Simplify the complex rational expression by the method of your choice. 1——x-6———-1 - 1 —- x-6

We are told to list all the elements of whole numbers not greater than 8 using both the set notation and the listing method.

SET NOTATION

Let 'x' be used to represent the whole numbers.

LISTING METHOD

The sequence in the question may be given as

1, 3, 9, 27

From this, the first term is 1 and the common ration is 3

Common ratio = 3/1 = 9/3 = 27/9

= 3

The laboratory technician has to combine 11 L  acid solution to get the desired concentration .

The volume of solute that has been dissolved in a specific volume of solvent or solution is known as the concentration of a solution. A solution with a significant concentration of dissolved solute is one that is concentrated. When there is just a minimal amount of dissolved solute in a solution, it is said to be diluted. The amount of a solute, or dissolvable substance, combined with the solvent, or other substance, determines the concentration of a solution in chemistry. C = m/V, where m is the mass of the solute dissolved and V is the total volume of the solution, is the accepted formula. Among the quantitative units of concentration are molarity, molality, mass percentage, parts per thousand, parts per million, and parts per billion.

The33 L batch is 40% acid, so 33 x 0.4 = 13.2 L of pure acid in the batch.

Let P = the number of liters of pure acid required, D = the number of liters of the 10 % solution.

Then P + 0.10 x D = 13.2.  

Also, P + D = 33

This equation can be solved simultaneously by substitution.

P = 33 - D

33 - D + 0.10 x D = 16.8

-D (1 - 0.10) = 13.2 - 33

-D =  -19.2/ 0.9

D = -22

P = 33 - 22

= 11 L

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I got the answer of 505 students

The product of the given expression will be -49 + 13√7.

Product of two entities may be used to increase the amount of those entities. A radical expression may be defined as an expression which along with numbers and variables contain square root symbol. Instead of square root there can be cube root, fourth root or of root with any power. For example, 1 + √4, 1 + ∛4 etc. We have the expression (7 - √7) (-6 + √7). The product of this expression will be

Product = (7 - √7) (-6 + √7)

Product = -42 + 7√7 + 6√7 - 7

Product = -49 + 13√7 which is the required expression.

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Answer:

[tex]-49 + 13\sqrt{7}[/tex]

Step-by-step explanation:

[tex](7 - \sqrt{7} )(-6 + \sqrt{7})\[/tex] Distribute.

[tex]7 * -6 + 7 * \sqrt{7} - \sqrt{7} * -6 - \sqrt{7} * \sqrt{7}[/tex] Multiply. Keep in mind [tex]- \sqrt{7} * \sqrt{7} = (-\sqrt{7})^{2} = - 7[/tex].

[tex]-42 +13\sqrt{7} - 7[/tex] Combine like radicals/terms.

[tex]-49 +13\sqrt{7}[/tex]

The angle addition postulate is the best justification for m∠XPD + m∠DPE = m∠XPE.

An angle bisector is a line segment that divides an angle into two equal parts.

The angle addition postulate states, if a line segment is in between an angle sum of two smaller angles created by the line segment, is equal to the measure of the larger angle.

We have an ∠XPE that is divided by a line segment PD which creates two smaller angles ∠XPD and ∠DPE.

∴ By angle addition postulate m∠XPD + m∠DPE = m∠XPE.

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Answer:

Domain: [-8, 2]

Range: [-4, 0]

Function: Yes

Step-by-step explanation:

The domain is the set of x-values and the range is the set of y-values.

A relation is a function if each x value corresponds to only one y-value.

Answer:

Slope = 0, y int = (0,4)

If there is no x variable, slope is 0. y = 4 so no matter what x is (which it will always be 0) the y intercept will always be 4

In order to evalute this expression, replace the variable placeholders with the numerical values, that is,

which gives

then, the answer is 26.

This is a linear relation. For linear relations, we have the general form:

Where 'a' is the slope and 'b' is the intercept.

In this problem, we have that the intercept b is 200, because that's the point where the line crosses the y-axis. For now we have something like:

(here y is C and x is m)

To find the slope we have to use the intercept point (0, 200) and another point on the line. We can see that one of those points is (200, 500).

