Marin writes the functions m(x) = startfraction 3 x over x + 7 endfraction and n(x) = startfraction 7 x over 3 minus x endfraction. Which equation must be true for m(x) and n(x) to be inverse functions?.

Answer:

The ordered pair that satisfies the system of equations is (7, -1)

Step-by-step explanation:

⭐What is a system of equations?

When we solve for an ordered pair that satisfies the system of equations, we are finding at what point do the equations intersect.

⭐How can we solve a system of equations?

For this problem, I find elimination to be the easiest. I will demonstrate how to use elimination to solve this system of equations.

⭐What is the elimination method?

We have the system: [tex]{ x+7y = 0\\\\2x - 8y = 22[/tex]. Let's eliminate the variable "x".

To do so, multiply the first equation by -2, then add both equations.

[tex]-2(x+7y = 0)\\-2x -14y = 0[/tex]

Now add this new equation with the second equation. This eliminates the x variable.

[tex]-2x - 14y = 0 \\+2x -8y = 22\\\\-22y = 22\\y = -1[/tex]

∴ y = -1

Next, we need to solve for the x variable. To do so, substitute the y variable into one of the equations we added and solve for x.

I will substitute y into the equation [tex]2x - 8y = 22[/tex], but you can also substitute it into [tex]-2x-14y = 0[/tex]

[tex]2x - 8y = 22[/tex]

[tex]2x-8(-1) = 22[/tex]

[tex]2x + 8 = 22[/tex]

[tex]2x = 14[/tex]

[tex]x = 7[/tex]

∴ The ordered pair that satisfies the system of equations is (7, -1)

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Answer:   The final balance is $9,013.73.

The total compound interest is $7,513.73.

Step-by-step explanation:

groceries has a higher population mean annual credit card charge

What is population mean?

A population is the complete set group of individuals, whether that group comprises a nation or a group of people with a common characteristic. In statistics, a population is the pool of individuals from which a statistical sample is drawn for a study.

The population mean can be calculated by the sum of all values in the given data/population divided by a total number of values in the given data/population.

Given that Bank of America’s Consumer Spending Survey collected data on annual credit card  charges in seven different categories of expenditures: transportation, groceries, dining out,  household expenses, home furnishings, apparel, and entertainment (US Airways Attache,  December 2003).

Sample size n =42

Mean difference d = 850

Std dev s = 1125

Point estimate of the difference is 0

95% confidence level would be

= 0A ± tcritical * stderrror

=  A ± 2.021*173.59

= (-350.83 , 350.83)

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Answer:

(- 3, - 7 )

Step-by-step explanation:

given

y = x - 4 ← substitute y = - 7 into the equation and solve for x

- 7 = x - 4 ( add 4 to both sides )

- 3 = x

then point is (x, y ) = (- 3, - 7 )

Answer:

(-3, -7)

Step-by-step explanation:

y=-7

y=x-4

-7 = x - 4  ==> since y=-7 and y=x-4, -7 = x-4

-7 + 4 = x - 4 + 4  ==> solve for x by adding 4 on both sides

-3 = x

x = -3

x=-3, y=-7 ==> (-3, -7)

The number of the students in the sixth grade will be 132 students.

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 proportion of sixth and seventh graders is 11 to 9. In the event that there were 108 seventh graders.

The ratio of the number of students in the sixth and seventh will remain constant.

Let 'x' be the number of students in sixth grade. Then the equation is given as,

x / 108 = 11 / 9

Simplify the equation, then we have

x / 108 = 11 / 9

x = 108 × 11 / 9

x = 12 × 11

x = 132

The number of the students in the sixth grade will be 132 students.

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Before the change maple tree was 240 cm longer than cherry tree when the heights of a maple tree and a cherry tree currently have a ratio of 5:2. if the maple tree grew 20 centimeters, and 20 centimeters was cut off the top of the cherry tree, the ratio of their heights would be 3:1.

One quantity can be expressed as a fraction of another using a ratio, which is a number. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects.

