3) Decide if each of the following statements are true or false. If true, give a mathematical explanation. If false, give a counterexample.

a) If a quadrilateral is a square, then it is a rectangle.

b) If a quadrilateral has a pair of parallel sides, then it must have a pair of opposite
sides that are congruent.

c) If the diagonals of a quadrilateral are perpendicular to each other, then the
quadrilateral is a rhombus.

d) If a quadrilateral has one right angle, then all of its angles must be right angles.

e) Write the converse of each of the statements in a)–d) above. Which is true?

f) Write the contrapositive of each of the statements in a)-d) above. Which is true?

The difference in rainfall between the wettest and driest months is 3.97 inches.

A bar graph is a graphical depiction of information, amounts, or numbers using bars or strips. They are utilized to contrast and compare various data types, frequencies, or other measurements of several categories of data.

On the graph, there are two axes. The numerical data is displayed against the category data on one axis, which is used to depict the numerical values.

Given the graph which shows the rainfall of the wettest and driest months,

here red blocks are for the driest months and blue blocks show the wettest months,

From the graph, we can see that the wettest month has a rainfall height of 2.3 inches

The driest month has a rainfall of -1.67 inches

So the difference between the two will be;

2.3 - (-1.67)

=  2.3 + 1.67 = 3.97 inches

Hence the difference is 3.97 inches.

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The complete question is,

The bar graph shows the differences in a city’s rainfall from the historical average. What is the difference in rainfall between the wettest and the driest months? Write your answer as a decimal.

The difference in rainfall between the wettest and the driest months is inches.

The amount invensted at 5% and 7% are 3500 and 4500 respectively.

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.

Given that, an amount $8000, is invested at 5% and 7%, with annual interest is $490,

For this we will establish the a system of equations,

x + y = 8000......(i)

0.05x + 0.07y = 490

Multiplying by 100,

5x + 7y = 49000.....(ii)

Multiplying eq(i) by 5,

5x + 5y = 40000

Subtract eq(i) from eq(ii)

2y = 9000

y = 4500

Put y = 4500 in eq(i)

x = 8000 - 4500

x = 3500

Hence, the amount invensted at 5% and 7% are 3500 and 4500 respectively.

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The difference in rainfall between the wettest and driest months is the amount of precipitation.

Precipitation refers to any form of moisture that falls from the atmosphere to the ground, including rain, snow, sleet, hail, and other forms of precipitation. Precipitation is an important aspect of the Earth's water cycle, as it provides the water that replenishes rivers, lakes, and aquifers, and sustains the growth of plants and animals.

The amount of precipitation that falls in a given area can vary widely, depending on many factors such as geography, temperature, and prevailing weather patterns. For example, areas near the equator tend to receive more rainfall than areas located closer to the poles, and areas with high elevations tend to receive more snow than areas that are closer to sea level.

The distribution of rainfall and other forms of precipitation across a region can also be affected by the prevailing winds, air masses, and topographical features. For example, mountainous areas may receive more rainfall due to the prevailing winds and the way that air masses interact with the terrain.

The difference in rainfall between the wettest and driest months is the amount of precipitation that occurs in the wettest month minus the amount of precipitation that occurs in the driest month. This difference can vary greatly depending on the location and climate of a region.

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Answer:

A

Step-by-step explanation:

please memorize this formula for area of sphere

A=4π r²

so d = 22, which means r=11

so A = 4* π*11² = 4*121*π =484π = 1519.76

x = 15/2

do u need an explanation?

The sum of the measures of the exterior angles of the polygon is,  360°

An angle is a mathematical term, which we can define, when two straight lines or rays meet at a common endpoint. The common point is called the vertex of an angle. The word angle comes from a Latin word named ‘angulus,’.

Interior angles:- The inner angle made by the intersection of two polygonal sides.

Exterior angles:- The outer angle made by the intersection of two polygonal sides.

Given that,

A polygon,

Having 9 equal sides,

The sum of the measures of the exterior angles of the polygon = ?

The sum of each interior & exterior angles are 180°

Suppose, interior angles  are respectively

a, b, c, d, e, f, g, h, i,

Now, exterior angles are respectively

180°-a, 180°-b, 180°-c, 180°-d, 180°-e, 180°-f, 180°-g, 180°-h, 180°-i,

The sum of the measures of the exterior angles of the polygon =

180°-a  + 180°-b +180°-c +180°-d + 180°-e + 180°-f  + 180°-g +180°-h + 180°-i,

1620 - (a + b + c + d + e + f + g + h + i)

Sum of all the interior angles  = (9-2)x180°

                                                  =  1260°

The sum of  the exterior angles of the polygon =  1620 - 1260°

                                                                               =   360°

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The least number of plates and cups she can buy is 24. She will buy 3 packs of plates and 2 packs of cup

The ratio can be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects.

Given, ria is buying plates and cubs for a party. she wants the same numbers of each. Plates are sold in packs of 8. cups are sold in packs of 12.

Plates = 8 per pack

Cups = 12 per pack

the Lowest common multiple of 8 and 12

8 = 16, 24, 32, 40, 48, 56, 64, 72, 80

12 = 24, 36, 48, 60, 72

The Lowest common multiple of 8 and 12 is 24

The least number of plates and cups she can buy is 24

Packs of plates = 24 plates / 8 per pack

= 3 packs

She will buy 3 packs of plates

Packs of cups = 24 / 12 per pack

= 2 packs

She will buy 2 packs of cup

Therefore, The least number of plates and cups she can buy is 24. She will buy 3 packs of plates and 2 packs of cup

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AB vector is a vector whereas AB bar is a line segment.

What is a vector ?

The vectors are described as an object containing both significance and course. Vector describes the motion of an item from one point to any other. Vector math may be geometrically picturised via the directed line segment.

The duration of the phase of the directed line is known as the value of a vector and the angle at which the vector is inclined shows the path of the vector. The start line of a vector is referred to as “Tail” and the finishing factor (having an arrow) is referred to as “Head.”

The difference is in their names itself.

AB vector is a vector whereas AB bar is a line segment.

A vector has a direction and a magnitude while a line segment ( scalar ) has only magnitude.

Therefore, AB vector is a vector whereas AB bar is a line segment.

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Answer:

sec 30° = 1/cos 30° = 2.

Step-by-step explanation:

The secant function (sec) is the reciprocal of the cosine function. So, sec(x) = 1/cos(x). The value of cosine at 30 degrees is sqrt(3)/2, and its reciprocal is 2/sqrt(3), which can be simplified to 2. Hence, sec(30°) = 2.

Answer:

[tex]\angle A= 27.2 \textdegree\\\angle B=37.3 \textdegree\\\angle C=115.5 \textdegree\\[/tex]

[tex]a=38.5[/tex] ft

[tex]b=51[/tex] ft

[tex]c=76[/tex] ft

Step-by-step explanation:

Here is the formula for the Law of Sines.

[tex]\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}[/tex]`

In this example we are given

[tex]\angle A =27.2 \textdegree\\\angle C=115.5 \textdegree\\c=76.0[/tex]

Angle B

The sum of the interior angles in a triangle add up to 180º. Given 2 angles, we can evaluate the 3rd.

[tex]180\textdegree-115.5\textdegree-27.2\textdegree=37.3 \textdegree[/tex]

[tex]\angle B=37.3 \textdegree[/tex]

Side a

We can use the Law of Sines formula  [tex]\frac{a}{\sin A}=\frac{c}{\sin C}[/tex]  to evaluate side a.

Inserting our values into the equation gives us

[tex]\frac{a}{\sin 27.2}=\frac{76}{\sin 115.5}[/tex]

Cross multiply to evaluate side a.

[tex]76*\sin 27.2=a*\sin 115.5[/tex]

Divide both sides by [tex]\sin 115.5[/tex].

[tex]\frac{76*\sin 27.2}{\sin 115.5} =a[/tex]

[tex]38.49=a[/tex]

Side b

We can use the Law of Sines formula  [tex]\frac{b}{\sin B}=\frac{c}{\sin C}[/tex]  to evaluate side b.

Inserting our values into the equation gives us

[tex]\frac{b}{\sin 37.3}=\frac{76}{\sin 115.5}[/tex]

Cross multiply to evaluate side b.

[tex]76*\sin 37.3=b*\sin 115.5[/tex]

Divide both sides by [tex]\sin 115.5[/tex].

[tex]\frac{76*\sin 37.3}{\sin 115.5} =b[/tex]

[tex]51.03=b[/tex]

[tex]\angle A= 27.2 \textdegree\\\angle B=37.3 \textdegree\\\angle C=115.5 \textdegree\\a=38.5\\b=51\\c=76[/tex]

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sin(A) / a = sin(B) / b = sin(C) / c

where A, B, and C are the angles of the triangle, and a, b, and c are the lengths of the sides opposite those angles.

