find the value of n in each equation the name the property that is used

The simplification of the expression will be; 15t³  + 9t² + 14y

Those expressions that might look different but their simplified forms are the same expressions are called equivalent expressions. To derive equivalent expressions of some expressions, we can either make them look more complex or simple.

Given that the expression as 8t³ + 8y + 7t³ + 6y + 9t²

Now combining like terms;

8t³  + 7t³ + 9t² + 8y + 6y

Simplify;

15t³  + 9t² + 14y

It cannot be solved further because of unlike terms in the expression.

Therefore, the simplification of the expression will be; 15t³  + 9t² + 14y

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we have the functions

so

The IQR of the given series 2.9, 5.7, 10.0, 13.2, 21.1 is 15.4

In the given question, a five number summary is given as follows

2.9, 5.7, 10.0, 13.2, 21.1

We need to find the IQR

So, first we'll find the median of the given series

The middle value in a sorted, ascending or descending list of numbers is known as the median, and it has the potential to describe a data collection more accurately than the average does.

So, the given series is already in ascending order. And the middle value is 10.0. So the median is 10.0

Now to find the IQR the given formula will be used,

IQR = Q3 - Q1

Where Q3 is the last term in lower series and Q1 is the last term in upper series

Lower series - 2.9, 5.7

Upper series - 3.2, 21.1

Q3 = 5.7 , Q1 = 21.1

IQR = Q3 - Q1 = 21.1 - 5.7 = 15.4 ( IQR is always positive)

Hence, the IQR of the given series 2.9, 5.7, 10.0, 13.2, 21.1 is 15.4

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Answer:

44,000

Let me know if its wrong

6.

(a)

The slope for the side AB is:

The slope for the side BC is:

The slope for the side DC is:

And the slope for AD is:

(b) According to the previous results:

(c) Since it has two pairs of parallel sides, also, The opposite sides are of equal length, we can conclude that this figure is a parallelogram

We will determine the angle as follows:

We know that the whole circle contains 360°, so we determine the angle of 0.35 as follows:

So, the measure of the central angle for sector C is 126°.

Given:

The probability that a baby that is born is a boy is 0.52.

The probability that a baby that is born is a girl is 0.48.

To find:

The probability that the family has 0, 1, or 2 girls.

Explanation:

Using the binomial distribution,

Here,

The probability that the family gets 0 girl child is,

The probability that the family gets 1 girl child is,

The probability that the family gets 2 girl children is,

So, the probability that the family has 0, 1, or 2 girls is,

a) The tree diagram is,

b) The binomial distribution table for p(X) is,

ANSWER

EXPLANATION

Given:

Also,

One of the zeros: x = 4

Desired Outcome:

List the remaining zeros using radicals and i.

Simplify the polynomial using x - 4 = 0

Determine the remaining polynomials by simplifying x^2 - 2x + 17 = 0 using the quadratic formula

where:

a = 1,

b = -2

c = 17

Substitute the values

We have the next inequality

where x is the rent of each person

The maximum rent each will pay is $500

sin C = 3/5

Given:

CB = 32

AC = 40

AB = 24

To find:

sin C

To determine sinC, we will apply the sine ratio:

Step 1

compatible numbers are the numbers that are easy to add, subtract, multiply, or divide mentally.

Step 2

Math problem

455 + 229

Compatible numbers

455 + 225 = 680

680 is close to 455+229 = 684

Step 3:

Hence

By compatible numbers, 455 + 229 is more than 650.

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

Since the coop is in square shape The fencing is in the shape of a square

So equation is 4x=20, x=5

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

The completed worksheet is the following:

This worksheet involves three measures of central tendency: Mean, Median, Mode and Range

Mean: To get the mean of a dataset, add up all the data and divide by the number of datum (or inputs)

Median: To get the median of a dataset, sort the data in ascending order, and choose the central datum.

For example, if you have a dataset with 7 inputs, sort it in ascending order and select the 4th datum, as there would be 3 values above and 3 below (Hence it being the central datum).

Mode: The mode is the most repeated value of a dataset.

Range: The range is the difference between the biggest and smallest values of a dataset.

A quadratic function describes the relationship between the number of products x and the overall profits for a company.

The roots of the quadratic function are given as x = 0 and x = 28. We also know the graph's vertex is located at (14, -40).

The quadratic equation can be written in terms of its roots x1 and x2 as:

Substituting the given values:

We can find the value of a by plugging in the coordinates of the vertex:

Solving for a:

Substituting into the equation:

The graph of the function is given below:

The company actually loses money on their first few products, but once they hit 28 items, they break even again.

The worst-case scenario is that they produce 14 items, as they will have a profit of -40 dollars. The first root tells us the profit will be 0 when 0 products are sold.

we have that

Distributive property is the product of a factor and a sum (or difference) equals the sum (or difference) of the product

In this exanple

6x*0=0

Is not the product of a factor and a sum or difference

Problem

We have the following expression given:

f(x)= -2(5)^x

And we want to find f(2)

Solution

so we can do the following:

f(2)= -2 (5)^2 = -2*25 = -50

Population decreasing rate is

18% monthly

Actual population = 500

Then

In 1 month decreases (500/100)• 18 = 90

Population = 500-90= 410

No find (410/100)•18 = 73.8

410-73.8= 336.2

In 3 months

(336.2/100) •18 = 60.5

336.2 - 60.5 = 276 fishes

ANSWER IS 276 fishes remain

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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We have to find the number x for which 64 is the 2/3.

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%

4 cats and 14 dogs.

Explanation:

Data :

Amount of cats : c = ?

Cost per cats : $1.50

Amount of dogs : d = ?

Cost per dogs : $6.50

Total spent for dogs and cats : $97.00

Total number of dogs and cats : 18

Formulas:

1.50c + 6.50d = 97.00

c + d = 18

Solution:

c + d = 18 => c = 18 - d

1.50(18 -d) + 6.50d = 97.00

27 - 1.50d + 6.50d = 97.00

27 - 1.50d + 6.50d - 27 = 97 -

ANSWER:

A.

STEP-BY-STEP EXPLANATION:

We have the following function:

To find the zeros of the function we must set the function equal to 0 in the following way:

We reorganize the equation in order to be able to factor and calculate the zeros of the function, like this:

Therefore, the zeros are:

And in its factored form the expression would be:

Brandy will get a tip of $2.778

Here, we want to get the amount of tip Brandy will get

In the question, the tip is 15% of $18.52

That will mathematically be;

Answer: We have to find the radio stations in 2015, which is 13.8% more than the radio stations in 2005 which were 744:

Given:

Equation of a circle on a graph with center(3, -2).

To find:

Equation of a circle.

Explanation:

General eqution of a circle is

Solution:

From the graph, we can see that center is (3, -2) and radius equal 3.

So, equation of a circle is

Hence, this is the equation of a circle.

No

A relationship is called a proportional relationship if it has two variables that are realated by the same ration. In this case there will be a proportionality constant.

In this table:

Let Height be represented as H

Let Time be represented as T

For the relationship to be a proportional relationship, it must obey the relation:

When T = 3, H = 15

Using H = kT

15 = 3k

k = 15 / 3

k = 5

When T = 6, H = 30

H = kT

30 = 6k

k = 30 / 6

k = 5

When T = 12, H = 45

H = kT

45 = 12k

k = 45 / 12

k = 3.75

Since the constant of proportionality is the the same for the three cases in the table, the scenario is not a proportional relationship

Answer:

Step-by-step explanation:

(3,9)

(-5*3) +( 3*9) > 12

-15 + 27 > 12

12 > 12

not true

(-5,5)

(-5*5) + (3*5) > 12

-25 + 15 > 12

-10 > 12

not true

(3,-6)

(-5*3) + (3*-6) > 12

-15 + -18 > 12

-33 > 12

not true

(-2,-5)

(-5*-2) + (3*-5) > 12

10 + -15 > 12

5 > 12

not true

(2,8)

(-5*2) + (3*8) > 12

-10 + 24 > 12

14 > 12

(-6,0)

(-5*-6) + (3*0) > 12

30 + 0 > 12

30 > 12