Unit 8: Polygons & Quadrilaterals
Homework 7: Trapezoids

Note that where Tom Harris is 24 years old and he wishes to purchase a $7,000 value 10-year term insurance, his annual premium will be:  $290.5.

Gross premiums written in the insurance sector are the sum of direct and assumed premiums written before subtracting ceded reinsurance. Direct premiums written are the premiums on all policies issued by the company's insurance subsidiaries throughout the fiscal year.

To compute Tom's insurance premium we must use the information given as well as the table above:

Given:

Tom's Age = 24 years

Value of Insurance Cover Requested = $7,000

Type of Insurance cover requested = 10-Year Term

The rate for the Type of Insurance Cover requested: Since he 24 and wants a 10-year term, the rate applicable from the table is; 4.15%

Thus, his annual premium  = 7000 * 4.15%
= 29050/ 100
= $290.5

Thus, Tom Harris' annual insurance premium is: $290.5

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a) The possible rational zeroes of the function are: ±1, ±2, ±3, ±6

b) The possible number of positive, negative, and imaginary roots of the function are: 0 to 2 positive roots, 0 to 2 negative roots, An odd number of imaginary roots.

What is Descartes' Rule?

The number of real zeros in a polynomial function is determined using Descartes' rule of sign. It states that the number of positive real zeros in a polynomial function f(x) is equal to or fewer than the number of changes in the sign of the coefficients.

a) To find the possible rational zeroes of the function, we can use the Rational Root Theorem, which states that if p/q is a rational zero of a polynomial with integer coefficients, then p must divide the constant term (in this case, -6) and q must divide the leading coefficient (in this case, 2).

The possible rational zeroes of the function are: ±1, ±2, ±3, ±6

b) To use Descartes' Rule of Signs to determine the number of positive, negative, and imaginary roots of the function, we count the number of sign changes in the coefficients of the polynomial. In this case, the signs are +, +, -, +, +, so we have two sign changes. Descartes' Rule of Signs states that a polynomial with n sign changes will have either n or n-2 positive roots. Since n=2 in this case, the polynomial can have either 0 or 2 positive roots. The same is true for negative roots. Additionally, if the degree of the polynomial is odd and the leading coefficient is positive, the polynomial will have an odd number of imaginary roots.

Therefore, The possible number of positive, negative, and imaginary roots of the function are:

0 to 2 positive roots

0 to 2 negative roots

An odd number of imaginary roots.

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The results of the expressions are;

1)  192

2) 3

3) 1024

We have to note that when we say that there is an expression, the implication of that is that the equality sign is missing in the mathematical statement as it has been written.

We know that;

1) a*b

a=8

b=24

8*24

= 192

2)  b/a

b/a

b=24

a=8

24/8

= 3

3)  (a+b)^2

a=8

b=24

(8+24)^2

= 1024

This is the way that we can be able to obtain all the expressions that we have in the question that is shown here.

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Missing parts;

Use a = 8 and b = 24 to work out the value of these expressions. b) ab c) b/a d) (a + b)^2

Answer: Undifined!

Step-by-step explanation: Division by zero is considered an invalid operation in mathematics because there is no number that can be multiplied by zero to produce the original number. In other words, there is no single valid answer to dividing by zero. Example: You have 0 cookies and you want to share them among 9 friends. There's no way to share, since you don't have cookies haha!

Answer:

Step-by-step explanation:

An expression without a value is referred to as being undefined; it has an indeterminant form. When a number is divided by zero, it usually has no specified meaning. Mathematically, we can't divide by zero because the result is an equation we can't compute.

Step-by-step explanation:

The equivalent expression in the form of a product is:

(8x) * (4x + 6)

The average rate of change of g(x) = -x3 + 2 is therefore -51/5 from x = -1 to x = 4.

