What are the answers and how do I find them please help I’m so confused

Answer:

8 + 6i

Step-by-step explanation:

add the like terms:

(3 + 4i) (5 + 2i)

(3 + 5) (4i + 2i)

8 + 6i

In conclusion each bride's guest used approximately 1.38 tissues at the wedding.

How to determine?

To approximate the number of tissues used per bride's guest, we can divide the total number of tissues used by the total number of guests:

Total guests = 120 (groom's guests) + 185 (bride's guests) = 305

Total tissues used = 270 (bride's guests) + 152 (groom's guests) = 422

Approximate number of tissues used per bride's guest = Total tissues used / Total guests who attended the wedding

≈ 422 / 305

≈ 1.38

Therefore, each bride's guest used approximately 1.38 tissues at the wedding.

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The value of original number is found to be 8.

The given word problem is-

if thrice a number is increase by 11 , the result is 35 .

Let the number be 'x'

Thrice the number: 3x

Result is increased by 11: 3x + 11

The result becomes: 35

The equation forms:

3x + 11 = 35

Solving the equation:

3x = 35 - 11

3x = 24

x = 24/3

x = 8

Thus, the value of original number is found to be 8.

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Answer: $0.56 cents per inch

Step-by-step explanation: 2 feet = 24 inches 13.44/24 = 0.56

The required sum of all the even k numbers which are less than 50 is given by 600.

the sum of even k numbers less than 50,

Set of even numbers less than 50.

Even numbers are those that can be divided by 2 without a remainder.

Set of even numbers less than 50 are,

{2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48}

Sum of the first k even numbers in this set.

k = n/2,

where n is the total number of even numbers in the set

here, n = 24

Use the formula for the sum of the first n natural numbers,

sum = (n /2 ) ( First term + last term )

Plugging in n = 24, we get,

⇒ sum = ( 24 / 2 ) ( 2 + 48 )

⇒ sum = 12 × (50)

⇒ sum = 600

Therefore, the sum of even k numbers less than 50 is equal to 600.

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The given question is incomplete, I answer the question in general according to my knowledge:

Find the sum of even k numbers less than 50?

After answering the given query, we can state that Since 11 is an integer and the only other number that is closer to it is 11, 11 is the nearest integer to 11.

Integers can be zero, a positive integer, or a negative integer indicated by a minus sign. An additive inverse of a positive number that it corresponds to is a negative number. A group of integers is commonly represented in mathematical notation by a bold Z or a bold "mathbb Z". An integer is a positive, negative, or zero number that is not a percentage. (pronounced IN-tuh-jer). Integer instances include -5, 1, 5, 8, 97, and 3,043. Non-integer instances include the numbers 1.43, 1 3/4, 3.14, and others. A group of integers and their antipodes is known as an integer set. Fractions and decimals are not included in the collection of integers.

Since 11 is an integer and the only other number that is closer to it is 11, 11 is the nearest integer to 11.

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a = at(t) + an(n) + zk/r(t).

To write a in the form at(t) an(n) without finding t and n, we need to use the given equation r(t) = (ysint)i (ycost)i ztk and rearrange the terms to get a in terms of t and n.

First, we can separate the terms involving t and n:

r(t) = (ysint)i + (ycost)i + ztk

Next, we can factor out t and n from the terms involving them:

r(t) = t(ysini) + n(ycosi) + zk

Now we can rearrange the equation to get a in terms of t and n:

a = t(ysini) + n(ycosi) + zk/r(t)

Finally, we can write a in the form at(t) an(n):

a = at(t) + an(n) + zk/r(t)

where at(t) = ysini and an(n) = ycosi.

Therefore, the final expression for a in the form at(t) an(n) without finding t and n is a = at(t) + an(n) + zk/r(t).

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Among the followings A, C, D, and F subsets of P2 are subspaces of P2.

The subsets of P2 that are subspaces of P2 are A, C, D, and F.

A. {p(t) | p′(t)+4p(t)+9=0} is a subspace of P2 because it satisfies the criteria of being closed under addition and scalar multiplication.

B. {p(t) | p′(0)=p(4)} is not a subspace of P2 because the derivative of p(0) does not equal p(4).

C. {p(t) | p(2)=0} is a subspace of P2 because it satisfies the criteria of being closed under addition and scalar multiplication.

D. {p(t) | p′(t) is constant } is a subspace of P2 because it satisfies the criteria of being closed under addition and scalar multiplication.

