Could anyone solve both and say how they did it? asked my teacher and she didnt help ​

Answer: In a parallelogram, opposite sides are equal in length and parallel, so if we subtract the vectors AB and BC from each other, we will get the vector for CD.

Given A = (4,0), B = (1.5,0), and C = (-3,-5), we can calculate the vectors AB and BC as follows:

AB = B - A = (1.5, 0) - (4, 0) = (-2.5, 0)

BC = C - B = (-3, -5) - (1.5, 0) = (-4.5, -5)

Next, we subtract these vectors to find the vector for CD:

CD = BC - AB = (-4.5, -5) - (-2.5, 0) = (-2, -5)

Finally, we add the vector CD to vertex C to find vertex D:

D = C + CD = (-3, -5) + (-2, -5) = (-5, -10)

So, the ordered pair for vertex D is (-5, -10).

Step-by-step explanation:

The slope of the points in this table is equal to 2.

In Mathematics, the slope of any straight line can be determined by using this mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Based on the information provided, we can logically deduce the following slope and data points on the line:

Substituting the given points into the slope formula, we have the following;

Slope, m = (-1 + 3)/(-1 + 2)

Slope, m = 2/1

Slope, m = 2.

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The missing words in the statement are mean and absolute deviation respectively.

The mean absolute deviation (MAD) is a measure of the average magnitude of the differences between individual values in a data set and the mean of the data set. It is calculated by first finding the absolute value of the difference between each data point and the mean, summing these absolute values, and then dividing by the number of data points. The resulting value provides a measure of the "typical" or average deviation of individual data points from the mean, without considering the direction of the deviation (positive or negative). The mean absolute deviation is often used as a summary statistic for data that is not normally distributed or when the variance or standard deviation are not meaningful.

The mean of the absolute deviation between the mean of the data set and the individual numbers in the data set is referred to as the mean absolute deviation (MAD).

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The difference of the data between the mean of the data set and individual numbers in the data set is called the deviation.

Mean Absolute Deviation (MAD) is a measure of the average distance between the values in a dataset and the mean of that data set. It is calculated by finding the absolute difference between each value and the mean, summing them, and dividing by the total number of values. MAD is commonly used as a way to describe the variability or dispersion of a set of data.

In other words, the mean absolute deviation (MAD) is the average distance between each data value and the mean of the data set.

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The ratio of used books to all books is 7 : 13 and  the ratio of new books to used books is 6 : 7

If there are 13 books on a shelf. 6 of these books are new.

(a) The ratio of used books to all books

Number of all books = 13

Number of used books = total no. of books - no. of new books

                                       =  13 - 6

                                       = 7

So, ratio of used books to all books

= no. of all books : no. of total books

= 7 : 13

Thus, the ratio of used books to all books = 7 : 13

(b) The ratio of new books to used books

Number of new books = 6

Number of used books = 7

So, the ratio of new books to used books

= no. of new books : no. of used books

= 6 : 7

Thus, the ratio of new books to used books = 6 : 7

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Answer:

Step-by-step explanation:

If Boden's account has a principal of $600 and a simple interest rate of 3.9%, then the interest he earns each year can be calculated as follows:

Simple Interest = Principal * Rate * Time = $600 * 3.9% * 1 = $23.40

So, after one year, the amount of money in the account will be $600 + $23.40 = $623.40

This process can be repeated for multiple years to find the amount of money in the account for a specific time period.

Cynthia's percent error in her fourth lab report was 4.38%.

Percent error is a measure of the accuracy of a numerical result, expressed as a percentage of the difference between the actual value and the calculated or measured value. It is calculated using the formula -

Percent Error = (|Actual value - Calculated value| / Actual value) * 100

In order to calculate Cynthia's percent error, we will use the formula:

Percent Error = (|Accepted Value - Measured Value| / Accepted Value) * 100%

For the mean of her four measured values (0.7325), the percent error would be:

Percent Error = (|0.77 - 0.7325| / 0.77) * 100% = 4.38%

So, the answer to be entered rounded to two decimal places is 4.38.

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The solution of a system of equations can be determined by dividing the coefficients of variables.

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

Solution of system of equations :-

Let the two system of equations be

a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0

1) Unique solution or one solution :-

The solution of the system of equations will be unique when,

a₁ / a₂ ≠ b₁ / b₂

2) Infinite solutions :-

The solution of the system of equations will have infinitely many solutions when,

a₁ / a₂ = b₁ / b₂ = c₁ / c₂

3) No solution :-

The solution of the system of equations will have no solutions when,

a₁ / a₂ = b₁ / b₂ ≠ c₁ / c₂

Hence, the solution of a system of equations can be determined by dividing the coefficients of variables.

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The diagram that represent the distance and the journeys is added as an attachment

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

Using the above as a guide, we have the following:

Next, we create the diagram (see attachment)

The attached figure represents the required diagram

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Answer:

3000

Step-by-step explanation:

8 x 375 = 3000

Nice work on getting part (a) correct.

The 261% falls in the "250-300%" range, so they pay 8.5% of their yearly income toward health insurance.

8.5% of $65,500 = 0.085*65500 = 5567.50

That represents the yearly contribution. Divide that by 12 to find the monthly contribution.

5567.50/12 = 463.95833 = 463.96 approximately

Then round to the nearest dollar to get 464

For the first part of the question, here is my classification of each statement:

A) True. The domain of the function is all real numbers.

B) False. The range of the function is all real numbers.

C) False. The function has no x-intercepts.

D) False. The center of symmetry is (0, 0).

For the second part, the transformations performed from function f to function g are:

A) Function f is translated to the left 3 units.

For the third part, the transformations performed from function f to function g are:

A) Function f is translated to the right 3 units.

B) Function f is translated up 3 units.

For the last part, you would need to find the x and y-intercepts of the polynomial function, and plot them on the graph. The x-intercepts can be found by setting x=0 in the equation and solving for y. The y-intercept can be found by setting y=0 and solving for x. Once the intercepts are found, you can plot them on the graph and connect them to form the graph of the polynomial function.

Answer:

See below for answers and explanations

Step-by-step explanation:

Problem 1

Problem 2

Problem 3

I cannot read your problem

Problem 4

[tex]f(x)=x^3+3x^2-4x-12\\0=x^3+3x^2-4x-12\\0=x^2(x+3)-4(x+3)\\0=(x^2-4)(x+3)\\0=(x-2)(x+2)(x+3)\\x_1=-3,\,x_2=-2,\,x_3=2[/tex]

Hence, the graph of the function would have points at (-3,0) (-2,0) and (2,0).

Step-by-step explanation:

this is the process and figure is cointerior

The number of biology textbooks sold =  156

The number of psychology textbooks sold = 95

An equation is a mathematical term, which indicates that the value of two algebraic expressions are equal. There are various parts of an equation which are, coefficients, variables, constants, terms, operators, expressions, and equal to sign.

For example, 3x+2y=0.

Types of equation

1. Linear Equation

2. Quadratic Equation

3. Cubic Equation

Let x be the number of biology textbooks sold. Then, the number of psychology textbooks sold was x - 61.

The combined total of the two types of textbooks sold was 251, so we can write an equation:

x + (x - 61) = 251

Expanding the right side:

2x - 61 = 251

Adding 61 to both sides:

2x = 312

Dividing both sides by 2:

x = 156

the number of psychology textbooks sold =  x - 61

                                                                      =  156 - 61

                                                                      =  95

So, 156 biology textbooks were sold and 95 psychology textbooks were sold.

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The value of measure ∠2 is, 135°.

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

In the house,

⇒ m ∠1 = 45°

We know that;

An exterior angle of a triangle is the sum of two opposite angle of a triangle.

Hence, We can formulate;

⇒ m ∠2 = m ∠1 + 90°

⇒ m ∠2 = 45° + 90°

⇒ m ∠2 = 135°

Thus, We get;

⇒ m ∠2 = 135°

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The value of the expression is A = 4p ( 3 - 2 ) = 4p

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

A = 12p - 8p   be equation (1)

On simplifying the equation , we get

Taking the common factor as 4p in the expression , we get

A = 4p ( 3 - 2 )

On further simplification , we get

A = 4p

Therefore , the value of A is 4p

Hence , the expression simplified is 4p

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Answer:

1. True

2. False

3. True

4. False

Step-by-step explanation:

Given function:

[tex]f(x)=4(x-2)^3+2[/tex]

The point-of-symmetry of a cubic graph is its point of inflection.

To find the x-value of the point of inflection of a cubic function, differentiate the function twice:

[tex]f'(x)=12(x-2)^2[/tex]

[tex]f''(x)=24(x-2)[/tex]

Set the second differentiated function to zero and solve for x:

[tex]\implies 24(x-2)=0[/tex]

[tex]\implies x-2=0[/tex]

[tex]\implies x=2[/tex]

Substitute the found value of x into the original function to find the y-value of the point of inflection:

[tex]\implies y=4(2-2)^3+2[/tex]

[tex]\implies y=4(0)^3+2[/tex]

[tex]\implies y=0+2[/tex]

[tex]\implies y=2[/tex]

Therefore, the point of symmetry of the cubic function is (2, 2).

The inverse of a cubic function its reflection in the line y = x.

As the point of symmetry is (2, 2), then its reflection in the line y = x is also (2, 2).

So the point of symmetry on f⁻¹(x) is (2, 2).

The given function has an unrestricted domain and range.

The domain of the inverse function is the range of the function.

The range of the inverse function is the domain of the function.

Therefore, as the domain and the range of the original function are unrestricted, so are the domain and range of the inverse function.

The inverse of a cubic function with an unrestricted domain is its reflection across the line y = x.

Therefore, the graphs of f⁻¹(x) and f(x) are reflections across the line y = x.

To find the inverse of the given function, swap x and y:

[tex]\implies x=4(y-2)^3+2[/tex]

Rearrange to make y the subject:

[tex]\implies x-2=4(y-2)^3[/tex]

[tex]\implies \dfrac{x-2}{4}=(y-2)^3[/tex]

[tex]\implies \sqrt[3]{\dfrac{x-2}{4}}=y-2[/tex]

[tex]\implies y=\sqrt[3]{\dfrac{x-2}{4}}+2[/tex]

Replace y with f⁻¹(x):

[tex]\implies f^{-1}(x)=\sqrt[3]{\dfrac{x-2}{4}}+2[/tex]

As we have already established, the domain and range of the inverse function are unrestricted.  As each x-value has only one y-value associated with it, f⁻¹(x) is a function.

Answer:

$4.25 for 64 fluid ounces = $0.06640625 per fluid ounce

297 miles on 11 gallons of gas = 27 miles per gallon

124 feet in 10 seconds = 12.4 feet per second

Step-by-step explanation:

The calculation of uncertainty depends on various factors, including the method used, the distribution of the data, and the number of data points. In some cases, the calculated uncertainty may be lower than the actual deviation of the data, especially if the data is not normally distributed or if the number of data points is small.

It's also important to keep in mind that uncertainty is a measure of the spread of the data, not the absolute deviation from the mean. In other words, if the data is tightly clustered around the mean, the calculated uncertainty will be low, even if the maximum deviation from the mean is relatively high.

If you think your calculated uncertainty is not accurately representing the spread of your data, you may want to consider using a different method for calculating uncertainty, or checking the underlying assumptions of the method you are using to ensure that it is appropriate for your data set.

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The uncertainty of a group of data represents the range of possible values that the data could reasonably have and is not expected to exceed the actual mathematical value of the data.

The uncertainty of a group of data is determined by factors such as measurement error and natural variability in the data & represents the range of possible values that the data could reasonably have. It is not expected to exceed the actual mathematical value of the data because the mathematical value represents the best estimate of the true value based on the available data.

The uncertainty is a measure of the limitations and potential sources of error in the data and helps to quantify the level of confidence that can be placed in the mathematical value.

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Domain is all real numbers and Range is all real numbers less than or equal to -2.

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

The given function is  f(x) = -x⁴+ 2x²-x-2

Domain is all real numbers.

