In a scale drawing, a rectangle has a length of 6.1 inches. The actual rectangle has a length of 85.4 inches.

A quadrilateral with at least one pair of parallel sides is called, in American and Canadian English, a trapezoid. In British and other forms of English, a (North American) trapezoid is called a trapezium. The transposition of these two terms was a result of an error in Charles Hutton's mathematical dictionary.

In Euclidean geometry, a trapezoid is a convex quadrilateral by definition. The bases of the trapezoid are the parallel sides. If the remaining two sides are parallel, they are referred to as the legs (or lateral sides); if not, the trapezoid is a parallelogram, and there are two pairs of bases. As opposed to the particular examples below, a scalene trapezoid is a trapezoid without equal sides.

The Greek mathematician Euclid identified five different quadrilateral shapes, of which four had two sets of parallel sides (the square, rectangle, rhombus, and rhomboid in English) and one did not (a trapezia, meaning "a table," which comes from "four" and means "a foot; end, boundary, edge").

In his commentary on the first book of Euclid's Elements, Proclus (412–485) developed two varieties of trapezia: one pair of parallel sides, or a trapezium (v), divided into isosceles (equal legs), and scalene (unequal) Similar to how cuboid and rhomboid both mean "resembles," trapezia with no parallel sides is a trapezoid, trapezoeidé, or literally "trapezium-like."

English followed Proclus's arrangement until the late 18th century, when a prominent mathematical lexicon produced by Charles Hutton in 1795 endorsed a transposition of the terms without providing an explanation. Although this error was fixed in British English around 1875, it remained in American English till the present..

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The thing that P(W) represents is A. It denotes the probability of screening a driver and finding that he or she is not intoxicated.

The value is 0.99257

It should be noted that probability simply means the likelihood that something will happen or occur based on the information given.

From the information, the man observed a sobriety checkpoint conducted by a police department, he saw drivers were screened and were arrested for driving while intoxicated.

P(W) = 0.000743

Therefore, those that are not intoxicated will be:

= 1 - P(W)

= 1 - 0.000743

= 0.99257

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Elizabeth is correct in evaluating the expression.

All the students are evaluating the expression

48÷4×2+2

For evaluating such an expression the order of operations need to be used.

The order of operations are:

So the expression 48÷4×2+2 is solved as:

48÷4×2+2

= 12 × 2 + 2

= 24 + 2

= 26

So 26 is the right answer and it is given by Elizabeth.

So Elizabeth is correct(26).

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The ball to rise 45 meters in 3 seconds.

How do you find the solutions of a quadratic equation?

here

Function : [tex]H= 30t-5t^{2}[/tex]

height = 45m

then [tex]30t-5t^{2} = 45[/tex]

simplify the quadratic equation ⇒ [tex]6t-t^{2} -9=0[/tex]

⇒ [tex]t^{2} -6t+9=0[/tex]

⇒ [tex](t-3) (t-3)=0\\t=3.[/tex]

 time required to  reach 45m = 3 sec.

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Each label should be dragged to the correct location in the equation as follows:

100 yards/1 × (3) feet/1 yards × (12) inch/1 foot × (2.54) cm/1 inch × 1 (meter)/100 cm = (91.44) meter

A conversion factor can be defined as a number that is typically used to convert (change) a number in one (1) set of units to another, either by dividing or multiplying.

Generally speaking, an appropriate conversion factor to an equal value must be used when it is necessary to perform any mathematical conversion.

Conversion:

1 yard = 0.9144 meter

100 yards = X meters

Cross-multiplying, we have:

X = 0.9144 × 100

X = 91.44 meters.

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Answer:

A. The perimeter of the image is 4 times as large as the perimeter of the pre-image.

Explanation:

To answer this question, we use an example.

Given the pre-image:

• A square with side length 1 cm

• Perimeter = 4 x 1 = 4cm

If the square is dilated by a scale factor of 4:

• Side length = 4cm

• Perimeter = 4 x 4 =16cm

We see therefore that 'The perimeter of the image is 4 times as large as the perimeter of the pre-image.'

The correct choice is A.

The equation y = - 2x + 4 matches the line

How to find the equation?

The line passes through two points .