The slope of the secant line connecting two points on a function across an interval represents the average rate of change of that function over that interval. We must determine the slope of the secant line that connects the points (-1, g(-1)) and (4, g(4)) in order to calculate the average rate of change of g(x) = -x³ + 2 from x = -1 to x = 4.

g(-1) = -(-1) (-1)

4³ + 2 = -1 + 2 = 1 \sg(4) = -4^3 + 2 = -52 + 2 = -50

The secant line's slope is therefore ((-50) - 1) / (4 - (-1)) = -51 / 5

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Answer:1. y=2x+3

             2. y=-1x-2  

             3. y=-3x+4

             4= y=3x+0

Answer:

To solve the expression [(4r²t)³]², you need to follow the order of operations (PEMDAS):

Calculate the expression inside the outermost parenthesis first: (4r²t)³ = (4 * r^2 * t)^3, where r and t are variables.

Raise the result to the power of 3: (4 * r^2 * t)^3 = 64 * r^6 * t^3.

Raise the result to the power of 2: (64 * r^6 * t^3)^2 = 4096 * r^12 * t^6.

So, [(4r²t)³]² = 4096 * r^12 * t^6.

Step-by-step explanation:

The amount of compound remaining from a 84-ounce sample after seven weeks is 4.32 ounces.

Given a half-life of 5 days and a sample of 84 ounces, the exponential decay function can be represented as:

A(t) = 84 * (1/2)^(t/5)

Where A(t) represents the amount of the compound remaining after t days.

To find the amount of compound remaining after 7 weeks

7 weeks * 7 days/week = 49 days,

we can substitute t = 49 into the function:

A(49) = 84 * (1/2)^(49/5)

A(49) = 84 * (1/2)^9.8

A(49) ≈ 4.32 ounces

So, the amount of the compound remaining after 7 weeks would be approximately 4.32 ounces.

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1. [tex]m\angle BOC=45^{\circ}[/tex] since angles on a straight line add to [tex]180^{\circ}[/tex]

2. [tex]m\angle DOE=60^{\circ}[/tex] because vertical angles are congruent

3. [tex]m\angle AOE=120^{\circ}[/tex] because vertical angles are congruent

Answer:

9.818 years after 2008

Step-by-step explanation:

Y_A = 0.35 * X + 9.6

Y_B = 0.9 * X + 6.5

Equal in year X = (Y_B - Y_A) / (0.35 - 0.9) = (6.5 - 9.6) / (-0.55) = 9.818 years after 2008

X = 9.818 + 2008 = 2018.818

Y_A = 0.35 * (2018 - 2008) + 9.6 = 14.3 billion

Y_B = 0.9 * (2018 - 2008) + 6.5 = 15.3 billion

The quantity that will be left after 35 seconds would be =-71.5%

The quantity of radioactive Beryllium-11 isotope that was used to start the experiment = 100%

The rate at which the isotope decays= 4.9%/second

The quantity that will remain after 35 seconds = ?

That is;

4.9% = 1 second

x% = 35 seconds

make X the subject of formula;

X = 4.9×35

X= 171.5

The quantity that will be left = 100-171.5 = -71.5%

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The measure of angle 4 is 90 degrees

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

The rectangle

Also, we have

<5 = 12x -3

<6 = 10x + 9

Angles 5 and 6 add up to 90

So, we have

12x - 3 + 10x + 9 = 90

Evaluate the like terms

22x = 84

So, we have

x = 3.82

The angles in a triangle add up to 180

So, we have

<4 + 12 * 3.82 - 3 + 10 * 3.82 + 9 = 180

Evaluate

<4 = 90

Hence, the measure o this angle is 90 degrees

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Answer:1/6 can be represented as a fraction of a whole unit, where the whole unit is divided into 6 equal parts. Each of these parts represents 1/6 of the whole.

1/2, on the other hand, represents half of the whole unit, so it is twice as much as 1/6.

To visualize this, you can think of a ruler divided into 6 equal parts. 1/6 would represent 1 mark on the ruler, while 1/2 would represent 3 marks. To have the same length as 1/2, you need to add up 3 marks, or 3 copies of 1/6.

