formula of tan: tan A = opposite/adjacent=BC/A Band, tan C = opposite/adjacent=AB/BC.

Thus, tan A = BC/AB tan C = AB/BC Taking the ratio of these two equations, we have: tan A/tan C = BC/AB ÷ AB/BC Tan A * tan C = BC^2/AB^2So, the product of tan A and tan C is equal to `(BC)^2/(AB)^2`.

Answer: `(BC)^2/(AB)^2`.

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Answer: 1935825

Step-by-step explanation:

The exponential function is A = $2000 × (1 + .03)⁴⁰ and the amount is $6524.1.

Let a be the initial value and x be the power of the exponent function and b be the increasing factor.

The exponent is given as

y = a(b)ˣ

y = a (1 ± r)ˣ

The rate is 6% for 20 years semiannually. Then the rate is given as,

r = 0.06 / 2

r = 0.03

Then the time is given as,

x = 20 (2)

x = 40

Then the exponential function is given as,

A = $2000 × (1 + 0.03)⁴⁰

A = $2000 × (1.03)⁴⁰

A = $2000 × 3.262

A = $6524.1

The exponential function is A = $2000 × (1 + .03)⁴⁰ and the amount is $6524.1.

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Answer:

FA: Chord

BO: Radius

CO: Radius

DO: Radius

EO: Radius

CE: Diameter

Step-by-step explanation:

Hello!

Some lines in a circle:

Segment FA

This has endpoints inside the circle, but doesn't go through the center. This is a chord.

Segment BO

BO has an endpoint on the center and and an endpoint on the perimeter. This is a radius.

Segment CO

This is also a radius, it has an endpoint on the center and another endpoint on its perimeter.

Segment DO

This is a radius, it has n endpoint on the center and another endpoint on the perimeter

Segment EO

Another radius, with a an endpoint on the center and another endpoint on the perimeter.

Segment CE

A diameter. It has two endpoints on the perimeter of the circle and goes through the center of the circle.

Answer:

-18 in my opinion loss

Step-by-step explanation:

if they suck they suck depends on the team

The slope-intercept formula is one of the formulas used to determine a line's equation. Y = mx + b is the slope-intercept formula for a line with slope m and y-intercept b. Any point on the line is (x, y) in this case.

Using a straight line's slope and the location of its y-axis intersection, the slope intercept equation can be used to determine the general equation of the line. Y = mx + b is the equation in slope intercept form.

One of the formulas used to get a line's equation is the slope-intercept formula. Y = mx + b is the slope-intercept formula for a line with slope m and y-intercept b. Any point on the line is (x, y) in this case.

The variables we'll use in our function will be as follows:

m = slope, and b = y-intercept.

It is written as y = mx + b. The m and b variables are changed to numbers, while the x and y variables stay as letters (for example, y = 2x + 4, slope = 2, and y-intercept = 4).

The slope and intercept from an equation are used in the following video through a few examples.

y = mx + b

The slope and intercept are the two integers that make up this equation, which is why it is known as the slope-intercept form.

Remember, the slope (m) is the amount being multiplied to x and the intercept (b) is the number being added or subtracted

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The z score associated with the highest 10% is closest to: option (c) 1.28

-To find the z score associated with the highest 10%, first determine the percentage that corresponds to the lower 90%, since the z score table typically represents the area to the left of the z score.

- Look up the 0.90 (90%) in a standard normal distribution  (z score) table, which will give you the corresponding z score.

-The z score closest to 0.90 in the table is 1.28, which corresponds to the highest 10% of values.

Therefore, the z score associated with the highest 10% is closest to 1.28.

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Answer:

296%

Step-by-step explanation:

Total number of biscuits sold = 720

70% of 720 = 0.7 x 720

                   = 504

Amount of 504 biscuits sold = 504 x 25p

                             = 12600p

But 100p = £1

So that,

12600p = £126

30% of 720 = 0.3 x 720

                    =  216

But, she sold 216 biscuits at 4 for 60p.

The amount of 216 biscuits sold = \(\frac{216}{4}\) x 60p

                                      = 54 x 60p

                                      = 3240p

                                      = £32.40

Total amount on sales = £126 + £32.40

                            = £158.40

But her cost price is £40.

Profit = £158.40 - £40

         = £118.40

Her percentage profit = \(\frac{118.40}{40}\) x 100

                                    = 296%

The population of sunfish in the small lake decreased from 800 at the beginning to 736 after the first year. Data for the second year is missing due to a wildfire, but the population was recorded as 623 during the third year.

To explain further, the recorded population numbers indicate a decline in the sunfish population over the observed period. At the beginning, there were 800 sunfish. However, after the first year, the population decreased to 736. This suggests a reduction in the number of sunfish, potentially due to various factors such as predation, disease, or environmental changes.

Unfortunately, data for the second year is missing due to the wildfire, so we cannot determine the specific population change during that period. However, in the third year, the biologist recorded a population of 623 sunfish. This further indicates a decline in the sunfish population from the initial count.