[tex](x_1, y_1) = (2, 0)\\\\(x_2, y_2) = (0, 4)[/tex]

We know that slope (m) is given by,

[tex]m =\frac{y_2 -y_1}{x_2 -x_1} \\\\m =\frac{4-0}{0-2} \\\\m= -\frac{4}{2} \\\\m= -2[/tex]

We know the slope- intercept form of an equation is:

y = mx+ c    ----(1)

Let us substitute the point  [tex](x_1, y_1)[/tex]  and m in (1)

y = mx+ c

0 = -2(2) +c

c = 4

Let us substitute c and m in (1)

The slope- intercept form of the equation is:

y = -2x + 4

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Answer:

4x-5

Step-by-step explanation:

Answer:

32

Step-by-step explanation:

Since l and m are parallel, the value of 2x is equal to 64.

64/2 = 32

Answer:

It is trapezium.

Step-by-step explanation:

1÷2×h[b1+b2]

Loretta would not have paid any taxes last year because her total earnings were below the €8625 threshold.

What is Percentage ?

A Percentage is a figure or ratio that is stated as a fraction of 100 in mathematics. Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent symbol, "%," is frequently used to indicate it. A % is a number without dimensions and without a measurement system.

The total amount paid in tax from Cary's last year earning is £9640
Total earning last year = €34 500

Tax on earnings :
First €3500 = 0%
€3500 to €10 500 = 25%
Earnings above €10 500 = 35%
Therefore, tax paid on €34 500 :

Tax percentage × amount earned

First €10 500 earned = (25% × 10,500) = 2625

Excess above €10 500 = (34500 - 10500) = 24000

25% × 24000 = 6000

Therefore, the total tax amount = €(2625 + 6000) = €8625

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In the picture there is a straight line which has a point where the 2 lines intersect. The angles are 90°, 30° and a is 60°.

Given that,

In the picture there is a straight line which has a point where the 2 lines intersect.

The angles are 90° and 30°.

We have to find the angle a.

A straight angle in geometry is an angle with a vertex point that is at 180 degrees. In essence, it creates a straight line with sides that face away from the vertex. "Flat angles" is another name for it.

So, we get,

90°+30°+a=180°

a=180°-90°-30°

a=180°-120°

a=60°

Therefore, the angle a is 60°.

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For the given mapping diagram, we have that: C. Yes (one y-value for each x-value) it represent a function.

A function can be defined as a mathematical expression which is used to define and represent the relationship that exists between two or more variables. This ultimately implies that, a function is typically used for uniquely mapping an input variable to an output variable.

A domain can be defined as the set of all real numbers for which a particular function is defined and these include the following: {1, 2, 3, 4}.

In conclusion, we can reasonably infer and logically deduce that this mapping diagram represent a function because it has the different input values (x-values) for different output values (y-values).

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The inequality expression given as 2 - |6 + 12x| > -28 has a solution of -3 < x < 2

From the question, the inequality is given as

2-|6+12x|>-28

Rewrite properly as

2 - |6 + 12x| > -28

Subtract 2 from both sides

- |6 + 12x| > -30

Divide both sides by -1

|6 + 12x| < 30

Remove the absolute bracket

So, we have the following representation

-30 < 6 + 12x < 30

Add -6 to all sides of the inequality

So, we have

-36 < 12x < 24

Multiply through by 1/12

So, we have

-3 < x < 2

Hence, the solution to the expression is -3 < x < 2

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Answer:

Step-by-step explanation:

45 degrees -67/6

Based on the numbers to be divided of 1,060 ÷ 33 to get a quotient, the mixed number in the simplest form is 32¹/₂ .

Finding the quotient of two numbers means that one of the numbers would have to divide the other number.

The quotient in this case is:

= 1,060 ÷ 33

= 32.1212

To convert this to mixed number, divide the decimal portion by the relevant power of 10:
= 32 + 1212/10,000

= 32 + 4/32

= 32 + 1/8

= 32¹/₂

In conclusion, the quotient of 1,060 ÷ 33 is 32¹/₂ .

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Answer: 3 5/8 hours

Step-by-step explanation:

2 + 1 = 3

1 / 4 = 2 / 8

3 / 8 + 2 / 8 = 5 / 8

The length of the missing side z would be 17 units which is determined by Pythagoras's theorem.

A right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

According to Pythagoras's theorem,

⇒ a² + b² = c²

Here, a = 8  b = 15 and c = z

⇒ (8)² + (15)² = z²

⇒ 64 + 225 = z²

Apply the addition operation,

⇒ 289 = z²

⇒ z² = 289

⇒ z = √289

⇒ z = 17

Therefore, the length of the missing side z would be 17 units.

