solve for x. each figure is a parallelogram

The value of the equation from binomial expansion is

a) A = 81x⁴ + 108x³y + 54x²y² + 12xy³ + y⁴

b) B = x⁶ - 12x⁵y + 60x⁴y² - 160x³y³ + 240x²y⁴ - 192xy⁵ + 64y⁶

The general term of the binomial expansion is Tr+1 = nCr x^n-r y^r . Here the coefficient values are found from the pascals triangle or using the combinations formula, and the sum of the exponents of both the terms in the general term is equal to n.

( x + y )ⁿ = ⁿCₐ ( x )ⁿ⁻ᵃ ( y )ᵃ

Given data ,

Let the equation be represented as A

Now , the value of A is

a)

A = ( 3x + y )⁴

On simplifying the equation , we get

From binomial expansion , ( x + y )ⁿ = ⁿCₐ ( x )ⁿ⁻ᵃ ( y )ᵃ

Substituting the values in the equation , we get

( 3x + y )⁴ = ⁴C₀ ( 3x )⁴ ( y )⁰ + ⁴C₁ ( 3x )³ ( y ) + ⁴C₂ ( 3x )² ( y )² + ⁴C₃ ( 3x ) ( y )³ + ⁴C₄ ( 3x )⁰ ( y )⁴

On further simplification , we get

( 3x + y )⁴ = 81x⁴ + 108x³y + 54x²y² + 12xy³ + y⁴

Hence , the equation is A = 81x⁴ + 108x³y + 54x²y² + 12xy³ + y⁴

b)

B = ( x - 2y )⁶

On simplifying the equation , we get

From binomial expansion , ( x + y )ⁿ = ⁿCₐ ( x )ⁿ⁻ᵃ ( y )ᵃ

Substituting the values in the equation , we get

( x - 2y )⁶ = ⁶C₀ ( x )⁶ ( -2y )⁰ + ⁶C₁ ( x )⁵ ( -2y ) + ⁶C₂ ( x )⁴ ( -2y )² + ⁶C₃( x )³(-2y)³ + ⁶C₄ ( x )² ( -2y )⁴ + ⁶C₅ ( x )¹ ( -2y )⁵ + ⁶C₆ ( x )⁰ ( -2y )⁶

On further simplification , we get

( x - 2y )⁶ = x⁶ - 12x⁵y + 60x⁴y² - 160x³y³ + 240x²y⁴ - 192xy⁵ + 64y⁶

Hence , the equation is

B = x⁶ - 12x⁵y + 60x⁴y² - 160x³y³ + 240x²y⁴ - 192xy⁵ + 64y⁶

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The system of equations has at least one solution if the determinant of the coefficient matrix is not equal to zero.

A system of linear equations is a set of two or more linear equations with the same variables. These equations can be solved to find the values of the variables that satisfy all the equations simultaneously.

In this problem, we have a system of three linear equations: x + 2y + 3z = a, 4x + 5y + 6z = b, and 7x + 8y + 9z = c.

The goal is to find all the points (a, b, c) in space for which the system has at least one solution.

To find the points (a, b, c) in space, we need to find out if the system of equations is consistent or inconsistent. If the system is consistent, it means that there exists at least one solution to the system of equations.

This can be determined by finding the determinant of the coefficient matrix, which is the matrix formed by the coefficients of the variables in the system of equations.

If the determinant is not equal to zero, then the system is consistent, and it has at least one solution.

This means that the points (a, b, c) in space are those for which the system of equations is consistent and has a solution.

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Answer:

2300000

Step-by-step explanation:

This might be written as x2-25x-2200 = 0, since the park's area is 2200 m2, and its length is.xm.

A rectangle is a polygon with four direction perpendicular in Euclidean plane geometry. You may also refer to it as an equiangular quadrilateral, meaning that every one of its vertices are equal. A straight angle may also present in the parallelogram. Rectangles with four evenly sized sides are called squares. Four 90º vertices and equivalent parallel sides make up a quadrilateral with the characteristics of a rectangle. As a result, it's also known as a georeferencing rectangle. A rectangle is also referred to as a parallelogram since its separate angles are parallel and equal.

given

Park's rectangular length is x meters.

Park width is equal to (x-25)m since width is 25 m shorter than length.

The park has a 2200 m2 area.

Rectangle's area is known to be length times breadth.

Therefore;

x*(x-25)=2200 about division x²-25x = 2200

This might be written as x2-25x-2200 = 0, since the park's area is 2200 m2, and its length is.xm.

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Answer:

first car: 25 gallons

second car: 40 gallons

Step-by-step explanation:

1) 35 miles/gallon                           consumption=distance/volume

2) 40 miles/gallon                           distance=consumption*volume

2475 miles = d1 + d2

                   = 35*v1    +   40*v2

v1 + v2 = 65

v2 = 65 - v1  

2475 = 35*v1 + 40*(65 - v1)

2475 = 35*v1 + 2600 - 40*v1  /-2600

-125 = -5*v1

v1 = 25 gallons

v2 = 65 - v1

v2 = 40 gallons

The area of the shaded shape is 60 [tex]m^{2}[/tex].

This question uses the area formula for rectangles, which states that the area of a rectangle is equal to its length multiplied by its width.

The formula for the area of a rectangle is A = lw, where l is the length of the rectangle and w is the width of the rectangle

To work out the area of the shaded shape, we need to calculate the area of the rectangle (5m x 12m) and subtract the area of the smaller rectangle (8m x 9m).

The area of the rectangle = 5m x 12m = 60[tex]m^{2}[/tex]

The area of the small rectangle = 8m x 9m = 72[tex]m^{2}[/tex]

Therefore, the area of the shaded shape = 60[tex]m^{2}[/tex] - 72[tex]m^{2}[/tex] = -12[tex]m^{2}[/tex]

The answer is 60[tex]m^{2}[/tex].

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Answer:

The percentage error in x can be calculated as follows:

Percentage error = (Estimated value - Actual value) / Actual value * 100

Let x be the actual value and y be the estimated value such that y > x.

Percentage error = (y - x) / x * 100

This formula calculates the absolute error in terms of a percentage of the actual value.

Answer:

hundreds

Step-by-step explanation:

Answer:

j(x) = f(g(x)) = f(0.25x) = 0.75x - 5

The number which describes the average change in weight per day of Ignacio is equal to 0.4 pounds per day.

Number of days Ignacio done the dieting is equal to 30 days

Total weight lost by Ignacio in 30 days = 12 pounds

Let 'x' be the change in weight per day of Ignacio after dieting.

Weight lost in 30 days = 12 pounds

Average weight change per day is:

⇒ 1 day = ( 12 / 30 )  pounds per day

⇒ 1 day = ( 2/ 5 ) pounds per day

⇒ 1 day = ( 0.4 ) pounds per day

Therefore, the average weight change per day by Ignacio is equal to 0.4pounds per day.

The above question is incomplete, the complete question is:

Write a numerical statement to represent the problem. Then simplify the numerical expression to answer the question. After dieting for 30 day, Ignacio has lost 12 pound. What number describe his average weight change per day?

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The value of y if (1, y, −9) is perpendicular to vector v is  38/5.

Given vector v = 2i - 5j - 4k and vector c = 1i + yj - 9k

In the question, we are told that we need to find y if vector v and vector c are perpendicular. So, if two vectors are perpendicular their dot product is zero

So,  vector v.vector c = 0

(2i - 5j - 4k ).(i + yj - 9k)  = 0

                    2(1) - 5(y) - 4(-9) = 0

                           2 - 5y + 36 = 0

                                    5y = 38

                                      y = 38/5

Hence, the value of y is 38/5.

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Word problem with steps for linear equation is given below.

An equation containing variables with its highest power as one is called linear equation.

Question:

Mother is as five times as old as daughter. After 3 years, the mother will be four four times as old as her daughter. What are their present age?

Solution

Let x  represents the age  daughter.

Mother is as five times as old as daughter. i.e., 5x

After 3 years, the mother will be four four times as old as her daughter.

⇒5x+3=4(x+3)

5x+3=4x+12

⇒5x-4x=12-3

⇒x=9.

Their present age of daughter is 9 and mother is 5*9=45.

Hence, present age of mother and daughter is 45 and 9 respectively.

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Answer:

3:10

Step-by-step explanation:

In order to find the ratio of red to green sweets, we first need to find the ratio of yellow to green sweets. We know that the ratio of yellow to green is 1:5 and we also know that the ratio of red to yellow is 3:2.

We can use this information to find the ratio of red to green by cross-multiplying the ratio of red to yellow and the ratio of yellow to green.

So (3:2) x (1:5) = (3:10)

This means the ratio of red to green is 3:10.

Alternatively, we can find the ratio of red to green by using the following formula:

(red:yellow) x (yellow:green) = (red:green)

So (3:2) x (1:5) = (3:10)

The ratio of red to green is 3:10.