Given,

Current ratio = 5:2

Let y equal the height of the cherry tree, and x represent the height of a maple tree.

x/y = 5/2

New ratio = 3:1

x+20/y-20 = 3/1

Cross multiplying,

x + 20 = 3(y - 20)

x = 3(y - 20) -20

Equating values in x/y = 5/2

3(y-20) - 20/y = 5/2

5y = 2(3y - 60) -20

5y = 6y - 160

y = 160

Now, for value of x,

Equating values in x = 3(y - 20) -20

x = 3(160 - 20) - 20

x = 480 - 60 - 20

x = 400

For the height,

400 - 160

240

Before the change maple tree was 240 cm longer than cherry tree when the heights of a maple tree and a cherry tree currently have a ratio of 5:2. if the maple tree grew 20 centimeters, and 20 centimeters was cut off the top of the cherry tree, the ratio of their heights would be 3:1.

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Step-by-step explanation:

(3-2)^2+y^2=4

(9-4)+y^2=2^2

the power of y and 2 should be cut now

5+y=2

5-2=y

3=y

y=3

:. the area of enclosed by a circle is 3 cm

If the discriminant, b² - 4ac is positive

From the question, we have the following equation of discriminant

The discriminant (d) is calculated as

d = b² - 4ac

The solutions of a quadratic equation are dependent on the following conditions

This means that "d > 0, the quadratic equation has 2 different real solutions" implies that the discriminant is positive

Hence, the complete statement is (b) positive

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The probability that there is at least two 4s in the three throws is 0.05 or 5%

Probability

In statistics, probability deals with the possibility of happening of the events.

Given,

Here we know that the throw a fair die three times. if we observe the first throw is a 4.

And we need to find the probability that there is at least two 4s in the three throws.

According to the given question, we know that the dice is thrown 3 time.

Then the sample space of the given event is 216.

Here we know that the first throw has 4.

And we need to find the probability of getting two 4s in the 3 throws,

So, the possible number of events are.

=> {444, 441, 442, 443, 445, 446, 414, 424, 434, 454, 464}

So, the total possible number is 11.

Then the probability is,

=> 11/216

=> 0.05 or 5%

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Answer:

17

Step-by-step explanation:

Using PEMDAS:

5² + 2(-8 ÷ 2)​

5² + 2(-4)

25 - 8

17

Answer:

See below

Step-by-step explanation:

1).  A = k / (B^3)   <==== this becomes   A = 512/(B^3)  when you use the                                                                               answer from 2).      (below)

2).     When A = 64  and B = 2 :

           64 = k / (2^3)

              64 = k / 8

                   k = 64*8 = 512

Answer:

x = 1 or x = -1

Step-by-step explanation:

The only number square root and get 1 is 1 and -1. Because 2022 is an even number, so -1 will work in this case, and the final answer will be positive 1!

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The solution to the equation are x=a

The given equation is sin (2x) = a and 0 < x < pi/2

Sin(2x) = sin x, 0≤x≤2п  ........................... (eq. 1)

Using the trigonometrical formula,

sin(2x) = sin xcosx

Let us subtract the formula from equation 1

2sinxcosx = sinx

Therefore, 2sinxcosx-sinx = 0

Let us remove common terms to get

sinx(2cox-1)=0

Now, sinx=0

x= 0, [tex]\pi[/tex], [tex]2\pi[/tex]

Also, 2cos x =1

This means that cos x = 1/2

By implication, x=cos⁻¹(1/2)

That is to say that x= [tex]\frac{\pi }{3} , \frac{5\pi }{3}[/tex]

In conclusion, the value of [tex]\pi[/tex] is a as a single integer

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The algebraic form of the statement is b/4 + 7 = 2 and the value of b is -20.

Given the statement; the quotient of a number b and four plus seven is two.

First, we convert the statement into an algebraic equation.

Now, combine the terms and equality sign.

b/4 + 7 = 2

Next, solve for the numerical value of b.

b/4 + 7 = 2

Subtract 7 from both sides

b/4 + 7 - 7  = 2 - 7

Simplify the left-hand side

b/4 = 2 - 7

Subtract 7 from 2

b/4 = -5

Next, multiply both sides by 4

b/4 × 4 = -5 × 4

b = -5 × 4

b = -20

Therefore, the numerical value of b is -20.

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The angles GBD, GBD and G measures 90 , 90, 52 degree respectively.

GB is the diameter given.

AD is the tangent given.

The tangent makes 90 degree angle with diameter.

hence the angle GBD will be : 90°

Similarly, GBA will also be 90°

The angle GBA is given as 38°

Hence the angle G will be = 90 - 38 =52

All points in a plane that are at a specific distance from a specific point, the centre, form a circle. In other words, it is the curve that a moving point in a plane draws to keep its distance from a specific point constant. The radius of a circle is the separation between any point on the circle and its centre.

The radius must typically be a positive integer. A degenerate situation is a circle with radius equal to zero (one point). Except when otherwise specified, this article discusses circles in Euclidean geometry, namely the Euclidean plane.

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The solution for the system of equations would be x = 2 and y = 3.

The general equation of a straight line is -

where -

[m] → is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] → is the y - intercept i.e. the point where the graph cuts the [y] axis.

We have the graph of y = 5 - x.

Refer to the image of the graph attached. It shows the graph of -

and

The common point of intersection will be the solution for the system :

Therefore, the solution is x = 2 and y = 3.

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Therefore the balance after a year comes out to be $3552.80 and the balance comes out to be after compounded annually is $3552.50

Compound interest is the interest on savings that is computed using both the original principal and the interest accrued over time.

It is believed that Italy in the 17th century was where the idea of "interest on interest" or compound interest first emerged. It will accelerate the growth of a sum more quickly than simple interest, which is only applied to the principal sum.

Money multiplies more quickly through compounding, and the higher the

Here,

The Liam deposits $3,500 in a saving account that pays 1.5% interest,

Thus rate=1.5% and principle amount =3500

Therefore it is compounded quartely ,

The balance after year=

C=P[tex]e^{rt}[/tex]

C=3500*[tex]e^{1.5*4}[/tex]

C=3552.80

Therefore the balance after a year comes out to be $3552.80

Therefore the balance comes out to be after compounded annually is

$3552.50

So there is only $0.30 difference between the amounts

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Answer:

  C = (5, 4)

Step-by-step explanation:

You want the coordinates of point C, located 3/4 of the way from A(-4, -2) to B(8, 6).

That point is ...

  C = A +3/4(B -A)

  C = (-4, -2) + (3/4)((8, 6) -(-4, -2))

  C = (-4, -2) + (3/4)(8+4, 6+2) = (-4, -2) + (3/4)(12, 8) = (-4, -2) +(9, 6)

  C = (-4 +9, -2 +6)

  C = (5, 4)

__

Additional comment

Equivalently,

  C = (3B +A)/4 = (3(8, 6) +(-4, -2))/4 = (24 -4, 18 -2)/4 = (5, 4)

The method shown above may be more intuitive. The formula shown here is a result of simplifying the one used above.

When computing the weighted average of the coordinates, the nearest point (B) gets the higher weight (3/4).

Answer:

y = x + 2

Step-by-step explanation:

Use the slope-intercept form:

y=mx+b

M represents the slope of the line

B represents the y-intercept

The factor is -3x(x - 4) and value of x is 4.

Define Algebraic Expression

An expression that includes variables, constants, and algebraic operations is known as an algebraic expression (addition, subtraction, etc.)

Define Factorization

Factorization or factoring consists of writing a number or another mathematical object as a product of several factors, usually smaller or simpler objects of the same kind.

Given expression,

-3x² + 12x

Take -3x common

⇒ -3x(x - 4)

Now, if you want to find the value of x then write it in standard form like this

-3x(x - 4) = 0

Now, find x

x - 4 = 0

x = 4

Hence, the factor is -3x(x - 4) and value of x is 4.

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The vertex form of the equation is in the form of y = a(x-h)^2 + k.

Step 1: Use the formula below to solve for a.

a = -1/4 * (4 - 12) = -1

Step 2: Use the formula below to solve for h.

h = -b/(2a) = 12/(2(-1)) = -6

Step 3: Use the formula below to solve for k.

k = f(h) = -(-6)^2 + 12(-6) - 4 = 36

Therefore, the vertex form of the equation is y = -(x+6)^2 + 36.

A vertex, or particular point, is a place where two or more lines or edges meet in a mathematical object. Angles, polygons, polyhedra, and graphs are where vertices are most frequently seen. Nodes and vertices in a graph are the same thing.

