What is the reason for each step in the solution of the equation?
4x−1=−2(x+1)

Answer:

[tex]a=22\\b=6\\c=14\\d=8[/tex]

Step-by-step explanation:

So (Didn't even know what it was until now), is a square where all rows, columns, and diagonals sum up to the same number.

So, from the diagonal of 7, 15, and 23, but adding them up, we can tell that each row, column, and diagonal should sum up to 45.

If we know that, you can solve it either arithmetically or algebraically (I'm going to sovle them algebraically)

Here are the equations I used to solve for each:

[tex]7+16+a=45\\23+a=45\\a=22\\\\24+15+b=45\\39+b=45\\b=6\\\\15+16+c=45\\31+c=45\\c=14\\\\14+23+d=45\\37+d=45\\d=8[/tex]

Any further questions? Just leave a comment.

29) 3[tex]e^{2i}[/tex] = – 1.248 + 2.728 i (conversion from polar form to rectangular a+bi form of complex number)

3[tex]e^{2i}[/tex] = 3 (cos[tex]2^{c}[/tex] + i sin[tex]2^{c}[/tex]) = 3 ( – 0.416 + i 0.909) = – 1.248 + 2.728 i

33) 3[tex]e^{\frac{5\pi i}{4} }[/tex] = – 2.12 + 2.12 i (conversion from polar form to rectangular a+bi form of complex number)

3[tex]e^{\frac{5\pi i}{4} }[/tex] = 3 (cos[tex](\frac{5\pi }{4})^{c}[/tex][tex]\frac{5\pi }{4}^{c}[/tex] + i sin[tex](\frac{5\pi }{4})^{c}[/tex] ) = 3 ( – 0.707 + i 0.707) = – 2.12 + 2.12 i

37) – 4 i =  4[tex]e^{\frac{3\pi}{2}i}[/tex] (conversion from rectangular a+bi form to polar form of complex number)

– 4 i =   0 – 4 i = [tex]\sqrt{0^{2}+(-4)^{2}}[/tex][tex]e^{i tan^{-1}\frac{-4}{0} }[/tex] =  4[tex]e^{\frac{3\pi}{2}i}[/tex]

41) – 3 + 4 i = 5 [tex]e^{2.214i}[/tex] (conversion from rectangular a+bi form to polar form of complex number)

– 3 + 4 i = [tex]\sqrt{(-3)^{2}+(4)^{2}}[/tex][tex]e^{tan^{-1}\frac{4}{-3}i}[/tex] = 5 [tex]e^{(\pi - 0.927)i}[/tex] = 5 [tex]e^{2.214i}[/tex]

49) 5 – i = [tex]\sqrt{26}e^{-0.197i}[/tex] (conversion from rectangular a+bi form to polar form of complex number)

5 - i = [tex]\sqrt{5^{2}+1^{2}}e^{tan^{-1}(\frac{-1}{5})i}[/tex]  = [tex]\sqrt{26}e^{-0.197i}[/tex]

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The function operation ( f + g )(x) of the functions f( x ) = 4x + 1 and g( x ) = x² - 5 is x² + 4x - 4.

A function is simply a relationship that maps one input to one output.

Each x-values must have one y-value to qualify as a function.

Given the data in the question;

First, set up the function operation

( f + g )(x) = f(x) + g(x)

Replace the function designators f(x) and g(x) with the actual functions.

( f + g )(x) = f(x) + g(x)

( f + g )(x) = ( 4x + 1 ) + ( x² - 5 )

Collect and add like terms

( f + g )(x) = 4x + 1 + x² - 5

( f + g )(x) = 4x + x² - 5 + 1

( f + g )(x) = 4x + x² - 4

Reorder the function

( f + g )(x) = x² + 4x - 4

Therefore, the function operation ( f + g )(x) is  x² + 4x - 4.

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The net image of a figure is a visual representation of the original figure.

From the given net image, the solid that has the net image can be said to be a traingular

By using algebra resolution methods for systems of linear equations, we find that the equation of the form f(x) = a · x² + b · x + c that passes through the three points is equal to f(x) = (5 / 2) · x² + (3 / 2) · x.

