M is the midpoint of the diagonals. Use the properties of rotations to show that the measures of both pairs of opposite sides are equal in length.

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 measure of the side of the partial rectangle is 7 cm

The perimeter P of a rectangle is given by the formula, P=2 ( L + W) , where L is the length and W is the width of the rectangle.

Perimeter P of rectangle = 2 ( Length + Width )

Given data ,

Let the perimeter of the rectangular figure be represented as P

Now , the equation will be

The length of the rectangle 1 = 12 cm

The width of the rectangle 1 = 6 cm

The length of the rectangle 2 = 15 cm

The width of the rectangle 2 = 5 cm

Now , let the unknown length be represented as A

And , A = length of the rectangle 1 - width of the rectangle 2

Substituting the values in the equation , we get

The unknown length A = 12 cm - 5 cm

On simplifying the equation , we get

The unknown length A = 7 cm

Hence , the unknown length of the rectangle is A = 7 cm

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The probability of selecting all bottles of the same variety is P(A) = 6/46656 = 0.00013.

The probability of selecting two bottles of each variety when randomly selecting 6 bottles can be calculated using the formula P(A) = n(A) / n(S), where n(A) is the number of possible ways to select two bottles of each variety and n(S) is the total number of possible ways to select 6 bottles. In this case, n(A) is equal to 6! / (2!2!2!) = 90 and n(S) is equal to 6^6 = 46656. So, the probability of selecting two bottles of each variety is P(A) = 90/46656 = 0.0019.

The probability of selecting all bottles of the same variety when randomly selecting 6 bottles can be calculated using the same formula. In this case, n(A) is equal to 6, which is the number of ways to select 6 bottles of the same variety, and n(S) is equal to 46656. So, the probability of selecting all bottles of the same variety is P(A) = 6/46656 = 0.00013.

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$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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Based on the information in the graph, the length of DF is 3.87 cm, the length of XF is 4.89 cm. The point 2cm from E is 5cm from X and the angle of D is 60°.

To find the length of the side DF we must apply the Pythagorean theorem substituting the values that we know as shown below:

To find the length of the side DF we must apply the Pythagorean theorem substituting the values that we know as shown below:

The point 2cm from E would lie on the line EX at 2cm from E and 5cm from X.

To calculate the angle of D we can use a compass, in this case, we know that the angle of X is 90°, so the other 90° that make up the triangle are distributed between point F and D. However, we know that F has a angle less than D so we can infer that F has an angle of 30° and D has an angle of 60° which we can check with a compass.

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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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By alternating internal angles, angles 1 and 2 are equivalent.

What does the triangle's angle sum property entail?

According to the triangle's "angle sum property," the inner angles of a triangle add up to 180 degrees.

1. Angles 1 and 2 complement one another. Angles 2 and 3 compliment one another.

These angles are linear, hence their sum is 180 degrees.

2.m angle

Angle 1 + m2 Equals 90° Angle m2 + m3 = 90°

Equals makes a straight angle

3. m angle1 plus m angle2 equals m angle2 plus m angle3

= 180 degrees when the total of the two sides

4. m angle2 equals m angle

= The total of the two sides is equal

5. m angle1 = m angle3

= The total of the two sides is equal

6.Angle1 and Angle3 are congruent.

Alternate interior angles are what they are.

Angle 1 and Angle 3 are therefore equivalent based on the triangle's characteristics.

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Answer:

20 students went to college.

Step-by-step explanation:

In order to find a percent of a number you must do the number multiplied by the percent divided by 100. For example, the formula is (x*%) divided by 100. 25*80 = 2000. 2000/100 = 20 students. Hope I helped!

Answer:

80% of 25 students

80÷100 × 25 = 20

therefore , 20 students went to college.

The algebraic expression that represents the amount that Sohail got is given as follows:

[10(x - 8)]².

His break lasted x days and he was out of station for 8 days, hence the number of days that Sohail worked is given as follows:

x - 8 days.

Each day he earned Rs 10, hence the total amount earned can be modeled as follows:

10(x - 8).

After the amount was squared, the expression is given as follows:

[10(x - 8)]².

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Answer:

Step-by-step explanation:

Simply substitute for y in the equation if y = 12.

2 + y + 1  ->  2 + (12) + 1 = 15

The x-coordinate of the solution to the system of equations is 3.

Graphical solutions of a system of equations are a way of finding the intersection points of all the equations given.

A system with two or more than two equations has a solution only when they have a common intersection point.