E. {p(t) | 6) =2} is not a subspace of P2 because the derivative of p(6) does not equal 2.

F. {p(t) | p(−t) =p(t) for all t} is a subspace of P2 because it satisfies the criteria of being closed under addition and scalar multiplication.

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The mean number of cars owned for this sample is 3.00.

To find the mean number of cars owned for this sample, we will use the formula for calculating the mean:
Mean = (sum of all values) / (number of values)

Let's assume that the sample is given as: 1, 2, 3, 4, 5
Find the sum of all values. In this case, the sum is 1 + 2 + 3 + 4 + 5 = 15.
Find the number of values. In this case, there are 5 values.

Divide the sum of all values by the number of values to find the mean. In this case, the mean is 15 / 5 = 3.

Overall, Mean, median and mode are all measures of central tendency in statistics. In different ways they each tell us what value in a data set is typical or representative of the data set. The mean is the same as the average value of a data set and is found using a calculation. Add up all of the numbers and divide by the number of numbers in the data set.

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The Student t-distribution would be the most appropriate method for calculating the margin of error for the population mean in this case.

The most appropriate method for calculating the margin of error for the population mean in this case would be the Student t-distribution. This is because the sample size is relatively small (16 school children) and the population distribution is assumed to be uniformly distributed.

The Student t-distribution is used when the sample size is small and the population distribution is unknown or not normally distributed.

In contrast, the Normal z-distribution is used when the sample size is large (usually over 30) and the population distribution is assumed to be normally distributed.

More advanced statistical techniques, such as bootstrapping or Bayesian methods, may be used when the sample size is small and the population distribution is unknown, but these techniques are more complex and may not be necessary in this case.

Therefore, the Student t-distribution would be the most appropriate method for calculating the margin of error for the population mean in this case.

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To find the log of 45.3 using a calculator, first enter 45.3 into the calculator, then press the "log" key. This should give you the result of 1.654221564 rounded to the nearest ten-thousandth.

Knowing the nature of logarithms, in mathematics, logarithms are the opposite or inverse of exponents or exponents. In simple terms, logarithms can be interpreted as an inverse or the opposite of the power used in determining the power of a base number.

So the point is that by studying logarithms, you will be able to find the exponential value of a number whose exponent is known.

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The simplified expression after the subtraction is given as follows:

-20.2m - 11.8.

The subtraction expression for this problem is defined as follows:

(2y + 14.6m + 3.8) - (34.8m + 15.6 + 2y).

The negative sign means that the sign of each term on the parenthesis preceded by the negative sign is exchanged, hence:

2y + 14.6m + 3.8 - 34.8m - 15.6 - 2y.

When you combine like terms, you are simplifying an expression by grouping together terms that have the same variables and exponents.

The like terms are given as follows:

Hence the simplified expression is:

-20.2m - 11.8.

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The particular solution of the differential equation dy/dx=(x−2)e−2y satisfying the initial condition y(2)=ln(2).y(x) = ln(2)+ln(x-1)

The particular solution of the differential equation dy/dx=(x−2)e−2y satisfying the initial condition y(2)=ln(2) is y(x) = ln(2)+ln(x-1).

To solve this equation, we use the method of integrating factor. First, we multiply the entire equation by the integrating factor e2y, to get:

e2y dy/dx=(x-2)

Integrating both sides with respect to x, we get:

e2y dy = (x-2)dx

Integrating again with respect to y, we get:

e2y = x-2 + c

where c is a constant.

Now, to satisfy the initial condition y(2)=ln(2), we put x=2 in the equation above and get:

e2ln(2) = 0 + c

or c=e2ln(2).

Therefore, the equation becomes:

e2y = x-2 + e2ln(2)

Rearranging the equation, we get:

y(x) = ln(2)+ln(x-1).

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The expressions that represent the costs of the wood, nails, and hammer. ford are:

Let's start by using variables to represent the cost of nails and the cost of the hammer.

Let x be the cost of nails.

Then, according to the problem statement, the cost of the hammer is $5 more than the cost of the nails, so the cost of the hammer is x + 5.

The cost of the wood is $5 more than the cost of the hammer, so the cost of the wood is (x + 5) + 5 = x + 10.

