Give an example of a problem that can be made easy to solve
mentally by using the
commutative property of multiplication. Write a relevant
equation.

The value of a(t) is -1 and b(t) is 55 + \(e^t\)

No, the given equation y' - y = 55 + \(e^t\) is not in the standard form of a first-order linear differential equation.

In the method for solving a first-order linear differential equation, an integrating factor is a function used to transform the equation into a form that can be easily solved.

For an equation in the standard form y' + a(t)y = b(t), the integrating factor is defined as:

μ(t) = e^∫a(t)dt

To solve the equation, you multiply both sides of the equation by the integrating factor μ(t) and then simplify. This multiplication helps to make the left side of the equation integrable and simplifies the process of finding the solution.

To put it in standard form, we need to rewrite it as y' + a(t)y = b(t).

Comparing the given equation with the standard form, we can identify:

a(t) = -1

b(t) = 55 + \(e^t\)

Therefore, The value of a(t) is -1 and b(t) is 55 + \(e^t\)

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The context that represents exponential decline or decay among the options provided is the car that depreciates at a rate of 7.3% per year.

Exponential decay is the continuous reduction of an entity at a fixed percentage rate over time.

The car's value reduces every year by 7.3%, and therefore it represents an exponential decay or decline.

The other given options are:An elevator descends at a rate of 24 feet per second.

This context represents linear decay or decline because the rate of descent is constant, and the value decreases linearly with time.

Money invested in a savings account grows at an annual rate of 2.2%.

This context represents exponential growth because the rate of growth is proportional to the total amount of money invested in the savings account, and hence the growth is exponential.

A population of 150 bacteria doubles every minute.

This context also represents exponential growth because the bacteria's growth is proportional to the total number of bacteria present, and hence the growth is exponential.

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A publisher needs to send many books to a local book retailer and will send the books in a combination of small and large boxes. Each small box can hold 20 books and each large box can hold 35 books.

The system of equation will be x+y = 7 and 20x+35y = 225.

Let x be the no of small boxes and y be the no. of large boxes.

Given here each small box can hold 20 books and each large box can hold 35 books.

A total of 7 boxes were sent.

So, x+y = 7.......equation 1

Also given that 7 boxes can hold 225 books altogether.

So, 20x+35y = 225.....equation 2

Hence the system of equation will be x+y = 7 and 20x+35y = 225.

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Evaluate using a suitable identity:  (997)³

991026973

Given:

(997)³

To solve this using an appropriate identity;

i. Rewrite by splitting the value in bracket (997) into a difference of two numbers. i.e

(997)³ = (1000 - 3)³

ii. Use the appropriate identity

Since the split from (i) above gave a cube of the difference of two numbers,  we can apply the following identity for finding the cube of the difference of two numbers;

(a - b)³ = a³ - b³ - 3ab(a - b)

In this case;

a = 1000

b = 3

(iii) Substitute the values of a and b into the identity equation and solve;

(1000 - 3)³ = 1000³ - 3³ - 3(1000)(3)(1000 - 3)

(1000 - 3)³ = 1000000000 - 27 - 9000(997)

(1000 - 3)³ = 1000000000 - 27 - 8973000

(1000 - 3)³ = 991026973

Therefore,

(997)³ = 991026973

====================================================

Explanation:

The two points given are

C = (x1,y1) = (2,-1)

D = (x2,y2) = (5,3)

Use the distance formula

\(d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(2-5)^2 + (-1-3)^2}\\\\d = \sqrt{(-3)^2 + (-4)^2}\\\\d = \sqrt{9 + 16}\\\\d = \sqrt{25}\\\\d = 5\\\\\)

The distance from C to D is 5 units. This is the same as saying segment CD is 5 units long.

In the given word problem, they all start to mow their lawns at the same time, Beth will finish first.

Let's assume that Beth's lawn has an area of x, so Andy's lawn has an area of 2x, and Carlos' lawn has an area of (1/3) × 2x = (2/3)x. Let's also assume that Beth's lawn mower can mow at a rate of 1 unit of area per hour, so Carlos' mower can mow at a rate of 1/2 = 0.5 units of area per hour, and Andy's mower can mow at a rate of 1/3 units of area per hour.  We can calculate the time it will take each person to mow their lawn by using the formula:

Time = Area / Rate.

Beth's time = x / 1

                   = x hours

Carlos' time = (2/3)x / 0.5

                    = (4/3)x hours

Andy's time = 2x / (1/3)

                    = 6x hours

According to these facts, it is quite clear that Beth would finish first followed by Carlos and Andy would finish last.

