classify the following triangle. Check all that apply.
A. right
B. acute
C. scalene
D. isosceles
E. equilateral
F. abtuse

Probability that a randomly selected point falls in the white area is; 84.1%

The formula for area of a circle is;

A = πr²

where r is radius.

Thus;

A_circle = π * 4² = 50.265 cm²

Now, formula for area of triangle is;

A_tria = ¹/₂ * base * height

A_tria = ¹/₂ * 4 * 4 = 8 cm²

Thus;

Area of white portion = 50.265 cm² - 8 cm²

Area of white portion = 42.265  cm²

Thus;

Probability that a randomly selected point falls in the white area is;

P(White area) = 42.265/50.265 = 0.8408

= 84.1%

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68.27% of values are within 2 standard deviations of the mean.

Normal distribution, also known as the Gaussian distribution, is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean.

Given that, five hundred values are normally distributed with a mean of 125 and a standard deviation of 10 approximately.

Here, X=125 and σ=10

The percent of the values lies between the interval 115-135 is calculated as follows;

P(115<X<135)=P(115-125/10 < X-μ/σ <135-125/10)

= P(-1<Z<1)

= 0.6827 (Obtained from the standard normal distribution table)

Therefore, 68.27% of values are within 2 standard deviations of the mean.

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The point that is a solution to the inequality 2x - у < 10 is (2, -5)

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

2x - y < 10

Next, we make the variable y the subject of the formula

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

-y < 10 - 2x

Divide both sides by -1

y > 2x - 10

Assume a value for x

y > 2 * 2 - 10

So, we have

y > -6

This means that the possible y value at x = 2 is -5

Hence, the point is (2, -5)

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Using subtraction as an arithmetic operator, the quantity to feed the second cat is 1/4 can

Subtraction is an arithmetic operation in which the difference between two numbers is found. It is symbolized by a minus sign (-) and is the inverse of addition.

To determine the extra food needed to feed the second cat, we need to subtract the quantity required to feed the first cat from the combined quantity to feed both cats now.

3/8 - 1/8 = (3 - 1) / 8 = 2/8 = 1/4

The quantity to feed the second cat is 1/4 can

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The system of equations for the number of weeks (x) when you both donate the same number of items (y) is 14 + 3x; 8 + 5x.

Let

number of weeks = x

number of items = y

Your equation:

y = 14 + 3x

Your friend:

y = 8 + 5x

Equate y

14 + 3x = 8 + 5x

14 - 8 = 5x - 3x

6 = 2x

divide both sides by 2

x = 6/2

x = 3 weeks

Therefore, it will take 3 weeks for you both to donate the same number of items.

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The statement is false because adding a vector to a set of vectors can increase its span, but the new span is not necessarily the same as the original span.

The statement is false. To prove this, consider three vectors u1, u2 and u3 that span R3, and a vector u4 that is not a linear combination of

u1, u2 and u3.

The span of

{u1, u2, u3, u4}

will be a subset of the span of

{u1, u2, u3}.

This means that the span of

{u1, u2, u3, u4}

will contain all the vectors that the span of {u1, u2, u3} contains, plus the vector u4. However, it does not necessarily mean that the span of

{u1, u2, u3, u4} will be the same as the span of {u1, u2, u3},

as there may be other vectors that are in the span of

{u1, u2, u3, u4}

but not in the span of {u1, u2, u3}. Hence, the statement is false.

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The complete question is

Determine if the statement is true or false, and justify your answer. If (u1, u2, u3) spans R3, then so does (u1, u2, uz, u). O False. Consider u4 =0 True, the span of a set of vectors can only increase (with respect to set containment) when adding a vector to the set. O True, since the span of {ul, u2, u3, u4} is a subset of the span of {u1, u2, us), O False. Consider u4 = 0. The span of {u1, u2, u3, u4} is a subset of the span of {u1, u2, us}, but the span of {u1, u2, u3, u4} is not the same as the span of {u1, u2, us}.

Answer:

Step-by-step explanation:

Answer: 14.9 feet

Step-by-step explanation:

To find the distance above the ground that the top of the ladder touches the wall, we can use the Pythagorean Theorem.

We can set up the equation as follows:

a^2 + b^2 = c^2

Where c is the length of the ladder (15 feet), a is the distance above the ground that the top of the ladder touches the wall, and b is the distance that the bottom of the ladder is from the wall (2 feet).

Substituting these values and solving for a, we get:

a^2 + 2^2 = 15^2

a^2 + 4 = 225

a^2 = 221

a = sqrt(221)

Rounding to the nearest tenth, we get a = 14.866 feet. This is the distance above the ground that the top of the ladder touches the wall.

Therefore, X = 14.9 feet.

Answer:

14.9

Step-by-step explanation:

[tex] {a}^{2} + {b}^{2} = {c}^{2} \\ {2}^{2} + {b}^{2} = {15}^{2} \\ 4 + {b}^{2} = 225 \\ 4 - 4 + {b}^{2} = 225 - 4 \\ {b}^{2} = 221 \\ \sqrt{ {b}^{2} } = \sqrt{221} \\ b = 14.866 \\ b = 14.9[/tex]

Answer:

[tex]y=-3x-3[/tex]

Step-by-step explanation:

[tex]y+15=-3(x-4) \\ \\ y+15=-3x+12 \\ \\ y=-3x-3[/tex]

Using the vertical angles theorem, the equation created is: 3x - 3 = 2x + 13

The value of x = 16.

To solve the problem given, use the vertical angles theorem to create an equation then find the value of x.

(3x - 3)° and (2x + 13)° are vertical angles, therefore, based on the vertical angles theorem, the equation created is:

3x - 3 = 2x + 13

Combine like terms:

3x - 2x = 3 + 13

x = 16

The value of x is: 16.

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If leg ab = 9 cm and leg cd = 12 cm then the perimeter of this trapezoid will be 46cm.

Angle bisector in geometry refers to a line that splits an angle into two equal angles. Bisector means the thing that bisects a shape or an object into two equal parts.  If we draw a ray that bisects an angle into two equal parts of the same measure, then it is called an angle bisector.

Step-by-step explanation:

It is given that the angle bisector AC divides the trapezoid ABCD into two similar triangles Δ ABC and Δ ACD.

Let us first find the corresponding sides of triangles Δ ABC and Δ ACD.

Since AC is the angle bisector of ∠A,

∠DAC = ∠CAB --- (1)

Also, since ∠DAC and ∠ACB are alternate interior angles,

∠DAC = ∠ACB --- (2)

From (1) and (2),

∠CAB = ∠ACB

Therefore, in Δ ABC,

BC = AB (sides opposite to equal angles are equal)

So, BC = 9 cm.

Now, since ∠DAC = ∠ACB and ∠DAC = ∠CAB, we can take either ∠ACB or ∠CAB as the angle corresponding to ∠DAC. Let us take ∠ACB as the corresponding angle of ∠DAC.

So, the side opposite to ∠DAC in Δ ACD is the corresponding side to the side opposite to ∠ACB in Δ ABC.

That is, the side CD in Δ ACD is the corresponding side to the side AB in Δ ABC.

Now, suppose if the side BC in Δ ABC corresponds to side AD of Δ ACD, then the remaining side AC of Δ ABC should correspond to side AC of Δ ACD which is not possible since they are congruent.

So, the side BC in Δ ABC should correspond to side AC of Δ ACD and the remaining side AC of Δ ABC should correspond to side AD of Δ ACD.

Therefore, we have,

[tex]\frac{AB}{CD} =\frac{BC}{AC} =\frac{AC}{AD}[/tex]

But, [tex]\frac{AB}{CD} =\frac{9}{12} =\frac{3}{4}[/tex]

Therefore,[tex]\frac{BC}{AC} =\frac{3}{4}[/tex]

[tex]\frac{9}{AC} =\frac{3}{4}[/tex]

[tex]AC=(\frac{4}{3} )(9)[/tex]

AC = 12 cm

Also,

[tex]\frac{AC}{AD} =\frac{3}{4}[/tex]

[tex]\frac{12}{AD} =\frac{3}{4}\\AD=(\frac{4}{3} )(12)[/tex]

AD = 16 cm

Now, the perimeter of the trapezoid = AB + BC + CD + AD

= 9 + 9 + 12 + 16

= 46 cm

Therefore, the perimeter of this trapezoid will be 46cm.

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The perimeter of this trapezoid will be 46cm.

Now, According to the question:

Angle bisector in geometry refers to a line that splits an angle into two equal angles. Bisector means the thing that bisects a shape or an object into two equal parts.  If we draw a ray that bisects an angle into two equal parts of the same measure, then it is called an angle bisector.

An angle bisector AC divides a trapezoid ABCD into two similar triangles △ABC and △ACD.

The leg AB=9 cm and the leg CD=12 cm.

Given that AC is the angle bisector of angle A, therefore:

∠DAC = ∠CAB     ----- (1)

∠DAC = ∠ ACB      (alternate interior angles)       ---- (2)

From (1) and (2):

Sides opposite to equal angles are equal, therefore:

BC = AB

Hence, BC = 9 cm

Side BC in triangle ABC should correspond to side AC of triangle ACD and the remaining side AC of triangle ABC should correspond to side AD of triangle ACD.

Therefore, we have

[tex]\frac{AB}{CD} = \frac{BC}{AC} =\frac{AC}{AD}[/tex]

[tex]\frac{AB}{CD}[/tex] = [tex]\frac{9}{12}=\frac{3}{4}[/tex]

Therefore, [tex]\frac{BC}{AC}=\frac{3}{4}[/tex]

[tex]\frac{9}{AC}=\frac{3}{4}[/tex]

AC = 4/3 × 9

AC = 12cm

also, [tex]\frac{AC}{AD} =\frac{3}{4}[/tex]

12/AD = 3/4

AD = 4/3 ×12

AD = 16cm

Now, the perimeter of the trapezoid = AB + BC + CD + AD

= 9 + 9 + 12 + 16

= 46 cm

Therefore, the perimeter of this trapezoid will be 46cm.

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The complete question is this:

An angle bisector AC divides a trapezoid ABCD into two similar triangles △ABC and △ACD. Find the perimeter of this trapezoid if the leg AB=9 cm and the leg CD=12 cm.

The equation representing vertical stretching of y = x³ by a factor of 4, will be y = 4x³.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

The function y = x³, and we need to b it vertically by a factor of 4. So, this can be simply done by multiplying the function (x³) by 4.

Therefore, the b representing vertical stretching of y = x³ by a factor of 4, will be y = 4x³.

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The equation y = x³ with a vertical stretched by a factor of 4 is y = x³ + 4.

Option A is the correct answer.

It is the movement of the shape in the left, right, up, and down directions.

The translated shape will have the same shape and shape.

There is a positive value when translated to the right and up.

There is a negative value when translated to the left and down.

We have,

y = x³

Vertically stretched by a factor of 4 means,

y = x³ + 4

Thus,

y = x³ + 4 is the equation.

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The 24 paper squares cannot be used to make quilts with 5 rows of paper squares.

It is important to note that an expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. in this case, it is vital to note that they have at least two terms which have to be related by through an operator.

In this case, the 24 paper squares cannot be used to make quilts with 5 rows of paper squares. The appropriate number will be:

= 5 × 5

= 25

Also multiples of 5s can be used

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The equation of the line that includes the point (–4,2) and has a slope of –14 is y - 2 = -14x - 56.

The equation of a line in point-slope form is expressed as;

y - y₁ = m( x - x₁ )

Where x and y are the coordinates and m is the slope.

Given the data in the question;

Point (-4,2)

To find the equation of the line that includes the point (–4,2) and has a slope of –14, we can use the point-slope form of the equation of a line, which is:

y - y₁ = m( x - x₁ )

Substituting the values given in the problem, we get:

y - 2 = -14(x - (-4))

Expanding the right side of the equation and simplifying, we get:

y - 2 = -14x - 56

Therefore, the equation of the line in point slope form is y - 2 = -14x - 56.

