Simplify the rational expression . x^2+9x+20/x+7The quotient is , and the remainder is .

The dimensions are either 4 units by 2 units or 2 units by 4 units.

To draw a rectangle with a perimeter of 12 units and an area of 8 square units, we need to find the dimensions of the rectangle first.

Let  l be the length of the rectangle and w be the width of the rectangle.

We know that the perimeter of a rectangle is given by: P = 2(l + w) =12

12 = 2(l + w) ,6 = l + w

Also, the area of a rectangle is given by: A = l * w = 8

Now, we need to find a pair of numbers  l  and  w  that satisfy both equations:  6 = l + w and  8 = l * w

One such pair is l = 4  and  w = 2 , because ( 4 + 2 = 6 ) and ( 4 * 2 = 8 ).

This rectangle has a length of 4 units and a width of 2 units, with a perimeter of 12 units and an area of 8 square units.

Without additional context or an image, we can't definitively determine which number the point A represents in your question.

The point A represents the number 0.1.

Points on a number line represent numbers. The numbers between 0 and 1 can be represented as decimals. The point A is located between 0 and 1, closer to 0, so it represents the number 0.1.

Therefore, the correct answer is option a. 0.1.

Unfortunately, without further context such as a diagram or graph, it's not possible to definitively identify which number Point A would represent. In a standard coordinate system, points are typically represented as pairs of numbers (x, y) which indicate their position on the grid. In a number line, each point corresponds to a specific number. Please provide additional details or an image to get a more accurate answer.

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Answer:

Edge Checklist:

Find the third year’s salary by multiplying the second year’s salary by 1.05

Find the fourth year’s salary by multiplying the third year’s salary by 1.05.

Find the fifth year’s salary by multiplying the fourth year’s salary by 1.05.

The salaries form a geometric sequence because the athlete’s salary changes by a common ratio of 1.05 each year.

The value of the equation y = 3x^2 - 18x + 15 can be found by substituting different values of x and calculating the corresponding value of y.

The value of the equation y = 3x^2 - 18x + 15 can be found by substituting different values of x and calculating the corresponding value of y. For example, if we substitute x = 1, we get y = 3(1)^2 - 18(1) + 15 = 0. So, when x = 1, y is 0.

To find more values, we can create a table of values by substituting different x values into the equation. The resulting values of y can be plotted on a graph to see the pattern and shape of the equation.

Table of Values:

This equation represents a quadratic function in the form of y = ax^2 + bx + c, where a = 3, b = -18, and c = 15.

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Brand had 2 5/12 cups of chili left over from the second batch (option A). This was determined by solving the equation 1 1/3 + x = 3 3/4 using improper fractions and subtraction.

To find out how many cups of chili were left over from the second batch, we need to solve for x in the equation 1 1/3 + x = 3 3/4. Firstly, convert the mixed numbers to improper fractions: 1 1/3 becomes 4/3 and 3 3/4 becomes 15/4.

Now the equation looks like this: 4/3 + x = 15/4. To find x, subtract 4/3 from both sides of the equation.

15/4 - 4/3 = (15*3 - 4*4)/(4*3) = 45/12 - 16/12 = 29/12.

Now convert the improper fraction back to a mixed number. 29/12 is 2 and 5/12. So Brand had 2 5/12 cups of chili left over from the second batch (option A).

Option D, which is x + 2y^2 - 7, is a trinomial as it contains exactly three terms.

A trinomial is an algebraic expression with three terms.

These terms are usually separated by '+' or '-' signs. Let's examine the options given to identify a trinomial:

Therefore, Option D is the correct answer as it is the expression that contains exactly three terms, making it a trinomial.

The equation q^2=36 has two solutions because both a positive and a negative number squared can result in a positive number. The solutions are q=6 and q=-6, illustrating the concept of integer powers and square roots.

To solve the equation q squared equals 36 (q2 = 36), we look for the number that, when multiplied by itself, gives the product of 36. In mathematics, finding a value that satisfies this condition involves taking the square root of both sides of the equation. Thus, we have two potential solutions since both positive and negative values can be squared to yield a positive result.

The square root of 36 is 6, so our equation gives us two possible solutions: q = 6 or q = -6. This demonstrates the concept of integer powers, where for instance, raising 4 to the power of 3 (43) means multiplying 4 by itself three times. When dealing with the square root, we are essentially doing the opposite: we are asking what number multiplied by itself gives us the original number under the square power.

Final answer:

To divide 660 grams in a 4:7 ratio, you first calculate the value of each part by dividing 660 grams by 11 (the sum of the ratio parts), resulting in 60 grams per part. Then multiply 60 grams by 4 to get 240 grams, and by 7 to get 420 grams, giving you two portions that comprise the ratio 4:7.

Explanation:

To divide 660 grams in the ratio 4:7, first add the two parts of the ratio together to find the total number of parts. This is 4 + 7 = 11 parts in total. The ratio indicates that for every 11 parts of the total weight, 4 parts should be in one portion and 7 parts in another. To find the weight of each part, divide the total weight (660 g) by the total number of parts (11).

660 g ÷ 11 = 60 g per part

Now, to get the weights for the two portions:

For the 4 parts: 60 g/part × 4 = 240 grams

For the 7 parts: 60 g/part × 7 = 420 grams

Thus, 660 grams divided in the ratio 4:7 of  gives two portions of 240 grams and 420 grams, respectively.

It will take 4 yrs for Rajeev to reach 200$

To find out after how many years Rajeev will have at least $200 in his account, we can use the formula for compound interest. P = $175, A = $200, r = 0.04, n = 1, and t = ? Substituting these values into the formula and solving for t, we find that it will take approximately 7.38 years for Rajeev to have at least $200 in his account.

To find out after how many years Rajeev will have at least $200 in his account, we can use the formula for compound interest, which is given by:

A = P(1 + r/n)^(nt)

Where:

In this case, we have:

Substituting these values into the formula, we get:

$200 = $175(1 + 0.04/1)^(1t)

Simplifying the equation, we have:

1.1429 = (1.04)^t

To solve for t, we can take the logarithm of both sides:

log(1.1429) = log((1.04)^t)

Using logarithmic properties, we have:

t log(1.04) = log(1.1429)

Dividing both sides by log(1.04), we get:

t = log(1.1429)/log(1.04)

Using a calculator, we find that t ≈ 7.38

Therefore, it will take approximately 7.38 years for Rajeev to have at least $200 in his account.

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Final answer:

To find 300% of the difference between 23 and 27, you first calculate the difference, which is 4, and then multiply by 3, giving the result of 12.

Explanation:

The question asks us to calculate 300% of the difference between 23 and 27. First, let's find the difference between these two numbers: 27 - 23 = 4. Now, to find 300% of 4, we multiply 4 by 3 (since 300% is the same as multiplying by 3): 4 imes 3 = 12. Therefore, 300% of the difference between 23 and 27 is 12.This is the final answer.

The number sentences that solves the problem are;

B. (2 × 16) + (3 × 16) = 80
D. 16 × (2 + 3) = 80

To determine the number sentence, we have from the information given that;

Then, we can say that in each bag, there are;

= 3 + 2
= 5 objects

Now, in 16 of the goodies bag, the number of objects would be;

= 5 ×16

= 80 objects

Therefore, the sentences are in options B and D

Answer:  √3 and √2 are irrational numbers;

                [tex]-\dfracP{1}{16}[/tex] and 0 are rational numbers.

Step-by-step explanation:  We are given to classify the following numbers as rational or irrational:

[tex]\sqrt{3},~~-\dfrac{1}{16},~~0,~~\sqrt{2}.[/tex]

Rational number:   The digits after the decimal are either repeating or terminating.

Irrational number:  The digits after the decimal are non-terminating and non-terminating.

(a) We have

[tex]\sqrt{3}=1.732050807568877~.~.~.[/tex]

Since the digits after the decimal are non-terminating and non-repeating, so √3 is an IRRATIONAL number.

(b) We have

[tex]-\dfrac{1}{16}=-0.0625.[/tex]

Since the digits after the decimal are terminating, so [tex]-\dfrac{1}{16}[/tex] is a RATIONAL number.

(c) We have

[tex]0=0.000.[/tex]

Since the digits after the decimal are  terminating, so [tex]0[/tex] is a RATIONAL number.

(d) We have

[tex]\sqrt{2}=1.414213562373095~.~.~.[/tex]

Since the digits after the decimal are non-terminating and non-repeating, so √2 is an IRRATIONAL number.

Final answer:

Triangles with two complementary angles must be right triangles. Since these angles add up to 90 degrees, the side between them is part of a right triangle. There can be many different right triangles that satisfy these conditions, but all must have a 90-degree angle. (Option D)

Explanation:

The question asks about the conditions that define a certain type of triangle. With two angles being complementary, they add up to 90 degrees. In geometry, a complementary pair of angles adds up to 90 degrees, which means that the two angles in question must be acute angles that add up to form a right angle. Therefore, the triangle with two complementary angles must be a right triangle.

Since the triangle can have many different dimensions for the other sides and angles while keeping the side between the complementary angles at 12 centimeters, we can infer that there are infinite variations of this triangle, each with different measures for the remaining side and angle. However, all those triangles must satisfy the condition of being right triangles.

Thus, the correct answer to this question is:

D. Exactly one triangle exists with the given conditions, and it must be a right triangle.