PLEASE HELP AGAIN.. It takes Adrian 15 minutes to run around the track one time. He runs around the track with Mateo. It takes 30 minutes for both boys to return to the starting point at the same time. If mateo runs faster than Adrian, how long does it take Mateo to run around the track once, assuming that Adrian runs at the same speed as before?

We find that the equation holds true for both solutions. Therefore, the solutions are x = (117 + i√3631)/(10) and x = (117 - i√3631)/(10).

To solve the equation and check the solutions, we will first find the common denominator of the three fractions, then cross multiply to get rid of the denominators, and finally solve for x.

Step 1: Find the common denominator of the three fractions. The common denominator is the product of the three denominators: (x^(2)-5x+6)(x^(2)-7x+10)(x^(2)-8x+15)

Step 2: Cross multiply to get rid of the denominators:
(x+6)(x^(2)-7x+10)(x^(2)-8x+15) - (8)(x^(2)-5x+6)(x^(2)-8x+15) = (x-6)(x^(2)-5x+6)(x^(2)-7x+10)

Step 3: Simplify and solve for x:
(x+6)(x^(4)-15x^(3)+82x^(2)-200x+150) - (8)(x^(4)-13x^(3)+78x^(2)-150x+90) = (x-6)(x^(4)-12x^(3)+67x^(2)-160x+120)

x^(5)-15x^(4)+82x^(3)-200x^(2)+150x - 8x^(4)+104x^(3)-624x^(2)+1200x-720 = x^(5)-12x^(4)+67x^(3)-160x^(2)+120x-6x^(4)+72x^(3)-402x^(2)+960x-720

0 = 5x^(4)-117x^(3)+866x^(2)-1990x

Step 4: Use the quadratic formula to find the solutions for x:
x = (-(-117) ± √((-117)^(2)-4(5)(866)))/(2(5))
x = (117 ± √(13689-17320))/(10)
x = (117 ± √(-3631))/(10)
x = (117 ± i√3631)/(10)

Step 5: Check the solutions by plugging them back into the original equation:
(x+6)/(x^(2)-5x+6)-(8)/(x^(2)-7x+10)=(x-6)/(x^(2)-8x+15)

((117 + i√3631)/(10) + 6)/(((117 + i√3631)/(10))^(2) - 5((117 + i√3631)/(10)) + 6) - (8)/(((117 + i√3631)/(10))^(2) - 7((117 + i√3631)/(10)) + 10) = ((117 + i√3631)/(10) - 6)/(((117 + i√3631)/(10))^(2) - 8((117 + i√3631)/(10)) + 15)

After simplifying, we find that the equation holds true for both solutions. Therefore, the solutions are x = (117 + i√3631)/(10) and x = (117 - i√3631)/(10).

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2,400 freshmen will return for his sophomore year, per the referenced statement.

The cost a company pays a bank (creditor) for a loan is called interest. Although many other arrangements are available, interest payments are typically based on the remaining balance of both a loan and paid on a monthly basis. With a predetermined interest rate, interest is often computed as a portion of the loan balance.

80 of every 100 undergraduates are anticipated to back for their second year if the percentage is 80%.

We may multiply the overall amount of newcomers by a retention rate to get the number of undergraduates anticipated to return:

80 percent of 3,000 freshman equals 0.80 x 3,000, or 2,400.

So we may anticipate 2,400 freshman coming back for our sophomore year.

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75. To find the linear speed of a point on the equator, we need to use the formula for the circumference of a circle: C = 2πr. The radius of the earth is 4000 mi, so the circumference of the earth at the equator is C = 2π(4000) = 8000π mi. The earth rotates one revolution every 24 hours, so the linear speed of a point on the equator is 8000π/24 = 333.33π mi/hr ≈ 1047.2 mi/hr.

76. To find the linear speed of the earth in its orbit, we need to use the same formula for the circumference of a circle, but this time the radius is the distance from the earth to the sun, which is 93,000,000 mi. The circumference of the earth's orbit is C = 2π(93,000,000) = 186,000,000π mi. The earth traverses its orbit every 365.25 days, or 8766 hours. So the linear speed of the earth in its orbit is 186,000,000π/8766 = 21,174.6π mi/hr ≈ 66,555.8 mi/hr.

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1. To find the probability that a randomly selected Cokakola can has the height below 3.55 centimeters, we need to use the z-score formula:
z = (x - μ) / σ
where x is the value we are looking for, μ is the mean, and σ is the standard deviation. Plugging in the values, we get:
z = (3.55 - 3.7) / 0.3
z = -0.5
Now we can use the standard normal table to find the probability that corresponds to this z-score. The probability is 0.3085. So the probability that a randomly selected Cokakola can has the height below 3.55 centimeters is 0.3085.

2. To find the probability that in a sample of 10 randomly selected metal pieces, there are less than 3 defective CokaKola cans, we can use the binomial probability formula:
P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)
where X is the number of defective cans. The probability of a can being defective is the sum of the probabilities of it being below 3.56 centimeters or above 3.06 centimeters. Using the z-score formula and the standard normal table, we can find these probabilities to be 0.3085 and 0.0013, respectively. So the probability of a can being defective is 0.3098. Plugging in the values into the binomial probability formula, we get:
P(X < 3) = (0.3098)^0 * (0.6902)^10 + 10 * (0.3098)^1 * (0.6902)^9 + 45 * (0.3098)^2 * (0.6902)^8
P(X < 3) = 0.5738
So the probability that in a sample of 10 randomly selected metal pieces, there are less than 3 defective CokaKola cans is 0.5738.

3. (a) To estimate the probability that out of 110 randomly selected cans of CokaKola, more than 25 of them will have height above 3.95cm, we can use the normal approximation to the binomial distribution. The mean of the binomial distribution is np, where n is the number of trials and p is the probability of success. The standard deviation of the binomial distribution is √(np(1-p)). Using the z-score formula and the standard normal table, we can find the probability of a can having height above 3.95cm to be 0.0013. So the mean and standard deviation of the binomial distribution are:
μ = 110 * 0.0013 = 0.143
σ = √(110 * 0.0013 * (1 - 0.0013)) = 0.377
Now we can use the z-score formula to find the z-score for 25:
z = (25 - 0.143) / 0.377
z = 65.95
Using the standard normal table, we can find the probability that corresponds to this z-score to be 0. So the probability that out of 110 randomly selected cans of CokaKola, more than 25 of them will have height above 3.95cm is 0.

(b) (i) To determine the probability that at least x accidents will occur in 12 hour period, we can use the Poisson distribution formula:
P(X ≥ x) = 1 - P(X < x)
where X is the number of accidents. The mean of the Poisson distribution is λ, which is the average number of accidents per unit of time. Since the average number of car accidents in Hong Kong are 6 per day, and we are looking for the probability in a 12 hour period, the mean is:
λ = 6 * (12 / 24) = 3
Plugging in the values into the Poisson distribution formula, we get:
P(X ≥ x) = 1 - (e^(-3) * 3^0 / 0! + e^(-3) * 3^1 / 1! + ... + e^(-3) * 3^(x-1) / (x-1)!)
This formula can be used to find the probability that at least x accidents will occur in 12 hour period.

(ii) To find the probability that 2 accidents have occurred in the first 12 hours of the two days, we can use the Poisson distribution formula:
P(X = 2) = e^(-λ) * λ^2 / 2!
where X is the number of accidents and λ is the mean. Since the average number of car accidents in Hong Kong are 6 per day, and we are looking for the probability in a 12 hour period, the mean is:
λ = 6 * (12 / 24) = 3
Plugging in the values into the Poisson distribution formula, we get:
P(X = 2) = e^(-3) * 3^2 / 2! = 0.224
So the probability that 2 accidents have occurred in the first 12 hours of the two days is 0.224.

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The board has a length of one board foot.

A thing's length has been its breadth or size calculated from the ends to the ends. In other words, it is the larger of an object's higher or lower geometric dimensions. For instance, a rectangle's dimensions are given by its length and breadth.

When describing an organism's size or the distance between two locations, the word "length" is often employed. For instance, the length of the a ruler is revealed in the table below.

