What is the reason for each step in the solution of the equation?

18−2x=4x

Drag and drop the reasons into the boxes to correctly complete the table.

A total of 2587 students attended the collage

From the question, the given parameters are:

The above parameters implies that

Number of students that attended = 56% x Total number of students

Represent the total number of students with x

So, we have the following representation

Number of students that attended = 56% * x

Where

x = 4620

So, we have

Number of students that attended = 56% x 4620

Evaluate the products

Number of students that attended  = 2587.2

Approximate

Number of students that attended = 2587

Hence, 2587 of the students attended the collage

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To have $600,000 for retirement in 35 years at 5% interest, one would need to deposit $528.13 in the account each month.

Periodic deposits are monthly cash inflows into a retirement account that accumulates interest by compounding.

To find periodic deposits, we can use an online finance calculator, defining the parameters as follows.

N (# of periods) = 420 months (35 years x 12)

I/Y (Interest per year) = 5%

PV (Present Value) = $0

FV (Future Value) = $600,000

Results:

Monthly Deposits (PMT) = $528.13

Sum of all periodic deposits = $221,814.60

Total Interest = $378,185.40

Thus, monthly deposits of $528.13 can accumulate to $600,000 in 35 years at 5% interest.

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The equation of the vertical asymptote for the graph of the rational number g(x) = 6/x-1 is x - 1 = 0 or x = 1.

Given function:

g(x) = 6/x-1

vertical asymptote for any function is denominator is equal to zero.

x - 1 = 0

x = 1.

Therefore the equation of the vertical asymptote for the graph of the rational number g(x) = 6/x-1 is x - 1 = 0 or x = 1.

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Answer:

Step-by-step explanation:

Answer:a, c and d

Step-by-step explanation:bc i got it right on edge

Answer:

Step-by-step explanation:

A. -1/3x

B. -x

c.-5/4x

The numeric value of the expression -b + 8x when b = 5 and x = -6 is given as follows:

-53.

To find the numeric value of a function or of an expression, we replace each instance of the variable/variables in the function or in the expression by the value/values at which we want to find the numeric value.

In this problem, the expression is given as follows:

-b + 8x.

The values at which the numeric value is to be found are:

b = 5, x = -6.

Hence:

Thus the numeric value of the expression is obtained as follows:

-5 + 8(-6) = -5 - 48 = -53.

The problem is given by the image at the end of the answer.

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It would take 8 months of membership for the total money paid of $321.91.

An equation is an expression that shows the relationship between two or more numbers and variables. A variable can either be dependent or independent. A dependent variable depend on other variable while an independent variable does not depend on other variables.

Let x be the number of months subscribed. Hence,

For Fitness :

Total payment = 33.99 x + 49.99

if you paid a total of $321.91 then the number of months subscribed will be;

321.91  = 33.99 x + 49.99

33.99 x = 321.91  - 49.99

33.99 x = 271.92

x = 271.92/33.99

x = 8

It would take 8 months of membership for the total money paid of $321.91.

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From the given equation y = A(x-h)² +k it is identified that this quadratic function represents the parabola with vertex (h, k).

As given in the question,

Given equation is :

y = A(x-h)² +k

Standard basic parabola equation is y = x² where parabola pass through (0, 0) .

In the given quadratic function y = A(x-h)² +k , it represent equation of parabola which is U shaped .

Value of A > 0 then it open in upward direction .

Value of A <0 then it is open in downward direction.

Vertex of the given parabola y = A(x-h)² +k  is (h, k).

Line of symmetry is given by vertical line x =h.

Therefore, from the given equation y = A(x-h)² +k it is identified that this quadratic function represents the parabola with vertex (h, k).

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The width of the rectangle is given as w = p/2 - l which is derived from perimeter of rectangle

The perimeter of a rectangle is the total distance covered by its boundaries or the sides. Since there are four sides of a rectangle, thus, the perimeter of the rectangle will be the sum of all four sides.

In this question, we simply need to make the width (w) the subject of formula.

The equation given is

p = 2w + 2l

p = 2w + 2l

p = 2(w + l)

p / 2 = w + l

w = p/2 - l

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Answer:

d the last one I think

Step-by-step explanation:

I am not really sure

Answer:

D.) 6.67 X 10^2

The probability expression when converted from odd's expression is 8/17

From the question, we have the following odd parameters

Odd = 8 to 9

To start with, we need to express the odd as ratio

So, we have the following representation

Odds ratio = 8 : 9

Solving further, we need to express the ratio as fraction

So, we have the following representation

Odds fraction = 8/9

To convert the above odd's expression to probability expression, we make use of the following equation

This is represented as

P = Odds/(Odds + 1)

Substitute the known values in the above equation

So, we have the following equation

P = (8/9)/(8/9 + 1)

Evaluate the sum

This gives

P = (8/9)/(17/9)

Express the quotient as product

P = (8/9) * (9/17)

Evaluate

P = 8/17

Hence, the probability is 8/17

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Answer:

[tex] \sf Root \: of \: x \: are \: \dfrac{3}{2} \: and \: \dfrac{ - 6 \pm \sqrt{ - 108} }{8} [/tex]

Step-by-step explanation:

[tex] \rm \implies 8 {x}^{3} - 27 = 0 \\ \\ \rm \implies (2 \times 2 \times 2) {x}^{3} - (3 \times 3 \times 3) = 0 \\ \\ \rm \implies {(2x)}^{3} - {3}^{3} = 0 \\ \\ \boxed{ \rm {a}^{3} - {b}^{3} = (a - b)( {a}^{2} + ab + {b}^{2} )} \\ \\ \rm \implies (2x - 3)( {(2x)}^{2} + (2x)(3) + {3}^{2} ) = 0 \\ \\ \rm \implies 2x - 3 = 0 \: and \: 4 {x}^{2} + 6x + 9 = 0 \\ \\ \rm \implies x = \frac{3}{2} \: and \: x = \frac{ - 6 \pm \sqrt{36 - 144} }{8} \\ \\ \rm \implies x = \frac{3}{2} \: and \: x = \frac{ - 6 \pm \sqrt{ - 108} }{8} [/tex]

Addition of the given polynomial functions (5a³ + 4a² - 3a + 2) and (a³ - 3a² + 3a - 9)​ gives 8a³ + a² - 7

A polynomial function is a function in an equation, such as the quadratic equation or the cubic equation, that only uses non-negative integer powers or only positive integer exponents of a variable.

Addition of polynomial is achieved term by term

= (5a³ + 4a² - 3a + 2) + (a³ - 3a² + 3a - 9)​

= 5a³ + 3a³+ 4a² - 3a²- 3a + 3a + 2 - 9

= 8a³ + a² - 7

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The completion of the inventory table is as follows:

Some of the inventory methods that are used in completing the inventory table are:

                                    Units    Unit Cost    Total Cost

Jan. 1      Beg. Inventory  10       $7.00            $70

Apri. 11    Purchases        30     $12.00          $360

May 17    Purchases        40     $13.00          $520

Dec. 5    Purchases        20    $15.00           $300

Total                              100                        $1,250

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Answer:

x = 15

Step-by-step explanation:

A segment joining the midpoints of two sides of a triangle is half the length of the third side , then

x + 3 = [tex]\frac{1}{2}[/tex] × 36 = 18 ( subtract 3 from both sides )

x = 15

Answer:

5 hours 15 minutes

Step-by-step explanation:

using the relationship

time = [tex]\frac{distance}{speed}[/tex] = [tex]\frac{273}{52}[/tex] = 5.25 hours = 5 hours 15 minutes

The z-score of a person who scored 128 on the exam is equal to 2.9

A z-score is also referred to as a z-value or standard score and it can be defined as a measure of the distance between a raw score and the mean, when standard deviation units are used.

Mathematically, the z-score of a given sample score in a normal distribution can be calculated by using this formula:

[tex]z=\frac{x\;-\;u}{\sigma}[/tex]

Where:

Substituting the given parameters into the formula, we have;

Z-score, z = (128 - 70)/(20)

Z-score, z = 58/20

Z-score, z = 2.9

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Answer:

8%

Step-by-step explanation:

Step-by-step explanation:

why ? the same pattern your saw yourself, as the handwritten numbers indicate.

it is 1:118.

event on the left is multiplied by 118 to create the numbers on the right.

The equation for the word problem the difference of ten times a number and six is fourteen is (10x-6 = 14) and the value of x is 2.

According to the question,

We have the following information:

The difference of ten times a number and six is fourteen.

Now, let's take the number to be x.

So, we have the following expression:

10x-6 = 14

Now, moving 6 from the left hand side to the right hand side will result in the change of the sign from minus to plus:

10x = 14+6

10x = 20

x = 20/10

x = 2

Hence, the equation for the word problem the difference of ten times a number and six is fourteen is (10x-6 = 14) and the value of x is 2.

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On October 28, Lee received proceeds of $71,153.66 from the discounted note.

Discounting a note involves receiving immediate cash by selling it to a financial institution at a discount.

The implication of discounting a note is that the receiver gets less than the maturity value.

The maturity value is the face value of the note plus the computed interest.

Face value of the note receivable = $70,000

Interest rate = 6.34%

Note period = 120 days

July 26 - October 28 = 94 days

Maturity value of the note receivable = The Face Value + Interest

= $71,459.07 [$70,000 + ($70,000 x 6.34% x 120/365)]

Bank discount rate = 6%

The discount period from October 28 to Nov 22 = 26 days (120 - 94)

Bank discount = Maturity Value x Discount Rate x Discount Period

= $305.41 ($71,459.07 x 6% x 26/365)

Proceeds = Maturity value - Bank discount

= $71,153.66 ($71,459.07 - $305.41)

Thus, by discounting the note receivable at LB Bank at 6%, Lee received $71,153.66 instead of the $71,459.07 it would have received at maturity.

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The expected value if you play this game will be -$0.205.

Let the number of gold, silver, and black marbles be P1, P2, and P3, respectively.

Given, The bag contains,

Number of gold marbles (P1)  = 3

Number of silver marbles (P2) = 5

Number of black marbles (P3) = 26

Also given,

The winning value if a gold marble is selected = $3

The winning value if a silver marble is selected = $2

The losing value if a black marble is selected = $1

Probability = Expected value/ Sum of the total number of events

Probability of picking a gold marble,

P1 = 3/ (3+ 5+ 26)

   = 3/34.

Probability of picking a silver marble,

P2 = 5/ (3+ 5+ 26)

   = 5/34.

Probability of picking a black marble,

P3 = 26/ (3+ 5+ 26)

   = 26/34.

The expected value if you play the game will be,

Value = ($3) P1 + ($2) P2 + (-$1) P3

         = ($9/34) + ($10/34) - ($26/34)

         = - ($7/34)

         = -$ 0.205

Thus, you will face a loss of 0.205 cents.

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Answer: Look at the graph

Step-by-step explanation:

The proof to the above diagram is ∠1 + ∠3 = 180

Supplementary angles are angles whose sum equals 180°

If angle A + angle B = 180°, then both angles are said to be supplementary, meaning angle A is the supplement of Angle B.

∠2 ≅ ∠3. This means ∠2 is approximately equal to ∠3

Also ∠1 + ∠2 = 180°( sum of angles on a straight line)

making ∠2 the subject of the equation

∠2 = 180 - ∠1

But ∠2 ≅ ∠3, which we can say that ∠2 = ∠3

substituting ∠2 for ∠3 in the equation, we have

∠3 = 180 - ∠1

which is further simplified as,

∠1 + ∠3 = 180°

Which  means both angles are also supplementary.

In conclusion,  both angles are supplementary as ∠1 + ∠3 = 180

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The next three terms in the sequence are  -1/16, 1/32, -1/64

The correct option is option C)

What is a sequence?

A sequence is an set of values separated by commas Referring to a generalized rule. They have a relation among them. One of the common sequences are arithmetic progression

We are given a sequence of -1, 1/2, -1/4, 1/8,

We have to describe the next three terms of the sequence

If we notice closely the given sequence is an geometric sequence

Hence they have a common factor known as common ratio

in it we divide a term by its previous term

Hence

Ratio= (1/2)/-1

Ratio = -1/2

Now to find the next terms we multiply this with the last term we get

1/8*-1/2= -1/16

Now Hence the next three terms are -1/16, 1/32, -1/64

The correct option is option c)

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