For a line with points (x1, y1) and (x2, y2), the slope is find like:

In this problem, the slope is:

Then, we have the equation that represents the relationship between the mileage and the cost:

x² +3x+9 and x² + 9 are prime polynomials.

A whole number higher than 1 whose only elements are 1 and itself is referred to as a prime number. A whole number that may be split evenly into another number is referred to as a factor. 2, 3, 5, 7, 11, 13, 17, 19, 23 and 29 are the first few prime numbers. Composite numbers are those that have more than two components. A prime number is one that can only be divided without leaving a residue by itself and one.

Given Data

x² +9

x² + 9 cannot be divided into factors of rational numbers. It is a prime polynomial as a result.

x²+3x+9

It is impossible to factorize x² + 3x + 9 using rational values. It is a prime polynomial as a result.

x²-9

Factoring x² - 9 results in (x - 3)(x + 3). It is not a prime polynomial, therefore.

-2x² +8

The factorization of -2x² + 8 results in -2(x - 2)(x + 2). It is not a prime polynomial, therefore.

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You have the following expression:

-10 - (5 - 9)²

In order to simplify the previous expression you proceed as follow:

- 10 - (5 - 9)² simplify terms inside parenthesis

= -10 - (-4)² solve the parenthesis

= -10 - 16 simplify

= -26

Hence, the simplified expression is -26.

Answer: 25%

Explanation:

Probability is expressed as

number of favorable outcomes/number of total outcomes

From the information given, the spinner has 4 equal spaces. Thus,

number of total outcomes = 4

number of favorable outcomes = number of blue spaces = 1

Thus,

the probability of spinning the spinner and having it land on blue = 1/4 x 100

the probability of spinning the spinner and having it land on blue = 25%

Solution

For this case we have the following:

When we apply the division we got:

Option A is correct

Option D is correct

Option E is correct

Final answer: A, D, E

The distance covered by Natalie in kilometers will be 2.24 kilometers.

Multiplication or division by a numerical factor, selection of the correct number of significant figures, and unit conversion are all steps in a multi-step procedure.

Given that Natalie walked 1.4 miles in one hour. The distance covered by Natalie in kilometers will be calculated as:-

The value of 1 mile is equal to 1.4 kilometers.

1 miles = 1.6 kilometers

1.4 miles = 1.4 x 1.6 kilometers

1.4 miles = 2.24 kilometers

Therefore, the distance covered by Natalie in kilometers will be 2.24 kilometers.

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The 28th term of the given arithmetic sequence is 219

any arithmetic sequence can be solved once we identify the aa1 term and the an term because then we have to simply find the common difference and solve further by substituting the value in the below mentioned equation.

Given the arithmetic sequence = 3,11, 19, 27

a₁ = 3

a₂ = 11

a₃ = 19

a₄ = 27

the common difference or d = a₂ - a₁

this implies d = 11 - 3 = 8

Therefore the 28th term of the given arithmetic sequence is

a₂₈ = a₁ + ( n - 1 ) d

a₂₈ = 3 + ( 28 - 1 ) 8

     = 3 + 27 × 8

     = 3 + 216

     = 219

Thus a₂₈ = 219

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Given the model for the height of a ball:

To hit the ground, the height must be h(t) = 0. Then:

We use the general solution for a quadratic equation:

From the problem, we identify:

Using the formula:

We only take the positive value (because the time is always positive!). Then, the answer is:

Answer:

i know that if i just answered the question quick then it would have been better for you but i also need help with something but i know something that will help you

Step-by-step explanation: go to cymath ans type it in it will help you and you can use it on school laptops so im kind of helping future you

we have the following:

replacing:

17. (1, 0) and (5, 5)

therefore,

19. (0, -1) and (3, -5)

therefore,

21. (1, 9) and (6, 2)

therefore,

In the problem, we are already given 2 pairs of sides that are congruent: AB and ED, and AD and BE.

Using the reflexive property of congruence, we also know that segment BD is congruent to itself.

We have therefore used three pairs of sides that are congruent to prove that △ABD ≅ △EDB.

This means that we used the SSS Postulate to prove the congruence of the two triangles.

Answer:

[tex]2x + 5 \\ (2 \times 10) + 5 \\ 20 + 5 \\ = 25[/tex]

Answer:

0.825 inches per hour

Step-by-step explanation:

Invasive weed species can grow quickly. One variety grows up to 1.65 ft per day. How fast in inches per minute can this weed grow?

FACTS:

the weed grows up to 1.65 feet per day

there are 12 inches in 1 foot

there are 24 hours in 1 day

First, lets figure how many inches the weed can grow in one day:

= daily growth in feet per day * inches in 1 foot

= 1.65 feet * 12 inches

= 19.8 inches a day

If the weed can grown 19.8 inches a day, and there are 24 hours in a day:

= growth in inches per day/24 hours in 1 day

=19.8/24

= 0.825 inches per hour

From a perfect square trinomial

We know that:

Now, let's use this for the trinomial given:

We know that:

Solving for b,

This way, the complete perfect square trinomial is:

Ans: Option A

The frequency for the given distribution of the class interval 1.00 - 1.09 is 3, which are 1.07, 1.05 and 1.07.

The frequency of a repeating event is its number of instances per unit of time. In some cases, it is also referred to as temporal frequency or ordinary frequency to emphasise differences with spatial and angular frequencies, respectively. One (event) per second is equal to one hertz (Hz), which is how frequency is expressed.

The period is the reciprocal of the frequency because it is the length of time for one cycle in a repeating event. For instance, the period, T—the space between beats—of a heart beating at a frequency of 120 beats per minute (2 hertz), is equal to 0.5 seconds (60 seconds divided by 120 beats).

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The area to be recarpeted is 361 sq. m.

What is area?

The measurement that describes the size of a location on a horizontal or contour is called area. Surface area refers to the area of an extended surface or the border of a tri object, whereas the area of a horizontal region or flat area corresponds to the area of a form or planar laminate. Area can be interpreted as both the amount of substance with a specific thickness required to create a model of the shape or as the quantity of paint required to completely cover a surface in a single coat. It is the two-dimensional equivalent of the volume of a solid or the length of a curve, both of which are one-dimensional concepts (a three-dimensional concept).

given the area is in form of square

So, the area of floor = 19x19 = 361 sq. m.

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Looking at f(x) and g(x), we can see that g(x) is made by f(x) multiplied by -6.

Since the function was multiplied by a negative value, that means we had a reflection over the x-axis.

Also, if the function was multiplied by a constant value, that means we had a vertical stretch by a factor equal to the absolute value of the constant.

Therefore the correct options are A and D.

From the information given in the word problem, the oldest child of Mrs. Danforth must be 13 years old.

Given:

Since the bags are distributed according to the proportion of their ages, then, we say

5 bags x 16 candies =80 candies.

80 / 4 = 20 candies per child

Given that his 4-year-old sister gets 20 -12 = 8 candies, then:

8/4 = 2 candies per year for each child's age.

Given that Cameron will gain 20 + 2 =22 candies, then:

22 / 2 = 11 years is Cameron's age.

22 candies of Cameron + 8 candies for youngest sister=30

80 - 30 = 50 candies for the remaining older children.

Since Cameron is the 2nd youngest, it means the remaining 2 siblings must be 12 and 13 years respectively:

So that: 12 x 2 = 24 candies for the 3rd oldest

And 13 x 2 = 26 candies for the oldest child. So, the total allocations of all the candies would be:

8 + 22 + 24 + 26 = 80 candies.

Therefore, the most senior child must be 13 years old.

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Full Question

Mrs. Danforth packed 5 bags of fun-sized candies for her family's picnic. Each bag contains 16 pieces. She had intended to pass out the same number of candies to each of her 4 children. But Cameron, her second-youngest, argues that she should instead distribute the candies in proportion to the children's ages. All of the children have different ages. If Cameron can convince his mother to give out the candies his way, he will gain two candies while his four-year-old sister will lose twelve. How old is Mrs. Danforth's oldest child?

Answer

22a + 28

Explanation

The question asks us to simplify the given expression

2a + 4(7 + 5a)

The first step is to open the bracket

2a + 4(7 + 5a)

= 2a + 28 + 20a

= 2a + 20a + 28

= 22a + 28

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