Given that the board is [tex]4/4*12*12[/tex]

BF = (thickness in inches x width in inches x length in inches) / [tex]144[/tex]

BF = (1 inch x 12 inches x 12 inches) / 144

BF = 144 cubic inches / 144

BF = 1 board foot

Therefore, the board is 1 board foot in size.

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The equation that expresses how many cases Tamera used in her downstairs bathroom is: Downstairs cases = Total cases - Upstairs cases

We know that Tamera purchased a total of 31 cases of tile, and used 17 cases in her upstairs bathroom. Therefore, the number of cases she used in her downstairs bathroom can be found by subtracting the number of cases used in her upstairs bathroom from the total number of cases:

Downstairs cases = Total cases - Upstairs cases

Downstairs cases = 31 - 17

Downstairs cases = 14

Therefore, Tamera used 14 cases of tile in her downstairs bathroom.

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The discussion-based assessment is meant to provide you with an opportunity to reflect on the topics and skills you have learned, as well as identify any areas you may need additional support in.

The conversation should be guided by your instructor, who will ask questions to ensure you understand the material, as well as provide feedback and advice on how to improve your understanding and performance.

At the end of the assessment, you and your instructor should have a clear understanding of your progress and where you need to focus your efforts moving forward.

The instructor should also provide feedback on your performance and suggest strategies for improvement. Additionally, you should have an understanding of the topics you need to work on and the resources available to you to help you improve.

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The complete question is:

Discussion-based Assessment

A student using a computer to study once you have completed the lesson and assignments, please contact your instructor to complete your discussion-based assessment. You and your instructor will discuss what you have learned up to this point in the course to make sure you're ready to move on to the next lesson. What does it mean?

The value for k has to be taken, to ensure that the probability, that - when we take a distance measurement y in practice - this distance measurement lies inside the interval [x – ko, x + ko), equals 99% is  0.516.

To find the value of k that ensures that the probability that the distance measurement lies inside the interval [x – ko, x + ko) equals 99%, we can use the standard normal distribution table.

First, we need to find the z-score that corresponds to the 99% probability. This is found by looking at the standard normal distribution table and finding the z-score that corresponds to a cumulative probability of 0.995 (since the probability is split between both sides of the mean, we need to look for 0.995 instead of 0.99).

The z-score that corresponds to 0.995 is approximately 2.58.

Now, we can use the formula for the z-score to find the value of k:

z = (y - x)/o

Since we are looking for the value of k that corresponds to the interval [x – ko, x + ko), we can plug in the values for the z-score and the standard deviation:

2.58 = (x + ko - x)/0.2

Solving for k, we get:

k = 2.58 * 0.2

k = 0.516

Therefore, the value for k that ensures that the probability that the distance measurement lies inside the interval [x – ko, x + ko) equals 99% is 0.516.

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The image of the point (-1, -2, 0) under a dilation with center (0, 0, 0) and scale factor 3 is (-3, -6, 0).

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

Center = (0, 0, 0).

Point = (-1, -2, 0)

Scale factor = 3

A dilation with center (0, 0, 0) and scale factor k multiplies the coordinates of a point by k.

So, to find the image of the point (-1, -2, 0) under a dilation with scale factor 3, we multiply each coordinate by 3:

(-1, -2, 0) --> (3(-1), 3(-2), 3(0))

Image = (-3, -6, 0)

Hence, the image of the point (-1, -2, 0)is (-3, -6, 0).

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The image of the figure under a dilation with scale factor 3/2 is attached

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

Center = (0, 0).

Point = (6, 12), (8, 12) and (8, 8)

Scale factor = 3

A dilation with center (0, 0) and scale factor k multiplies the coordinates of a point by k.

So, to find the image of the point under the dilation with scale factor 3/2, we multiply each coordinate by 3/2:

Image = [(6, 12), (8, 12) and (8, 8)] * 3/2

Image = [(9, 18), (12, 18) and (12, 12)]

Hence, the image of the figure is attached

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The other root of the polynomial is 5 + 7i.

Polynomial, a mathematical expression made comprised of numbers and variables arranged in specific patterns. Polynomials are sums of monomials of the form ax^n, where n (the degree) must be a whole number and a (the coefficient) can be any real number. The greatest degree monomial in a polynomial determines the polynomial's degree. Polynomials can be prime or factorable into products of primes, just like whole numbers. As long as each variable's power is a non negative integer, they can include any number of variables. They serve as the foundation for solving algebraic equations.

As per the given data:

One root of a polynomial is 5 - 7i

For finding the other root:

Consider the quadratic formula:

[tex]x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex]

From here, we can observe that imaginary roots will always occur in a pair.

So if one root is a + ib the other will be a - ib.

Similarly, for 5 - 7i the other root will be 5 + 7i.

Hence, the other root of the polynomial is 5 + 7i.

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Answer:

The answer is 145°

Step-by-step explanation:

Angle 3 and 4 make a right angle (90°) Subtract 55 from 90.

90-55=35

Angle 3 and Angle 1 are vertical angles, hence they have the same measurement.

Angle 1 is 35°

Angle 1 and 2 make a 180° angle. Subtract 35 from 180.

180-35=145

The measurement of angle 2 is 145°

Answer:

Step-by-step explanation:

∠5 + ∠4 = 90 + 55 = 145

∠2 = ∠5 + ∠4 (vertically opposite angles)

∴ ∠2 = 145

Therefore, this is how much it would cost to purchase p pounds of chicken: Cost is equal to $3.75p – $1.75, with p≥  1.

The unitary method in mathematics is a strategy for resolving proportional issues. Finding the value of one unit of a quantity and using that value to calculate the value of a second quantity that is proportional to the first includes this technique. The unitary technique is frequently employed in a variety of real-world contexts, including engineering, finance, and food preparation. The unitary method can be used to determine the amount of flour required to make a different number of cookies, for instance, if a recipe asks for 2 cups of flour to make 12 cookies.

given

The price of 5 pounds of poultry without the coupon is:

$5 for five pounds at $3.75 per pound.

Jai saves $1.75 thanks to the coupon, making the total price for 5 pounds of chicken:

$18.75 - $1.75 = $17.00

Jai would therefore need to spend $17.00 in order to purchase 5 pounds of poultry using the coupon.

With the assumption that at least one pound is bought, we can use the following formula to write an expression for the price to buy p pounds of chicken:

Expense is equal to (price per pound) x (pounds) - (coupon amount)

where p is the number of pounds, $3.75 is the price per pound, and $1.75 is the value of the voucher.

Therefore, this is how much it would cost to purchase p pounds of chicken: Cost is equal to $3.75p – $1.75, with p≥  1.

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Answer:

George will be right by the rule of BODMAS

Step-by-step explanation:

If the students use BODMAS rule, division comes before addition

To find the value of r that makes the statement an identity, we need to set the two sides of the equation equal to each other and solve for r.

First, let's multiply both sides of the equation by (x-10) to eliminate the denominator:

(x^(2)-x-8) = (x-10)(x+9) + r

Next, let's expand the right side of the equation:

x^(2)-x-8 = x^(2) + 9x - 10x - 90 + r

Now, let's rearrange the equation and solve for r:

r = x^(2)-x-8 - x^(2) - 9x + 10x + 90

r = 90

Therefore, the value of r that makes the statement an identity is 90.

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a. R = 1820 - 25t
b. R = 1820 - 25(7) = 1345 billion barrels
c. The world's oil reserves will be depleted when R = 0, so 25t = 1820, t = 72.8 years

a. The linear equation for the remaining oil reserves, R, in terms of t, the number of years since now, is R = 1820 - 25t. This equation represents the starting amount of oil reserves (1820 billion barrels) and subtracts the amount that is depleted each year (25 billion barrels) multiplied by the number of years that have passed (t).
b. Seven years from now, the oil reserves will be R = 1820 - 25(7) = 1820 - 175 = 1645 billion barrels.
c. To find when the world's oil reserves will be depleted, we need to solve for t when R = 0. So we have:

0 = 1820 - 25t
25t = 1820
t = 1820/25
t = 72.8
So, if the rate of depletion isn't changed, the world's oil reserves will be depleted in about 72.8 years.

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The IQR is the difference between Q3 and Q1: IQR = Q3 - Q1 = 4 - 1 = 3 hours.

The presented graph displays a line or dot plot of a data set that indicates the average daily activity time of a group of individuals over the previous week.

We must locate the data set's middle value in order to get the median. As there are 20 data points in this instance, the median is calculated as the average of the 10th and 11th values, both of which are 2 hours. As a result, 2 hours is the median amount of exercise per day.

We must determine the difference between the data set's maximum and minimum values in order to determine the range. The ranges are 0 hours for the minimum and 5 hours for the highest. The range is therefore 5 - 0 = 5 hours.

Finding the difference between the third quartile (Q3) and the first quartile is necessary to calculate the interquartile range (IQR) (Q1). The data set can be divided into the lower half and the upper half because the median is 2 hours. 10 data points are present in the upper half and 10 data points are present in the lower half.

The median of the lower half of the data set must be located in order to determine Q1. The median is the average of the fifth and sixth values, both of which are one hour because there are ten data points in the lower half. Q1 is therefore 1 hour.

We must determine the median of the upper half of the data set in order to determine Q3. The median is the average of the fifth and sixth values, which are both 4 hours, as there are 10 data points in the upper half. Q3 is therefore 4 hours.

The IQR represents the variation between Q3 and Q1: IQR is equal to Q3 - Q1 (4 - 1 = 3 hours).

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According to the figure the congruent angles are: ∠BAC = ∠CDB, ∠ABD = ∠ACD, ∠ACB = ∠ADB and ∠CBD = ∠CAD

Congruent angles may be define as if two or more angles measures the same value. In other words, if two angles are congruent, they will have the same degree measure, and they will look identical when placed on top of each other. This is similar to the concept of congruent shapes or figures, where two shapes have the same size and shape.

According to the figure the points A, B, C, and D are consecutive points on Circle W (center) as shown in figure.

We need to find out the angles must be congruent to the angles of ABD, BAC, ACB and CBD.

according to the figure we have to get some values of congruent angles are:

∠BAC = ∠CDB,

∠ABD = ∠ACD,

∠ACB = ∠ADB and

∠CBD = ∠CAD

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Answer:

eight angles

Step-by-step explanation:

The total area of the painting and frame is 112 in²

An equation is an expression that shows the relationship between two or more numbers and variables. Equations can either be linear, quadratic, cubic and so on depending on the degree.

Let x represent the length of the smaller edge.

One edge of a painting is 6 in. longer than the other edge. Hence:

Longer edge = x + 6

The painting has a 2-inch-wide frame.

Smaller edge length with frame = x + 2 + 2 = x + 4

Longer edge length with frame = (x + 6) + 2 + 2 = x + 10

Total area = (x + 4)(x + 10)

Total area = x² + 14x + 40

The longer side of the frame is 14 inches long, hence:

x + 10 = 14

x = 4 in

Total area = x² + 14x + 40 = 4² + 14(4) + 40 = 112 in²

The total area is 112 in²

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The slope of the line as shown in the image attached below is: 2/3.

The slope of a line represents the ratio of the change in y (vertical) to the change in x (horizontal). It is a measure of the steepness of the line and tells us how much the y-value changes for each unit change in the x-value.

It is given as:

Slope (m) = rise/run.

The rise (blue line) = 2 units

The run (red line) = 3 units

Slope (m) = -2/3

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The base length of the isosceles triangular pieces with height 8 cm, side length 4cm and area of triangle is 64 cm² is equals to the 16 cm.

Isoceles triangle: The two sides of triangle which are equal in length are called "legs". In case of isosceles triangle, ABC (present above), AB and AC are the called "legs".

Steps to calculate the base of the triangle :

Now we have an isosceles triangle,

height of isosceles triangle, h = 8 cm

area of isosceles triangle, A = 64 cm²

we know that area of isosceles triangle

= ½ x base x height

=> base triangle = (2 x area of triangle)/ height

Substituting all known values,

=> base length of triangle = 2 x 64/8

=> base length = 16 cm

Hence, required base length is 16 cm.

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Complete question:

Calculate the base length of the isosceles triangular pieces with height 8 cm, side length 4cm and area of triangle is 64 cm².

Answer: I don't speak Spanish but the answer might be 21.4285714286 liters

Step-by-step explanation:

"An aluminum container has a capacity of 6 liters at 28 degrees Celcius. Determine the volume of the container when it is heated to 100 degrees Celsius."

The evaluated values of the function for the given values of x are:
f(-1) = 5
f(0) = 0
f(1) = -1
f(2) = 2
f(3) = 9

To evaluate the function f(x)=2x^2-3x for the given values of x, we simply plug in the given value of x into the function and solve for f(x).

(a) f(-1) = 2(-1)^2 - 3(-1) = 2(1) + 3 = 5

(b) f(0) = 2(0)^2 - 3(0) = 0 - 0 = 0

(c) f(1) = 2(1)^2 - 3(1) = 2 - 3 = -1

(d) f(2) = 2(2)^2 - 3(2) = 8 - 6 = 2

(e) f(3) = 2(3)^2 - 3(3) = 18 - 9 = 9

Therefore, the evaluated values of the function for the given values of x are:
f(-1) = 5
f(0) = 0
f(1) = -1
f(2) = 2
f(3) = 9

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The value of the variable 'x' using the external angle theorem will be 84°.

The polygonal form of a triangle has a number of flanks and three independent variables. Angles in the triangle add up to 180°.

The exterior angle of a triangle is practically always equivalent to the accumulation of the interior and opposing interior angles. The term "external angle property" refers to this segment.

The graph is completed and given below.

By the external angle theorem, the equation is given as,

x + 180° - 154° + 180° - 110° = 180°

x + 26° + 70° = 180°

x + 96° = 180°

x = 84°

The value of the variable 'x' using the external angle theorem will be 84°.

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Answer:

0

Step-by-step explanation:

y = 1x + b

-3 = 1(-3) + b

-3 = -3 + b
+3   +3

0 = b

The quotient of the given values when expressed in a scientific notation would be = 1.7 × 10⁵

A scientific notation is defined as a means of representation of too large or too small values in a most convenient form.

The quotient of 3.91× 10⁷ and 2.3 × 10² means the division of 3.91× 10⁷ and 2.3 × 10².

That is ;

= 3.91× 10⁷/ 2.3 × 10²

= 3.91/2.3 × 10⁷/10²

= 1.7 × 10⁵ ( it is 10⁵ because since it's division the superscripts attached to 10 will be subtracted)

Therefore, the quotient value of the given expression above would be = 1.7 × 10⁵.

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The product AB is not equal to the product BA. This demonstrates the non-commutativity of matrix multiplication.

Matrix multiplication is non-commutative, which means that the product of two matrices can be different depending on the order in which they are multiplied. In other words, AB is not always equal to BA. Let's find the product of the given matrices A and B in both orders to demonstrate this.

First, let's find the AB Product:
AB = [[1,-4],[-2,4]] * [[-4,0],[4,3]]
= [(1 * -4) + (-4 * 4), (1 * 0) + (-4 * 3), (-2 * -4) + (4 * 4), (-2 * 0) + (4 * 3)]
= [[-20, -12], [16, 12]]

Now, let's find the product BA:
BA = [[-4,0],[4,3]] * [[1,-4],[-2,4]]
= [(-4 * 1) + (0 * -2), (-4 * -4) + (0 * 4), (4 * 1) + (3 * -2), (4 * -4) + (3 * 4)]
= [[-4, 16], [2, 4]]

As we can see, the product AB is not equal to the product BA. This demonstrates the non-commutativity of matrix multiplication.

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complementary mean they both add to 90 degrees

90 - 12.1 = 77.9

the other angle is 77.9 degrees

Answer: 77.9°

Step-by-step explanation:

Complementary angles are angles that, when added together, equal 90°.

So to find the complementary angle of an angle that measures 12.1°, you subtract:

90-12.1 = 77.9°

83/17 = 4.88235294118

Answer:

4.88, and 4.9 rounded to the nearest 10th and 5 round to the nearest whole number.

Step-by-step explanation: