The roof shingles are arranged so that each row has 7 fewer shingles than the row below it. If the first row has 75 shingles, how many shingles are in the 6th row?

All of the graphs and associated functions and equations serve as examples of quadratic functions.

The locations where the graph's line or curve crosses the x-axis are known as the zeros of a function. The line dividing a graph into equal halves is known as the axis of symmetry.

The minimum or greatest point on a graph is the vertex of a function. If a quadratic function expands upward, its vertex is lowest; if not, it is maximum.

The worksheet is given below:

Using the stated definitions, the worksheet's answers are:

Graph 1

Zeros: -4 and 0

Axis of symmetry: x = -2

Min or Max: Maximum

Vertex: (-2, 4)

Graph 2

Zeros: 2

Axis of symmetry: x = -2

Min or Max: Minimum

Vertex: (-2, 0)

Graph 3

Zeros: -3 and 3

Axis of symmetry: x = 0

Min or Max = Minimum

Vertex: (0, -9)

Graph 4

Zeros: -5 and -3

Axis of symmetry: x = -4

Min or Max = Maximum

Vertex: (-4, -1)

Graph 5

Zeros: 3 and 7

Axis of symmetry: x = 5

Min or Max = Minimum

Vertex: (5, -4)

Graph 6

Zeros: None

Axis of symmetry: x = 24

Min or Max = Minimum

Vertex: (2, 5)

Graph 7

Zeros: 1 and 5

Axis of symmetry: x = 3

Min or Max = Minimum

Vertex: (3, -4)

Graph 8

Zeros: -2 and 0

Axis of symmetry: x = -1

Min or Max = Maximum

Vertex: (-1, 1)

Graph 9

Zeros: 5

Axis of symmetry: x = 5

Min or Max = Minimum

Vertex: (5, 0)

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The length of the side ML of the trapezoid JKML is 58 units.

An open, flat object with four straight sides and one pair of parallel sides is referred to as a trapezoid or trapezium.

A trapezium's non-parallel sides are referred to as the legs, while its parallel sides are referred to as the bases. The legs of a trapezium can also be parallel. The parallel sides may be vertical, horizontal, or angled.

The altitude is the measurement of the angle perpendicular to the parallel sides.

The area of a trapezoid is (1/2)×(sum of the two parallel sides)×height.

We know the midsegment of a trapezoid is half of the sum of the two parallel sides.

Therefore, {(3x + 11) + (10x - 12)}/2 = 45.

3x + 11 + 10x - 12 = 90.

13x - 1 = 90.

13z = 91.

x = 91/13.

x = 7.

So, The length of ML is 10(7) - 12 = 70 - 12 = 58 units.

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here we are given that a 6ft high man is flying a kite with a string of length 100ft at an angle of elevation 52° . We would like to calculate the height of the kite above the ground. For figure refer to the attachment. We would have to make use of trigonometric ratios here as ,

In ∆ ABE ,

[tex]\longrightarrow \sin 52^o = \dfrac{AB}{AE} \\ [/tex]

[tex]\longrightarrow 0.8 =\dfrac{y}{100ft} \\ [/tex]

[tex]\longrightarrow y =0.8(100ft) \\ [/tex]

[tex]\longrightarrow y = 80ft \\ [/tex]

Now the total height above the ground will be ,

[tex]\longrightarrow h = y + h_{man} \\ [/tex]

[tex]\longrightarrow h = (80 + 6)ft\\ [/tex]

[tex]\longrightarrow\underline{\underline{ h = 86\ ft. }} \\ [/tex]

And we are done!

The value of x in the above triangle, according to the supplied assertion, is 21.

The Pythagorean Theorem states that the squared on the tangent line (the side across from the right angle) of a right triangle, or, in standard mathematical notation, a2 + b2, are equal to the numbers on the legs. A triangle is a two-half polygon in geometry that has 3 components and three vertices. The most important attribute of a triangle is that its inside angles sum to 180 degrees. The right triangle angle sum attribute is what is known as.

x+x+7/x+7 = 9+12/12

2x+7/x+7 = 27/12

8x+28 = 7x+49

8x-7x = 49-28

x = 21

Therefore, the of x is 21

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The rise and run may be used to determine the slope. Discover the y-intercept.

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For the given graph, the slope is 2/9, t the U.S. box office revenue in 2018 is 12  billion.

Given a graph depicting approximations of US box office earnings (in billions of dollars) from 2000 to 2012, what would you conclude?

We must calculate the graph's slope and y-intercept.

In order to overcome the issue, we are employing the point-slope form. Two points are obtained from the graph: (x1,y1) = (0,8) and (x2,y2) = (9, 10).

Consequently, slope is m = y2 - y1 / x2 - x1

⇒ 10 - 8/ 9 - 0 = 2/9

This is the graph's straight line's slope.

The point-slope form is given by y-y1 = m. (x-x1)

Meaning: y - 8 = m(x - 0)

The line's equation is then y = 2x/9 + 8, with 8 serving as the y-intercept.

• In this case, the y-intercept provides the beginning value, or 8 when x = 0. Here, the year 2000 is represented by the number 0, and the U.S. box office took in $8 billion in that year.

2 • The graph's straight line shape and slope (m) indicate that the U.S. box office's revenue is rising at a steady rate of $2 billion every two years. 2 year 9 is on the x-axis.

• Using the equation, y = 2, we may get the precise income in any year from 2000 through 2012.

The x axis in the graph corresponds to the year;

hence, the point at x = 0 denotes the year 2000 and the one at x = 12 denotes the year 2012.

In order to get the income for 2018, we must determine the value of y when x equals 18.

The formula is y = 2x/9 + 8

y = 2(18)/9 + 8

y = 12

That is, 12 billion dollars will be made at the U.S. box office in 2018.

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Complete Question -

If Pablo’s goal is to walk a total of 10(3/4) miles each week. He walked 2(1/4) miles on Sunday, 1(3/8) miles on Monday, and 1(7/8) miles on Tuesday , then the equation to find the number of miles he needs to walk is "15/8 + 11/8 + 9/4 + x = 43/4" .

the goal of Pablo to walk in a week is = 10(3/4) = 43/4  ;

the distance he walked on Sunday is = 2(1/4) = 9/4  ;

the distance he walked on Monday is = 1(3/8) = 11/8 ;

the distance he walked on Tuesday is = 1(7/8) = 15/8  ;

let the remaining distance be = x miles ;

So , this situation can be represented in equations as :

⇒ 15/8 + 11/8 + 9/4 + x = 43/4 ;

making the denominator same by taking LCM as 8  ,

we get ;

⇒  15/8 + 11/8 + 18/8 + 8x =  43/4

⇒  15/8 + 11/8 + 18/8 + 8x/8 = 43/4

⇒  15 + 11 + 18 + 8x = 8 × 43/4  ;

⇒  44 + 8x = 86  ;

⇒ 8x = 86-44 = 42 ;

⇒ x = 42/8 = 5.25

Therefore , Pablo still needs to cover 5.25 miles to reach his weekly goal .

The given question is incomplete , the complete question is

Pablo’s goal is to walk a total of 10(3/4)  miles each week. He walked 2(1/4)  miles on Sunday, 1(3/8)  miles on Monday, and 1(7/8)  miles on Tuesday. Write the equation that he can use to find the number of miles he needs to walk the rest of the week to reach his goal ?

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The Ruiz family's laptop has the greater initial resale value. During the first four years, the resale value of the Sawyer family's laptop decreases at an average rate faster than​ the resale value of the Ruiz family's laptop.

The initial resale value of the laptops for both families are the same, as the function f(x) models the resale value for both families and does not differentiate between them.

During the first four years, the average rate of change in the resale value of the Sawyer family's laptop can be found by finding the average rate of change of the function f(x) over the interval [0, 4]. The average rate of change during this interval can be approximated by finding the average rate of change over a smaller interval within [0, 4]. For example, finding the average rate of change over the interval [0, 1] and then multiplying by 4 to find the average rate of change over the entire interval [0, 4].

Correct Question :

The Sawyer and Ruiz families each bought a laptop computer at the same time resale values in dollars of the laptops are modeled by the given function where X is the number of years that each family has owned the laptop.

The ____ family's laptop has the greater initial resale value. During the first four years, the resale value of the Sawyer family's laptop decreases at an average rate ____ the resale value of the Ruiz family's laptop.

1st blank:

Ruiz

Sawyer

2nd blank:

slower than

equal to

faster than​

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The value of n is 1.03.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

Given;

3.2-5.1-3n+5=0

Now,

-3n=-3.2+5.1-5

-3n=-3.1

n=3.1/3

n=1.03

Therefore, the answer of given algebra will be 1.03

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Samuel pay 5.81 for the 3 bottles of juice.

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

We have to given that;

Samuel buys 3 bottles of juice that each have an original price of 2.80.

And, He uses a coupon for 35% off. Then, he is changed sales tax at a rate of 6.5%.

Here, The original cost of 3 bottles of juice = 3 × 2.80

                                                                  = 8.40

Now, He uses a coupon for 35% off.

Hence, The off price = 35% of 8.40

                               = 35/100 × 8.40

                               = 2.94

So, The amount of 3 bottles of juice = 8.40 - 2.94

                                                       = 5.46

And, He is changed sales tax at a rate of 6.5%.

Thus, The sales tax on bottles = 6.5% of 5.46

                                              = 6.5/100 × 5.46

                                              = 0.35

Thus, The actual amount of 3 bottles of juice = 5.46 + 0.35

                                                                    = 5.81

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We can start solving the problem using systems of equations. Let x be the cost of each balloon and y be the cost of each banner. We know from the problem that:

1x + 1y = 3 (the cost of 1 balloon and 1 banner is $3)

5x + 2y = 9 (the cost of 5 balloons and 2 banners is $9)

We can use the first equation to solve for one of the variables in terms of the other, and substitute that into the second equation. Then we can solve for the remaining variable.

From equation 1:

y = 3 - x

We can substitute this into equation 2:

5x + 2(3 - x) = 9

Which simplifies to:

5x + 6 - 2x = 9

3x = 3

x = 1

So each balloon costs $1

We can now substitute x=1 in the first equation:

1*1 + 1y = 3

y = 2

So each banner costs $2

Step-by-step explanation:

Let us assume the cost of

In first case , cost of 1 1 balloon and 1 banner is $3 . We can set up a equation as ,

1*x + 1*y = 3

x + y = 3 . . . . . (i)

In second case, cost of 5 balloons and 2 banners is $9 . So ,

5*x + 2*y = 9

5x + 2y = 9 . . . . . (ii)

From equation i and ii , we have ,

5(3-y) + 2y = 9

15 - 5y + 2y = 9

15 - 3y = 9

3y = 15 -9

3y = 6

y = 2

And we had ,

x + y = 3

x + 2 = 3

x = 3 - 2

x = 1

Hence,

and we are done!

Answer:

To find the function f(x), we need to use the Remainder Theorem. The Remainder Theorem states that if we divide a polynomial by x - a, the remainder will be equal to the value of the polynomial at x = a.

We know that f(x) divided by 3x + 1 leaves a remainder of 7, so we can set up the equation:

f(x) = (3x + 1)(2x^2 + 2x - 9) + 7

Expanding the left side of the equation, we get:

f(x) = 6x^3 + 2x^2 - 27x - 9 + 7

Simplifying, we get:

f(x) = 6x^3 + 2x^2 - 27x + 2

The function f(x) is in standard form.