Therefore, the expressions that represent the costs of the wood, nails, and hammer are:

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Answer:

∠ BCD = 42°

Step-by-step explanation:

the measure of the secant- tangent angle BCD is half the difference of the intercepted arcs, that is

∠ BCD = [tex]\frac{1}{2}[/tex] (EB - BD) = [tex]\frac{1}{2}[/tex] (157 - 73)° = [tex]\frac{1}{2}[/tex] × 84° = 42°

The given function f(x) = (1/2)(x-5)^2 - 6 is a transformation of the parent function f(x) = x^2. It has been horizontally shifted 5 units to the right, vertically stretched by a factor of 1/2, and vertically translated downward 6 units. There is no reflection.

The parent function in this case is the quadratic function f(x) = x^2.

The given function f(x) = (1/2)(x-5)^2 - 6 is a transformation of the parent function f(x) = x^2. Here are the transformations that were applied

Translation: The function has been shifted horizontally by 5 units to the right. This is because the term (x-5) appears inside the function.

Vertical stretch: The coefficient 1/2 indicates that the function has been vertically stretched by a factor of 1/2. This means that the graph of the function is narrower than the graph of the parent function.

Vertical translation: The term -6 indicates that the function has been shifted vertically downward by 6 units.

Reflection: There is no reflection in this case since there is no negative sign outside the function.

Overall, the given function is a horizontally shifted, vertically stretched, vertically translated version of the parent function f(x) = x^2.

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The image of T is the set of all vectors orthogonal to v, and the kernel of T is the set of all vectors parallel to v.

The image of the linear transformation T(X) = v x X is the set of all vectors that are orthogonal to v. This is because the cross product of two vectors produces a vector that is orthogonal to both of the original vectors. Therefore, any vector in the image of T must be orthogonal to v.

The kernel of T is the set of all vectors X such that T(X) = 0. In other words, it is the set of all vectors that are parallel to v. This is because if two vectors are parallel, their cross-product is 0. Therefore, any vector in the kernel of T must be parallel to v.
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The cοοrdinates οf the mid pοint M οf the line segment AB are ( 3,1 ) .

A midpοint οf a line segment is the pοint οn a segment that bisects the segment intο twο cοngruent segments. In οther wοrds, The midpοint is halfway between the twο end pοints.

Fοr the given line segment AB with cοοrdinates as (2, -3) and (4, 5) οf A and B respectively.

x₁ = 2           y₁ = -3                  (Cοοrdinates οf A)

x₂ = 4          y₂ = 5                   (Cοοrdinates οf B)

Midpοint οf a line segment = [ (x₁ + x₂ ) / 2   ;    (y₁ +  y₂) /2  ]

= [  (2 +4) /2  ;    (-3 + 5) / 2  ]

= [ 6/2  ;   2/2 ]

= (3,1)

=> Thus, the cοοrdinates οf M are (3,1).

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Answer: The answer is B)

If α and β are the zeroes of the polynomial x² - 7x + 10, then the value of α³ + β³ is = 133.

We know that "α" and "β" are the zeroes of the polynomial x² - 7x + 10,

we factor the polynomial by splitting the middle term ,

We get;

⇒ x² - 7x + 10 ⇒ x² - 2x - 5x + 10,

⇒ x(x - 2) -5(x - 2) ⇒ (x - 5)(x - 2).

So, we get that α = 5 and β = 2;

In order to find the value of the expression α³ + β³, we substitute, the values of α and β in the expression,

We get;

⇒ 5³ + 2³

⇒ 125 + 8

⇒ 133.

Therefore , the value of expression α³ + β³ is 133.

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The given question is incomplete, the complete question is

If α and β are the zeroes of the polynomial x² - 7x + 10 , find the value of α³+β³.

The exterior circumference of the regular polygon is: 20 x 8.13cm = 162.6cm

What is polygon ?

A polygon is a two-dimensional closed geometric shape made up of three or more straight sides connected by straight line segments. Polygons are named based on the number of sides they have. For example, a polygon with three sides is called a triangle, a polygon with four sides is called a quadrilateral, and so on.

Polygons can be regular or irregular. A regular polygon is a polygon with all sides of equal length and all interior angles of equal measure. An irregular polygon is a polygon with sides of different lengths and/or interior angles of different measures.

Some examples of polygons include:

Triangle: A polygon with three sides.

Square: A regular polygon with four sides of equal length and four interior angles of 90 degrees each.

Pentagon: A polygon with five sides.

Hexagon: A polygon with six sides.

Octagon: A polygon with eight sides.

According to the question:
The sum of the exterior angles of any polygon is always 360 degrees. In a regular polygon, all the exterior angles are equal, so each exterior angle of this regular polygon measures 360° divided by the number of sides.

Let's call the number of sides "n". Then we know that:

n x 18° = 360°

Solving for n, we get:

n = 360° / 18° = 20

So the regular polygon has 20 sides.

To find the exterior circumference of the polygon, we need to find the length of one exterior side. To do this, we can use trigonometry. The exterior angle and the interior angle of a regular polygon are supplementary, so each interior angle of this polygon measures:

180° - 18° = 162°

In a regular polygon, all the interior angles are equal, so we can use the formula for the sum of the interior angles to find the measure of each interior angle:

sum of interior angles = (n - 2) x 180°

20 x 162° = (20 - 2) x 180°

20 x 162° = 3240°

So each interior angle of the polygon measures 3240° / 20 = 162°.

Now, in a right triangle with one leg equal to half the side length (5.75cm) and the other leg equal to the tangent of half the interior angle (tan(81°) ≈ 5.98), the hypotenuse is equal to the length of one exterior side. Using the Pythagorean theorem, we can find the hypotenuse:

h = √(5.75^2 + 5.98^2) ≈ 8.13

Therefore, the exterior circumference of the regular polygon is:

20 x 8.13cm = 162.6cm (rounded to one decimal place)

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Answer:

g(-4) = 22

Step-by-step explanation:

To find g(-4), we must substitute it into the equation

We are given g(x) = - 5x + 2

g(-4) = - 5(-4) + 2

g(-4) = 20 + 2

g(-4) = 22

Answer:

[tex]\boxed{\mathtt{g(-4)=22.}}[/tex]

Step-by-step explanation:

[tex]\textsf{We are asked to identify g(-4).}[/tex]

[tex]\textsf{-4 is the substituted value for x. We should substitute -4 into the equation as well.}[/tex]

[tex]\large\underline{\textsf{Substitute:}}[/tex]

[tex]\mathtt{g(-4)=-5(-4)+2.}[/tex]

[tex]\large\underline{\textsf{Simplify the \bf{Right Side:}}}[/tex]

[tex]\mathtt{g(-4)=20+2.}[/tex]

[tex]\boxed{\mathtt{g(-4)=22.}}[/tex]

[tex]\large\underline{\textsf{Note:}}[/tex]

[tex]\textsf{Substitution will be used for problems such as these. If there is a number in the}[/tex]

[tex]\textsf{parentheses, it will likely be used mainly for the \underline{right} side of the equation.}[/tex]

The solution to the equation -8x + 7y + 9z = 5 is X = -8, Y = 7, and Z = 9.

To solve the equation, you will need to isolate the variables. First, subtract 9z from both sides of the equation:

=>-8x + 7y + 9z = 5
=>-8x + 7y = -4

Next, subtract -8x from both sides of the equation:

=>-8x + 7y = -4
=>7y = 4 + 8x

Finally, divide both sides of the equation by 7:

=>7y = 4 + 8x
=>y = (4 + 8x) / 7

Therefore, the value of X is -8, Y is (4 + 8x) / 7; Y is 7, and Z is  9.

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To find:-

Answer:-

We are here given that a frame of width 1cm is placed around the picture whose length is 6cm more than its breadth. So let's take the breadth be " x " , then its length will be, " x + 6 "

Answer 1 :-

For diagram refer to the attachment.

Length of the frame = AB = AI + IJ + JB

= 1 + x + 6 + 1

= ( x + 8 ) cm

Breadth of the frame = BC = JL + LG + GK

= 1 + x + 1

= ( x + 2 ) cm

So the perimeter can be calculated using the formula,

P = 2 ( l + b )

P = 2 ( x + 8 + x + 2) cm

P = 2 ( 2x + 10 ) cm

P = ( 4x + 20 ) cm

Hence the perimeter of the frame is ( 4x + 20 ) cm .

_________________________________________

Answer 2 :-

For finding the area of the frame , subtract the area of picture from the total area of picture and frame . Let the required area be " S " , then ;

S = ∆A

S = (x+8)(x+2) - x(x+6)

S = x² + 2x + 8x + 16 - ( x² + 6x )

S = x² + 10x + 16 - x² - 6x

S = ( 4x + 16 ) cm²

Hence the area of the frame is ( 4x + 16 ) cm² .

_________________________________________

Answer 3 :-

In answer 1 we found the perimeter of the frame to be ( 4x + 20 ) cm . So if width of the picture that is " x " is 15cm , then the perimeter can be calculated by substituting x = 15 , in the obtained expression as ,

P = ( 4*15 + 20 ) cm

P = ( 60 + 20 ) cm

P = 80 cm

Hence the perimeter of the frame is 80cm .

and we are done!

Answer:

[tex]\textsf{Perimeter of frame:} \quad P(x)=4x+20[/tex]

[tex]\textsf{Area of frame:} \quad A(x)=4x+16[/tex]

The perimeter of the frame is 80 cm.

Step-by-step explanation:

A rectangle is a two-dimensional shape where all the interior angles are  right angles (90°) and its opposite sides are equal in length and parallel.

The perimeter of a two-dimensional shape is the distance all the way around the outside.

Given a rectangular picture is 6 cm longer than it is wide:

If a frame 1 cm wide is placed around the picture, then the width and length will be extended by 2 cm. Therefore:

Since the perimeter of a rectangle is twice the sum of its width and length, the polynomial that represents the perimeter of the frame is:

[tex]\begin{aligned}\implies P(x)&=2(\sf width+length)\\&=2(x+2+x+8)\\&=2(2x+10)\\&=4x+20\end{aligned}[/tex]

The area of a rectangle is the product of its length and width.

The area of the frame is the area of the largest rectangle less the area of the picture. Therefore, the polynomial that represents this is:

[tex]\begin{aligned}\implies A(x)&=(x+2)(x+8)-x(x+6)\\&=x^2+10x+16-x^2-6x\\&=x^2-x^2+10x-6x+16\\&=4x+16\end{aligned}[/tex]

To find the perimeter of the frame if the picture is 15 cm wide, substitute x = 15 into the polynomial P(x):

[tex]\begin{aligned}x=15\implies P(15)&=4(15)+20\\&=60+20\\&=80\; \sf cm\end{aligned}[/tex]

Therefore, the perimeter of the frame is 80 cm.

Answer:

your equation is very simple

The answer is C. (x-6)(x-6).

Answer:

c) (x-6)(x-6)

Step-by-step explanation:

(x-6)(x-6) => x²-6x+36-6x => x² - 12x + 36.

The function of the given graph is: Option C:  f(x) = (x - 1)(x - 2)(x + 1)(x + 2).

A function's range is the set among all values that the function accepts, and its domain is the set of all values in which the function is defined.

A function's domain is indeed the set of all permitted input values, whereas its range is the set of all feasible output values. Imagine the graph getting compressed down to the x- or y-axis, and use that image to determine the graph's domain and range.

From the given graph, the function f(x) becomes zero for the domain of x at -2, -1 ,1 and 2.

Thus, -2, -1 ,1 and 2 are the factors of the function given.

Thus, the equation which depicts the graph shown is:

f(x) = (x - 1)(x - 2)(x + 1)(x + 2).

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Answer:

(-5,8)

Step-by-step explanation:

If we look at the graph, Point A is 5 to the left and it is going up 8. The x axis is the point's horizontal change and the y axis its its vertical change. Based on this information, we can count up and left to see its position.

In order to label points on the coordinate plane, we can use the template (x,y) which helps us label where the point is.

(-5,8)

Answer:(-5,8)

Step-by-step explanation:

The correct statement is D. As the risk of an investment increases, the opportunity of gains decreases.

This statement is true because when the risk of an investment increases, the potential gains may not be as great as when the risk is lower. This is because when the risk of an investment increases, investors may be less likely to invest in it due to the increased risk and therefore the potential return will be lower.For example, if an investment has a risk level of 10%, the potential return may be 5%. However, if the risk level of the same investment increases to 20%, the potential return may decrease to 4%. This is because investors may be more hesitant to invest in the riskier investment and therefore the potential return is lower.In addition, when the risk of an investment increases, its market value may also decrease. This is because investors tend to be more attracted to investments with lower risk levels, which can lead to a decrease in demand and therefore a decrease in the market value of the investment.

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The correct statement is D. As the risk of an investment increases, the opportunity of gains decreases.

This statement is true because when the risk of an investment increases, the potential gains may not be as great as when the risk is lower. This is because when the risk of an investment increases, investors may be less likely to invest in it due to the increased risk and therefore the potential return will be lower.For example, if an investment has a risk level of 10%, the potential return may be 5%. However, if the risk level of the same investment increases to 20%, the potential return may decrease to 4%. This is because investors may be more hesitant to invest in the riskier investment and therefore the potential return is lower.In addition, when the risk of an investment increases, its market value may also decrease. This is because investors tend to be more attracted to investments with lower risk levels, which can lead to a decrease in demand and therefore a decrease in the market value of the investment.

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