It is essential for the marine biologist to continue monitoring the sunfish population to understand the long-term trends and potential factors influencing their numbers. Further data collection and analysis will provide valuable insights into the dynamics and conservation of the sunfish population in the small lake.

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Answer:

To calculate the mean for this population, we need to sum all the values and divide by the total number of values:

Mean = (9 + 24 + 23 + 3 + 45 + 15 + 30 + 23 + 52 + 49 + 13 + 41 + 11 + 45 + 50 + 51 + 25 + 39 + 65 + 23 + 70) / 20

Mean = 622 / 20

Mean = 31.1

Therefore, the mean for this population is 31.1.

Answer:

9 ÷ 2

Step-by-step explanation:

or draw that small house thing over the 9 an place 2 to the left of it.

Answer:

Half;  twice

Step-by-step explanation:

In a circle, the radius is said to be the distance from the center of the circle to any point on the edge of the circle, it is denoted as "r". The radius is called a radii if it is more than one.. The radius of a circle is half the length of the diameter of a circle because the diameter of a circle is the distance of the line that passes through the center of a circle touching both edges of the circle. It is denoted as "d".

Thus,

2r = d

r = d/2

For example, if the radius of a circle is 10cm, the diameter of the circle will be calculated as: d = 2 * 10 = 20cm. Which means if the radius is 10cm, diameter will be 20cm.

Therefore, the radius of a circle is half the length of its diameter. the diameter of a circle is twice the length of its radius

To find all real solutions of the equation 8x²3 - 27x²2 - 50x + 75 = 0, we can factor it by grouping

How to do that?

8x²3 - 27x²2 - 50x + 75 = 0

=> (8x²3 - 50x) - (27x²2 - 75) = 0

=> 2x(4x²2 - 25) - 3(9x²2 - 25) = 0

=> (2x - 3)(4x²2 - 9x + 15) = 0

Using the quadratic formula to solve the quadratic factor, we get:

4x²2 - 9x + 15 = 0

=> x = [9 ± sqrt(81 - 4(4)(15))] / (2(4))

=> x = [9 ± sqrt(-191)] / 8

Since the discriminant of the quadratic factor is negative, it has no real roots, and therefore, the only real solution of the equation is:

x = (2x - 3) = 0

=> x = 3/2

Therefore, the only real solution of the equation 8x²3 - 27x²2 - 50x + 75 = 0 is x = 3/2.

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Answer:

y=x+6

Step-by-step explanation:

y=mx+b

The slope (m) can be found by putting the rise (1) over the run (1).

y=1x+b

The y-intercept is 6, so therefore b is 6.

y=x+6

Jared bought 7 cans of paint. Let the number of red paint cans that Jared bought be x. The number of black paint cans he bought would be 7 - x. A can of red paint costs $3.75 and a can of black paint costs $2.75.

He spent $22 in all. Therefore we can write:3.75x + 2.75(7 - x) = 22 Multiplying out the second term and collecting like terms gives:0.5x + 19.25 = 22Subtracting 19.25 from both sides:0.5x = 2.75Dividing by 0.5:x = 5.5Since Jared can't buy half a can of paint, we should round the answer to the nearest integer. Hence, he bought 5 cans of red paint and 2 cans of black paint. The total cost of the 5 cans of red paint would be 5 x $3.75 = $18.75.The total cost of the 2 cans of black paint would be 2 x $2.75 = $5.50.The total cost of all 7 cans of paint would be $18.75 + $5.50 = $24.25.We spent more than Jared's budget. The value of $24.25 exceeds Jared's budget of $22. Hence, there is a problem with this problem statement.

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Option C. which corresponds to the probability of approximately 0.0771 that there will be 8 occurrences within a period of ten minutes.

This problem follows a Poisson distribution, where the mean and variance of the distribution are equal to λ. Here, λ = 5, and we need to find the probability of having 8 occurrences in 10 minutes. The probability mass function of Poisson distribution is:

P(X = k) = (e⁽⁻λ⁾ * λᵏ) / k!

Substituting the given values, we get:

P(X = 8) = (e⁽⁻⁵⁾ * 5⁸) / 8!

P(X = 8) ≈ 0.0771

Therefore, the probability that there are 8 occurrences in ten minutes is approximately 0.0771, which corresponds to option C.

This problem follows a Poisson distribution, where the mean and variance of the distribution are equal to λ. Here, λ = 5, and we need to find the probability of having 8 occurrences in 10 minutes. The probability mass function of Poisson distribution is:

P(X = k) = (e⁽⁻λ⁾ * λᵏ) / k!

Substituting the given values, we get:

P(X = 8) = (e⁽⁻⁵⁾ * 5⁸) / 8!

P(X = 8) ≈ 0.0771

Therefore, the probability that there are 8 occurrences in ten minutes is approximately 0.0771, which corresponds to option C.

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The value of Mean ≈ 341.2

Median ≈ 319

Standard Deviation ≈ 307.8

To find the mean, median, and standard deviation of the number of members per component, we can use statistical software to analyze the data. Here are the results:

Mean:

The mean is the average value of the number of members per component. We calculate it by summing up all the values and dividing by the total number of components.

Mean = (114 + 261 + 319 + 183 + 654 + 313 + 58 + 98 + 335 + 324 + 52 + 125 + 342 + 66 + 321 + 893 + 690 + 798 + 201 + 74 + 632 + 216 + 76 + 155 + 161 + 304 + 530 + 1,110 + 93 + 631 + 75 + 344 + 264 + 1,120 + 122 + 45 + 304 + 192 + 316 + 63) / 39

Mean ≈ 341.2

Median:

The median is the middle value when the components are arranged in ascending order. If there is an even number of components, the median is the average of the two middle values.

Arranging the components in ascending order:

45, 52, 58, 63, 74, 75, 76, 93, 98, 114, 122, 125, 155, 161, 183, 192, 201, 216, 261, 264, 304, 304, 313, 316, 319, 321, 324, 335, 342, 344, 530, 631, 632, 654, 690, 798, 893, 1,110, 1,120

The median is the middle value:

Median ≈ 319

Standard Deviation:

The standard deviation measures the dispersion or spread of the values around the mean.

Using statistical software, we calculate the standard deviation for the given data:

Standard Deviation ≈ 307.8 (rounded to 1 decimal place)

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Answer:

1/10

Step-by-step

Answer:

Let a be the first term and d be the common difference.

3rd term = 1407

a+2d = 1407  ------- 1

10th term = 1183

a+9d = 1183  ------- 2

By solving 1 and 2, a = 1471 and d = -32

so the general term T(n) = 1471 + (n-1)(-32)

                                          = 1471 - 32n +32

                                          = -32n + 1503

-32n + 1503 \(\geq\) 0

            -32n \(\geq\) -1503

                  n \(\leq\) 46.96875

The number of positive terms = 46

? Do you need help with an assignment?

the roots of the quadratic equation [{(-x²) + 2x + 12} = 0] are (1 - √13) and

(1 + √13).

As per the question statement, we are provided with a linear equation

[{(-x²) + 2x + 12} = 0].

We are required to calculate the roots of the above mentioned equation.

To solve this question, we will first need to know the formula to calculate the roots of the quadratic equation [(ax² + bx + c) = 0], which goes as,

x = [{(-b) ± √(b² - 4ac)}/(2a)]

Now comparing the standard quadratic equation [(ax² + bx + c) = 0] with

[{(-x²) + 2x + 12} = 0], we get, [a = (-1)], (b = 2) and (c = 12), and substituting these values in the above mentioned formula to calculate the roots of any quadratic equation, we get,

x = [(-2) ± √{2² - (4* -1 * 12)}]/{2 * (-1)}

Or, x = [(-2) ± √{4 - (-48)}]/(-2)

Or, x = [{(-2) ± √(4 + 48)}/(-2)]

Or, x = [{(-2) ± √52}/(-2)]

Or, x = [{(-2) + √52}/(-2)], [{(-2) - √52}/(-2)]

Or, x = [-{2 - √52}/(-2)], [-{2 + √52}/(-2)]

Or, x = [{2 - √52}/2], [{2 + √52}/2]

Or, x = [{2 - √(13 * 4)}/2], [{2 + √(13 * 4)}/2]

Or, x = [{2 - 2√13}/2], [{2 + 2√13}/2]

Or, x = [2{1 - √13}/2], [2{1 + √13}/2]

Or, x = (1 - √13), (1 + √13)

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Answer: 476 ft³

Step-by-step explanation:

Volume = width x hight x length

        V = 4 ft x 17 ft x 7 ft

        v  = 476 ft³

Let's calculate the products and check if they indeed have the same value:

Product of 32 and 46:

32 * 46 = 1,472

Reverse the digits of 23 and 64:

23 * 64 = 1,472

As you mentioned, the products are the same. This phenomenon is not unique to this particular pair of numbers. In fact, it occurs with any pair of two-digit numbers whose digits, when reversed, are the same as the product of the original numbers.

To find two other pairs of two-digit numbers that have this property, we can explore a few examples:

Product of 13 and 62:

13 * 62 = 806

Reversed digits: 31 * 26 = 806

Product of 17 and 83:

17 * 83 = 1,411

Reversed digits: 71 * 38 = 1,411

As for determining if a given pair of two-digit numbers will have this property without actually performing the multiplication, there is a simple rule. For any pair of two-digit numbers (AB and CD), if the sum of A and D equals the sum of B and C, then the products of the original and reversed digits will be the same.

For example, let's consider the pair 25 and 79:

A = 2, B = 5, C = 7, D = 9

The sum of A and D is 2 + 9 = 11, and the sum of B and C is 5 + 7 = 12. Since the sums are not equal (11 ≠ 12), we can determine that the products of the original and reversed digits will not be the same for this pair.

Therefore, by checking the sums of the digits in the two-digit numbers, we can determine whether they will have the property of the products being the same when digits are reversed.