You can also think of this as converting 1/6 to a common denominator, which in this case is 6. 3 copies of 1/6 is equal to 3/6 or 1/2.

Step-by-step explanation:

1/6 can be represented as a fraction of a whole unit, where the whole unit is divided into 6 equal parts. Each of these parts represents 1/6 of the whole.

1/2, on the other hand, represents half of the whole unit, so it is twice as much as 1/6.

To visualize this, you can think of a ruler divided into 6 equal parts. 1/6 would represent 1 mark on the ruler, while 1/2 would represent 3 marks. To have the same length as 1/2, you need to add up 3 marks, or 3 copies of 1/6.

You can also think of this as converting 1/6 to a common denominator, which in this case is 6. 3 copies of 1/6 is equal to 3/6 or 1/2.

Answer:

( 0,1)

Step-by-step explanation:

y-4x=1

We want to find the y-intercept ( where it crosses the y-axis).

Let x = 0

y-4*0=1

y = 1

The coordinates of the y-intercept are ( 0,1).

The predicted interval for the given function is, f(x) ≥ 0 over the interval [-1,1]. So Option C is correct

Function is a relation between a set of inputs and a set of outputs which are permissible. In a function, for particular values of x we will get only a single image in y. It is denoted by f(x).

Vertical line test:-

Whenever we want to check whether a given expression is a function or not we can apply a vertical line test, in this test we check for a single image of x , we are getting a single image or more.

If we get more images then it will not be a function.

For example, let us take, y² = 4ax

y = ±√4ax

For single value of x we get two values of y

Hence, it will not be a function.

Given that,

The ordered pairs of the given function

(-3,15), (-2,-5), (-1,0), (0,5), and (1,0).

It can be observed from the values of f(x) with respect to x, that the function reaches zero at x = -1, then then reach up to 5 at x = 0 and then again reaches zero at x = 1

Hence, the value of f(x) remains positive within the interval of [-1,1].

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To locate the fractions we must divide the unit in the number of the denominator (point A). According to the information, each shell symbol means 2 shells. Mark found 4 fewer shells than Tania. Mark and Carlos found 10 more shells than Mei Ling. Lastly, the numbers are rounded to the nearest number.

To locate the fractions we must divide the unit in the part number that says the denominator of the fraction and locate the fraction in the numerator position as shown in the graph. They all go in the first position.

Based on the information in the graph, it can be established that:

To approximate the numbers we must identify which of the numbers in the graph is closest:

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Answer: 67.1 cm

Step-by-step explanation:

Using the Law of Sines:

[tex]\frac{i}{\sin I}=\frac{h}{\sin H}\\\\\frac{i}{\sin 24^{\circ}}=\frac{97}{\sin 144^{\circ}}\\\\i=\frac{97 \sin 24^{\circ}}{\sin 144^{\circ}}\\\\i \approx 67.1 \text{ cm}[/tex]

Answer:  67.1

Step-by-step explanation:

The fraction 6/5 represents the scale factor of one rectangle towards the other. The figure has been shown.

The scale factor is defined as the ratio of the modified change in length to the original length.

Here,
one rectangle = 6/5 [original rectangle]
one rectangle / original rectangle = 6 / 5
Scale factor [for the rectangle] = 6/5

Thus, the fraction 6/5 represents the scale factor of one rectangle towards the other. The figure has been shown.

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Answer: 4

Step-by-step explanation:

3x4+12

------------ (over)

6

12+12

---------

6

24

----- = 4

6

The correct inequality that represent the dogs could he have walked on Saturday is,

⇒ 100 + 12.50x > 210

A relation by which we can compare two or more mathematical expression is called an inequality.

We have to given that;

On Saturday, Dylan earned $100 for cleaning a local business.

And, He also walked dogs to earn money, charging $12.50 for each dog he walked.