Recall that a parabola's General Form is y = ax2 + bx + c. The x-coordinate of the vertices, which is x = - b/2a, must first be discovered in order to find the vertex from this form. You will use this number to replace x in the parabola equation once you have determined the x-coordinate of the vertex.

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The number of days required to complete his task is 9 days.

What is a graph?

The graph of a relation R is the set of all points (x, y) in a coordinate plane such that x is related to y through the relation R.

Stewart loves playing Genshin Impact so much that he “forgets” to do his schoolwork. It’s really starting to impact his grades and he has 36 overdue assignments. The semester is almost over, and he really needs to improve his grades. He can realistically complete 4 overdue assignments each day.

So he will complete 4 assignments each day and he has to complete the 36 overdue assignments.

The number of days required to do this = 36/4

                                                                  = 9 days.

Hence, the number of days required to complete his task is 9 days. and this relation can be expressed on the graph as

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The sales tax rate for a specific type of wood-frame door priced at $1480 is 25%, or $370.

Percentages are just fractions with a denominator of 100. We use the percent sign (%) beside a number to indicate that it is a percentage. For instance, if you answered 75 questions correctly out of 100 on a test (75/100), you would have received a 75%. A percentage is a relative value that represents one hundredth of a quantity. One percent (symbolized 1%) is a hundredth part; thus, 100 percent represents the entire amount and 200 percent specifies twice the given quantity. A percentage is a fraction of a whole expressed as a number between 0 and 100.

Here,

Sale tax=$370

Price of door=$1480

Sales tax percent=370/1480*100

=25%

The rate of sales tax for a particular type of wood-frame door is priced at $1480 is 25% that is $370.

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Answer:

Let X be the amount Jaheem invested in the first money market, and Y be the amount he invested in the second money market. We can set up the following system of equations to represent the given information:

X + Y = 10000 (1)

0.125X + 0.0825Y = 925 (2)

We can solve this system of equations using any method of your choice, such as elimination or substitution.

Using elimination, we can multiply equation (1) by 0.125 and equation (2) by 10,000 to eliminate Y:

1.25X + 1250Y = 1250000

125X + 82500Y = 9250000

Subtracting the first equation from the second gives us:

124X + 82350Y = 8037500

Y = (8037500 - 124X)/82350

Substituting this expression for Y into equation (1) and solving for X gives us:

X + (8037500 - 124X)/82350 = 10000

X = $7,500

Therefore, Jaheem invested $7,500 in the first money market and $2,500 in the second money market.

Step-by-step explanation:

SELF EXPLANATORY

Answer:

SSA

Step-by-step explanation:

If you have 2 triangles that have 2 congruent sides, and a congruent non-included angle, there is 2 possible values for the third side, so SSA does not work

Answer:

- 2

Step-by-step explanation:

the factors of a difference of square are

a² - b² = (a + b)(a - b)

(1 + [tex]\sqrt{3}[/tex] )(1 - [tex]\sqrt{3}[/tex] ) ← are the factors of a difference of squares , then

(1 + [tex]\sqrt{3}[/tex] )(1 - [tex]\sqrt{3}[/tex] )

= 1² - ([tex]\sqrt{3}[/tex] )²

= 1 - 3

= - 2

Answer:

f(x) / g(x) = x - 1   where x ≠ -1.

Step-by-step explanation:

f(x) / g(x) =   x² - 1 / x + 1

                = (x + 1)(x - 1) / (x + 1)

                = x - 1.

The fencing needed to enclose the garden is equal to the perimeter of the rectangle and it will be 5x + 56.

The perimeter of the rectangle: The sum of all the sides of the rectangle will be known as the perimeter of the rectangle.

Let L be the length and W be the width of the rectangle.

Then the perimeter of the rectangle will be

The perimeter of the rectangle = Sum of all the sides

If the gardener fences in the total rectangular area shown in the illustration instead of just the square area, he will need twice as much fencing to enclose the garden.

From the diagram, the length is 28 + x. And the width is x. Then the perimeters of the rectangle will be

P = 28 + x + 28 + x + x + x + x

P = 56 + 5x

The fencing needed is equal to the perimeter and will be 5x + 56.

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