Answer:

When the function f (x) is divided by 3x – 1, the quotient is 2x² – 3x + 6 a

Step-by-step explanation:

Step 1 Devisor = 3x - 1Quotient = 2x2 - 3x + 6Remainder = 7Dividend = f(

The probability that you win the game on your second draw is 1/1140.

We have an urn containing 17 balls marked LOSE and 3 balls marked WIN. You and the opponent take turns of a random selection of a single ball from the urn without replacement.

The person who picks the third WIN ball wins the game. It does not matter who picked the first two WIN balls.

If you first, we need to find the probability that you will win the game on your second draw.

Here we consider Y: you draw W first, O: opponent draws W first and

Y: you draw W second.

Then,

P(YOY) = P(W W W )

Where W is win.

P(YOY) = 3/20 × 2/19 × 1/18

P(YOY) = 1/1140

Therefore the probability that you win the game on your second draw is 1/1140.

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a^6 + b^6= (a^2 +b^2)(a^4-a^2b^2+b^2) is an identity. The reasoning is done below.

The term "operation" in mathematics refers to the process of computing a value utilizing operands and a math operator. For the specified operands or integers, the math operator's symbol has predetermined rules that must be followed. In mathematics, there are five basic operations: addition, subtraction, multiplication, division, and modular forms.

Given an expression  a^6 + b^6= (a^2 +b^2)(a^4-a^2b^2+b^2) we need to assure if its right or not

Let "x" = a² and "y" = b² thus the equation

x³ + y ³ = ( x + y)(x² + y² - xy)

Take L.H.S.

=> x³ + y³ = (x + y)³ - 3xy (x + y)

» Take (x + y) common

=> (x + y) [(x + y)² - 3xy (1)]

=> (x + y) [(x² + 2xy + y²) - 3xy]

Because (a + b)² = a² + 2ab + b²

=> (x + y) (x² + y² + 2xy - 3xy)

=> (x + y) (x² + y² - xy)

L.H.S. = R.H.S.

Take R.H.S.

=> (x + y) (x² - xy + y²)

=> x(x² - xy + y²) + y(x² - xy + y²)

=> x³ - x²y +xy² + x²y - xy² + y³

=> x³ + y³

L.H.S. = R.H.S.

therefore, a^6 + b^6= (a^2 +b^2)(a^4-a^2b^2+b^2) is an identity .

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Answer:

x = 4 cm

Area= 36 cm2

Step-by-step explanation:

x is the measurement of one side of the triangular shape above (4cm)

Area = (4)(9) = 36 (shaded face)

Hope this helps

A total of 31 child tickets were sold that day.

System of Equations:

Problems with two unknown values require a system of equations containing two variables.

A unique solution is obtained only when the lines formed by the equations intersect at only one point.

Let C be the number of child tickets and A be the number of Adult tickets

Now, like most coin, cost, or earnings problems, you can make a number balance and a money balance and get two equations for the two unknowns defined above:

4C=adults, because four times as many tickets were sold

6.50C+9.80(4C)=1436.80

6.50C+39.2C=652.50

45.7C=1436.80

C=31

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Answer: I got 13x^2+4x+7, I hope this helps

The probability that all three letters are identical is the product of the probability that each individual letter is identical, which is (1/26) * (1/26) * (1/26) = (1/26)^3.

The probability that all three letters selected are identical would be (1/26)^3, assuming that the pool of letters contains an equal number of each letter of the alphabet (a, b, c, ..., z) and that each letter is selected independently and with replacement. This is because there is only a 1 in 26 chance of selecting any given letter on the first draw, and the same is true for the second and third draws. Since all three draws are independent, the probability that all three letters are identical is the product of the probability that each individual letter is identical, which is (1/26) * (1/26) * (1/26) = (1/26)^3.

When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.

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Answer:

450 meters is 0.45 kilometers.

A boat can travel approximately distance 116 miles on 39 number of gallons of gasoline.

To calculate the distance a boat can travel on 39 gallons of gasoline, you must divide the distance (174 miles) by the amount of gasoline (58 gallons), and then multiply the result by the new amount of gasoline (39 gallons).

the distance a boat can travel on 39 gallons of gasoline, you must divide the distance (174 miles) by the amount of gasoline (58 gallons), and then multiply the result by the new amount of gasoline (39 gallons).

174 miles ÷ 58 gallons x 39 gallons = 116.37 miles

Therefore, a boat can travel approximately 116 miles on 39 gallons of gasoline.

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Answer:

433345344 Answer

Step-by-step explanation:

The angle of each measure is:

m<DEC= 129°

m∠BCE = 51°

m∠ADE = 57°

m∠EDB = 123°

m∠DBC = 57°

Angle of measure is the measure of an angle formed by two rays with a common endpoint. Angle of measure is important to many mathematical and scientific fields, including geometry, trigonometry, and physics.

In geometry, angles are used to define shapes and measure the size of an object. For example, angles are used to determine the angles of a triangle, or the angles between the sides of a rectangle. Angle of measure is also important in trigonometry, as it is used to calculate the lengths of sides and angles in a triangle, as well as the area of a triangle.

Angle of measure is also used in engineering, navigation, and surveying. When designing a building or structure, angles are used to determine the strength and stability of the structure, as well as the angles of the beams and walls. In navigation, angles are used to calculate the direction of a ship or aircraft. Finally, in surveying, angles are used to measure the angles between points on a map or a landscape.

Given,

m∠DEC= (12x-3)°, m∠BCE= (7x-26)°, and m∠DAE= 72°

∠DEC+∠BCE = 180°

12x-3+7x-26 = 180°

19x - 29 = 180°

19x = 180+29

x = 209/19

x = 11

Substitute x=11 in m∠DEC= (12x-3)°, we get

m∠DEC= 129°

Substitute x=11 in m∠BCE= (7x-26)°, we get

m∠BCE = 51°

To find m∠ADE,

m∠ADE + m∠DAE + m∠DEA=180°

m∠ADE + 72° + 51° = 180°

m∠ADE = 57°

To find m∠EDB,

m∠EDB + m∠ADE=180°

m∠EDB = 180° - 57°

m∠EDB = 123°

To find m∠DBC,

m∠DBC = m∠ADE are corresponding angles, so

m∠DBC = m∠ADE = 57°

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The price of the stock models exponential is 500, The rate of exponential growth or exponential decay is 19%.

A relation is a function if it has only One y-value for each x-value.

The given function is f(x) = 500(1 − 0.19 )x² models the price of a share of stock over time.

The quantity decreases slowly at regular intervals by a fixed percent.

The price of the stock models exponential is 500.

The rate of exponential growth or exponential decay is 0.19×100=19%

f(x) = 500(1 − 0.19 )x²

f(x)=500(0.81)x²

f(x)=500(0.81)x² is the equivalent function of  f(x) = 500(1 − 0.19 )x²

Hence, The price of the stock models exponential is 500, The rate of exponential growth or exponential decay is 19%.

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The equation relating the number of hours worked and the total amount earned will be y = 14x.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

From the table, the two points will be written as (1.25, 17.50) and (3.75, 52.50). Then the equation of the line is given as,

(y - 17.50) = [(52.50 - 17.50) / (3.75 - 1.25)](x - 1.25)

y - 17.50 = 14(x - 1.25)

y - 17.50 = 14x - 17.50

y = 14x

The equation relating the number of hours worked and the total amount earned will be y = 14x.

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The missing table is attached below.

The final step in solving the inequality is: C. x < 3.

To solve an inequality means to find the possible value of a variable in in inequality statement, which will also make it true.