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Answer:

700 is your answer i am pretty sure. If not i am super sorry

Answer:

630

Step-by-step explanation:

If she owns 70 and each went up by 10 then 70*10=700

700-70=630

I am sure it is correct but if not,sory if it is wrong

All real numbers n that is less than 14 when plugged in for x will be less than 14 in inequality .

What is inequality in math?

inequality  = 4n+ 13 ≤ 69

                 = 4n ≤ 69 - 13

                 = 4n ≤ 56

                 = n ≤ 56/4

                 = n ≤  14

Thus, all real numbers n that is less than 14 when plugged in for x will be less than 14.

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The ratio of boys to girls in the 9th grade is 7 : 9. Girls are 218

proportion of girls in total students are [tex]\frac{218}{9}[/tex] = 24.2

According to the question, given that

In class ratio of boys and girls is 7 : 9

and girls in the class are 218

Proportion of girls in total class = [tex]\frac{218}{9}[/tex]

                                                    = 24.2

Therefore, we get proportion of girls in the class is 24.2

When determining if two ratios or fractions are equivalent, the proportion formula is utilized. The proportional formula is as follows:

a : b :: c : d = a/b = c/d

Proportion Formula

a:b::c:d = a/b = c/d

where,

a, d = Extreme terms

b, c = Mean terms

The product of means equals the product of extremes is one of the various proportional formulas. You can write this as ad = bc.

Two additional proportional formulas that depend on direct or indirect variation are available. When two quantities x and y are in direct proportion, y = k x, and when x and y  are in indirect proportion, y = k/x, with k serving as the proportionality constant in both cases.

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Answer:

Step-by-step explanation:

                          [tex]\boxed {b_n=b_1q^{n-1}}[/tex]

[tex]b_{12}=-12,288\ \ \ \ \ q=2\ \ \ \ n=12[/tex]

[tex]-12,288=b_1(2^{12-1})\\\\-12,288=b_1(2^{11})\\\\-12,288=b_1(2048)[/tex]

Divide both parts of the equation by 2048:

[tex]-0.006=b_1[/tex]

[tex]Thus,\ b_1=-0.006[/tex]

The  system of equations that could be used to determine the price of each pound of raspberries and the price of each pound of grapes is:  44 x + 43 y = 217 , 45x + 18y = 144 .  Each pound of peaches cost $2 and each pound of grapes cost $3

x = price of each pound of peaches

y = price of each pound of grapes.

Given that yesterday,  he sold 44 pounds of peaches and 43 pounds of grapes for a total revenue of $217

So 44 x + 43 y = 217 be equation 1.

Also given that today he sold 45 pounds of peaches and 18 pounds of grapes for a total revenue of $144.

So 45x + 18y = 144 equation 2.

Multiplying equation 1 with 18 gives us,

792x +774y = 3906

Multiplying equation 2 with 43 gives us,  

1935x+774y = 6192

Solving these,

792x +774y = 3906

1935x+774y = 6192

---------------------------------------------

-1143 x=- 2286

x = 2286/ 1143

x = 2

Plug this value of x in equation 1 and solve for y, to get,

44 x + 43 y = 217

44 (2) + 43 y = 217

43 y = 217 − 88

43 y =129

y = 129/43

y = 3

Therefore each pound of peaches cost $2 and each pound of grapes cost $3

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Answer:

[2005]=25.29

Step-by-step explanation:

[tex]y = 7.41 + 2.98x[/tex]

Answer:

Point of intersection is the point where two lines or two curves meet each other. The point of intersection of two lines of two curves is a point.

Step-by-step explanation:

Hope it helps! =D

2 lines intersect at:

A point

In a plane, crossed lines square measure any 2 or a lot of lines that cross each other. The purpose of intersection, which may be found on all crossed lines, is wherever the crossed lines share a standard purpose.

Perpendicular lines square measure 2 lines that cross at associate angle of right angles.

Since the purpose of intersection is that the solely location wherever the 2 graphs meet once the lines cross, the coordinates of that location offer the solution to the equations involving the 2 variables.

There are not any solutions once the lines square measure parallel.

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Answer:

[tex]\frac{1}{12}[/tex] inch per hour

Hope this helps you!

Answer:

3811

Step-by-step explanation:

37X100= 3700

37X3=111

so 3700+ 111= 3811