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Answer:

Sometimes, the symbol – written on top of two letters is used to denote the segment. This is line segment CD (Figure 1 ). Figure 1 Line segment. It is written CD (Technically, CD refers to the points C and D and all the points between them, and CD without the refers to the distance from C to D.)

Step-by-step explanation:

Sometimes, the symbol – written on top of two letters is used to denote the segment. This is line segment CD (Figure 1 ). Figure 1 Line segment. It is written CD (Technically, CD refers to the points C and D and all the points between them, and CD without the refers to the distance from C to D.)

Answer:

Segment CD and CD are different description of the line segment between points C and D.

By default CD refers to line segment but it could also refer to arc in the circle or a ray.

Therefore it is always good to mention by words or notation what is it.

We need first to change the speed of miles per hour to meter per min, then compare both speeds

Since 1 mile = 1.61 km

Since 1 km = 1000 m, then

1 mile = 1 x 1.61 x 1000

1 mile = 1610 meters

Since 1 hour = 60 min, then

50 miles per hour = 50 miles / 1 hour

Multiply 50 by 1610

Multiply 1 h by 60

Simplify it

Since the other speed is 1250 meters per min

Since 1341 2/3 > 1250

Then you have to drive at 50 miles per hour

Answer:

-24

Step-by-step explanation:

The coefficients are   4    3  and  -2

 multiplied together = -24

(4)(3)(-2) = - 24

Let's begin with the line that goes from minus infinity to zero

the equation of this line is

because of the filled circle we know that this interval touch the zero

in inequality, this will be

then for the line that is between 0 and 2, we have a filled circle in the number two therefore we can touch this number

the interval will be

in inequality notation

the interval

in inequality notation

Therefore the piecewise function i

the correct option is the second one

Given:

The given endpoints are ( -2,10) and (-10, -12).

Required:

We need to find the midpoint of te given endpoints.

Explanation:

Consider the formua to find the midpoint.

Consider the points ( -2,10) and (-10, -12).

Final answer:

Answer:

X = 12.645 round to 12.7

Step-by-step explanation:

∆LMN ~ ∆OPQ

so the coresponding side ratio are proportional

LM/OP = LN/OQ

LM/OP = LN/OQ49/OP = 31/8 ... the u solve x

X = 12.645 round to 12.7

Answer:

The answer is 84.

Step-by-step explanation:

The given equation is

4x*2 + 2x -5 = 0

Here a= 4, b= 2, c= -5

Since Discriminant= b*2 -4ac

Putting values

Discriminant= (2)*2 - 4(4)(-5)

= 4 + 80

= 84

Since our Discriminant(84) is >0 and is not a perfect square so the roots of the given equation are unequal and irrational(real).

Answer:

Here is an example

Step-by-step explanation:

Answer:

1/12

Step-by-step explanation:

The probability of landing a dice on 2 is 1/6

and for a coin it's 1/2

2*6=12 so

1/12

The quality and credibility of the risk analysis requires a PM to define risk probability and impact, which can then be made into a Probability and Impact Matrix.

The quality and credibility of risk analysis in project management require a comprehensive approach that includes defining risk probability and impact. The probability of a risk event is the likelihood of it occurring, and impact is the magnitude of its consequences on project objectives. Once these factors are defined, they can be used to create a Probability and Impact Matrix, also known as a Risk Matrix, which is a useful tool for assessing and prioritizing risks.

The Probability and Impact Matrix is a grid that lists the probability of an event occurring on one axis and the impact of that event on project objectives on the other axis. The intersection of these two factors represents the level of risk associated with that event. By assigning a probability and impact score to each risk, the PM can prioritize them and allocate resources to mitigate or manage them accordingly.

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a) Using the Avrami equation with n = 1.2 and 90% completion in 180 seconds, the parameter k is found to be approximately 0.00397. b) The rate of transformation, r, is approximately 0.0367 per second.


a) The Avrami equation is given by the equation t = k * (1 – exp(-r^n)), where t is the transformation time, k is a parameter, r is the rate of transformation, and n is a constant (in this case, n = 1.2). Given t = 180 seconds and the transformation is 90% complete, we can rearrange the equation to solve for k: k = t / (1 – exp(-r^n)). By substituting the values, we find k ≈ 0.00397.
b) To determine the rate of transformation, we can rearrange the Avrami equation and solve for r: r = (-ln(1 – (t / k)))^(1/n). Plugging in the values t = 180 seconds and k ≈ 0.00397, and n = 1.2, we can calculate r ≈ 0.0367 per second. This represents the rate at which the transformation progresses per unit time.

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Answer:

-2 and -3

Step-by-step explanation:

a negative multiplied by a negative is a positive so -2 multiplied by -3 equals 6. And, -2 + -3 = -5

Answer:

32.5 minutes

Step-by-step explanation:

10/4 = laps per minute

(10/4) x 13 = minutes in 13 laps

32.5

Hope This Helps! •v•

(4.5/3) * 4 = 6

That is, the time per lap times the # of laps

Answer:

Move the variables to one side and the constants to the other through subtraction/additions to BOTH SIDES. Then, divide/multiply to get x = some constant.

Step-by-step explanation:

Try Khan Academy.

Answer:

Step-by-step explanation:

4²=16

5²=25

so √24 is between 4 and 5.

Answer: 56.25 = u

Step-by-step explanation:

1) Multiply 3 on both sides to leave u by itself

18.75 = u/3

18.75*3 = u

56.25 = u

The prove is as follows

Statement             Reason

line BC || line DA  Definition of parallelogram

Draw line AC        Unique line postulate

AC = CA                Reflexive property (common sides)

∠BAC = ∠DCA      Alternate interior angles

∠BCA = ∠DAC      Alternate interior angles

Δ ABC ≅ Δ CDA   ASA triangle postulate

AB ≅ CD               CPCTC theorem

BC ≅ DA               CPCTC theorem

The ASA (Angle-Side-Angle) postulate is a statement about the relationship between the angles and sides of triangles. It states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent. In other words, if two triangles have the same shape and size, then they are congruent.

CPCTC stands for "Corresponding Parts of Congruent Triangles are Congruent." This theorem states that if two triangles are congruent, then all their corresponding parts are congruent. In other words, if two triangles have the same shape and size, then all their angles and sides are congruent.

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To determine the measures of the angles of a polygon are necessary the concepts of algebra by using the formula of the sum of interior angles and creating equations and obtaining the measures of unknown angle.

First, it is important to remember the formula for the sum of interior angles of a polygon, which is (n-2) x 180°, where n is the number of sides of the polygon.

Next, you can use algebra concepts to solve for the unknown angle measures. For example, if you know the sum of the interior angles and the measures of some of the angles, you can create an equation and solve for the unknown angle measures.

Here is an example:
If a quadrilateral has interior angles of 70°, 110°, and 120°, you can use the formula (4-2) x 180° = 360° to find the sum of the interior angles. Then, you can create the equation 70° + 110° + 120° + x = 360° and solve for x to find the measure of the unknown angle.

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Answer:

Mean-69

Median-73

Mode- There is no mode

Range-36

Step-by-step explanation:

Answer:

Option (1)

Step-by-step explanation:

Equation of a quadratic function,

y = a(x - h)² + k

Here (h, k) is the vertex

From the picture attached,

Vertex of the parabola is (2, -5)

So the equation of the function will be,

y = a(x - 2)² - 5

Since, the graph passes through a point (0, 3)

3 = a(0 - 2)² - 5

3 = 4a - 5

4a = 8

a = 2

Equation will be,

y = 2(x - 2)² - 5

y = 2(x² - 4x + 4) - 5

y = 2x² - 8x + 8 - 5

y = 2x² - 8x + 3

But the shaded area is outside the graph so the quadratic inequality will be,

y ≤ 2x² - 8x + 3

Option (1) will be the answer.

Answer: A

Step-by-step explanation:

Equation of a quadratic function,

y = a(x - h)² + k

Answer:

D

Step-by-step explanation:

the best answer may be D because 9/3 =3 3×5=15

the formula for (f o g)(x) is Vx^3 + 12x^2 + 48x + 59, and it is simplified as much as possible.

To find the formula for (f o g)(x), we need to substitute g(x) into f(x) wherever we see x. So, we have:

(f o g)(x) = f(g(x))
= f(Vx+4)
= (Vx+4)^3 - 5

To simplify this answer, we can expand the cube of the binomial using the formula (a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3. So, we get:

(f o g)(x) = Vx^3 + 12x^2 + 48x + 59


To find the formula for (f o g)(x), you need to substitute g(x) into f(x). Here's the solution:

Step 1: Identify f(x) and g(x).
f(x) = x^3 - 5
g(x) = √(x + 4)

Step 2: Substitute g(x) into f(x).
(f o g)(x) = f(g(x)) = (√(x + 4))^3 - 5

Step 3: Simplify the expression.
(f o g)(x) = (x + 4)^(3/2) - 5

So, the simplified formula for (f o g)(x) is (x + 4)^(3/2) - 5.

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Answer:

Below.

Step-by-step explanation:

Yes.

-9 = 3/4x - 3     -6 = 3/4 x     x = -8

-6 = 3/4x - 3    -3 = 3/4 x     x = -4  (there's a pattern!)

0 = 3/4x - 3    3 = 3/4 x     x = 4

3 = 3/4x - 3    6 = 3/4 x     x = 8

Hope this helps!