Find the solution of the initial value problem 2
′′ − 3
′ + = 0, (0) = 2,

′
(0) = 1/2 . Then determine the maximum value of the solution and also find
the point where the solution is zero.

Answer:

Write

f

(

x

)

=

2

x

2

+

12

x

+

10

as an equation.

y

=

2

x

2

+

12

x

+

10

Step-by-step explanation:

Write

f

(

x

)

=

2

x

2

+

12

x

+

10

as an equation.

y

=

2

x

2

+

12

x

+

10

Answer:

What we know from the problem:

therefore tangent will be positive.

Adjacent Side = 1

Hypotenuse Side = 7

We need to find out:

Opposite Side = b

Using the Pythagorean Theorem: a² + b² = c²

1² + b² = 7²

b = 4√3

Lastly:

Tangent = Opposite/Adjacent

4√3 ÷ 1 = 4√3

Tangent = 4√3

The scale factor of HOPE to RSTU is 1.5

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

The shape

From the shape, we have the following parameters

Side length of HOPE = 8

Corresponding side length of RSTU = 12

Using the above as a guide, we have the following:

Scale factor of the dilation = Corresponding side length of RSTU/ Side length of HOPE

So, we have

Scale factor of the dilation = 12/8

Evaluate

Scale factor of the dilation = 1.5

Hence, the scale factor of the dilation is 1.5

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Required solution of the given equation 3.1 = -0.5 + 0.3x is x = 12.

What is equation?

A mathematical statement that asserts that two expressions are equal is called equation

. It is consist of variables, constants, and mathematical operations such as , subtraction, addition, division, multiplication . We can use equations in mathematics to model real-world situations or to solve problems. It can also be used to express relationships between quantities, to find unknown values, and to test hypotheses. Equations can be written in various forms, such as linear, exponential, trigonometric ,quadratic. Equation depends on the type of relationship being modeled.

Here given equation is 3.1 = -0.5 + 0.3x.

We are Simplifying it,

[tex]3.1 + 0.5 = 0.3x \\ 0.3x = 3.6 \\ x = \frac{3.6}{0.3} \\ x = 12[/tex]

So, required solution of the given equation is 12.

Therefore, option C is the correct answer.

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Correct question is "What is the solution to this equation? 3.1 = -0.5 + 0.3x A:x=6 B:x=3 C:x=12 D:x=0.8".

On solving the provided question ,we can say that In order to find holes in a mathematical proof or the boundaries of a theory or hypothesis, counterexamples might be helpful.

A sequence is a grouping of "terms," or integers. Term examples are 2, 5, and 8. Some sequences can be extended indefinitely by taking advantage of a specific pattern that they exhibit. Use the sequence 2, 5, 8, and then add 3 to make it longer. Formulas exist that show where to seek for words in a sequence. A sequence (or event) in mathematics is a group of things that are arranged in some way. In that it has components (also known as elements or words), it is similar to a set. The length of the sequence is the set of all, possibly infinite, ordered items. the action of arranging two or more things in a sensible sequence.

Evidence is utilised to back up a claim or argument in a direct proof. A direct proof's objective is to connect known facts or presumptions logically to the desired conclusion in order to show that a certain assertion is true. Direct proofs sometimes take the form of a series of logical stages that are combined to get the desired result.

A counterexample, on the other hand, is a solitary instance that refutes a claim or argument. A counterexample presents a particular situation in which a claim is wrong in order to demonstrate that the claim is not always true. In order to find holes in a mathematical proof or the boundaries of a theory or hypothesis, counterexamples might be helpful.

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The genotype ratio is:  1   TT : 1   Tt : 0  tt

The phenotype ratio is :  4   Tall :   0   Short

100 percent of the offspring will be tall.

Genotypic ratio is the ratio between the genetic makeup among the offspring population.

On the other hand, the ratio between the offspring population for an observable characteristic is the phenotype ratio.

The given test cross is between a homozygous tall parent and a heterozygous tall parent.

Using a Punnett square,

The result will be as shown below.

                     T                   t

          T        TT                 Tt

           T       TT                 Tt

Genotype :  1   TT : 1   Tt : 0  tt

Phenotype :  4   Tall :   0   Short

100 percent of the offspring will be tall.

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The polynomial function with fifth degree and given zeroes is 4x⁵ - 20x⁴ + 64x³ + 324x² - 432x.

The maximum power of the variable in a polynomial function is its degree. For instance, since 2 is the largest power of x, the polynomial function f(x) = 3x2 + 2x + 1 has a degree of 2. We only take into account the degree of the term with the highest power of x when a polynomial function comprises many terms. A polynomial with no x terms is a constant function, and thus has degree zero.

To determine the polynomial, we determine the zeroes.

Given that, 3 is a zero of multiplicity 3,-4 is the only other zero thus:

(x - 3)³(x + 4)

Now, for leading coefficient 4 we have:

4x(x - 3)³(x + 4)

Thus, solving the parentheses we have:

4x(x³ - 9x² + 27x - 27)(x + 4)

(4x⁴ - 36x³ + 108x² - 108x)(x + 4)

4x⁵ - 36x⁴ + 108x³ - 108x² + 16x⁴ - 144x³ + 432x² - 432x

4x⁵ - 20x⁴ + 64x³ + 324x² - 432x

Hence, the polynomial function with fifth degree and given zeroes is 4x⁵ - 20x⁴ + 64x³ + 324x² - 432x.

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Answer:

To factor the polynomial 40x^3 + 70x^2 + 30x, we can first factor out the greatest common factor of the terms, which is 10x:

10x(4x^2 + 7x + 3)

Next, we can factor the quadratic expression inside the parentheses. We need to find two numbers that multiply to give 4 × 3 = 12 and add to give 7. These numbers are 4 and 3:

10x(4x + 3)(x + 1)

Therefore, the factored form of the polynomial is:

10x(4x + 3)(x + 1)

Answer: -13/17

Step-by-step explanation: To find the slope of the line that passes through the points (-9, 7) and (8, -6), you can use the slope formula:

slope = (y2 - y1) / (x2 - x1)

where (x1, y1) = (-9, 7) and (x2, y2) = (8, -6)

Substituting the values in the formula, we get:

slope = (-6 - 7) / (8 - (-9))

slope = -13 / 17

Therefore, the slope of the line that passes through the points (-9, 7) and (8, -6) is -13/17.

Answer:

[tex]\frac{-14}{17}[/tex]

Step-by-step explanation:

Slope is the change in y's (-9,7) (8,-6) over the changes in x's (-9,7)(8,-6).  You find the changes by subtraction

[tex]\frac{-6-7}{8-(-9)}[/tex] = [tex]\frac{-14}{8+9}[/tex] = [tex]\frac{-14}{17}[/tex]

Helping in the name of Jesus.

The values of the variables are;

x = 7

y = -9

From the information given, we have that;

5x−y=44

−3x−y=−12

Using the elimination method of solving simultaneous equations

Subtract equation (2) from equation (1), we get;

5x - y - (-3x - y) = 44 - (-12)

Now, expand the bracket

5x - y+ 3x + y = 56

collect the like terms

5x + 3x = 56

add the terms

8x = 56

Make 'x' the subject of formula

x= 7

Now, substitute the value of x in equation (2)

-3x - y = -12

-3(7) - y = -12

expand the bracket

-21 - y= - 12

collect like terms

-y = 9

y = -9

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If the train was travelling nonstop for 5.5 hours, it would travel approximately 90 km. This can be estimated by observing the graph and finding the corresponding distance for 5.5 hours on the y-axis.

Graph is a data structure composed of nodes (vertices) and edges. It is a non-linear data structure that is used to represent relationships between objects, events, or ideas. Graphs are widely used in computer science, mathematics, engineering, and other fields for representing various types of data. Graphs can be used to represent a wide variety of data sets, including networks, social relationships, and even biological systems. Graphs can also be used to identify patterns, trends, and correlations in data.

The graph below shows the relation between time (hours) and distance (km) for a train trip that lasted from 0 to 7 hours.

The line of best fit is a linear line with a positive slope, indicating that the distance travelled increases as the time spent travelling increases. Therefore, it can be estimated that if the train was travelling nonstop for 5.5 hours, it would travel approximately 90 km. This can be calculated by observing the graph and finding the corresponding distance for 5.5 hours on the y-axis, which is approximately 90 km.

In conclusion, if the train was travelling nonstop for 5.5 hours, it would travel approximately 90 km. This can be estimated by observing the graph and finding the corresponding distance for 5.5 hours on the y-axis.

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Complete questions as follows-
On the grid below, draw a graph of the relationship between  and  for a trip that lasted from 0to 7 hours.  8Time (hours) If the train was traveling nonstop, how many  would it travel in 5.5 hours?

When both t and d are zero, we can immediately see that c = 0 because the train begins at rest. Additionally, the rate of change is the constant speed, making m = 95. Thus, d = 95t is the necessary relationship.

A graph is a type of data structure that consists of edges and nodes (vertices). It is a non-linear data structure intended to depict connections between things, occasions, or concepts. Graphs are frequently used to represent numerous forms of data in computer science, mathematics, engineering, and other disciplines. A wide range of data sets, including networks, social relationships, and even biological systems, can be represented using graphs. Graphs can also be used to spot trends, correlations, and patterns in data.

The necessary equation should be d = mt +c,

Where the arbitrary real constants m and c are used.

When t = 1, d = 95

so that 95= m+c ---> (1)

Also, when t=2, d = 190,

hence 190 = 2m+c ---> (2)

When the first equation is taken out and the second equation is added back in,

we get 2m+c-m-c = 190-95 or, m = 95.

When this value of m is substituted in the first equation,

we get 95 = 95+c so that c = 95-95 = 0.

Thus, the require3d equation is d = 95t. Since 95*3 = 285 and 95*4= 380, All of the given facts are satisfied by this equation.

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The complete question and graph attached below,

The correct option is D, the x-intercept is 2pi

To find this, we need to solve the equation:

y = cos(x/2) = 0

Remember that the cosine function is zero for the arguments pi and (3/2)pi.

Then the x-intercepts are:

x/2 = pi

x/2 = (3/2)pi

Solving these:

x = 2pi

x = 3pi

From these the one that appears in the options is 2pi, at option D.

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Answer:

The answer in the simplest form is (32y-3)/8

Step-by-step explanation:

1/4(13y-3)+1/8(6y+3)

13y/4-3/4+6y/8+9/8

(13y-3)/4+(6y+9)/8

[2(13y-3)+(6y+9)]/8

[26y-6+6y+9]/8

C.L.T

[26y+6y-6+9]/8

(32y-3)/8

The equation that represents the town's population after 6 years is:

P = 2.33 × 10¹ (1.07)⁶

What is the rate?

In mathematics, the rate is a measure of the change in one quantity with respect to another quantity. It is typically expressed as a ratio between the two quantities.

The initial population is 2.33 × 10¹.

After one year, the population will be:

P₁ = 2.33 × 10¹ + 0.07 × 2.33 × 10¹

P₁ = 2.33 × 10¹ (1 + 0.07)

After two years, the population will be:

P₂ = P₁ + 0.07 P₁

P₂ = P₁ (1 + 0.07) = 2.33 × 10¹ (1 + 0.07)²

After three years, the population will be:

P₃ = P₂ + 0.07 P₂

P₃ = P₂ (1 + 0.07) = 2.33 × 10¹ (1 + 0.07)³

And so on, until after six years:

P₆ = 2.33 × 10¹ (1 + 0.07)⁶

Simplifying the expression, we get:

P₆ = 2.33 × 10¹ (1.07)⁶

Therefore, the equation that represents the town's population after 6 years is:

P = 2.33 × 10¹ (1.07)⁶

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The distance from point C to A that is AC = 7.5 cm and CB = 10.5 cm.

While distance and displacement appear to have the same meaning, they actually have very different definitions and implications. Displacement is the measurement of "how far an object is out of place," whereas distance refers to "how much ground an object has covered during its motion."

Distance is the sum of an object's movements, regardless of direction. Distance can be defined as the amount of space an object has covered, regardless of its starting or ending position.

Let us suppose the distance between C to A = x.

Now, for C to B we have = 3 + x

Given, AB = 18

Thus,

AC + CB = AB

x + (x + 3) = 18

2x + 3 = 18

2x = 15

x = 7.5

Now, CB = 3 + x = 3 + 7.5 = 10.5

Hence, the distance from C to A that is AC = 7.5 cm and CB = 10.5 cm.

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Answer:

8

Step-by-step explanation:

x^2-4x=32

Subtract from both sides:

x^2-4x-32=32-32

Simplify the expression

x^2-4x-32=0

To find the coefficients, use the standard form of a quadratic equation:

ax^2+bx+c=0

x^2-4x-32=0

a coefficient =1

b coefficient =-4

c coefficient =-32

Find the factors which product equals to coefficient a multiplied by coefficient c:

a coefficient ∙ c coefficient = 1 ∙ -32 = -32

List the factors of -32:

1, 2, 4, 8, 16, 32

Because the product of coefficient a and coefficient c equals a negative number (-32) one factor needs to be positive and the other one negative.

From the list of factors, find a pair which sum equals to the b coefficient.

b coefficient = -4

This pair doesn't work.

1*-32=-32

2*-16=-32

2-16=-14

Found it - this pair does the trick:

4*-8=-32

4-8=-4

The product of 4 and -8 equals to coefficient a(1) multiplied by coefficient c (-32) and their sum equals to coefficient b (-4).

The percent of the total time teens spend using the Internet and doing chores is the time they spend listening to the radio is 55.56%.

Time spent using the internet = 4 hours

Time spent doing chores = 4 hours

The time spent listening to the radio = 10 hours

The total time spent during the week is 4 + 4 + 10 = 18 hours

The percentage of this total time that is spent listening to the radio is:

(10 hours / 18 hours) x 100% =55.56%

This is basic arithmetic operations and is used in calculation of numbers.

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North Division’s direct fixed expenses for February is $34000.

Segment margin = Contribution margin - Direct fixed expenses

We are given that the North Division's segment margin for February is $18,000, and its contribution margin is $52,000. Let X represent the North Division's direct fixed expenses:

$18,000 = $52,000 - X

Solving for X, we get:

X = $52,000 - $18,000

X = $34,000

Therefore, the North Division's direct fixed expenses for February is $34,000.

The answer is: Multiple Choice $34,000.

Hence, North Division’s direct fixed expenses for February is $34000.

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Complete question:

American Manufacturing Incorporated operates two divisions with the following selected information for the month of February: North Division South Division Sales $ 120,000 $ 90,000 Contribution margin $ 52,000 $ 40,000 Segment margin $ 18,000 $ 12,000 North Division’s direct fixed expenses for February is: Multiple Choice $34,000. $96,000. $60,000. $78,000.

Answer:

To find out how much change Luke should receive if he pays the cashier $20 for a Helmond that costs $19.67, we can subtract the cost of the Helmond from the amount of money Luke pays:

$20.00 - $19.67 = $0.33

Therefore, Luke should receive $0.33 in change.

Answer:

If 45% of the fruit on a table are apples, then 55% of the fruit are oranges (since the total percentage must add up to 100%).

The probability of selecting a piece of fruit that is not an apple is equal to the percentage of oranges on the table, which is 55%.

Therefore, the probability of selecting a piece of fruit that is not an apple is 55%.

Angle measure in radians 9π/5 3π/4

Angle measure in degrees 324° 135°

Note:

9π/5 can also be written as 1.8π radians or 324 degrees

3π/4 can also be written as 0.75π radians or 135 degrees

The table provides values for angle measures in radians and degrees. To convert between radians and degrees, The exact measures in radians for 9rt/5 is 3π/5 and for 3π/4 is 135°. The exact measure in radians for 20 degrees is π/9 and for 275 degrees is 55π/36.

An angle is a geometric figure formed by two rays or line segments that share a common endpoint, known as the vertex. It is used to measure the amount of rotation between the two rays or line segments.

A radian is a unit of measure for angles, where the measure of the central angle is equal to the length of the corresponding arc on the unit circle. It is equal to approximately 57.3 degrees.

According to thw given information:

The table displays measures of angles in radians and degrees. Radians are a unit of measurement for angles, and they relate the length of the arc of a circle to the radius of that circle. One radian is equivalent to the angle subtended at the center of a circle by an arc equal in length to the radius of the circle. Pi radians, or 180 degrees, represent a straight angle.

In the table, the first angle measure in radians is given as 9√5, which is an exact measure. The second angle measure in radians is given as 3π/4, which represents a quarter of the circumference of the circle, and is equal to 45 degrees. The first angle measure in degrees is given as 20°, which is the equivalent of π/9 radians, and the second angle measure in degrees is given as 275°, which is equivalent to 55π/36 radians.

Knowing how to convert between radians and degrees is important in many mathematical calculations, especially those involving trigonometry. Understanding the relationship between these units of measure can help to solve problems in many areas of mathematics and science.

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Answer:

325

Step-by-step explanation:

the product being multiplication is 65 * 5

The inequality is graphed on the number line is

Inequality can be graphed on a number line by shading the appropriate region of the number line.

To graph an inequality x > -7, follow these steps:

Plot the critical points on the number line. The critical points are the values of x that make the inequality true with an equal sign. For example, to graph the inequality x > -7, we plot the critical point x = -7 on the number line.

Determine the direction of the shading or line. If the inequality is "greater than" or "greater than or equal to," shade to the right of the critical point..

If the inequality includes "or equal to," use a closed circle at the critical point. If the inequality does not include "or equal to," use an open circle at the critical point.

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Answer:

[tex]-i\sqrt{7}[/tex]

Step-by-step explanation:

We can write this expression as:

[tex]-\sqrt{-1 \cdot 7}[/tex]

From here, we can take the square root of negative 1 ([tex]i[/tex]):

[tex]\boxed{-i\sqrt{7}}[/tex]

No further simplification can be done.

The engineer should consider a sample size of 325 electronic components to be 90% sure that the mean width will be within ± 0.3 mm.

To determine the required sample size, we can use the formula for the margin of error (ME) in the context of the normal distribution:

ME = (Z * σ) / √n

Where:

ME = Margin of error

Z = Z-score, which corresponds to the desired level of confidence (in this case, 90%)

σ = Standard deviation (3.3 mm in this problem)

n = Sample size

First, we need to find the Z-score corresponding to a 90% confidence level. This can be found using a Z-table or statistical software. The Z-score for a 90% confidence interval is approximately 1.645.

Now, we will rearrange the formula to solve for the sample size (n):

n = (Z * σ / ME)^2

We are given that the margin of error should be within ± 0.3 mm:

n = (1.645 * 3.3 / 0.3)^2

n ≈ (18.015)^2

n ≈ 324.54

Since we cannot have a fraction of a component, we round up to the nearest whole number to ensure the desired level of confidence:

n ≈ 325

The engineer should consider a sample size of 325 electronic components to be 90% sure that the mean width will be within ± 0.3 mm.

It took Emily 33.4 minutes to make dinner.

A mixed number is a kind of fraction that also has a proper fraction and a whole number. The number of whole units is represented by the whole number, and the fraction of a unit is represented by the proper fraction.

To solve the problem, we have to convert the mixed number  [tex]9 \frac{1}{10}[/tex]   to a decimal number:

⇒ [tex]9 \frac{1}{10} = 9 +\frac{1}{10} = \frac{(9*10)+1}{10}[/tex]

⇒ [tex]\frac{91}{10}[/tex]  =  9.1

This means that Emily finished making dinner 9.1 minutes sooner than the cake.

To find out how long it took Emily to make dinner, we can subtract 9.1 from the cake baking time:

⇒ 42.5 - 9.1 = 33.4 minutes

Therefore, it took Emily 33.4 minutes to make dinner.

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The value of the angle x is 108 degrees

To determine the value, we need to note that the sum of the angles on a straight line is 180 degrees.

Also, parallel lines are lines that do not meet or intersect each other on any side of a plane

From the information given, we have that;

x + 72 = 180

now, collect the like terms in the equation, we have;

x = 180 - 72

subtract the values

x  = 108 degrees

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