For 5 years, Gavin has had a checking account at Truth Bank. He uses a bank ATM 2 times per month and a nonbank ATM once a month. He checks his account statement online. How much money would Gavin save per month if he switched to Old River Bank?

The most appropriate choice for polynomial will be given by

1) Zeroes of P(x) = 2, [tex]\frac{2 + \sqrt{2}i}{3}[/tex], [tex]\frac{2 - \sqrt{2}i}{3}[/tex]

where [tex]i = \sqrt{-1}[/tex]

2) Zeroes of P(x) = 3, 2i, -2i

3) Roots are 2i, -2i, [tex]\frac{3}{2}[/tex]

4) Roots are 0, 1, [tex]2 + \sqrt{5}[/tex], [tex]2 - \sqrt{5}[/tex]

What is a polynomial?

An algebraic expression of the form [tex]a_0 + a_1x +a_2x^2 + a_nx^n[/tex] is called a polynomial of degree n.

[tex]1) P(x ) = 3x^3 -10x^2 + 10x -4\\P(2) = 3(2)^3 - 10(2)^2 +10(2) - 4\\[/tex]

        [tex]= 24 -40 + 20 -16\\= 0[/tex]

(x - 2)  is a factor of P(x)

[tex]P(x) = 3x^2(x - 2) -4x(x - 2) +2(x-2)\\[/tex]

        = [tex](x - 2)(3x^2 - 4x + 2)[/tex]

        [tex]=(x-2)(x -a)(x - b)[/tex]

where,

[tex]a = \frac{-(-4)+\sqrt{(-4)^2 - 4\times 3\times 2}}{2\times 3}\\a =\frac{ 4 + \sqrt{-8}}{6}\\a = \frac{4 + 2\sqrt{2} i}{6}\\a = \frac{2(2 + \sqrt{2}i)}{6}\\a = \frac{2 + \sqrt{2}i}{3}[/tex]

[tex]b = \frac{-(-4)-\sqrt{(-4)^2 - 4\times 3\times 2}}{2\times 3}\\b =\frac{ 4 -\sqrt{-8}}{6}\\b = \frac{4 - 2\sqrt{2} i}{6}\\b = \frac{2(2 - \sqrt{2}i)}{6}\\b = \frac{2 - \sqrt{2}i}{3}[/tex]

Zeroes of P(x) = 2, [tex]\frac{2 + \sqrt{2}i}{3}[/tex], [tex]\frac{2 - \sqrt{2}i}{3}[/tex]

where [tex]i = \sqrt{-1}[/tex]

[tex]2) P(x) = x^3 - 3x^2+4x-12\\P(3) = (3)^3 - 3(3)^2 +4(3) -12\\ P(3) = 0[/tex]

(x - 3) is a factor of P(x)

[tex]x^2(x - 3) + 4(x - 3)\\(x - 3)(x^2 + 4)\\(x - 3)(x -a)(x-b)\\[/tex]

where,

[tex]a = \sqrt{-4}\\a = 2i[/tex]

[tex]b = -\sqrt{-4}\\a = -2i[/tex]

Zeroes of P(x) = 3, 2i, -2i

[tex]3) 2x^3 - 3x^2 +8x-12= 0\\[/tex]

x = 2 satisfies the equation

[tex]2x^2(x -\frac{3}{2}) + 8(x-\frac{3}{2})=0\\(2x^2+8)(x - \frac{3}{2}) = 0\\[/tex]

[tex]2x^2 + 8 = 0[/tex] or [tex]x - \frac{3}{2} = 0[/tex]

[tex]x^2 = -\frac{8}{2}[/tex] or [tex]x = \frac{3}{2}[/tex]

[tex]x^2 = -4[/tex] or [tex]x = \frac{3}{2}[/tex]

[tex]x = \sqrt{-4}[/tex] or [tex]x = \frac{3}{2}[/tex]

[tex]x = 2i[/tex] or [tex]x = -2i[/tex] or [tex]x = \frac{3}{2}[/tex]

Roots are 2i, -2i, [tex]\frac{3}{2}[/tex]

4)

[tex]x^4 - 5x^3 +3x^2 +x = 0\\x(x^3 -5x^2 + 3x +1) = 0\\[/tex]

[tex]x = 0[/tex] or [tex]x^3 -5x^2+3x +1 = 0[/tex]

For  [tex]x^3 -5x^2+3x +1 = 0[/tex]

x = 1 satisfies the equation

[tex]x^2(x -1) -4x(x-1)-1(x-1) = 0\\(x - 1)(x^2 - 4x -1) = 0\\[/tex]

[tex]x -1 = 0[/tex] or [tex]x^2 - 4x -1 = 0[/tex]

Roots are x = 1 or x = a or x = b

where,

[tex]a = \frac{-(-4) + \sqrt{(-4)^2 - 4\times 1 \times(-1)}}{2\times 1}\\a = \frac{4+\sqrt{20}}{2}\\a = \frac{4 + 2\sqrt{5}}{2}\\a = \frac{2(2 + \sqrt{5})}{2}\\a = 2 + \sqrt{5}[/tex]

[tex]b = \frac{-(-4) - \sqrt{(-4)^2 - 4\times 1 \times(-1)}}{2\times 1}\\b = \frac{4-\sqrt{20}}{2}\\b = \frac{4 - 2\sqrt{5}}{2}\\b = \frac{2(2 - \sqrt{5})}{2}\\b = 2 - \sqrt{5}[/tex]

Roots are 0, 1, [tex]2 + \sqrt{5}[/tex], [tex]2 - \sqrt{5}[/tex]

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A dime is 10% of a dollar = 10/100 x 100 cent = 10 cents

A quater is 25% of a dollar = 25/100 x 100 cent = 25 cents

Since Karen has 5 more quaters than dimes

let quaters = q

let dimes = d

Then Karen has 5q : d = $ 3.70

$ 3.70 = 3.70 x 100 cents = 370 cents

Solution

We have the function

The graph of the function is

Let Ashley can text x words in 60 minutes. Then equation for x is,

Thus, Ashley text 80 words in 60 seconds.

A 40% decrease represents subtraction.

So, the initial percentage is 100%, if it decreases by 40%, we get 60% as result.

Given the graph:

The length of the shadow = y - x.

• To find x:

• To find y:

Length of the shadow:

ANSWER

Length of the shadow = 11.4 m

Given data:

The given equation x+y=4.

Substitute 0 for x in the given equation.

0+y=4

y=4.

Substitute 0 for y in the given equation.

x+0=4

x=4

So, the graph of the equation must pass from (0,4) and (4,0).

Thus, the option (a) is correct.

We have to first determine the area of the square. The area of a square can be represented as follows

The number of each square feet each person will requre can be calculated as follows

Answer

The situation is not biased because it takes a random sample from each group.

The breadth of the room = 6 cm

Since the length of the room is twice its breadth

Then

Length of the room = 2 times 6cm = 12cm

The height of the room = 4cm

Since the shape of the room is a cuboid

The surface area of a cuboid is given as

Substitute l = 12, w = 6 and h = 4 into the formula

This gives

Simplify the expression

Therefore, the total surface area of the room is

Given,

A= (-7, 8, 1).

B= (8, 7, 7)

The value of ||AB|| is,

The value of A.B is ,

Hence, the value is 7.

Answer:

True.

The graph is linear, but not proportional.​

Explanation:

Given the graph in the attached image;

The graph is linear because it is a straight line graph.

A linear graph is always straight.

A proportional relationship in which the two components have a constant ratio.

The proportional graph is a straight line graph that passes through the origin (0,0).

Since the given graph does not pass through the origin, it is not a proportional graph.

Therefore, The graph is linear, but not proportional.​

a) To calculate the minimum payment of the balance, you calculate the 2% of $4273.56. You proceed as follow:

(2/100)(4273.56) = 85.47

Hence, the mimum payment of the balance is $85.47

b) You calculate the amount of interest charged this month as follow:

convert the annual percentage rate to decimal form:

21.1/100 = 0.211

divide the previous result by 12 to get the monthly interest rate:

0.2111/12 = 0.0175

multiply the previoues result by the balance:

0.0175 x 4273.56 = 75.143 ≈ 75.14

convert the monthly rate to a percentage:

0.0175 x 100 = 1.75%

Hence, the amount of interest was $75.14, which corresponds to a 1.75%

sin C = 3/5

Given:

CB = 32

AC = 40

AB = 24

To find:

sin C

To determine sinC, we will apply the sine ratio:

Answer:

Explanations:

According to the question, we need to determine which of the signs will fit in that will make the expression a binomial.

In simple terms, a binomial is a two-term algebraic expression that contains variable, coefficient, exponents, and constant.

We need to determine the required sign by using the trial and error method.

Using the positive sign (+) first, we will have:

Using the product sign, this will be expressed as:

According to the sum of two cubes;

Comparing this with the expression above, we will see that a = 3y^6 and

b = 4. This means that the resulting expression above can be written as a sum of two cubes to have;

Collect the like terms:

Bobby is right because the measurements were made smaller so the dilation factor must be a number less than 1, and 1/3 is less than 1

Answer:

The fraction form of the repeating decimal is;

Explanation:

We want to express the repeating decimal 0.2 (2 repeating) as a fraction.

let x represent the fraction;

Then subtract x from 10x;

Then we can divide both sides by the coefficient of x;

Therefore, the fraction form of the repeating decimal is;

We have the next data

70,89,75,36,80

First we will calculate the mean

(70+89+75+36+80)/5=70

mean=70

Then we will calculate the Median

36,70,75,80,89

median =75

Then we will calculate the mode because any value is repeated all the values given are the mode

mode:70,89,75,36,80

Range

89-36=53

Range =53

Answer: [tex]f(x)=x^3 -51x^2 -3x+153[/tex]

Step-by-step explanation:

By the conjugate root theorem, the roots are [tex]\sqrt{3}, -\sqrt{3}, 51[/tex].

Letting the leading coefficient be 1,

[tex]f(x)=(x-\sqrt{3})(x+\sqrt{3})(x-51)\\\\=(x^2 -3)(x-51)\\\\=x^3 -51x^2 -3x+153[/tex]

Kindly check below

Question 1) We can see that in the column "number of recipients" there is a Geometric Sequence whose common ratio is 5.

2) Therefore, we can fill in those gaps with the following:

3) Thus is the table.

We are asked to determine the perimeter of triangle LMN. To do that we will use the fact that the perimeter is the sum of the length of the sides of the triangle. Therefore, we have:

To determine the value of the length of "LM" we will use the formula for the euclidian distance:

Where:

Are the endpoints of the segment. For LM we have that the coordinates of the endpoints are:

Substituting we get:

Solving the operations:

Solving the operations:

Now, we use the endpoints of MN:

Substituting we get:

Solving the operations we get:

Now, we apply the equation for segment LN:

Solving the operations:

Now, we substitute in the formula for the perimeter:

Adding like terms:

In decimal form rounded to the nearest unit this is:

Therefore, the perimeter of the figure is 25.

To get the better deal of the two, we need to find the cost per area of pizza for each deal and compare.

Deal 1: 2 medium 14'' (round) pizza for $14 total

The area of a circle is calculated as

where r is the radius.

The area of the pizza is calculated to be:

Hence, the total area for the two pizzas will be:

The cost per square inch of pizza is, therefore, calculated to be:

The pizza costs $0.011 per square inch.

Deal 2: 1 large 20'' (round) pizza for $13 total

The area of the pizza is calculated to be:

Hence, the cost per square inch of pizza is calculated to be:

The pizza costs $0.010 per square inch.

CONCLUSION:

The better deal will be the deal with the lesser cost per square inch. As can be seen from the calculation, both deals are about the same price per square inch if approximated. However, without approximation, Deal 2 has a slightly lesser cost per square inch.

Therefore, DEAL 2 IS THE BETTER DEAL.

The given data is:

Rearrange the data in ascending order:

Given angles are corresponding angles, they are congruent (have the same measure):

Use the equation above to solve x;

You use the value of x=30 to find the measure of corresponding angles:

Remmy will pay $660 interest.

Step - by - Step Explanation

What to find? The amount of interest to be paid.

Given Parameters:

• Principal (P) = $8000

• Rate of interest(R) = 5.5

• Time(t in years) = 1.5

The formula for calculating simple interest is given below:

Where P is the principal.

R represents the rate.

T is the time given in years.

S.I is the simple interest.

Substitute the values into the formula and simplify.

= 660

Hen

Original Car price = $20,000

Price increase after 5 years = 25%

To calculate the price after 5 years, first multiply the original price (20,000) by the percentage increase in decimal form ( divided by 100) to obtain the increase amount:

20,000 x (25/100) = 20,000 x 0.25 = $5000

Finally, add the increase amount to the original price:

20,000+5,000 = $25,000

Answer:

b. 15 fl. oz

Explanation:

From the question, we are told that 3/4 cup of bleach is needed per 1 gallon of water.

Thus:

Next, we represent the result in the form of the given options:

Using the standard rate of conversion: 1 cup = 8 fl. oz

The volume of bleach added to 2.5 gallons of water is 15 fl. oz.

ANSWER:

The system can only be consistent and independent

STEP-BY-STEP EXPLANATION:

We have to:

• If a system has at least one solution, it is said to be consistent.

• If a consistent system has exactly one solution, it is independent.

• If a consistent system has an infinite number of solutions, it is dependent

• If a system has no solution, it is said to be inconsistent

We know that the system has 2 solutions, and we know that the system is only inconsistent when it has no solution, therefore the correct answer is:

The system can only be consistent and independent

The function f(x) is increasing for the intervals:

Lemons cost $4 for a bag of six, so using the unitary method, which states, "The unitary method is a process of finding the value of a single unit, and based on this value; we can find the value of the required number of units," $16 will be spent for 24 lemons.

The unitary method is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. A single or distinct unit is referred to by the word unitary. Therefore, the goal of this method is to establish values in relation to a single unit. The unitary method, for instance, can be used to calculate how many kilometers a car will travel on one litre of gas if it travels 44 km on two litres of fuel.

Here,

Let x be the cost of 24 lemons.

6 lemons for $4

24 lemons for $x

by unitary method,

cost of 1 lemon=$4/6

cost of 24 lemons,

=24*(4/6)

=$16

Using the unitary method, which states that "The unitary method is a process of finding the value of a single unit, and based on this value; we can find the value of the required number of units," $16 will be spent for 24 lemons since a bag of six costs $4.

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