what is the solution to the system 3x+2y=-3 and 9x +4y=3

The function y = (e⁻⁽ˣ⁺²⁾) / x + 2  increases along intervals of (-∞, 3) and decreases along (-3, -2), (-2, ∞) and the function y = 2x - 1 / (x - 1)² has no inflection points but  concave downwards along (-∞, 1) ∪ (1 ,∞)

An extremum (or extreme value) of a function is a point at which a maximum or minimum value of the function is obtained in some interval. A local extremum (or relative extremum) of a function is the point at which a maximum or minimum value of the function in some open interval containing the point is obtained.

The function given;

y = (e⁻⁽ˣ⁺²⁾) / x + 2

The extrema and intervals of increase or decrease of this function are

(-1, 1.63) and it increases along (-∞, 3) and decreases along (-3, -2), (-2, ∞)

2. The inflection points and intervals of concavity and convexity of the function

y = 2x - 1 / (x - 1)² are

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Using the radius of the Ferris wheel and the angle between the two positions, the time spent on the ride when they're 28 meters above the ground is 12 minutes

The radius of the Ferris wheel is 30 / 2 = 15 meters.

The highest point on the Ferris wheel is 15 + 4 = 19 meters above the ground.

The time spent higher than 28 meters is the time spent between the 12 o'clock and 8 o'clock positions.

The angle between these two positions is 180 degrees.

The time spent at each position is 10 minutes / 360 degrees * 180 degrees = 6 minutes.

Therefore, the total time spent higher than 28 meters is 6 minutes * 2 = 12 minutes.

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Answer:

b=0

Step-by-step explanation:

y=mx+b

-8=2(-4)+b

-8=-8+b

8+(-8)=b

0=b

b=0

The GCD of 5! and 7! is 2^3 * 3^1 * 5^1 = 120.

the greatest common divisor of 5! and 7! is 120.

To find the greatest common divisor (GCD) of 5! and 7!, we need to factorize both numbers and identify the common factors.

First, let's calculate the values of 5! and 7!:

5! = 5 * 4 * 3 * 2 * 1 = 120

7! = 7 * 6 * 5 * 4 * 3 * 2 * 1 = 5,040

Now, let's factorize both numbers:

Factorizing 120:

120 = 2^3 * 3 * 5

Factorizing 5,040:

5,040 = 2^4 * 3^2 * 5 * 7

To find the GCD, we need to consider the common factors raised to the lowest power. In this case, the common factors are 2, 3, and 5. The lowest power for 2 is 3 (from 120), the lowest power for 3 is 1 (from 120), and the lowest power for 5 is 1 (from both numbers).

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The image below shows the graph f(x) = |x| – 4

Hope this helps! :)

The solution of the expression, \(x^{\frac{9}{7} }\) is \(\sqrt[7]{x^{9} }\).

An expression is a combination of numbers, variables, functions such as addition, subtraction, multiplication or division etc.

Therefore, let's rewrite the expression to it's equivalent expression.

An equivalent expression is an expression that has the same value or worth as another expression, but does not look the same.

Therefore, using indices rule

\(x^{\frac{9}{7} }\) = \(\sqrt[7]{x^{9} }\)

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Answer:

Step-by-step explanation:

Based on the Triangle Inequality Theorem, the sets of side measurements that could form a triangle are:

13, 19, 7

25, 12, 13

18, 2, 24

The set of side measurements 3, 1, 5 could not form a triangle.

To determine which set of side measurements could form a triangle, we need to check if the sum of the lengths of the two shorter sides is greater than the length of the longest side. This is known as the Triangle Inequality Theorem.

Let's check each set of side measurements:

13, 19, 7:

The sum of the two shorter sides is 7 + 13 = 20, which is greater than the longest side (19). Therefore, this set of side measurements could form a triangle.

25, 12, 13:

The sum of the two shorter sides is 12 + 13 = 25, which is equal to the longest side (25). Therefore, this set of side measurements could form a triangle.

18, 2, 24:

The sum of the two shorter sides is 2 + 18 = 20, which is greater than the longest side (24). Therefore, this set of side measurements could form a triangle.

3, 1, 5:

The sum of the two shorter sides is 1 + 3 = 4, which is less than the longest side (5). Therefore, this set of side measurements could not form a triangle.

Based on the Triangle Inequality Theorem, the sets of side measurements that could form a triangle are:

13, 19, 7

25, 12, 13

18, 2, 24

The set of side measurements 3, 1, 5 could not form a triangle.

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Answer:

The answer is the last one

1/2 - (6.08-2)

Step-by-step explanation:

Answer/Step-by-step explanation:

40% = .40 (As a decimal)

$100 x .40= $40 {Mark-Up}
$40 is the Mark-up.

If Needed:

$100 + $40 = $140 [Final Price of the gymnastics mat]

[RevyBreeze]

Answer:

40/100

Step-by-step explanation:

it may be this or another answer which is 140 to 1400 to 140.000 but 40/100 sould be your answer.

We are told that the first week Lucy earns $50. We want to calculate the second week's earnings. Since earnings increase 10% every week, we will calculate 10% of 50 and then add it to 50. To calculate 10% of a number, we simply multiply the number by 0.1.

Then, the 10% of 50 would be

Now we add this quantity to 50. This would give the earnings of the second week. So, the earnings of the second week would be

From here, it is important to note that to increase a quantity by a 10% we simply multiply the quantity by the number (1+10/100). So, to calculate the earnings of week 3, we simply multiply the earnings of week 2 by (1+10/100)

This would be

Finally, we repeat the process for week 4, This would give

So we have

To calculate the earnings of all 4 weeks, we simply add this numbers, so we have

So in 4 weeks, Lucy earns 232.05

Answer:

The probability that the good exam belongs to Alice could be infered from the handwriting of the answer sheet. This s because, previously, the professor would have given them assignments which they submitted.

In the ones he marked, he was able to note the style of writing of alice and her good grades. Therefore, the style of writing (Handwriting ) in the exams with good grade will help him to determine that it belongs to Alice.

Step-by-step explanation:

Answer:

x = 5

Step-by-step explanation:

\(\frac{x}{2x - 3} = \frac{10}{14}\) --> Triangle Proportionality Theorem

10(2x - 3) = 14(x) --> Cross Multiplying

20x - 30 = 14x --> Distributing 10 and 14 to the parentheses

20x -30 - 14x + 30 = 14x - 14x + 30 --> Subtracting 14x and adding 30 on both sides

6x = 30 --> Simplifying

6x/6 = 30/6 --> Dividing 6 on both sides

x = 5 --> Simplifying

Hope this helped!

By the way, I'm not so sure you understand the concept of "Triangle Proportionality Theorem" since you asked a similar one before that. So I'll post an image that I found on the internet that explains it. :D

Answer:

Step-by-step explanation: Refer to the photo taken.

Answer:

Family. Family is what you make of it in Heart of a Samurai.

Language and Communication.

Principles.

Art and Culture.

Identity.

Change.

Society and Class.

Step-by-step explanation:

Hope this helps:)

Answer:

14.5833333333

Step-by-step explanation:

3.5x2.5=8.75, divided by 0.6 is 14.5833333333

Step-by-step explanation:

use length x width x height

Answer:

x = 4

m<AXC = 150

Step-by-step explanation:

m<1 + m<2 = m<AXC

102 + 10x + 8 = 6(6x + 1)

10x + 110 = 36x + 6

26x = 104

x = 4

m<AXC = 6(6x + 1)

m<AXC = 6(24 + 1)

m<AXC = 150

Answer:

Step-by-step explanation:

\(\sf 14=-6+2\left(2x+4\right)\)

\(\sf -6+2\left(2x+4\right)=14\)

\(\sf -6+2\left(2x+4\right)+6=14+\)

\(\sf 2\left(2x+4\right)=2\)

\(\sf \frac{2\left(2x+4\right)}{2}=\frac{20}{2}\)

\(\sf 2x+4=10\)

\(\sf 2x+4-4=10-4\)

\(\sf 2x=6\)

\(\sf \frac{2x}{2}=\frac{6}{2}\)

\(\sf x=3\)

Answer:

80 minutes

Step-by-step explanation:

Time taken to read 1 page = 15/6 = 2.5 minutes

time taken to read 32 page = 2.5 * 32 = 80 minutes

Answer:9,594 thats tha answer

Step-by-step explanation:

150 is base pay

5 is pay per shoe

The First mistake she made is simplifying 4(x+5) - 3x to be 4x+5-3x.

The mistake here is that she did not expand the 4(x+5) correctly. She forgot to multiply 4 by 5 to correctly expand the bracket. The correct expansion of "4(x+5)" is "4x + 20" and not "4x + 5"

The second mistake is that she simplified 4x+5-3x to be equal to 6. This is wrong.

"4x+5-3x" gives "x + 5" and not 6.

The correct simplification of the problem is as follows:

4(x+5) - 3x = 4x + 20 -3x

Collect like terms

=4x - 3x + 20

=x + 20

The correct answer should be x + 20

Answer:

Assuming normal distribution, the mean number of calls for a n-hour day is of \(m = n\mu\), in which \(\mu\) is the mean number of calls per hour, and the standard deviation is \(s = \sqrt{n}\sigma\), in which \(\sigma\) is the standard deviation of the number of calls per hour.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

N-instances of a normal variable:

For n-instances of normal variable, the mean of the distribution is: \(m = n\mu\), and the standard deviation is \(s = \sqrt{n}\sigma\)

What is the mean and standard deviation of the number of calls it receives for ​n-hour ​day?

Assuming normal distribution, the mean number of calls for a n-hour day is of \(m = n\mu\), in which \(\mu\) is the mean number of calls per hour, and the standard deviation is \(s = \sqrt{n}\sigma\), in which \(\sigma\) is the standard deviation of the number of calls per hour.

The rate of change of the volume is 871.2 ft³/sec

Rate of change of volume is the change in volume with time.

The rate of change of radius is 6 feet per second.

rate of change in volume = dv/dt

rate of change in radius = dr/dt

to find radius of the sphere;

V = 4/3 πr³

163 = 4/3 x3.14r³

r³ = 163× 3)/4×3.14

r³ = 488/12.56

r³ = 38.85

r = 3.4 feet

therefore

dr/dt = 1/4πr² × dv/dt

= 6 = 1/4×3.14× 3.4² × dv/dt

dv/dt = 6×4× 3.14× 3.4²

dv/dt = 871.2 feet³ per second

therefore the rate of change of the volume is 871.2 feet³ per second

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The two points with an x-coordinate of 2 and a distance of 5 from (-2, -4) are: (2, -4 + 2√13) and (2, -4 - 2√13)

What is distance formula?

Distance is a measurement of how far away two things or locations are, either numerically or occasionally qualitatively.

Distance formula: \(distance = \sqrt{((x2 - x1)^2 + (y2 - y1)^2)}\)

We can solve this problem using the distance formula, which gives us the distance between two points in a plane:

\(distance = \sqrt{((x2 - x1)^2 + (y2 - y1)^2)}\)

Let (x, y) be a point with an x-coordinate of 2. Then we can write the distance from (-2, -4) to (x, y) as:

\(distance = \sqrt{((x - (-2))^2 + (y - (-4))^2)}\)

Simplifying this expression, we get:

\(distance = \sqrt{((x + 2)^2 + (y + 4)^2)}\)

We know that the distance between (-2, -4) and (x, y) is 5. Therefore, we can write:

\(\sqrt{((x + 2)^2 + (y + 4)^2)} = 5\)

Squaring both sides, we get:

\((x + 2)^2 + (y + 4)^2 = 25\)

Expanding the left side, we get:

\(x^2 + 4x + 4 + y^2 + 8y + 16 = 25\)

Simplifying this expression, we get:

\(x^2 + 4x + y^2 + 8y - 5 = 0\)

To find all points with an x-coordinate of 2 that satisfy this equation, we can substitute x = 2 and simplify the resulting equation:

\(2^2 + 4(2) + y^2 + 8y - 5 = 0\)

Simplifying this equation, we get:

\(y^2 + 8y + 3 = 0\)

We can solve this quadratic equation using the quadratic formula:

y = (-b ± sqrt(b^2 - 4ac)) / 2a

where a = 1, b = 8, and c = 3.

Plugging in these values, we get:

y = (-8 ± sqrt(8^2 - 4(1)(3))) / 2(1)

Simplifying this expression, we get:

y = (-8 ± √52) / 2

y = (-8 ± 2√13) / 2

y = -4 ± √13

Therefore, the two points with an x-coordinate of 2 and a distance of 5 from (-2, -4) are: (2, -4 + 2√13) and (2, -4 - 2√13)

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The probability that the cupcake picked at random contains walnuts is given as follows:

0.4 = 40%.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

There are 30 cupcakes in a tin, hence the total number of outcomes is given as follows:

30.

The number of cupcakes with walnuts is given as follows:

Hence the probability that the cupcake picked at random contains walnuts is obtained as follows:

p = (3 + 9)/30

p = 12/30

p = 0.4.

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