Given the inequality, –2(5 – 4x) < 6x – 4, we can solve as follows:

Step 1: Apply the distributive property

–10 + 8x < 6x – 4

Step 2: Subtract 8x from both sides

–10 < –2x – 4

Step 3: Add 4 to both sides

–6 < –2x

Step 4: Divide both sides by -2

-6/-2 > -2x/-2

3 > x

x < 3

The final answer of the inequality is: C. x < 3.

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The the height of the rectangle 6.3cm

A rectangle is a polygon of four sides whose opposite sides are equall and parallel

The given parameters that will help us to solve for the height are

the area of a rectangle is the space the rectangle occupies

The area is denoted by :

Area= Lenght * Height

245 = 39 * h

h= 245/39

Height = 6.3cm

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MNOP is a parallelogram and ∠MQN ≅ ∠ORP.  MN ≅ PO. MN ║ PO. Using these statements, we can prove that the ΔMQN ≅ ΔORP.

A quadrilateral with two sets of parallel sides is referred to as a parallelogram. In a parallelogram, the opposing sides are of equal length, and the opposing angles are of equal size. Additionally, the interior angles that are additional to the transversal on the same side. 360 degrees is the sum of all interior angles.

Given that the quadrilateral MNOP is a parallelogram and ∠MQN ≅ ∠ORP.

To prove that ΔMQN ≅ ΔORP, the correct statements are:

MNOP is a parallelogram and ∠MQN ≅ ∠ORP.

MN ≅ PO

MN ║ PO

Using these statements, we can prove that the ΔMQN ≅ ΔORP.

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The value of the bulldozer at year 2.5 is 93593.67 and at year 5 is 66451.16.

A construction company bought a new bulldozer for $125,000. The bulldozer depreciates exponentially and after 2 years the value of the bulldozer is $80,000. What is the value at year 2. 5 and 5Let V0 be the initial value of the bulldozer, and k be the depreciation rate. We know that the value of the bulldozer after 2 years is V2 = V0 * e^(-k * 2) = 80000.

So, k = -ln(V2/V0) / 2.

The value of the bulldozer at year 2.5 can be calculated as:

V2.5 = V0 * e^(-k * 2.5)

The value of the bulldozer at year 5 can be calculated as:

V5 = V0 * e^(-k * 5)

Plugging in V0 = 125000 and k = -ln(V2/V0) / 2, we get:

V2.5 = 125000 * e^(-k * 2.5) = 93593.67

V5 = 125000 * e^(-k * 5) = 66451.16

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The solution to the equation 2-x³ = 4x + 3 is x=1.

What is an equation?

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").

To find the solution to the equation 2-x³=4x+3, we can set the two sides of the equation equal to each other and solve for x.

2-x³ = 4x + 3

x³ - 4x - 1 = 0

To solve this equation, factor it or use the cubic formula.

One possible solution is x = 1, which can be verified by substituting it back into the original equation.

Another way to find the solution graphically, we can plot the graphs of y = 2-x^3 and y = 4x+3 on the same coordinate plane. The points at which the two graphs intersect are the solutions to the equation.

The graph of y = 2-x^3 is a downward facing parabola and the graph of y = 4x+3 is a line with slope 4 and y-intercept 3.

The intersection point of the parabola and the line is the solution x=1

It is not possible to find the other solutions graphically because the parabola doesn't intersect with the line again.

Therefore, the solution is obtained as x = 1.

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Answer:

A. 190-25

Step-by-step explanation:

Answer:

A or B

Step-by-step explanation:

Because 190 - 125 will give you the difference of 190 and 125

The value of the coefficient of the variable 'x' is 3. Then the correct option is C.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

The equation is given below.

(x + 7)(x - 4) = x² + gx - 28

Simplify the equation, then we have

(x + 7)(x - 4) = x² + gx - 28

x² + 7x - 4x - 28 = x² + gx - 28

x² + (7 - 4)x - 28 = x² + gx - 28

3x = gx

g = 3

The value of the coefficient of the variable 'x' is 3. Then the correct option is C.

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