In this problem we must determine the coefficients of a quadratic equation that passes through the points (x₁, y₁) = (1, 4), (x₂, y₂) = (2, 13) and (x₃, y₃) = (4, 46). First, we need to create a system of linear equations by substituting on y and x thrice:

(x₁, y₁) = (1, 4)

a · 1² + b · 1 + c = 4

a + b + c = 4

(x₂, y₂) = (2, 13)

a · 2² + b · 2 + c = 13

4 · a + 2 · b + c = 13

(x₃, y₃) = (4, 46)

a · 4² + b · 4 + c = 46

16 · a + 4 · b + c = 46

Then, we find a system of three linear equations with three variables that offers an unique solution:

a + b + c = 4                             (1)

4 · a + 2 · b + c = 13                 (2)

16 · a + 4 · b + c = 46               (3)

There are different methods to find the solution to this system, we proceed to use algebraic substitution:

By (1):

c = 4 - a - b

(1) in (2) and (3):

4 · a + 2 · b + (4 - a - b) = 13

3 · a + b = 9                          (2b)

16 · a + 4 · b + (4 - a - b) = 46

15 · a + 3 · b = 42                  (3b)

By (2b):

b = 9 - 3 · a

(2b) in (3b):

15 · a + 3 · (9 - 3 · a) = 42

15 · a + 27 - 9 · a = 42

6 · a = 15

a = 15 / 6

a = 5 / 2

By (2b):

b = 9 - 3 · (5 / 2)

b = 9 - 15 / 2

b = 18 / 2 - 15 / 2

b = 3 / 2

By (1):

c = 4 - 5 / 2 - 3 / 2

c = 4 - 8 / 2

c = 4 - 4

c = 0

The coefficients of the quadratic equation are (a, b, c) = (5 / 2, 3 / 2, 0).

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The x intercept of the function y=(2/3)x-1 is 3/2 , and y intercept is -1 .

X intercept of a function is defined as the point where the graph crosses the x axis ,

and the y intercept of the function  is defined as the point where the graph crosses the y axis .

In the question ,

it is given that

the function is y= (2/3)x-1

to find the x intercept we substitute y as 0 in the equation

On substituting  y as 0  , in the equation , we get

0 = (2/3)x-1

1=(2/3)x

x=1*(3/2)

x=3/2

the x intercept is 3/2.

to find the y intercept we substitute x as 0 in the equation

On substituting  x as 0  , in the equation , we get

y=(2/3)*0-1

y=0-1

y= -1

so, the y intercept is -1 .

Therefore , the x intercept of the function y=(2/3)x-1 is 3/2 , and y intercept is -1 .

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Given:

TR = 11 Ft

∠RTS = 16°

Let's determine the length of Arc PS,

Step 1: Let's first determine the angle of Arc PS.

∠RTS = 16°

∠PTQ = 16° ; Vertical angle pair of ∠RTS

Since ∠QTR = ∠PTS under the rule of vertical angles, we can now determine the measure of ∠PTS or Arc PS.

We get,

Step 2: Let's determine the perimeter of the circle.

Step 3: Let's determine the length of Arc PS.

Therefore, the length of Arc PS is 31.47 ft.

Answer: 10/3

Step-by-step explanation:

[tex]\frac{2}{6}=\frac{x}{10}\\\\x=\frac{10}{3}[/tex]

SOLUTION

(a) From the information given in the question,

We will select a curve with 58 at its center which represents the mean and

41 and 75 at the left and right sides. That is gotten by subtracting and adding the standard deviation of 17.

Hence the answer is Graph D

(b) The region that represents less than 41 is seen in graph B

Hence graph B is the answer

(c) Option A

The probability is 0.1587 that a randomly selected cell phone plan in this population is less than $41 per month

The number of high-quality version downloads is 300.

Given:

Size of the standard version = 2.8 megabytes (MB).

Size of the high-quality version = 4.5 MB.

Total number of downloads = 870

Total download size = 2946 MB

Let the number of high-quality version downloads be x.

Then the number of standard version downloads will be 870 - x.

Now the sum of the number of downloads of each type multiplied by their sizes equals 2946 MB.