Two lines are labeled on x-y coordinate y = - x + 5 and y = x - 1.

Now, Adding these two equations we have,

2y = 4.    (x and - x cancells).

y = 2.

Now, Putting the value of 'y' in any of the equations we have,

2 = - x + 5.

x = 5 - 2.

x = 3.

so, The x-coordinate of the solution is 3.

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Variability around the mean or nominal dimension is a measure of quality because it helps to quantify the spread of data and the degree to which it deviates from the expected value.

By considering variability, manufacturers and designers can identify areas for improvement, determine tolerances for product specifications, and ensure consistency in production. Additionally, it helps to identify outliers and inconsistencies in the data which can be indicative of defects or issues in the production process. Furthermore, considering variability helps to assess the risk of non-conformance and predict the performance of a product in real-world scenarios. In short, considering variability helps to improve the overall quality of products and ensure they meet customer expectations.

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Answer:

see below

Step-by-step explanation:

(x+ 2 4/5) * 2 = perimeter

so perimeter = 2x + 5.6

Answer:

Can 3. $2.40, Red Kidney Beans, 500g, Can. This can costs $0.0048 per gram.

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:

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:

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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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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1800 + 150x = y

150x is the money she makes a month

Y is the total

enjoy :D

The linear model that could be used to determine which plan would be less expensive based on the number of visits he makes is given as follows:

Second graph (top right graph, where the two lines intersect).

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

For the plan with the set price, we have that:

Hence it costs less for a lower number of visits.

For the plan with the set price plus the fee, we have that:

Hence it costs less for a higher number of visits.

Meaning that the second graph is the correct graph in this problem.

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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

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).

A library has 2500 books.40% of the books are fiction, number of not fiction books are 1500.

A percentage is a relative figure that represents one tenth of a quantity. Since one percent (symbolised as 1%) is equal to one tenth of anything, 100 percent stands for everything, while 200 percent refers to double the amount specified.

Total amount of book in library are 2500 ,

Out of that 40% are fiction so the number of the non fiction books are 60%

so 60% of 2500 will give us the value of non fiction books,

Number of non fiction = 2500 x 60%

= 2500 x 60/100

= 25 x 60

= 1500

Therefore,  Number of non fiction books are 1500.

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Answer:

an = - 7n+35

Step-by-step explanation:

In an arithmetic sequence, the difference between consecutive terms is constant. To find this difference, we can subtract the first term from the second term and the second term from the third term, etc.

a2 - a1 = 21 - 28 = -7

a3 - a2 = 14 - 21 = -7

Since the difference between consecutive terms is the same, we can conclude that the difference is -7.

The nth term in an arithmetic sequence can be found using the formula: an = a1 + (n-1)d, where d is the common difference.

For this sequence, the nth term can be found as: an = 28 + (n-1)(-7) = 28 - 7(n-1) = 28 - 7n + 7 = 35 - 7n.

So, the formula for the nth term in this arithmetic sequence is an = - 7n+35

Step-by-step explanation:

this is the process and figure is cointerior

[tex]\textit{arc's length}\\\\ s = \cfrac{\theta \pi r}{180} ~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ s=22\\ r=4 \end{cases}\implies 22=\cfrac{\theta \pi (4)}{180}\implies 22=\cfrac{\theta \pi}{45} \\\\\\ (22)(45)=\theta \pi \implies \cfrac{(22)(45)}{\pi }=\theta \implies 315.13\approx \theta[/tex]

The solution to the monomial in standard form is  0.04b^19.

The term "polynomials in standard form" can also refer to a polynomial written in the decreasing order of the degree of the variable.

The degree of the polynomial is significant when writing it in its standard form since the terms are written in descending order of the power of x.

Given that:

= (-0.2b^6)^3*5b

Rewrite using the commutative property of multiplication

= 5(-0.2b^6)^3b

Apply the product rule to −0.2b^6

= 5(-0.2^3)(b^6)^3b

= 5(-0.008b^18)b

= 5(-0.008^19)

= 0.04b^19

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Answer:

£481.02

Step-by-step explanation:

To calculate, you can multiply the original cost by the increase percentage (expressed as a decimal) and add that to the original cost:

£466.98 * 1.032 = £480.9936

£480.9936 + £466.98 = £481.02

Rounding to 2 decimal places, the answer is £481.02.

Answer:

No se puede determinar la edad de cada hijo con la información proporcionada.

Step-by-step explanation: