L Pretest: Unit 2Question 5 of 21Which of the following represents the factorization of the polynomial functiongraphed below? (Assume it has no constant factor.)55

Solution

For this case we have a total cake representing 1

We also know that 1/3 of the cake was left over so then 1/3

And we want to share to 4 friends so we can do this:

1/3 * 1/4 = 1/12

So then each friend will recieve 1/12

Area of the base = 10 x 3 = 30 in^2

Area of the lateral walls = 10 x 2.5 x 2 = 50 in^2

Area of the triangles = 3 x 2 /2 x 2 = 6 in^2

Total area = 30 + 50 + 6

= 86 in^2

The answer is Angle ACB

The angle is form from both line A and C

Step-by-step explanation:

this simply means to put first 5, then 9 and then 12 in place of the x in the function and calculate the 3 results.

a.

after 5 years it is worth

V(5) = -1500×5 + 21000 = -7500 + 21000 = $13,500

b.

after 9 years it is worth

V(9) = -1500×9 + 21000 = -13500 + 21000 = $7,500

c.

V(12) = $3000

means that after 12 years the car is worth only $3000.

let's check

V(12) = -1500×12 + 21000 = -18000 + 21000 = $3000.

correct.

The null hypothesis is H0: P = 0.31 and the alternative hypothesis is Ha: P > 0.31.

The null hypothesis is simply to predict that there is no effect of relationship between the variables.

The alternative hypothesis is to state the research prediction of a relationship or effect. In this case, the newsletter publisher believes that more than 31% of their readers own a Rolls Royce.

The null hypothesis is P = 0.31. while the alternative hypothesis will be that it's greater than 0.31.

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Exponent rule is the following:

Answer

Step-by-step explanation

First, we need to convert the 48'' into minutes. Using the conversion factor: 1' = 60'', we get:

Then, 14 minutes and 48 seconds are equivalent to 14 + 0.8 = 14.8 minutes. To convert this amount of minutes into degrees we need to use the conversion factor 1° = 60', as follows:

In consequence, 6° 14’ 48’’ is equivalent to 6 + 0.247 = 6.247°

Given:

It is given that the perimeter of a quarter circle is 3.57 km.

To find :

The radius of the quarter circle.

Explanation :

The perimeter of the quarter circle is

Substitute the value of perimeter in the above formula

Answer

Hence the radius of a quarter circle is 1.39 km.

It is to be noted that a relations in math can be represented in 8 different ways. See the examples below.

The relation in mathematics is the relationship between two or more sets of values.

The various types of relations and their examples are:

Empty Relation

An empty relation (or void relation) is one in which no set items are related to one another. For instance, if A = 1, 2, 3, one of the empty relations might be R = x, y, where |x - y| = 8. For an empty relationship,

R = φ ⊂ A × A

Universal Relation

A universal (or complete) relation is one in which every member of a set is connected to one another. Consider the set A = a, b, c. R = x, y will now be one of the universal relations, where |x - y| = 0. In terms of universality,

R = A × A

Identity Relation

Every element of a set is solely related to itself via an identity relation. In a set A = a, b, c, for example, the identity relation will be I = a, a, b, b, c, c. In terms of identity,  I = {(a, a), a ∈ A}

Inverse Relation

When one set includes items that are inverse pairings of another set, there is an inverse connection. For example, if A = (a, b), (c, d), then the inverse relation is R-1 = (b, a), (d, c). As a result, given an inverse relationship,

R-1 = {(b, a): (a, b) ∈ R}

Reflexive Relation

Every element in a reflexive relationship maps to itself. Consider the set A = 1, 2, for example. R = (1, 1), (2, 2), (1, 2), (2, 1) is an example of a reflexive connection. The reflexive relationship is defined as- (a, a) ∈ R

Symmetric Relation

If a=b is true, then b=a is also true in a symmetric relationship. In other words, a relation R is symmetric if and only if (b, a) R holds when (a,b) R. R = (1, 2), (2, 1) for a set A = 1, 2 is an example of a symmetric relation. As a result, with a symmetric relationship, aRb ⇒ bRa, ∀ a, b ∈ A.

Transitive Relation

For transitive relation, if (x, y) ∈ R, (y, z) ∈ R, then (x, z) ∈ R. For a transitive relation, aRb and bRc ⇒ aRc ∀ a, b, c ∈ A

Equivalence Relation

If a relation is reflexive, symmetric and transitive at the same time, it is known as an equivalence relation.

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It is found that a relations in math can be represented in 8 different ways.

The relation in mathematics is defined as the relationship between two or more sets of values.

There various types of relations and their examples:

An empty relation (or void relation) is one in which no set items are related to one another.  if A = 1, 2, 3, one of the empty relations might be R = x, y, where |x - y| = 8.

R = φ ⊂ A × A

Universal Relation; It is one in which every member of a set is connected to one another.

R = A × A

Identity Relation; Every element of a set is solely related to itself via an identity .

In a set A = a, b, c, for example, it is I = a, a, b, b, c, c. I

n terms of identity,  I = {(a, a), a ∈ A}

Inverse Relation; When one set of data includes items that are inverse pairings of another set, there is an inverse connection.

For example, if A = (a, b), (c, d), then the inverse is; R-1 = (b, a), (d, c).

R-1 = {(b, a): (a, b) ∈ R}

Equivalence Relation; When a relation is reflexive, symmetric and transitive at the same time, it is calles as an equivalence relation.

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A person who watches TV 11.5 hours can do 36 sit-ups.

Define Regression Analysis

Regression analysis is a mathematical measure of the average relationship between two or more variables in terms of the original units of the data

Given,

y = ax +b

a = -1.073

b = 27.069

r² = 0.434281

r = -0.659

No. of hours TV watched = 11.5 hours

we have , y = ax + b

where, a = 1.073 , b = 27.069 and x = 11.5 hours

put this value in given equation,

y = 1.073 * 11.5 + 27.069

After calculating, we get

y = 39.4085 or 39

Therefore, a person who watches TV 11.5 hours can do 36 sit-ups.

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La variable x asociada al sistema geométrico con dos ángulos alternos externos es igual a 23.

En esta pregunta tenemos un sistema geométrico conformado por dos líneas paralelas atravesadas por una tercera línea. Este conjunto incluye dos ángulos alternos externos, que guardan la siguiente relación según la geometría euclídea:

6 · x - 28 = 4 · x + 18

A continuación, despejamos la variable x:

6 · x - 4 · x = 28 + 18

2 · x = 46

x = 23

El valor de la variable x es 23.

No existen preguntas en español sobre ángulos alternos externos, por lo que se añade una pregunta en inglés.

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To find the median of a set of numbers, the first step is:

1 - Put the numbers in crescent order

This set of numbers is already in crescent order, so we can skip this step

2 - Count how many numbers there are in the set.

In our set we have 8 numbers, so in this case, the median of the set will be the average value between the two central numbers (that is, the fourth and fifth numbers)

The fourth number is 27, and the fifth number is 53, so the median is the average of these two numbers:

So the median of this set of numbers is 40.

Solution

Given a rectangular pan and two round pans

The volume, V, of the rectangular pan is 234 in³

A round pan is in the form of a cylinder

To find the volume, V, of the a round pan, the formula is

Where

Substitute the variables into the formula above

Since, there are two round pans, the volume of the two round pans will be

nce, the volume of the two round pans is 201.06 i³.

Since the volume of the two round pans (201.06in³) is less than the volume of the rectangular pan (234in³), the rectangular pan will hold more.

Hence, the answer is rectangular pan (option a)

The general form of a logarithmic function is:

Where a is the coefficient and b is the base. In the given picture, we can see that the coefficient is equal to 1, while the base is equal to 2.

We have to calculate the present value PV of a annuity.

The payment is yearly and it is P=60,000.

The interest rate is 5% (r=0.05), compounded annually (m=1).

The number of periods is n=20 years.

Then, we can use the formula for the present value of a annuity:

Answer: the company must set aside $747,720.

The graph of the given equations as;

-2x-y ≥2

The graph of the inequality y ≥-2

The graph of the inequality, x ≥-4

Now, the graph for the set of the system as;

...

We have two equations, the first is a circle, which we can identify by the characteristic form of the equation:

The second is a quadratic equation:

We know that Sasha got the bag to land in the edge of the circle defined by the hole, equation 1.

So, to know the points at which the bag landed, we can look for th eintersection of the two equations, which is the same as solving a system of equations:

Since we have been given alternatives, we can check them to get the correct answer.

The first option is (-1,-2) or (-2,1). Since the sign of the alternatives are the only thing that change and the circle equation doesn't differenciate the signs, the best equation to test first is the second one. Let's try that for (-1,-2).

We got y = 5, which is not -2, so this alternative is incorrect.

Let's got for the second alternative, (1.-2) or (2,1):

This is also incorrect.

The third alternative is (-1,2) or (-2,-1), we already saw that for x = -1, y = 5, which makes this alternative also incorrect.

Let's check if the last one will be correct, (1, 2) or (2, -1). We already saw that for x = 1, y = 2 in the second equation, let's check if this is also correct for the first:

One of the results is y = 2, so this also checks out.

The other point is (2,-1), let's check in both equations:

Checks out, and:

And the "y" checks out too.

So, the correct alternative is the last one: (1, 2) or (2, -1).

We can calculate the slope of a line using the formula

Let's say that

Therefore

Using the formula

The slope of the line passing through points (-8, 8) and (7,8) is 0. Which means it's a constant function (horizontal line).

Let's begin by listing out the information given to us:

The coldest temperature ever recorded on earth (T1) = -135.8 Fahrenheit

The hottest temperature ever recorded on earth (T2) = 134 Fahrenheit

The difference between the two temperature = Hottest - Coldest temperature

SOLUTION

perimeter of rectangle = 88cm

let the widht be x

now, according to question

lenght = 3x ( as it is triple of width)

formula of rectangle perimeter

88cm = 2* (length + width)

88cm = 2(3x+x)

88cm = 4x (2 will be transported to left )

88/2 cm = 4x

( 2 become in divide as in right it was in multiply)

44 cm = 4x

x= 44/4

x= 11cm

according to question,

width of rectangle = x = 11 cm

Let the coordinates of the pre-image which is point A be (x,y)

The point after the translation left 2 units and down 5 units is B(-8, -11)

To get the x coordinate

we were tolt that the point was move 2 units left

So this implies x = -8+2 = -6

To get the y coordinates, we wre told that the point was moved down 5 units

This implies y = -11+ 5 = -6

Therefore, the coordinates of the pre-image point A is (-6, -6)

Given the following question:

Your answer is 10.

Here, we want to get the length of the third side

Mathematically, we can get this by the use of Pythagoras' theorem

It states that the square of the length of the hypotenuse equals the sum of the squares of the two other sides

Let the missing side be s

From the diagram, we have the hypotenuse as 25 (the hypotenuse is the longest side and it is the side that faces the right angle

We have this as;

if he removes his lowest score the average increases, then if we remove 80 the new average is

new average is 92.5

Using the exponent rules, 10^-2 can be expressed as follows:

Substituting into the expression in scientific notation, we get:

The triangle is isosceles, since two of its sides are equal. Besides, the little triangles ABD and CBD are congruent and this can be concluding using the criterion SSS , since they share one side, and the other sides are equal. Then the angles are congruent, and the angles ADB and CDB are congruent and have the same measure. Then

Then, the measure of angle CDB is 32 degrees.

SOLUTION

Comparing the graphs and the options, it follows that each line on the graph represents 5 points. This means the person 6 obtained a score of 45, comparing this to the person 3, it means the person 3 obtained a score of 35.

So the answer is 35.

For the rating since person 6 has the highest possible score, which is 45, person 3 score becomes

so we can classify person 3 as very good

The equation:

4x² - 5 = 3x + 4

First, we need to re-arrange in the form : ax² + bx + c

4x² - 5 = 3x + 4

4x² - 3x -5 -4 = 0

4x² - 3x -9 =0

comparing the above with ax² + bx + c

a= 4 b= -3 c=-9

we will then substitute the values into the quadratic formula: