explain what it means to solve a system of equations

The sets of lengths that are Pythagorean triples are:

A. 10, 24, 26

D. 9, 40, 41

E. 15, 20, 25

A Pythagorean triple can be described as a set of three numbers of the side lengths of a right triangle whereby the square of the longest side is equal to the sum of the squares of the two other sides.

For 10, 24, 26, we have:

10² + 24² = 26²

676 = 676 [true]

The set, 10, 24, 26 is a Pythagorean triple.

For 14, 48, 49, we have:

14² + 48² = 49²

2,500 = 2,401 [not true]

The set, 14, 48, 49, is NOT a Pythagorean triple.

For  9, 12, 16, we have:

9² + 12² = 16²

225 = 256 [not true]

The set, 9, 12, 16, is NOT a Pythagorean triple.

For  9, 40, 41, we have:

9² + 40² = 41²

1,681 = 1,681 [true]

The set, 9, 40, 41, is a Pythagorean triple.

For  15, 20, 25, we have:

15² + 20² = 25²

625 = 625 [true]

The set, 15, 20, 25, is a Pythagorean triple.

The correct set of options are, A, D, and E.

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The angle between the stick and the base of the box is 77. 9 degrees

To determine the angle between the stick and the base, we have to know the trigonometric identities.

These identities are;

From the information given, we have;

sin A = FB/AB

Given that;

GB = 14.5cm

AB = 18. 6cm

substitute for the length of the sides, we have;

sin A = 14.5/18. 6

Divide the values, we have;

sin A = 0. 7796

Find the inverse sine

A = 77. 9 degrees

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The measures of central tendency of the first psychology exam in a semester are the average score, which was an 85.

The correlation coefficient and the range of scores from 95 to 65 are not measures of central tendency either.

The standard deviation is a measure of variability, not central tendency, that the measures of central tendency of the first psychology exam are the average and median scores. This states that the mode, correlation coefficient, range of scores, and standard deviation are not measures of central tendency.

Hence, the measures of central tendency for the first psychology exam in a semester are the average score (85) and the median score (80).

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The measures of central tendency for the psychology exam scores include the average, median, and mode.

The measures of central tendency of the first psychology exam in a semester include the average score, median score, and mode (most frequently occurring score).

The average score on the exam was 85, which represents the mean of all the scores.

The median score on the exam was 80, which represents the middle value when all the scores are arranged in order.

The most frequently occurring score was 82, which represents the mode of the scores.

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Answer:

The last choice

Step-by-step explanation:

All of the other choices have two of the same x values. A function can not have two of the same x values so it is the last choice.

The Volume generated when the region between the curves is rotated around the y - axis is 1216500335.46

Volume of the curves:

The volume of the solid formed by revolving the region bounded by the curve x = f(y) and the y-axis between y = c and y = d about the y-axis is given by

V = π ∫dc [f(y)]2dy.

The cross-section perpendicular to the axis of revolution has the form of a disk of radius R = f(y).

Given,

y = x³

Here we have to find the volume along to the y axis.

With limit as y = 0 and y = 27.

When we apply the values it can be written as,

=>\(V=\pi \int\limits^0_{27} {(x^3)^2} \, dx\)

\(\implies V=\pi \int\limits^0_{27} {(x^6)} \, dx\)

Apply the limits then we get,

\(\implies V = \pi [0^6 - (27)^6]\)

=> V = π [0 - 387420489]

=> V =   π x 387420489

=> V = 1216500335.46

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Answer:

75 degrees

Step-by-step explanation:

Complementary angles equal 90 degrees together. That is the case with angle X and Y. Set an equation to describe the situation.

Y=1/5X

X=5Y

Now, set another equation:

X+Y=90

Substitute the first equation into the second one.

5Y+Y=90

6Y=90

Y=15

Substitute this once again:

X+15=90

X=75

Answer: (0,-6)

Step-by-step explanation:

To find the y-intercept, we can rewrite the equation into slope-intercept form.

3x+5y=-30            [subtract both sides by 3x]

5y=-3x-30             [divide both sides by 5]

y=-3/5x-6

Now that the equation is in slope-interceot form, we know that the y-intercept is -6, we know that the answer is (0,-6).

Answer:

(B (4, 7 ) = (1, 12 )

Step-by-step explanation:

given

B (x, y ) = (x - 3, y + 5 ) , then

B (4, 7 ) = (4 - 3, 7 + 5 ) = (1, 12 )

Answer:16

Step-by-step explanation:

Answer:

20 % of 80 is 16.000

Step-by-step explanation:

Hope this Helps! :3

Answer:

0.8

Step-by-step explanation:

__0.8__

5/ 4.0

-._0__

4 0

-_4_0_

0. 0

I try showing u the working

When, bisecting diagonal of length 8 inch bisects the diagonal is equal halves then the length of the bisected diagonal is 8.66 inch.

In kite, one diagonal is bisects the other diagonal in two equal halves.

Let x and (8-x) be the lengths of the two parts of the bisecting diagonal.

Let y be the length of the bisected diagonal in half.

The legs of a right triangle with hypotenuse 5 are then x and y.

\(5^2=y^2+x^2\\\\y^2=5^2-x^2...i\)

The legs of a right triangle with hypotenuse 7 are (8-x) and y.

\(7^2=(8-x)^2+y^2\\\\y^2=7^2-(8-x)^2....ii\)

Equating both the equations i and ii,

\(5^2-x^2=7^2-(8-x)^2\\\\25-x^2=49-(64+x^2-16x)\\\\25-x^2=49-64-x^2+16x\\\\25=-15+16x\\\\40=16x\\\\x=2.5\)

substitute x in eq. i,

\(y^2=25-2.5^2\\\\y^2=25-6.75\\\\y^2=18.25\\\\y=4.33\)

Hence, the length of bisected diagonal is 2(4.33)=8.66 inch.

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Answer:

115 lbs = 52.16 kilograms

Step-by-step explanation:

115 pounds is a little over 52kg

Answer:

cool :))))))))) good luck

A random variable X follows a Poisson distribution with parameter λ = 10. The mean of X is 3. The standard deviation of X is 1.535. The variable θ is equal to 10. The equation xh = p × r = 38 × 10. The equation for the standard deviation is sd = n + (1 − 8).

The Poisson distribution has a parameter λ which represents the average rate of occurrence of an event. In this case, λ = 10.

The mean of a Poisson distribution is equal to its parameter. Therefore, the mean of X is 10.

The standard deviation of a Poisson distribution is the square root of its parameter. Hence, the standard deviation of X is √10 ≈ 3.162.

The variable θ is given as 10.

The equation xh = p × r = 38 × 10 implies that xh, which is not defined, is equal to the product of p and r, which is 380.

The equation for the standard deviation, sd, is n + (1 − 8). However, it seems to be incomplete or unclear in its current form.

Please provide additional clarification or correction for the last equation to provide a more accurate explanation.

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Answer:

p = 35°

Step-by-step explanation:

Angles on a straight line add up to 180° so:

2p + 5 + 3p = 180° (simplify)

5p + 5 = 180° (subtract 5 from both sides)

5p = 175° (divide both sides by 5)

p = 35°

Hope this helps!

Answer:

p=35

Step-by-step explanation:

You have to add the two together and set them equal to 180, so 2p+5+3p=180 so 5p=175, so p=35.

(1) For the equation x^2y'' - xy' - x - 3y = 0, with the substitution x = e^t, the general solution is y(x) = C1 * x^3 + C2 * x^(-1/2) + C3 * x. (2) For the equation x^3y''' + 6x^2y'' + 4xy' - 4y = 0, with the substitution x = e^t, the general solution is y(x) = C1 * x + C2 * x^(-2/3) + C3 * x^(-2).

To find the general solutions for the given differential equations, we will use the substitution x = e^t.

(1) For the equation x^2y'' - xy' - x - 3y = 0, we substitute x = e^t and differentiate with respect to t using the chain rule. We have:

dy/dt = dy/dx * dx/dt = dy/dx * (d/dt(e^t)) = dy/dx * e^t

Next, we substitute the derivatives into the differential equation:

(e^t)^2(dy/dx + d^2y/dx^2) - e^t(dy/dx) - e^t - 3y = 0

Simplifying the equation, we have:

e^(2t)(dy/dx + d^2y/dx^2) - e^t(dy/dx) - e^t - 3y = 0

Dividing through by e^t, we get:

dy/dx + d^2y/dx^2 - dy/dx - 1 - 3y/e^t = 0

Simplifying further, we have:

d^2y/dx^2 - 4y = 1

This is a second-order linear homogeneous differential equation. We can solve it using standard methods such as the characteristic equation.

(2) For the equation x^3y''' + 6x^2y'' + 4xy' - 4y = 0, we substitute x = e^t and differentiate with respect to t:

dy/dt = dy/dx * dx/dt = dy/dx * (d/dt(e^t)) = dy/dx * e^t

d^2y/dt^2 = d^2y/dx^2 * (dx/dt)^2 + dy/dx * d^2x/dt^2 = d^2y/dx^2 * (e^t)^2 + dy/dx * 0 = e^(2t)d^2y/dx^2

d^3y/dt^3 = e^(3t)d^3y/dx^3

Substituting these derivatives into the differential equation, we have:

(e^t)^3(d^3y/dx^3) + 6(e^t)^2(d^2y/dx^2) + 4(e^t)(dy/dx) - 4y = 0

Simplifying, we have:

e^(3t)(d^3y/dx^3) + 6e^(2t)(d^2y/dx^2) + 4e^t(dy/dx) - 4y = 0

Dividing through by e^t, we get:

d^3y/dx^3 + 6dy/dx + 4y/e^t - 4y/e^(2t) = 0

Simplifying further, we have:

d^3y/dx^3 + 6dy/dx + 4y - 4y/e^t = 0

This is a third-order linear homogeneous differential equation. We can solve it using standard methods such as finding the characteristic equation.

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Answer:

2.1

Step-by-step explanation:

1.35% is the percentage change in the population of the city that grew from the years 2010 to 2020.

The population of the city = 89,000

Percentage in the growth of people from 2010 to 2015 = 6.8%

Percentage in the decline of people from  2015 to 2020 = 4.9%

The formula to calculate the percentage change is:

percentage change = (new value - old value) / old value x 100%

To calculate the population of the city after the growth of 6.8%

Population in 2015 = 89,000 x (1 + 6.8/100)

Population in 2015 = 95,012

To calculate the population of the city after the decline of 4.9%

Population in 2020 = 95,012 x (1 - 4.9/100)

Population in 2020 = 90,199.88

Population in 2020 = 90,200

The total change in the percentage of growth of population in the city is:

percentage change = (new population - old population) / old value * 100%

percentage change = (90,200 - 89,000) / 89,000 x 100%

percentage change = 1,200 / 89,000 x 100%

percentage change = 1.35%

Therefore, we can conclude that the population in the city grew by 1.35% from 2010 to 2020.

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Carl is correct the value of x by using the side splitter theorem is 6

\(\frac{6}{3} = \frac{12}{x}\)

Required

Is Carl correct?

The side splitter theorem is a theorem that states that when a line passes through the two sides of a triangle and is parallel to the third remaining side, the line divides the two sides proportionally.

Using the side splitter theorem, the proportion is:

\(\frac{AB}{BC} = \frac{AE}{ED}\\\)

This gives:

\(\frac{6}{3} = \frac{12}{x}\)

This proportion is equivalent to Carl's.

Hence, Carl is correct.

Solving further: Cross Multiply

6 * x = 12 * 3

6x = 36

Make x the subject

\(x=\frac{36}{6}\)

x =6

Carl is correct the value of x by using the side splitter theorem is 6

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Answer:

every year the branches increase 75%

Step-by-step explanation:

Answer:

\(x=13\)

Step-by-step explanation:

The angle on a straight line is always 180 degrees.

Thus,

\((12x-26)+50=180\)

Remove the brackets:

\(12x-26+50=180\)

\(12x+24=180\)

Subtract 24 from both sides:

\(12x+24-24=180-24\)

\(12x=156\)

Divide both sides by 12:

\(\frac{12x}{12}=\frac{156}{12}\\\)

\(x=13\)

Answer:

x = 13

Step-by-step explanation:

Because it is the "Correct Answer"

Frank cannot recover the reward because he was unaware of the reward being offered by Emma.

In order to claim the reward, one typically needs to have knowledge of the reward prior to finding and returning the lost item or fulfilling the specified condition. Since Frank was unaware of the reward, he would not have had the opportunity to intentionally seek the dog with the expectation of receiving the reward. As a result, Emma is not obligated to provide the reward to Frank in this situation.

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Sathish will pay $64.8

When Satish is alone, kilometres:

Beginning at 150 kilometres and ending at 150 kilometres will be travelled 300 kilometres in total

When Satish is with friends, the total kilometres travelled is 2100 km:

And when Satish went alone he travelled 300 km

When Satish is with friends, total kilometres travelled: 2100-300 = 1800 km

Gas consumed in litres when Satish is alone: 100 kilometres use 6 litres of gas.

300 kilometres at 6 x 3 equals 18 litres.

So, when Satish is with friends, litres of gas are consumed: 100 kilometres use 6 litres of gas.

So, 6 × 18 for 1800 kilometres is equal to 108 litres.

Gas prices when Satish is on his own:

$1.2 per litre

18 x $1.2 = $21.6

Gas prices when Satish is travelling with friends

$1.2 per litre

108 x 1.2 = $129.6

Cost for each friend = $129.6/3 = $43.2

Satish will pay: Cost when travelling with friends + Cost when travelling alone

=$43.2+ $21.6

=$64.8

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Answer:

11) 75.2

12) 44.2

Step-by-step explanation:

angles formed by intersecting lines tangent to a circle are the same length.

11)

Perimeter = 2(5) + 2(12) + 2(11.4) + 2(9.2) = 75.2

12)

Perimeter = 2(4) + 2(8) + 2(5.3) + 2(4.8) = 44.2

The algebraic representation of (x,y)-> (5x, 5y) represents transformation of  dilate by a scale factor of 5.

Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size. The x and y coordinates of the original figure are multiplied by the scale factor to discover spots on the dilated image when a dilation in the coordinate plane has the origin as the centre of dilation. The algebraic representation of the dilation is (x, y) for scale factor k. (kx, ky). K > 1 for enlargements.

Given,

The algebraic representation of (x,y)-> (5x, 5y) represent transformation given below:

(B) dilate by a scale factor of 5

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The probability that the sample mean will be less than 8 is about 0.0384 or 3.84%.

Now, for the probability that the sample mean will be less than 8, we need to first find the standard error of the mean.

The formula for the standard error of the mean is:

standard error of the mean = standard deviation / square root of sample size

In this case, the standard error of the mean is

8 / √(50) = 1.13

Next, we can use the standard normal distribution to find the probability that the sample mean will be less than 8.

We can convert the sample mean to a z-score using the formula:

z = (sample mean - population mean) / standard error of the mean

In this case, the z-score is:

z = (8 - 10) / 1.13

z = -1.77

Using a standard normal distribution table or calculator, we can find the probability that a z-score is less than -1.77 is about 0.0384.

Therefore, the probability that the sample mean will be less than 8 is about 0.0384 or 3.84%.

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After d days, the number of lily pads in the pond can be calculated using the formula 2^d. So, if d is the number of days, then the number of lily pads after d days would be 2^d.

Each day, the number of lily pads doubles. So, on the first day, there is 1 lily pad. On the second day, the number doubles to 2. On the third day, it doubles again to 4, and so on. This doubling pattern continues for d days.

To calculate the number of lily pads after d days, we raise 2 to the power of d (2^d). This is because each day, the number of lily pads doubles, which can be represented as 2^1, 2^2, 2^3, and so on. By substituting the value of d into the equation, we can find the number of lily pads after d days.

For example, if d = 5, then the number of lily pads after 5 days would be 2^5 = 32. This means that there would be 32 lily pads in the pond after 5 days.

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The correct answer is (C) g'(-6).

We have to use the Chain Rule of Differentiation in order to find h'(-2).

Therefore, we have:

h(x) = f(g(x))

So,

h'(x) = f'(g(x)) \cdot g'(x)

The expression above can be written as:

h'(x) = f'(u) \cdot g'(x)

where $u = g(x)$.

Now, let's find h'(-2):

h'(-2) = f'(u) \cdot g'(-2)

We have been given that g(-2) = 6 and g'(-2) = 8.

However, we still need to know f'(u) in order to calculate h'(-2).

Therefore, the correct answer is (C) g'(-6).

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Answer: The critical points of g(t) occur at t = ±sqrt(-d/2) if d < 0. If d ≥ 0, then dg(t)/dt is always greater than or equal to zero, so g(t) has no critical points.

Step-by-step explanation:

To find the critical points of g(t), we need to find the values of t where the derivative dg(t)/dt is equal to zero or does not exist.

Using the given information, we have:

dg(t)/dt = 4ct^3 + 2dct

Setting this equal to zero, we get:

4ct^3 + 2dct = 0

Dividing both sides by 2ct, we get:

2t^2 + d = 0

Solving for t, we get:

t = ±sqrt(-d/2)

Therefore, the critical points of g(t) occur at t = ±sqrt(-d/2) if d < 0. If d ≥ 0, then dg(t)/dt is always greater than or equal to zero, so g(t) has no critical points.

Note that we also need to assume that c is nonzero, since if c = 0, then dg(t)/dt = 0 for all values of t and g(t) is not differentiable.

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