Answer:

Step-by-step explanation:

The ratio of red : yellow = 3:2 and yellow:green = 1:5

So, the ratio of red : yellow : green = 3:2:5

To find the ratio of red: green, we can find the ratio of red : yellow : green and then divide the red and green portions.

So, the ratio of red: green = (3/(3+2+5)) : (5/(3+2+5)) = 3/10 : 5/10 = 3:5

Answer:

Salvador has traveled 584 - 396 = 188 kilometers so far.

Number of ml of 40% sugar = x = 1000mL

Number of ml of 85% sugar used = y = 800mL

A general rule is that the algebraic expression should take any of the following forms: addition, subtraction, multiplication, and division. Bring the variable to the left side and the other values to the right side in order to find the value of x. To determine the answer, simplify the values.

Let the number of ml of 40% sugar be x and 85% sugar used be y

System of equations is given as:

x + y = 1800mL ....... (1)

x = 1800 - y

40% × x + 85% × y = 60% × 1800mL

0.4x + 0.85y = 1080.... (2)

We substitute 1800 - y for x in (2)

0.4(1800 - y) + 0.85y = 1080

simplifying the above equation, we get

720 - 0.4y + 0.85y = 1080

- 0.4y + 0.85y = 1080 - 720

0.45y = 360

y = 360/0.45

y = 800mL

Solving for x

x = 1800 - y

substitute the value of y in the above equation, we get

x = 1800 - 800

x = 1000mL

Therefore, the number of ml of 40% sugar = x = 1000mL

Number of ml of 85% sugar used = y = 800mL.

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Answer: Graph A is your answer

Step-by-step explanation:

Graph A becuase since it makes the same bobble-heads each hour and in 2 hours it made 120 then it makes 60 an hour. So 60x5 is 300 so Graph shows the relationship between the amount of time the machine runs and the number of bobble-head toys built.

Answer:

the 45 tickets

Step-by-step explanation:

In the 20 tickets deal, you'll spend USD 1.333333333333333 per ticket; in the 45 tickets deal, you pay USD 0.6 per ticket.

Answer: The last option.

Step-by-step explanation:

         The statement that can be used to prove that vertical angles ∠1 and ∠3 are congruent is;

             m∠1 + m∠2 = m∠2 + m∠3

       This is because we know that m∠1 + m∠2 is a straight line and that m∠2 + m∠3 is a straight line. Straight lines are equal to 180 degrees, so the vertical angles must be congruent.

The function f(x) is 3/x³ if f'(x) is 1/x²

Given that,

f'(x) is 1/x²

To find : f(x)

Differentiation is the opposite of integration. In other words, reversing the differentiation process merely results in integration. The example below demonstrates it:: y = x2 => dy/dx = 2x. So, ∫ (dy/dx) dx = ∫ 2x dx = x2 together represent the integration of the function with respect to the  x.

f(x) ---> differentiation  ------> f'(x)

f'(x)---> integration ------> f(x)

f(x) = ∫ f'(x)

f(x) = ∫ 1/x²

f(x) = 3/x³

Therefore, function f(x) is is 3/x³ if f'(x) is 1/x² .

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The diameters is 49​ be the circumference of the circle is 154 cm.

When it comes to geometry, a circle's or ellipse's circumference is its perimeter. In other words, the circumference would be the length of the circle's arc if it were opened out and straightened out to a line segment. The radius surrounding any closed figure is known as its perimeter more generally.

The distance in a straight line around a circle is known as its circumference. Or, to put it another way, the circumference of a circle is the length of a straight line formed by opening up the circle.

A circle's perimeter is referred to as its circumference. By calculating the length it would take to walk around the world, we may determine the size of the earth.

Given : Diameter of the circle [tex]$=49 \mathrm{~cm}$[/tex] and value of [tex]$\pi=\frac{22}{7}$[/tex]

The circumference of the circle is given by [tex]$C=2 \pi r$[/tex] or in the form of a diameter the circumference of the circle is [tex]$C=\pi d$[/tex]

Now, we have given [tex]$\mathrm{d}=49 \mathrm{~cm}$[/tex] and value of [tex]$\pi=\frac{22}{7}$[/tex]

Substitute the value in the formula,

[tex]$& C=\pi d \\[/tex]

substitute the values in the above equation, we get

[tex]$& C=\frac{22}{7} \times 49 \\[/tex]

simplifying the equation, we get

C = 22 × 7

C = 154 cm

Therefore, the circumference of the circle is 154 cm.