Now, Let number of dogs = x

Then, We get;

The correct inequality that represent the dogs could he have walked on Saturday is,

⇒ 100 + 12.50x > 210

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X2 + 7x + 10 = 0 has roots -5 and -2, the answer.

x2 + 7x + 10 = 0 is a mathematical equation.

x2 + 5x + 2x + 10 = 0 [dividing the middle term] is another way to express the aforementioned equation.

After factoring 2 from the second term of the expression, 2x + 10, and x from the first term of the expression, (x2 + 5x), the expression may be broken down into its constituent parts.

We obtain the factorized equation as follows: x (x + 5) + 2 (x + 5) = 0.

Now we can calculate (x + 2) (x + 5) = 0 by utilizing the distributive property.

The result of separately equating both terms with 0 is,

The equation x2 + 7x + 10 = 0 has -5 and -2 as its roots.

The Complete Question is :

How to Find the roots of the equation x2 + 7x + 10 = 0?

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The expression can be written as: a * b + 5.

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

The product of a and b increased by 5.

The product of a and b is represented as

a * b

Increased by 5 means

a * b + 5

So, the expression is a * b + 5

The expression "a * b + 5" represents the mathematical operation of first multiplying two values, 'a' and 'b', and then adding 5 to the result.

The '*' symbol is used for multiplication, and the '+' symbol is used for addition.

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Answer:

25 is X

Step-by-step explanation:

Answer:

25

Step-by-step explanation:

1+3=4

4+5=9

9+7=16

16+9=25

3+2=5

5+2=7

7+2=9

The function at its maximum value will be at point (9,2) and its value is 51 which can be derived keeping in mind the constraints that have been given.

The maximum value of any kind of a function is the place where the said function reaches its highest point, or vertex, on a graph. If your kind of quadratic equation has something as a negative of a term, it will also have a maximum value.

There are a bit of three ways to find that maximum, depending on which form of a quadratic function you have got.

here, we have,

Herein we can find the closed region ABC from the three equations or constraints given

and can mark the points as

A = (2,2)

B = (5, 2)

C = (9, 2)

if we put up the values of the points, we get

at (9, 2) ,

z=5x+3y

 =45+6

  =51 that is the maximum value amongst the three.

Thus, the maximum point of the function can be calculated as (9,2)

How do you extract out the maximum or minimum value of a function?

We will at first set out the first derivative of the function to absolute zero and then solve for x to get the exact critical point.

If we then take the second derivative or f’’(x), there in we can find out whether this point will be a maximum or minimum. If the second derivative is seen as positive, it will be a minimum value

What is the maximum value of a function called?

The maximum or minimum value that is calculated over the entire function is called an “Absolute” or “Global” maximum or minimum of the function.

There is presence of only one global maximum (and only one global minimum) but there can be several that is more than one local maximum or minimum

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Answer:

Step-by-step explanation:

The graph of y = 2x + c is a straight line with a slope of 2 and a y-intercept of c. The value of k cannot be determined from the equation alone, as it depends on the value of the constant c. To find the value of k, you would need additional information such as the coordinates of a point on the line or the x and y values that correspond to a specific k.

Answer:

16.7%

Step-by-step explanation:

84 - 70 = 14

14 divided by 84, times 100 = 16.7%

So, it increase by 16.7%

The larger television is Vehicle Viewing, explanation is mentioned below,

The diagonal of a television refers to the length of a line segment connecting two opposite corners of the screen. It is a way of measuring the size of the television screen, rather than its width or height. The diagonal measurement gives a good indication of the overall screen size and is commonly used as a specification for television screens.

Given that,

Two television,

Vehicle Viewing having diagonal 75 inches

Traveling TV Co having diagonal 8.5 inches

larger television =?

Vehicle Viewing, Inc. has the larger television with a diagonal of 75 inches compared to Traveling TV Co.'s diagonal of 8.5 inches.

This can be determined by simply comparing the two diagonal measurements given.

Hence, the larger television is Vehicle Viewing.

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