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Answer:

[tex]-\frac{10}{3}[/tex]

Answer:

-3 1/3

Step-by-step explanation:

Answer:

[tex]\dfrac{a-4\sqrt{a+1}+5}{a-3}[/tex]

Step-by-step explanation:

Given rational expression:

[tex]\dfrac{\sqrt{a+1}-2}{\sqrt{a+1}+2}[/tex]

To rationalize the denominator, multiply the numerator and denominator by the conjugate of the denominator.

The conjugate of a binomial is where we change the sign between the two terms of the binomial.  So the conjugate of √(a+1)+2​ is √(a+1)-2​.

Therefore:

[tex]\implies \dfrac{\sqrt{a+1}-2}{\sqrt{a+1}+2} \cdot \dfrac{\sqrt{a+1}-2}{\sqrt{a+1}-2}[/tex]

[tex]\implies \dfrac{(\sqrt{a+1}-2)(\sqrt{a+1}-2)}{(\sqrt{a+1}+2)(\sqrt{a+1}-2)}[/tex]

[tex]\implies \dfrac{(a+1)-4\sqrt{a+1}+4}{(a+1)-4}[/tex]

[tex]\implies \dfrac{a-4\sqrt{a+1}+5}{a-3}[/tex]

The product of  [tex]$ (5 \times 10^6)(8.2 \times10^{-9})[/tex] is  [tex]$ 4.1 \times 10^{-2}[/tex]  in scientific notation.

Numbers that are either too large or too small to be conveniently written in decimal form can be expressed using scientific notation. It is also known as "scientific form" in Britain, and it is frequently used by scientists, mathematicians, and engineers for difficult calculations involving large numbers. It is commonly referred to as "SCI" display mode on scientific calculators.

Scientific notation is a way to express numbers in terms of a decimal number between 1 and 10, but not 10 itself multiplied by a power of 10.

The standard for scientific notation is N × 10ᵃ

Given to find product of

⇒ [tex]$ (5 \times 10^6)(8.2 \times10^{-9})[/tex]

⇒ [tex]$ (5 \times 8.2 )10^{6 +(-9)}[/tex]

⇒ [tex]$ (5 \times 8.2 )10^{-3}[/tex]

⇒ [tex]$ (41 )10^{-3}[/tex]

⇒ [tex]$ 4.1 \times 10^{-2}[/tex]

Thus, The product of  [tex]$ (5 \times 10^6)(8.2 \times10^{-9})[/tex] is  [tex]$ 4.1 \times 10^{-2}[/tex]  in scientific notation.

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It is found that there is a 0.493 = 49.3% probability that it takes more than 3 customers who buy an eligible item to find one who purchased the extended warranty.

Formula for Binomial probability distribution:

[tex]P(X=x)=C_{n}_,_x_.p^x.(1-p)^{n-x}[/tex]

The parameters are:

x is the number of successes.

n is the number of trials.

p is the probability of a success on a single trial.

It is given that 21% of customers purchase extended warranty, hence p=0.21.

The probability that it takes more than 3 customers who buy an eligible item to find one who purchased the extended warranty is the probability that none of the first three buy, which is P(X = 0) when n = 3, hence:

[tex]P(X=x)=C_{n}_,_x_.p^x.(1-p)^{n-x}\\P(X=x)=C_{3}_,_0_.(0.21)^0.(0.79)^{3}\\=0.49[/tex]

0.493 = 49.3% probability that it takes more than 3 customers who buy an eligible item to find one who purchased the extended warranty.

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The amount of candy that each person got, given the number of people that Tammy shared the candy with, and the amount of candy, is 3 / 32 pounds

To find the amount of candy that each person got, you need to divide the amount of candy that Tammy had , by the total number of people that she shared the candy with.

The amount of candy that each person got was therefore :

= Amount of candy / Number of people

= 3 / 4 ÷ 8

= 0. 75 / 8

= 0. 09375 pounds

= 3 / 32 pounds

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The function is

y = 4x - 9

The slope of the function is 4 and the y- intercept is -9.

For x= 3,  y = 3

Each element of X receives precisely one element of Y when a function from one set to the other is used. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Initially, functions represented the idealized relationship between two changing quantities.

A function is a procedure or a relation that links each element of a non-empty set A, at least one element of another non-empty set B, to another element of the first non-empty set A. In mathematics, a relation f between two sets, A and B, is referred to as the function's domain and co-domain.

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a connection between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain. The usual way to refer to a function is as f(x), where x is the input.

The function is

y = 4x - 9

here the slope of the function is 4 and the y- intercept is -9

So, the line intersect the y-axis in (0,-9) and x axis at (0,9/4)

The missing value when x = 3

y = 4*3 - 9 = 3

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Reason:

The equation is t = 1.5p

The input p leads to the output t.

The domain only cares about the input. It's the set of allowed inputs. Since p refers to a number of something, we can only work with whole numbers {0,1,2,3,4,...} which is why Bonnie is correct.

Unfortunately Buffy is incorrect because something like p = 2.7 isn't allowed in the domain. It's a real number, but not a whole number. It doesn't make sense to have a fractional or decimal amount of pens.

The value of each part is AC = 18 cm, CD = 54 cm, DE = 108 cm, and

EB = 72 cm. This can be solved using the concept of mathematical operators.

A collection of numbers and operations is an expression in mathematics. The following are the parts of a math expression that do a math operation:

Operands: Operands are the numbers that an operation uses. The terms that are given to the operands vary according to the kind of operation.

Operator: An operator is the symbol that denotes a math operation, such as: division, addition, subtraction, and multiplication.

Given that,

length of wooden plank AB is 252 cm

divides it into four parts by inserting the points C, D and E

parts of plank are AC, CD, DE, EB

CD = 3AC,

DE = 2CD, and

DE = 2(3AC)

DE = 6AC

EB = 4AC

AB = AC + CD + DE + EB

substitute the values we get,

AB = AC + 3AC + 6AC + 4AC

252 = 14AC

AC = 252/14 = 18cm

CD = 3AC = 3(18) = 54 cm

DE = 6AC = 6(18) = 108 cm

EB = 4AC = 4(18) = 72 cm

Hence length of each part is AC = 18 cm, CD = 54 cm, DE = 108 cm, and

EB = 72 cm.

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Answer:

C) 2hours and 3 minutes

Step-by-step explanation:

rate x number of people x time =  1 job

Rate:

[tex]\frac{1}{18(100)}[/tex]   To get 1 job done, it takes 18 people and 100 minutes  (1 hours + 40 minutes is 60 + 40 or 100 minutes

[tex]\frac{1}{18(100)}[/tex] x 12 x time = 1

[tex]\frac{12}{1800}[/tex] t = 1   Multiply both sides by [tex]\frac{1800}{12}[/tex]

t = [tex]\frac{1800}{12}[/tex] = 150

The time is 150 minutes, which is the same as 2 hours and 30 minutes.

Therefore , the solution of the given problem of ordered pair comes out to be The exponential equation y = 2ˣ could produce the set C.

"Ordered pairs" are two variables that are presented together in a way that suggests a specific order. The first and second elements, accordingly, in an order pair, represent the x- and y-coordinates. As seen in the sample below, close parentheses are utilized to represent the ordered pair.

Here,

Given :

Since a⁰  = 1, the point (0,1) appears on the graph of any exponential function with the formula y =  aˣ.

Therefore, C is the only option available.

Examine it:

1/2 = a⁻¹, a = 2,

2 = a¹, a = 2,

4 =a²,= a = 2.

The exponential equation y = 2ˣ could produce the set C.

Therefore , the solution of the given problem of ordered pairs comes out to be The exponential equation y = 2ˣ could produce the set C.

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The total number of questions is 10 + 15 = 25.

Let x be the number of questions worth 5 points and let y be the number of questions worth 2 points. The total number of points can be calculated by the following formula: x*5 + y*2.

For example, if there are 10 questions worth 5 points and 15 questions worth 2 points, the total number of points is calculated by 10*5 + 15*2 = 100.

In order to calculate the average points per question, we divide the total number of points by the total number of questions. This can be formulated as (x*5 + y*2) / (x + y).

For the example above, the average points per question can be calculated as (10*5 + 15*2) / (10 + 15) = 100 / 25 = 4. This means that the average points per question is 4 points.

Finally, if we want to calculate the total number of questions, we can use the formula x + y. Continuing with the example, the total number of questions is 10 + 15 = 25.

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14 questions worth 5 points and 15 questions worth 2 points

In this question we have been given that Mr. Martin’s math test worth 100 points, has 29 questions and each problem is worth either 5 points or 2 points.

We have been given a system of equations:

x + y = 29                                ................(1)

5x + 2y = 100                          ................(2)

Assuming x be the number of questions worth 5 points and let y be the number of questions worth 2 points, we need to find the number of questions of each point value.

i.e., we need to find the value of x and y

From equation (1),

x = 29 - y                      ..............(3)

Subatitute above value of x in equation (2)

5(29 - y) + 2y = 100  

145 - 5y + 2y = 100

-3y = 100 - 145

-3y = -45

y = 15

Subatitute above value of y in equation (3)

x = 29 - 15

x = 14

Therefore, there are 14 and 15 questions worth 5 and  2, respectively.

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Answer:

6 (c)

Hope this helps

The most common method for finding complex roots of polynomials is the use of the Durand-Kerner Method. This method is based on the Newton-Raphson Method and takes advantage of the fact that complex numbers can be represented by a pair of real numbers.

1. Initialize a set of initial guesses for the roots of the polynomial.

2. Calculate the value of the polynomial at each of the initial guesses.

3. Calculate the derivative of the polynomial at each of the initial guesses.4. Calculate the new root value by subtracting the value of the polynomial at the current guess divided by the derivative of the polynomial at the current guess.

5. Repeat steps 3 and 4 until the values of the roots converge.

6. The final set of roots is the answer.

The most common method for finding complex roots of polynomials is the use of the Durand-Kerner Method. This method is based on the Newton-Raphson Method and takes advantage of the fact that complex numbers can be represented by a pair of real numbers.

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Answer:

  y = 2x +4

Step-by-step explanation:

You want an equation of the line through point P(0, 4) parallel to y = 2x.

The parallel line will have the same slope, so can be written in the form ...

  y = 2x +b

where 'b' is the y-intercept.

The point (0, 4) is the y-intercept, telling you b=4.

An equation for the line is y = 2x +4.

__

Additional comment

"An equation" covers a lot of territory. The equation we found can be written several other ways, including ...

<95141404393>

The area is given by 0.4291 units.

The points of intersection are given by,

y = 1+sin2x=e^(x/2). The y-intercept ( x = 0 ) for both are the same 1.

So, one common point is (0, 1). Glory to Socratic utility, the other is

approximated graphically to 4-sd as 1.136.

Now, the area is

∫(f−g)dx,   for x from 0 to 1.136

∫((1 + sin(2x)) − (eˣ/₂)dx, for x from 0 to 1.136

=[(x − 1/2cos(2x)) − (2eˣ/₂)], between 0 and 1.136

=(1.136 − 1/2cos(2.272) − 2e^1.16/2) (−5/2)

=0.4291 units.

The limit of a function in mathematics is a key idea in calculus and analysis regarding the behavior of that function close to a specific input.

Informally, a function f gives each input x an output f(x). If f(x) approaches L as x approaches input p, we say that the function has a limit L at that location. More specifically, any input that is sufficiently close to p when f is applied forces the output value arbitrarily close to L.

The term "limit" is also used in the definition of the mathematical term "derivative," which in one-variable calculus refers to the maximum value of the slope of secant lines on a function's graph.

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The number that is both a multiple of 7 and 4 and is the smallest positive integer of the two is 28 .

A multiple in mathematics refers to the outcome of multiplying two numbers together.

This means that the multiples of 4 can therefore be found to be:

4, 8, 12, 26, 20, 24, 28, 32, 36, 40

The multiples of 7 would also be:

7 , 14 , 21 , 28 , 35 , 42 , 49

Given these list of multiples, the multiple that appears in both sets and is the smallest to appear is 28. This makes 28 the smallest positive integer that is a multiple of 7 and 4.

Find out more on multiples at https://brainly.com/question/23058175

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