Answer: 58.5

Step-by-step explanation: 65.00 - 10% = 58.5

Answer: $58.50

Step-by-step explanation: Orignal Price: $65.00

10% discount = -$6.50

$65.00 - $6.50 = $58.50.

The exponential function from the table is f(x) = 2 [tex](0.5)^x[/tex].

The graph is given below.

Option D is the correct answer.

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

The exponential function is given as,

f(x) = m[tex]a^x[/tex]

Now,

From the table,

2 = m[tex]a^0[/tex]

m = 2

1 = m[tex]a^1[/tex]

m = 1/a ____(1)

0.5 = m[tex]a^2[/tex]

m = 0.5/[tex]a^2[/tex] _____(2)

Now,

From (1) and (2).

1/a = 0.5/[tex]a^2[/tex]

a = 0.5

Now,

f(x) = 2 [tex](0.5)^x[/tex]

Thus,

The exponential function is f(x) = 2 [tex](0.5)^x[/tex].

The graph is given below.

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The expression to represent the given statement is:33 - (2 * 22 * ½x)

The expression "33 - (2 * 22 * ½x)" represents a mathematical calculation. Breaking it down, we start with the product of 2 multiplied by 22, which equals 44. Then, we multiply the result by ½x, where ½ represents one-half and x is a variable. This gives us the term 44 * ½x. Finally, we subtract this term from 33. In simpler terms, we have 33 minus half of 44 times x. The expression allows us to compute the value of the expression based on the input for the variable x, providing a way to evaluate the equation numerically.Let's dive deeper into the explanation.

The given expression is "33 - (2 * 22 * ½x)".

To simplify it, let's break it down step by step:

The term "2 * 22" is a multiplication operation that calculates the product of 2 and 22, resulting in 44.

Next, we have "½x". Here, ½ represents one-half, or 0.5. Multiplying 0.5 by x gives us 0.5x.

Putting it together, we have the term "44 * ½x". This means multiplying 44 by 0.5x, resulting in 22x.

Finally, we subtract the term "22x" from 33, giving us the expression "33 - 22x".

In summary, the expression represents the number 33 minus the product of 22 and the value of x, denoted as 22x. This expression allows us to calculate the result by substituting a specific value for x. It provides a way to compute the numerical outcome based on the given mathematical relationship.

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The graph of the function y = f(x + 16) is a transformation of the original function f. This transformation has shifted the graph of f to the right by 16 units on the x-axis. This means that the value of x in the original function has been increased by 16, which has an effect on the corresponding value of y in the transformed function.

For example, if the point (a, b) is on the graph of f, then the point (a + 16, b) will be on the graph of y = f(x + 16). The x-coordinate of the point has been increased by 16, and since the transformation is a horizontal shift, the y-coordinate remains unchanged.

In summary, the graph of y = f(x + 16) is a reflection of the graph of f about the vertical axis. The transformation has the effect of shifting the graph to the right, but preserving the shape and overall form of the original function.

The correct statements regarding the translation from function f(x) to function g(x) are given as follows:

A translation happens when either a figure or a function are moved horizontally or vertically.

The four translation rules for functions are given as follows:

The translations for this problem are defined as follows:

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The area of the given rectangle will be A = 9x² - 64 yards².

What is a rectangle?

Rectangles are quadrilaterals having four right angles in the Euclidean plane of geometry. Various definitions include an equiangular quadrilateral, A closed, four-sided rectangle is a two-dimensional shape. A rectangle's opposite sides are equal and parallel to one another, and all of its angles are exactly 90 degrees.

The area of the rectangle is A = a*b

Given is l =(3x+8) yards

b = (3x-8)yards

So the area of the rectangle is A = l*b

A = (3x+8)(3x-8)

A = 3x² - 8²

A = 9x² - 64

hence the area of the given rectangle will be A = 9x² - 64 yards².

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the equation of  line passes through points (0, -3) and (4, -1) is 4y  = 3x -12.

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.

Given, an equation of a line in the graph.

Since the graph shows that the line passes through points (0, -3) and (4, -1).

The slope-intercept form of the equation of a line

y=mx+b,

where m is the slope

b is the y-intercept (value of y at x =0)

since

slope = (y - y')/(x -x')

In our case,

slope (m) = (-1 - (-3))/(4 -0)

m = 3/4

b = -3

Thus, the equation of the line:

y = 3/4x - 3

or, 4y  = 3x -12

therefore, the equation of the line will be 4y  = 3x -12.

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The value of x is given as follows:

x = 24.

The measure of angle DFE is given as follows:

<DFE = 62º.

To obtain the measures, we consider that the sum of the measures of the internal angles of a triangle is of 180º.

The internal angle measures for this problem are given as follows:

Hence the value of x is obtained as follows:

180 - 5x + 14 + 44 + 3x - 10 = 180

228 - 2x = 180

2x = 48

x = 24.

The measure of angle DFE is obtained as follows:

<DFE = 3(24) - 10

<DFE = 72 - 10

<DFE = 62º.

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Answer: D. [tex]5\sqrt{3}[/tex]

Step-by-step explanation:

[tex]\tan 30^{\circ}=\frac{x}{15}\\\\x=15 \tan 30^{\circ}\\\\x=5\sqrt{3}[/tex]

The truth about the pattern that we have here is that all of the numbers are:    odd.

In the number pattern given, each term is 2 less than the previous term. Starting from 13, we have 11 (13 - 2), 9 (11 - 2), and 7 (9 - 2). All of these numbers are odd, making answer D the correct choice.

A. All the numbers are multiples of 3: This is not true, as 9 is the only number that is a multiple of 3.

B. All the numbers are even: This is not true, as all of the numbers are odd.

C. All of the numbers are prime: This is not true, as 9 is not a prime number.

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Answer: 540°.

Step-by-step explanation:

by

Answer:

0.955

Step-by-step explanation:

Height= volume x pi x radius squared (h = V x pi x r^2)

Volume (V) = 243

Height (h) = ?

Pi = 3.14

Radius (r) = 9

Diameter to radius = 18/2 = 9

h = 243 x 3.14 x 9^2

=0.955

x > -2

Inequalities compare the values of 2 expressions.

Solving for x

To solve the inequality, we need to isolate x. First, add 4 to both sides.

Then, divide by 5.

Finally, divide both sides by -1. When multiplying or dividing an inequality by a negative, switch the direction of the sign.

Interpreting the Answer

Verbally, the answer is that x is greater than or equal to -2. This means that any x-value greater than -2 (including -2 itself) will make the original inequality, −5x−4 ≤ 6, true. For example, let's plug in 0.

This statement is true, which proves our answer is correct.

Answer:

Nope

Step-by-step explanation:

No, because if you add the angles of B and C (since they're asking for line BC), they must equal the angles of A and D (Since the other line was AD)

The sum of B and C is 90+45 which = 135

The sum of A and D is 90+135 which = 225

135 =/= 225

The value of function relating the number of people, n, to the cost, C is,

⇒ C (n) = 7n ; if 0 < n < 15

           = 105n ; if n ≥ 15

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

A museum charges $7 per person for a guided tour with a group of 1 to 14 people or a fixed $105 fee for a group of 15 or more people.

Hence, he value of function relating the number of people, n, to the cost, C is,

⇒ C (n) = 7n ; if 0 < n < 15

           = 105n ; if n ≥ 15

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Based on the manufacturing overhead applied to production during the period of $432,000, the fixed manufacturing overhead cost is $286,200.

The manufacturing overhead applied is determined as the product of the predetermined overhead rate and the actual machine hours consumed during the period.

Estimated machine hours to be worked = 55,000 hours

Actual machine hours during the period = 54,000 hours

Total manufacturing overhead applied to production = $432,000

Estimated variable manufacturing overhead per machine hour = $2.70

Total variable manufacturing overhead = $145,800 ($2.70 x 54,000)

Fixed manufacturing overhead (MOH) cost = $286,200 ($432,000 - $145,800)

Thus, the fixed manufacturing overhead cost is the difference ($286,200) between the total overhead cost applied and the variable manufacturing overhead cost.

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Answer:The length of AC to one decimal place in the trapezium is 18.1 cm

Step-by-step explanation: Using Pythagoras theorem, we can find the length AC

Pythagoras theorem

c² = a² + b²

Therefore, draw a line from the point B to the line AD and call it line BX.

BX ║ CD

Therefore,

16² - 7² = BX²

256  - 49 = BX²

BX² = 207

BX = √207

BX = 14.3874945699

BX = 14.4 cm

Therefore,

11² + 14.4² = AC²

121 + 207.36 = AC²

AC = √328.36

AC = 18.120706388

AC = 18.1 cm

Answer:

x intercept: (0,0)

Step-by-step explanation:

y intercept: (0,0)