So the equation is,

4.5x + 2.8(870 - x) = 2946

4.5x + 2436 - 2.8x = 2946

1.7x = 2946 - 2436

1.7x = 510

x = 510/1.7

x = 300

Therefore, the number of high-quality version downloads is 300.

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The height of the building is 118. 89 feet

Trigonometric identities are simplify defined as arithmetic expressions or equations relating to many trigonometric functions, and is also known for holding true for all the values in the domain of the functions.

The different  types of trigonometric identities includes;

The trigonometric ratios for major identities are;

sine = opposite/hypotenuse

tangent = opposite/adjacent

cosine = adjacent/hypotenuse

From the information given;

cos 43 = x/170

cross multiply

x = cos 43(170)

expand the bracket

x = 124.33 feet

To determine the height of the building is the opposite side

sin 73 = x/ 124.33

cross multiply

x = sin 73(124.33)

expand the bracket

x = 118. 89 feet

Hence, the value is 118. 89 feet

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olution

e have the following statement:

If < ABC and < CBD are supplementary angles then m < ABC and m< CBD = 180º represents the definition of:

A) supplementary angles

6 possible values of squares that she can move.

What is possibility or probability?

Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur i.e., how likely they are going to happen, using it.

it is already known that Oris has to move 7 squares (because 3 + 4 = 7), yet she has another 6 sets of possibilities because a dice has 6 facets.

Hence she has 6 different possible numbers of squares she can move.

The possibilities are:

-8 squares (if she rolls a 1)

-9 squares (if she rolls a 2)

-10 squares (if she rolls a 3)

-11 squares (if she rolls a 4)

-12 squares (if she rolls a 5)

-13 squares (if she rolls a 6)

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1) An equation that models the problem is x = 30,600 - 1,440t, where x is the value after t years.

2) After 8 years of straight-line depreciation, the car's value will be $19,080.

Depreciation is an accounting term that refers to the periodic expensing of the cost of a long-term asset.

Using depreciation, a reporting entity annually recognizes the cost of an asset used for many years.

Intangible long-term assets use amortization or depletion instead of depreciation to describe the same meaning.

Price of an automobile in 2003 = $30,600

Annual depreciation = $1,440

The car's value after t years = $19,080.

Value after t years = 30,600 - 1,440t

If 19,080 = 30,600 - 1,440t

1,440t = 30,600 - 19,080

1,440t = 11,520

t = 8 (11,520/1,440)

t = 8

= 8 years

Check:

x = 30,600 - 1,440t

x = 30,600 - 1,440(8)

x = 30,600 - 11,520

x = 19,080

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Answer: 71%

Explanation:

100% - total earth surface

29% - earth surface uncovered by water

100 - 29 = 71% of surface covered by water

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \: y = x² +6x -16[/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

The values of x for which the curve cuts/touches the x - axis are roots of that particular polynomial.

So, the values of x, when y = 0 are the roots of the given quadratic function.

that is : x = -8 and x = 2

And it can be represented as :

[tex]\qquad \tt \rightarrow \: (x - h1)(x - h2)= 0[/tex]

[ h1 and h2 represents roots of the quadratic function ]

[tex]\qquad \tt \rightarrow \: (x -2)(x + 8) = 0[/tex]

It can be further simplified as :

[tex]\qquad \tt \rightarrow \: {x}^{2} -2x +8x -16 = 0[/tex]

[tex]\qquad \tt \rightarrow \: x {}^{2} +6x -16 = 0[/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

the probability of winning a lottery game out of all the games played is 0.16.

We are given that:

In a lottery game, the chances of win are = 4 in 25

So, this means that:

if a person plays 25 games of lottery, then he will probably win 4 games out of them.

So, we get that:

Total games = 25

Win games = 4

Probability = win games / total games

Substituting the values, we get that:

Probability = 4 / 25

P = 0.16

Therefore, we get that, the probability of winning a lottery game out of all the games played is 0.16.

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The difference between expression (-3x²-xy-3y²) - (6x²-4xy+y²) is  

(-9x²+3xy-4y²).

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement.

Numbers and arithmetic operators make into a mathematical numerical expression. There are no symbols for undefined variables, equality, or inequality.

Unknown variables, integers, and arithmetic operators are the components of an algebraic expression. There are no symbols for equality or inequality in it.

= (-3x²-xy-3y²) - (6x²-4xy+y²)

=  -3x²-xy-3y² - 6x²+4xy-y²

= (-9x²+3xy-4y²)

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The correct answer is:  
     [A]:  " ∡2 is supplementary to ∡3 " .

___________________

The other answer choices given—which are correct statements—only prove that " a || b " {that is:  "Line A" is parallel to "Line B".}

___________________

Given the figure of an object consists of a cylinder and a rectangular prism.

We will find the volume of the cylinder using the following formula:

As shown, the diameter of the base = d = 3 ft

So, the radius = r = d/2 = 3/2 = 1.5 ft

And the height = h = 4 ft

Use π = 3

so, the volume of the cylinder will be as follows:

Now, we will find the volume of the rectangular prism using the following formula:

As shown, the length = l = 7 ft

The width = w = 4 ft

The height = h = 4 ft

So, the volume of the rectangular prism will be as follows:

So, the total volume of the object will be =

So, the answer will be V = 139 ft³

Step-by-step explanation:

On a horizontal number line, -43 is located to the left of -35. TRUE because -43 is farther away (to the left) from 0 than -35.

The value of x such that f(x) and g(x) have equal values is 3

Linear equations are equations that have constant average rates of change.

Note that the constant average rates of change can also be regarded as the slope or the gradient

From the question, we have

f(x) = -2x + 4

g(x) = 2x - 8

The question implies that the functions have equal values

This means that

f(x) = g(x)

Substitute f(x) = -2x + 4 and g(x) = 2x - 8 in f(x) = g(x)

So, we have the following equation

-2x + 4 = 2x - 8

Collect the like terms

2x + 2x = 8 + 4

Evaluate the like terms

4x = 12

Divide both sides of the equation by 4

x = 3

Hence, the value of x such that the equations are equal is 3

See attachment for the graph of the functions

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Answer:

24

Step-by-step explanation:

divide the sides added together by the middle

The set T can be rewritten by listing its elements as T = {-4}.

         Set A = {a, b, c, d}. These are the elements of set A: a, b, c, and d.

Given:

Set T is equal to  {x | x is an integer and -5 < x < -3}.

By examining the interval in the set, the set can also be written as something else. 

It should be noted that the interval consists of two inequalities combined so that x > -5 and x < -3.

As -4 > -5 and -4 < -3 via the number line so it is the only element listed in the required set notation.

Hence, the set can be rewritten as

T = {-4}

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The complete question is: "Rewrite the set T by listing its elements. Make sure to use the appropriate set notation.

T = {x | x is an integer and -5 < x < -3}."

Answer:

11

Step-by-step explanation:

This will form triangle VWX. So we have values for ∠VWX and ∠XVW but we don't have value for ∠WXV.

Since ∠WXV and ∠WXY are supplementary angles

=> ∠WXV + ∠WXY = 180

=> ∠WXV = 180 - ∠WXY

So the angles of triangle VXY

∠VWX + ∠XVW + ∠WXV = 180

(x + 14) + (x + 9) + (180 - (5x - 10)) = 180

x + x - 5x + 14 + 9 + 180 + 10 = 180

-3x + 213 = 180

-3x = - 33

x= 11

How many pounds of Virginia peanuts does Sergio use?

Assume he is making 10 lb of the $3.40 mixture

Let x = no. of pounds of the Virginia ($3.50) peanuts

Then (10-x) = no. of pounds of the Spanish ($3) peanuts

The Equation:

3.5x + 3(10-x) = 3.4(10)

3.5x + 30 - 3x = 34

.5x = 34 - 30

x = 4/.5

x = 8 pounds of Virginia peanuts

:

(b)How many pounds Spanish peanuts does Sergio use?

Spanish peanuts must be 2 pounds since the total is 10 pounds

:

Check:

3.5(8) + 3(2) = 3.4(10)

28 + 6 = 34

First, we find the value of r:

Then r is calculated as follows:

Multiplying

Simplify

Apply exponential properties

Applying the limit, the solution is

So, r = 0.4 and since r is less than 1, the series converges.

Answer: From the ratio test, r = 0.4. The series converges.