The complete question is:

Find the circumference of circle whose diameter is 49cm, pi = 22 by 7

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Answer:

I think the y= (-7)

The following equation is m=d-10+k×i represent the total amount in account(m) in dollar.

Although the question does not specify the options, but I have specified my answer as follows:

Given:

The equation representing the total amount in the account, m, when starting with d dollars and being charged a 10$ fee.

Account Opening Charges: $10

Starting amount: $d

The total amount in the account: $m

Let us say the depositor deposits an amount $k for 'i' number of months

Banks deduct their charges from the account balance itself, hence account opening charges are deducted from the bank balance.

I have assumed an amount $k invested every month. You can remove that term as per the requirement of the question.

The total amount at a point in time = starting amount - Account Opening Charges + monthly deposit till that time

⇒m=d-10+k×i

This equation shows that the total amount in the account will be equal to the initial deposit minus the fee charged by the bank.

Therefore, the following equation is m=d-10+k×i.

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The measure of arc FQ is given as follows:

155º.

The measure of arc FQ is obtained applying the two secant theorem in the context of this problem.

From the theorem we have that the angle of 40º represents half the difference between the angle measures of arcs FQ and TR = 75º.

Applying the two secant theorem, the angle measure of arc FQ is given as follows:

(FQ - 75)/2 = 40

FQ - 75 = 80

FQ = 75 + 80

FQ = 155º.

Meaning that the last option represents the correct option in the context of this problem.

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Applying the two-tangents theorem, the value of x is: 5.

The Two-Tangents Theorem says that if a single point outside a circle is used to draw two tangent lines, they will have the same length.

Since point J is formed by the two tangents, KJ and MJ, therefore:

KJ = MJ

Substitute:

4x + 7 = 7x - 8, find x

Combine like terms:

4x - 7x = -7 - 8

-3x = -15

-3x/-3 = -15/-3

x = 5

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The equation 120(b - 0.75) = 60 can you use to find the amount of money, b, smart start normally charges for a blue ribbon

Ms. Avila ordered 120 blue ribbons from the smart start school supplier.

Smart start reduced the price of each blue ribbon by $0.75.

The total came to $60.

To express the problem in equation we have to read the question carefully and write the equation according to question.

Let the price of 1 blue ribbon = b

If he reduce the price by 0.75, then the price of blue ribbon = (b - 0.75)

She buy total blue ribbons = 120

So the price of 120 blue ribbons = 120(b - 0.75)

But the total cost is $60.

So the equation is:

120(b - 0.75) = 60

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The time when the projectile has an instantaneous velocity of zero is a = 10 seconds.

The instantaneous velocity of a projectile at time t can be found by taking the derivative of its position function with respect to time. The velocity function is given by:

v(t) = ds(t)/dt = -32t + 320

The time at which the projectile has an instantaneous velocity of zero is when the velocity function is equal to 0. We can find this time by solving the equation:

-32t + 320 = 0

32t = 320

t = 10

Therefore, the time at which the projectile has an instantaneous velocity of zero is a = 10.

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--The given question is incomplete; the complete question is

"A projectile is fired vertically upward and has a position given by s(t) = -16T^2+320t+336 for 0 ≤ t ≤ 21.

Identify the time at which the projectile has an instantaneous velocity of zero; call this time = a."--

Answer: x/4+2=5

Step-by-step explanation:

Step-by-step explanation:

The data displayed below is numerical data.

Tally Chart:

10 |

19 |

17 |

14 |

11 |

18 |

16 |

17 |

18 |

15 |

13 |

12 |

14 |

15 |

16 |

18 |

19 |

20 |

16 |

15 |

11 |

10 |

15 |

20 |

12 |

14 |

Note: The above tally chart is just a representation of the data, the actual tally chart should be made on paper with tally marks.

According to the scatter plot below, when x = 5, the value of y is 1.

A scatter plot is a form of plot or mathematical diagram that displays values for two variables for a collection of data using Cartesian coordinates. One more variable can be presented if the points are programmed. A scatter plot is a collection of dots drawn on two axes, horizontal and vertical. Scatter plots are useful in statistics because they illustrate the amount, if any, of correlation between the values of observed quantities or events (called variables). With a particular confidence interval, a scatter plot might imply several types of relationships between variables. Weight and height, for example, would be on the y-axis, whereas height would be on the x-axis. Positive (increasing), negative (falling), or null correlations exist (uncorrelated).

Here,

Based on the scatter plot below, when x=5 then value of y is 1.

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