What is the exact solution to the system of equations shown on the graph? A. (-1 3/5, 4 1/5) B. (-1 1/5, 4 3/5) C. (-1 5/6, 6 2/3) D. (-1 1/5, 4 5/6)

[tex]~~~~~~~~~~~~ \textit{Amortized Loan Value} \\\\ pymt=P\left[ \cfrac{\frac{r}{n}}{1-\left( 1+ \frac{r}{n}\right)^{-nt}} \right]\implies pymt=P\left[ \cfrac{\frac{r}{n}}{1-\left(\frac{n}{n+r}\right)^{nt}} \right][/tex]

[tex]~~~~~~ \begin{cases} P= \begin{array}{llll} \textit{original amount deposited}\\ \end{array}\dotfill & \begin{array}{llll} 48000 \end{array}\\ pymt=\textit{periodic payments}\\ r=rate\to 6.1\%\to \frac{6.1}{100}\dotfill &0.061\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &6 \end{cases}[/tex]

[tex]pymt=48000\left[ \cfrac{\frac{0.061}{12}}{1-\left(\frac{12}{12+0.061}\right)^{12 \cdot 6}} \right] \\\\\\ pymt=48000\left[ \cfrac{\frac{61}{12000}}{ ~~ \frac{18249137}{59666181} ~~ } \right] \implies {\Large \begin{array}{llll} pymt \approx 797.77 \end{array}}[/tex]

well, Linda is paying that much every month for 6 years or namely 72 months, so the total for those 72 months will simply be 72(797.77) ≈ 57439.44.

hmmmm what's the interest?  well, if we simply subtract the principal from the total amount Linda is paying that'll be 57439.44 - 48000 ≈ 9439.44.

The equation which represents the solution for x in terms of a as required is; Choice 4; 2a + 1.

As evident in the task content; the given equation is to be solved for the variable, x in terms of a;

( x - 1 ) / 2 - a / 4 = 3a / 4

( x - 1 ) / 2 = 3a / 4 + a / 4

(x - 1) / 2 = a

x - 1 = 2a

x = 2a + 1.

Ultimately, the answer choice which correctly expresses x in terms of a is; Choice 4; 2a + 1.

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When the amount is accrued by the interest given for the number of months given, the amount becomes $ 1, 231. 56

The accrued amount when given the amount, the interest rate, and the number of periods, can be found by using the future value formula which is :

= Amount x ( 1 + rate ) ^ number of periods

The amount is $ 1, 200

The rate is given as an annual rate and so needs to be converted to a periodic rate in months :

= Rate / Number of months in year

= 3. 9 % / 12

= 0. 325 %

The future value becomes :

= 1, 200 x ( 1 + 0. 325 %) ⁸

= 1, 200 x 1. 00325 ⁸

= 1, 200 x 1.026297680

= $ 1, 231. 56

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The proof to show that ΔTSV ≅ ΔRSV, given that V is the midpoint of TR.

Two right angled triangles are said to be congruent if they have the same corresponding properties when compared.

A midpoint is said to divide a given line into two equal parts. So that the measure of length of the two parts are exactly the same. It may be determined by bisecting the line.

The following is the proof that ΔTSV ≅ ΔRSV;

<RSV ≅ <TSV                                   (definition of an angle bisector)

<RVS ≅ <TVS                                   (definition of right angle)

RS ≅ TV                                            (sides of congruent triangles)

RT = RV + VT                                    (addition property of a line bisector)

RV ≅ VT                                            (definition of a midpoint)

Therefore it can be deduced that;

ΔTSV ≅ ΔRSV                              (Side-Angle-Angle congruency theorem)

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The Correct answer is option b. The proportion of this population that lies at or below x=87 is 0.3085.

We can conclude that the proportion of this population that lies at or below x=87 is 0.6915 because the graph shows that the area under the curve to the left of x=87 is 0.3085. However, we cannot conclude that the proportion of this population that lies at or below x=87 is 0.3085 because this statement is contradictory to the information provided in the graph.

The area under the curve to the left of x=87 represents the proportion of the population that lies at or below x=87, so it cannot also be equal to the proportion of the population that lies at or above x=87.

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Answer:

A-There is no solution

Step-by-step explanation:

if you put 2x-6 into a calculator you'll get -12 and if you add that to 6x2 you'll end up with zero.

if you do 6x-6 you get -36 add that to 36 you'll get zero again

so (-6,2) is incorrect

if you do 2x3+6x0 you get you'll get 6

if you do 6x2+18x0 you get 12

so (3,0) is incorrect

it wouldn't be infinitely many solutions either because the equations would have to be the same therefore the answer is

A-there is no solution

That's the best I can explain it sorry if it's confusing.

also, the X in this is for the multiplication in case you're confused have a nice day/night :)

Note that there is no solution for the system of equations given above (Option A)

A set of simultaneous equations is a finite collection of equations for which common solutions are sought in mathematics. It is also known as a system of equations or an equation system.

Given:

2x + 6y = 12 .......................1

6x + 18y = 18 ......................2

We will attempt to solve the above system of equations using Substitution Method.

In equation (1) , makes x the subject of the expression. Thus,

2x + 6y = 12

2x + 6y + (−6y) = 12+ (−6y) (Add -6y to both sides)

2x = −6y + 12

2x/2 = -6y + 12/2 (Divide both sides by 2); thus

x = -3y + 6  ..........................(3)

Substitute the above expression 3 into (2) above. That is:

6x + 18y = 18

6(−3y+6) + 18y = 18

-18y + 36 + 18y = 18

36 = 18 (Add -36 to both sides);

0 = - 18

Since the above expression is illogical, that is -18 ≠ 0, therefore, we must conclude that the above problem has no solution.

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The equation in completing the square method is x= 3.15 or -3.15

Completing the square is a method of solving a quadratic equation where by the left hand side of the equation is made a perfect square.

The given equation is y=x^2+x-8

Using the completing the square method, take the constant to the RHS to get

x²+x=8

Then make the LHS a perfect square

x²+x+1/4 = 8+1/4

Factorize the RHS and simplify RHS to have

x²+5/4x +1/4=(32+1)/4

Factorize (x²+1/4c)² = 32/4

(x + 1/4)= ±√33/4

x+1/4 =±√8.25

x=--.025+2.9 or -0.25-2.9

x = 2.65 or -3.15

Thertefore, by completing the square x = x = 2.65 or -3.15

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The category of the numbers are

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

50 1/3 divided 50 1/4

This means that the individual numbers are

50 1/3 and 50 1/4

From the above numbers, we have

The greater the denominator, the smaller the number

This means that:

The greater number is 50 1/3, the smaller number is 50 1/4 and the numbers are close to one another

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Answer:

Step-by-step explanation:

The correct two - way frequency table for the data on High School Students, and the kind of band they want to play at the school dance, is:

                                                     Rap          Rock           Country      Total

Grades 9 - 10                                40              30                55              125

Grades 11 - 12                                60              25                35              120

Total                                              100              55                90             245

Option A is therefore correct.

In a two-way frequency table, there will be totals for both the rows and the columns.

The totals for the rows in this instance are:

Grade 9 - 10 totals :

= 40 + 30 + 55

= 125

Grade 11 - 12 :

= 60 + 25 + 35

= 120

The totals for the columns are:

Rap totals :

= 40 + 60

= 100

Rock :

= 30 + 25

= 55

Country :
= 55 + 35

= 90

Two-way frequency tables allow for us to be able to conclude on the event described by looking at totals from both the columns and the rows. This gives a clearly understanding on preferences and categories.

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Answer:2  hope this helps it was right on my test

Step-by-step explanation: it was right on the test i took

Answer:

y = -1x + 4

Step-by-step explanation:

First find the slope (m):

m = (0-6)/(4-(-2)) = -6/6 = -1

y = mx + b

Plug one of the points into the equation: (pick (4,0))

0 = -1(4) + b

b = 4

Now you have the complete equation:

y = -1x + 4

The probability the second card drawn is also a heart is 12/51.

Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.

We know that, probability of an event = Number of favourable outcomes/Total number of outcomes

1) The probability the first card drawn is a heart is 13/52= 1/4. Since that heart is NOT returned to the deck, there are now 51 cards, 12 of them hearts. The probability the second card drawn is also a heart is 12/51. Since that heart is NOT returned to the deck there are now 50 cards, 11 of them hearts.

2) You draw cards with replacement from a standard deck until you have drawn 4 black cards.

Here, 22/48

= 11/24

4) The probability that the kth face card is drawn on the xth turn

Probability =k/x

Therefore, the probability the second card drawn is also a heart is 12/51.

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The graph has a y-intercept at (0, 1) and is decreasing over the interval. Then the correct option is C.

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

The exponential function is given below.

f(x) = (1/3)ˣ

The value of the function at x = 0 will be given as,

f(0) = (1/3)⁰

f(0) = 1

As the value of the variable 'x' increases, then the value of the variable 'y' decreases. Then the function is a decreasing function.

Then the correct option is C.

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The percent decrease in pay, given the amount the staff started making after the merge, is 10 %

To find the percent decrease in pay, you first need to find the absolute decrease in pay, since the boutique merged with another store. This absolute decrease is:

= Historical pay - Current pay

= 10 - 9

=  $ 1

The percentage decrease in pay would then be :

= Absolute decrease in pay / Historical pay x 100 %

= 1 / 10 x 100 %

= 10 %

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The value of p is 7 and the median number of liters is 18.

Simply put, the mean is the average of the values in the given set.

When a collection of data is supplied and ordered in order, the median is the middle value.

Given that the mean number of liters is:

The mean is represented as follows:

[tex]m = \frac{16(11) + 17(10) + 18(p) + 19(4) + 20(8)}{11+10+p+4+8} = 17.7[/tex]

[tex]m=\frac{582+18p}{33+p} = 17.7[/tex]

[tex]582 +18p = 17.7(33+p)[/tex]

[tex]582 +18p = 584.1 + 17.7p\\18p-17.7p = 584.1 - 582\\0.3p = 2.1\\p = 7[/tex]

The value of p is 7.

Now arrange the table in ascending order for the motorist.

The median represents the median value and hence the median is 18.

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Sales increased until 2000 and then generally decreased. Hence, option C is the most appropriate answer to this question.

From the given graph,

The 0 on the x-axis denotes the year 1997, the 1 on the x-axis denotes 1998, and so on.

We can clearly see that the graph is neither steadily increasing nor steadily decreasing. Hence, options A and B are ruled out.

Sales never remained steady from 1997 to 2009 since the graph showed upward and downward movements. Hence, option D is wrong.

We can see the Graph is moving up from 1997 to 2000 and then moving down from 2000 to 2009.

Thus, sales increased from 1997 to 2000 and decreased from 2000 to 2009, so we can say they generally decreased after 2000.

Hence, option C is the correct answer.

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The complete question is -

Based on the graph, which of the following best describes the general trend in music album sales from 1997 through 2009?

A) Sales generally increased each year since 1997.

B) Sales generally decreased each year since 1997.

C) Sales increased until 2000 and then generally decreased.

D) Sales generally remained steady from 1997 through 2009.

The two teams whose win/loss records are proportional will be team 1 and term 2.

A ratio is a group of sequentially ordered numbers a and b expressed as a/b, where b is never equal to zero. When two objects are equal, a statement is said to be proportional.

The table below shows the number of all-time wins and losses for three basketball teams.

                   Wins          Losses

Team 1.      2,222           1,916

Team 2.      1,392           928

Team 3.     2,289          1,526

The ratio of the number of wins to losses for each team is calculated as,

For team 1, then we have

⇒ 2,222 / 1,916

⇒ 1.1597

For team 2, then we have

⇒ 1,392 / 928

⇒ 1.5

For team 3, then we have

⇒ 2,289 / 1,526

⇒ 1.5

The two teams whose win/loss records are proportional will be team 1 and term 2.

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Answer:negative it would be -2

Step-by-step explanation:

Answer:

negative.

Step-by-step explanation:

36/-18=-2

Answer:

A -1/4

B 1/6

Step-by-step explanation:

To find the slope from (-7, 5) to (-3, 4), we can use the slope formula:

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

Substituting in the coordinates of the two points, we get:

slope = (4 - 5) / (-3 - (-7))

= (-1) / 4

= -1/4

Therefore, the slope from (-7, 5) to (-3, 4) is -1/4.

To find the slope from (-3, 4) to 3,5, we can use the slope formula again:

slope = (5 - 4) / (3 - (-3))

= 1 / 6

= 1/6

Therefore, the slope from (-3, 4) to 3,5 is 1/6.

The slopes from Parts A and B tell us that the relationship between all the points in the table is that the y-values are increasing as the x-values increase, but the rate of change is different between the two pairs of points. Specifically, the y-values are increasing more quickly (at a slope of 1/6) as the x-values increase from (-3, 4) to 3,5 than they are (at a slope of -1/4) as the x-values increase from (-7, 5) to (-3, 4).

Answer:

Disagree with Chen

Explanation below

Step-by-step explanation:

The vertex of a quadratic function is either the minimum or maximum of that function.

We can find the value of x for which the minimum or maximum occurs by differentiating the  function with respect to x, setting the differential to 0 and solving for x.

We have

[tex]f(x) = ax^2+bx+c = 0[/tex]

Differentiating with respect to x we get

[tex]f'(x) = 2ax+b[/tex]

Setting this first derivative to 0 gives us
[tex]2ax+b =0[/tex]

[tex]2ax = -b\\[/tex]

[tex]x = -\dfrac{b}{2a}[/tex]

So the vertex will occur at

[tex]x_v = -\dfrac{b}{2a}[/tex]

Substitute this value of [tex]x _v[/tex]into the original function to get the corresponding value of [tex]y_v[/tex] for the vertex

[tex]f(x_v) = a\left(-\dfrac{b}{2a}\right)^2 +b\left(-\dfrac{b}{2a}\right) + c\\\\\\= a\left(\dfrac{b^2}{4a^2}\right) - \dfrac{b^2}{2a} + c\\\\\\= \dfrac{b^2}{4a} -\dfrac{b^2}{2a} + c\\\\\\[/tex]

[tex]\dfrac{b^2}{4a} -\dfrac{b^2}{2a} = -\dfrac{b^2}{4a}\\\\[/tex]

giving us

[tex]f(x_v) = -\dfrac{b^2}{4a} + c\\\\[/tex]

The right hand side can be simplified by multiplying throughout by 4a giving

[tex]f(x_v) = \dfrac{-b^2 + 4ac}{4a}\\\\\\[/tex]

which can be re-written as

[tex]f(x_v) = -\dfrac{b^2-4ac}{4a}[/tex]

But this is nothing but the y-coordinate of the vertex ie [tex]y_v[/tex]

So the vertex will occur at the point

[tex]\left(-\dfrac{b}{2a}, -\dfrac{b^2-4ac}{4a}\right)[/tex]

Chen is therefore incorrect

The dimensions of the deck should be increased by 5 feet each

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

Length = 20 feet

Width = 25 feet

So, the area is

Area = 20 * 25

Evaluate

Area = 500

When increased by 50%, we have

(20 + x) *(25 + x) = 500 * 1.50

Evaluate

(20 + x) * (25 + x) = 750

Express 750 as 25 * 30

So, we have

(20 + x) * (25 + x) = 25 * 30

This means that

20 + x = 25

25 + x = 30

Solve for x

x = 5 and x = 5

This means that

Increment = 5

Hence, the lengths should be increased by 5 feet

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Answer: 5x+45=60 or 45x+5=60

Step-by-step explanation:

The sum of five times a number= 5x

times a number= x or n

is= equals sign

When we put it all together we get 5x+45=60

edit: If that is wrong try 45+5x=60

Hope this helps :)

Answer: 336

Step-by-step explanation:

6 x 8 = 48 x 7 =336

Answer:

1.8 × 10-6.

Step-by-step explanation:

The number of steps that Bert actually took while mowing the lawn is given as follows:

1875 steps.

The number of steps that Bert actually took while mowing the lawn is obtained applying the proportions in the context of this problem.

His prediction was 4% lower than the actual number of steps he took, hence we have that 100 - 4 = 96% of the total number x is equivalent to 1800 steps.

Hence the equation that is used to obtain the value of x is defined as follows:

0.96x = 1800

x = 1800/0.96

x = 1875.

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Answer:2/10

Step-by-step explanation:there are 2 sailor hats out of 10 hats meaning every 10 hats you pull you will get 2 sailor hats so this makes 2/10 correct