Range is all real numbers less than or equal to -2.

Relative Maximum is the function does not have any relative maximums.

Relative Minimum(s): The function does not have any relative minimums.

End Behavior as x approaches infinity, f(x) approaches negative infinity. This can be seen by observing that the leading term in f(x),

-x⁴ grows much faster than the other terms as x increases, so the overall value of f(x) becomes more and more negative as x approaches infinity.

Hence, Domain is all real numbers and Range is all real numbers less than or equal to -2.

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The original purchase price of the car before any of the discounts and taxes is,

⇒  $15,024

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.

Given that;

There is a 12% discount because of the Happy Easter Sale and another 5% discount because the purchaser is a valued customer. After these discounts the GST increases the price by 10%.

Here, the customer paid $14 000.

Now, Let the original price = x

Hence, We can formulate;

⇒ x - (12% of x) - 5% of x + 10% of x = 14,000

⇒ x - 12x/100 - 5x/100 + 10x/100 = 14,000

⇒ (100x - 12x - 5x + 10x) / 100 = 14,000

⇒ 93x/100 = 14,000

⇒ 93x = 1400000

⇒ x = $15,024

Thus, The original purchase price of the car before any of the discounts and taxes is,

⇒  $15,024

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Using the formula of area of rectangle and square, the cost of painting is Rs. 1335

The area of a rectangle is equal to the product of its length and width. Mathematically, it can be represented as:

Area = Length × Width

In this problem, we need to substitute the values and calculate the area of the rectangular wall and then subtract the area of the window from it.

Area of rectangle = 15 * 7 = 105m²

The area of the window is calculate by using the formula of area of square.

Area of square = 4 * 4 = 16m²

Area of wall painted = 105 - 16 = 89m²

The cost of painting one square meter = Rs. 15

1m² = Rs. 15

89m² = x

x = 15 * 89

x = Rs. 1335

The cost is Rs. 1335

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Answer:

Aled's mother paid £220.

Aled paid £44.

Gareth paid £396.

Step-by-step explanation:

1-(1/3)= 2/3 [fraction of amt. Aled and Gareth paid]

£660×(2/3)= £440 [amt. Aled and Gareth paid]

total units= 1+9

= 10

10 units= £440

1 unit= £440÷10

= £44

9 units= £44×9

= £396

£660×(1/3)= £220

Solving the provided question, we can say that by Pythagoras theorem VT² = 18² + 24² = 900  => VT =  [tex]\sqrt{1900} = 30[/tex]

The Pythagorean Theorem, sometimes known as the Pythagorean Theorem, is the basic Euclidean geometry relationship between a right triangle's three sides. According to this rule, the area of a square with the hypotenuse side equals the sum of the areas of squares with the other two sides. The Pythagorean Theorem, often known as the generic algebraic notation a2 + b2 = c2, states that the square that crosses the hypotenuse of a right triangle opposite the right angle equals the sum of the squares that span the sides of a right triangle.

Pythagoras theorem

VT² = 18² + 24² = 900  

VT =  [tex]\sqrt{1900} = 30[/tex]

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Step-by-step explanation:

You would need to start by finding how many students is 1/5 of them

So to find this out you would take 70 and divided it by 5

So 70/5 = 14

Take 70 and subtract 14 to get 56

Next find what 1/7 is

So 56/7 = 8

But because it’s 2 sevenths take the 1/7 and multiply by 2

8 x 2 = 16

So
Take the 56 and subtract 16 to get 40

To find the fraction form it would be

40/70 students

Just simplify now

4/7

Step-by-step explanation:

day 1

70*1/5= 14

70-14 = 56

day 2

2/7 * 56= 16

16+14 = 30.

Remaining students = 70 - 30 = 40

Answer: If 20% of the 60 students in the Geneva Middle School marching band play the trombone, then 60 * 20% = 12 students play the trombone. To shade the grid to show the percent, you can shade 20 out of 100 squares on the grid, or 1/5 of the total number of squares.

Step-by-step explanation:

$2,250 was invested at 2% and the remaining $3,500 was invested at 12%. The combined interest earned amount for the first year was $475.

The financial planner invested $5,750 of the couple's money. Let x be the amount of money invested in the savings account paying 2% annual simple interest and y be the amount of money invested in the riskier mini-mall development plan paying 12% annual simple interest. Since the combined interest earned for the first year was $475, we can write the equation 2x + 12y = 475. Since the total amount of money invested was $5,750, we can add the equation x + y = 5,750 to our system of equations. Solving the system of equations yields x = 2,250 and y = 3,500. Thus, $2,250 was invested at 2% and the remaining $3,500 was invested at 12%. The combined interest earned for the first year was $475.

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Answer:

  (d)  C'(-1, 14)

Step-by-step explanation:

You want the coordinates of C' after the point C(-1, -6) is reflected across the line y = 4.

Reflection across the horizontal line y=4 will not change the x-coordinate of the point, so C' has an x-coordinate of -1.

The point (-1, 4) on the line of reflection will be the midpoint of C and C', so we have ...

  (C +C')/2 = (-1, 4)

  C +C' = 2(-1, 4) = (-2, 8) . . . .  .multiply by 2

  C' = (-2, 8) -C

  C' = (-2, 8) -(-1, -6) = (-1, 8+6)

  C' = (-1, 14)

__

Additional comment

Effectively, the reflection across the line y=4 is the transformation ...

 (x, y) ⇒ (x, 8 -y)

Answer:

C'(-1, -6).

Step-by-step explanation:

the reflection across y = 4 for point C(-1, -6).

When reflecting a point across a horizontal line like y = 4, the y-coordinate remains the same, and the x-coordinate is inverted with respect to the line of reflection.

For point C(-1, -6), the y-coordinate remains -6, and the x-coordinate is inverted across y = 4:

New x-coordinate = -1

So, the reflected image of point C across y = 4 is C'(-1, -6).

None of the provided options match this reflection, so it seems there might be an error in the given answer choices. The correct reflection of point C(-1, -6) across y = 4 is C'(-1, -6).

By the 1/3 ratio, the value of x for the given figure is 33 units.

A ratio is an ordered pair of integers a and b, denoted by the symbol a / b, where b does not equal zero. A proportion is an equation that sets two ratios equal to each other. For example, if there is one boy and three girls, the ratio may be written as: 1: 3 (for every one boy, there are three girls). A ratio in mathematics illustrates how many times one number contains another. For example, if a dish of fruit contains eight oranges and six lemons, the orange-to-lemon ratio is eight to six (that is, 8:6, which is equivalent to the ratio 4:3).

Here,

4/12=3/x1=5/x2

1/3=3/x1

x1=9 units

1/3=5/x2

x2=15 units

12+15+9=33 units

The value of x for the given figure is 33 units by the ratio of 1/3.

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The perimeter and area of the figure are 40.8 units and 110 square units respectively.

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

The figure

Using the distance formula:

d = √[(x₂ - x₁)² + (y₂ - y₁)²],

where d is the distance between the points (x₁, y₁) and (x₂, y₂).

So, we have

AB = √[(8-8)² + (9-2)²] = 7

BC = √[(3-8)² + (13-9)²] = 6.4

CD = √[(-3-3)² + (9-13)²] = 7.2

DE = √[(-3+3)² + (9-13)²] = 9

EA = √[(8+3)² + (2-0)²] = 11.2

DB = √[(8+3)² + (9-9)²] = 11

Perimeter = AB + BC + CD + DE + EA.

Perimeter = 7 + 6.4 + 7.2 + 9 + 11.2

Perimeter = 40.8 units.

The figure is observed to be a trapezium ABDE and a triangle BCD.

Triangle BCD have base length DB = 11 with height from C to DB equal to 4.

Trapezium ABDE have sides AB and DE parallel to each other, and height DB = 11.

area of triangle BCD = 1/2 × 11 × 4 = 22 square units

area of trapezium ABDE = 1/2 × (7 + 9) × 11 = 88 square units

Total area ABCDE = 22 + 88

Total area = 110 square units

Hence, the perimeter and area of the figure are 40.8 units and 54 square units respectively.

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