What is the equation of the line that passes through the point (-3,4)(−3,4) and has a slope of -2−2?

Argon is the gas who would work best for something that needs a steady, nonreactive gas. (Ar).

When a neutral environment is required, argon is frequently used. In this manner, titanium and other volatile metals are produced. Additionally, it is used in the manufacture of incandescent bulbs to prevent air from corroding their filaments and by welders to safeguard the weld region.

A chemical substance in the periodic table's 18th group is argon. It is an expensive gas and the third most common gas in the atmosphere of the planet. Aside from nitrogen and oxygen, argon is the most prevalent gas in the atmosphere.

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The length of the rectangle is 10.5 units.

What is perimeter?

Perimeter is the distance of a two-dimensional shape. It is equal to the sum of the lengths of all the sides of the shape. The perimeter is measured in units, such as centimeters, meters, feet, or inches, depending on the unit of measurement used for the dimensions of the shape.

The perimeter of a rectangle is given by the formula:

P = 2l + 2w

where P is the perimeter, l is the length, and w is the width.

In this case, we know that the perimeter is 34 units, and the width is 6.5 units. So we can substitute these values into the formula and solve for the length:

34 = 2l + 2(6.5)

Simplifying, we get:

34 = 2l + 13

Subtracting 13 from both sides, we get:

21 = 2l

Dividing both sides by 2, we get:

l = 10.5

So the equation to determine the length of the rectangle is:

2l + 2w = P

Substituting the known values, we get:

2l + 2(6.5) = 34

Simplifying and solving for l, we get:

2l + 13 = 34

2l = 21

l = 10.5

Therefore, the length of the rectangle is 10.5 units.

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Complete question: The perimeter of a rectangle is 34 units, its width is 6.5 units. Write an equation to determine the length (l) of the rectangle.

The derivative of f(x) is (1/2)(9x - sin²(2x))^(-1/2) * (9 - 4sin(2x)cos(2x)).

What is a derivative?

A derivative is a mathematical concept used in calculus to determine the rate at which a function changes with respect to its input variable. It measures the instantaneous rate of change of the function at a specific point, and is calculated as the limit of the rate of change as the input variable approaches zero. The derivative is represented by the notation f'(x) or dy/dx, and can be used to find important information about the function, such as its slope, maxima and minima, and points of inflection.

What are expression?

In mathematics, an expression is a combination of numbers, symbols, and/or variables that are combined in some way using mathematical operations such as addition, subtraction, multiplication, division, or exponentiation.

To find the derivative of f(x) = √[9x - sin²(2x)], we can use the chain rule and the power rule of differentiation:

f(x) = √[9x - sin²(2x)]

f'(x) = (1/2)(9x - sin²(2x))^(-1/2) * (9 - 4sin(2x)cos(2x))

Using the chain rule, we first take the derivative of the expression inside the square root, which is 9x - sin²(2x), and then multiply it by the derivative of the expression inside the square root. The derivative of the expression inside the square root is:

(1/2)(9x - sin²(2x))^(-1/2) * (d/dx)(9x - sin²(2x))

Using the chain rule and the power rule of differentiation, we can find the derivative of 9x - sin²(2x) as:

d/dx (9x - sin²(2x)) = 9 - 4sin(2x)cos(2x)

Substituting this into the expression for f'(x), we get:

f'(x) = (1/2)(9x - sin²(2x))^(-1/2) * (9 - 4sin(2x)cos(2x))

So, the derivative of f(x) is (1/2)(9x - sin²(2x))^(-1/2) * (9 - 4sin(2x)cos(2x)).

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The derivative of f(x) is: f'(x) = (9 - 4sin(2x)cos(2x)) / [2√(9x - sin²(2x))].

Differentiation is a mathematical concept used to calculate the rate at which one quantity changes with respect to another. In calculus, it refers to the process of finding the derivative of a function, which gives the slope of the tangent line at any point on the function.

In the given question,

To find the derivative of f(x), we can use the chain rule and the power rule of differentiation.

f(x) = √[9x - sin²(2x)]

Let's first simplify the expression under the square root:

g(x) = 9x - sin²(2x)

Taking the derivative of g(x) gives:

g'(x) = 9 - 2sin(2x) * cos(2x) * 2

g'(x) = 9 - 4sin(2x)cos(2x)

Now we can use the chain rule to find f'(x):

f'(x) = [1/2(9x - sin²(2x))^(-1/2)] * g'(x)

f'(x) = [1/2√(9x - sin²(2x))] * [9 - 4sin(2x)cos(2x)]

Therefore, the derivative of f(x) is:

f'(x) = (9 - 4sin(2x)cos(2x)) / [2√(9x - sin²(2x))]

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By circle , 15 is the length of x .

What is a circle, exactly?

A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point. The line of reflection symmetry is formed by each line that traverses the circle.

                                Moreover, every angle has rotational symmetry around the center. With no sides or edges, a circle is a figure with a round shape. A circle can be characterized in geometry as a closed shape, a two-dimensional shape, or a curved shape.

AE² = EC . CD

10² = 5 * x

100 = 5 * x

100/5 = x

 20 = x

ED = 20 - 5   = 15

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By adding fractions that represent each of the amounts of cupcakes, we can see that you need 9 cupcakes for you and your friends.

Her we know that you want 3 halves of a cupcake for yourself, 8 halves for your friend, and 7 halves for your other friend.

So we just need to add all of these fractions, to do so, we need to solve the follwing opeartion:

3*(1/2) + 8*(1/2) + 7*(1/2)

3/2 + 8/2 + 7/2

All of these have the same denominator so we can directly add them up:

3/2 + 8/2 + 7/2 = (3 + 8 + 7)/2

(3 + 8 + 7)/2 = 18/2

18/2 = 9

You need 9 cupcakes for you and your friends.

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Complete question:

"I want 3 halves of a cupcake for myself, 8 halves for my friend, and 7 halves for our other friend. How many halves we need in total?"

Answer: the missing digit would be 2

721,846 rounded to the nearest ten thousand is 720,000

The total balance after four years when compounded continuously is $12,615.24.

A technique of calculating interest on a loan or investment where interest is compounded an endless number of times annually is called continuous compounding. Continuous compounding is a method of growing an investment or debt over time by continually adding interest earned over a relatively brief period of time to the principal. In financial computations where interest is earned or charged continuously, such in the bond or mortgage markets, continuous compounding is frequently utilised.

The compound interest is given as:

[tex]A = Pe^{(rt)}[/tex]

Substituting the values:

[tex]A = 12000 * e^{(0.0125 * 4)}\\A = 12000 * e^{(0.05)}[/tex]

A = 12000 * 1.05127

A = 12615.24

Therefore, the total balance after four years is $12,615.24.

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The probability of choosing a student who plays both basketball and baseball is approximately 0.4643.

It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to occur.

We can use the inclusion-exclusion principle to find the number of students who play both basketball and baseball.

Number of students who play both = Number of basketball players + Number of baseball players - Number of students who play neither

                                                           = 11 + 13 - 11

                                                           = 13

Therefore, out of 28 students, 13 play both basketball and baseball.

The probability of choosing a student who plays both sports can be calculated as follows:

P(plays both) = Number of students who play both / Total number of students

                      = 13/28

                      = 0.4643 (rounded to 4 decimal places)

So the probability of choosing a student who plays both basketball and baseball is approximately 0.4643.

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The fraction that is equivalent to 5/7 is 15/21

It is important to note that fractions are simply described as part of a whole number or element.

Also, equivalent expressions are defined as expressions that have the same solution but differ in the mode of arrangement of the values.

From the information given, we have;

The numerator be x

The denominator is 9 less than twice the numerator

This is represented as;

x/2x - 9 = 5/7

Cross multiply the values, we have;

7(x) = 5(2x - 9)

expand the bracket

7x = 10x - 45

collect the like terms, we have;

7x - 10x = -45

-3x = -45

Make 'x' the subject

x = 15

Then, the fraction = 15/21

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The chain rule is used when a function is composed of two or more functions, where one function is applied to the output of the other. In other words, it is used when a function is "nested" inside another function. Thus, option A is correct.

We can solve this problem by applying the chain rule and the product rule of differentiation. Let's begin by simplifying the expression inside the parentheses:

[tex]y = ex (e^-2x + 7)[/tex]

Now, let's apply the product rule:

[tex]dy/dx = (ex)'(e^-2x + 7) + ex(e^-2x + 7)'[/tex]

Using the chain rule, we can find (ex)':

[tex](ex)' = ex[/tex]

And using the chain rule again, we can find [tex](e^-2x + 7)':[/tex]

[tex](e^-2x + 7)' = (-2e^-2x)[/tex]

Substituting these values back into the original equation, we get:

[tex]dy/dx = ex(e^-2x + 7) + ex(-2e^-2x)[/tex]

Simplifying, we get:

[tex]dy/dx = ex(e^-2x + 7 - 2e^-2x)[/tex]

[tex]dy/dx = ex(e^-2x - e^-2x + 7)[/tex]

[tex]dy/dx = ex(7)[/tex]

Therefore, the answer is A) 7.

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The expressions in a single exponent are 9³/9⁹ = 9⁻⁶ and 14⁻³ * 14¹² = 14⁹

Diego's mistake is multiplying the expressions, wrongly

Expression 1

Given that

9³/9⁹

To solve, we make use of the law of indices

So, we have

9³/9⁹ = 9⁻⁶

Expression 2

Here, we have

14⁻³ * 14¹²

Using the law of indices, we have

So, we have

14⁻³ * 14¹² = 14⁹

Diego's expression is given as

6⁴ * 8³ = 48⁷

The mistake in Diego's expression is that he multiplied 6 and 8, and then add the exponents

This is incorrect, and the actual solution is

6⁴ * 8³ = 1296* 512

6⁴ * 8³ = 2¹³ × 3⁴

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Answer:

the answer is f-1(x) = 5 - ln (x - 6)/ln (3) (I guess?)

The compound interest rate of the given information for which the annual rate of the bank account is = 3.9%.

What about compound interest?

Compound interest refers to the interest that is earned not only on the principal amount of a loan or investment but also on any interest that has been previously earned. In other words, it is the interest calculated on the initial principal and on the accumulated interest of previous periods. This compounding effect can result in significant growth over time, as the interest earned in each period is added to the principal, and the interest earned in subsequent periods is calculated on the new, larger principal amount. Compound interest is often used in long-term savings and investment accounts, such as retirement funds or fixed deposits, as it can result in a higher return than simple interest over time.

According to the given information:

In this case we know that;

⇒ A = [tex]P(1 + r)^n[/tex]

⇒ A = amount

⇒ P = principal

⇒ r = rate

⇒ n = number of years

⇒ 710.89  = 658.20[tex](1 + r)^2[/tex]

⇒ 710.89/658.20 = [tex](1 + r)^2[/tex]

⇒ 1.08 = [tex](1 + r)^2[/tex]

⇒ ln(1.08) =ln [tex](1 + r)^2[/tex]

⇒ 0.077 = 2ln[tex](1 + r)[/tex]

⇒ 0.077/2 = ln(1 + r)

⇒ ln[tex](1 + r)[/tex] = 0.0385

⇒ 1 + r = 1.039

⇒ r = 1.039 - 1

⇒ r = 0.039

⇒ r = 3.9%

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1. Batman spent $99 this month after starting with $57 and ending with a balance of -$42.

2. The average change in Barbie's position each minute in the scuba diving is -7.3 meters.

3. The change in Ms. Blue's weight after one year of dieting and losing 4 pounds monthly is -48 pounds.

Initial balance in the bank account = $57

Final balance at month-end = $-42

The total amount spent = $99 ($57 + $42)

Thus, when $99 is taken away from $57, the balance is $-42.

Initial position = -2.1 m

Final position = -38.6 m

Change in position = -36.5 m (-38.6 - -2.1)

The number of minutes used to change position = 5 minutes

The average change per minute = -7.3 m (-36.5 ÷ 5)

The quantity of pounds lost per month = 4 pounds

The period of dieting = 1 year = 12 months

The total change in weight after one year of dieting = -48 pounds (-4 x 12)

Thus, these three problems are solved using mathematical operations.

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Answer:

  148 cm²

Step-by-step explanation:

You want the surface area of a cuboid with edge lengths 4 cm, 5 cm, and 6 cm.

The formula is shown in your problem statement.

It can be made easier to compute using a little rearranging:

  SA = 2LW +2LH +2WH

  SA = 2(LW +LH +WH)

  SA = 2(LW +H(L +W))

The choice of dimensions for L, W, and H doesn't matter.

  SA = 2(4·6 +5(4+6)) = 2(24 +5(10)) = 2(74) = 148 . . . . cm²

The surface area is 148 cm².

The survey results, it can be estimated that approximately 17.93% of adult Americans have seen a ghost at some point in their lives[tex] (718/4,005 = 0.1793)[/tex].

However, it is important to note that this estimate is based on a sample and there may be some degree of error or variability.

Additionally, the term "supernatural experiences" may encompass a wide range of phenomena beyond just seeing ghosts, so the estimate may not accurately reflect the prevalence of all types of supernatural experiences in the population.

In the given survey on supernatural experiences, 718 out of 4,005 adult Americans reported having seen a ghost. Assuming this sample is representative of the adult American population, you can calculate the proportion of adults who have seen a ghost.

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The probability that the cupcake picked at random contains walnuts is given as follows:

0.4 = 40%.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

There are 30 cupcakes in a tin, hence the total number of outcomes is given as follows:

30.

The number of cupcakes with walnuts is given as follows:

Hence the probability that the cupcake picked at random contains walnuts is obtained as follows:

p = (3 + 9)/30

p = 12/30

p = 0.4.

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A square is not created when a plane slices through a cone.

What is square?

A square is a geometrical shape that has four equal sides and four equal angles of 90 degrees.

What is cone?

A cone is a three-dimensional geometric shape that tapers smoothly from a flat base to a pointed top or apex. It looks like a funnel or an ice cream cone.

When a plane intersects or slices through a cone, it creates a variety of different shapes depending on the angle of the plane and the position of the cone.

If the plane intersects the cone at an angle perpendicular to its base, it will create a circle. If the plane intersects the cone at an angle that is not perpendicular to its base, it will create an ellipse.

If the plane intersects the cone at an angle that is parallel to one of its generators (the lines that can be drawn from the vertex of the cone to any point on its base), it will create a parabola. If the plane intersects the cone at an angle that is not parallel to one of its generators, it will create a hyperbola.

Therefore, a square is not created when a plane slices through a cone.

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Answer:

The geometric mean of 9 and 6 is 4/3

Step-by-step explanation:

The geometric mean of 8 and 6 is [tex]4\sqrt{3}[/tex]

The geometric mean of two numbers [tex]x_1[/tex] and [tex]x_2[/tex] is given by the formula:

[tex]GM=\sqrt{x_1\times x_2}[/tex]

The two given numbers are 8 and 6

That is, [tex]x_1=8[/tex] and [tex]x_2=6[/tex]

Substitute [tex]x_1=8[/tex]  and [tex]x_2=6[/tex] into the formula [tex]GM=\sqrt{x_1\times x_2}[/tex]

[tex]GM=\sqrt{8\times 6}[/tex]

Simplifying further:

[tex]GM=\sqrt{48}[/tex]

[tex]GM=4\sqrt{3}[/tex]

Therefore, the geometric mean of 8 and 6 is [tex]4\sqrt{3}[/tex]

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Answer:

<AOB = 112

<AOD = 68

<DOC = 112

Hoped this helped

: )

275 miles can be driven in one day on a budget of $100.

an inequality is defines as a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on either sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa.

The rental car costs $45 a day and $0.20 a mile. So, for a budget of $100, the inequalities can be written as

45+.20m≤ 100

Where m= no.of miles

No.of miles can be travelled in 100

.2m=100-45

m=55/.2

m=275miles

Hence,275 miles can be driven in one day on a budget of $100.

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Using ratios, we can find the average weight of the adult bear to be 250 pounds and the angles of the triangles are 10°, 75° and 95°.

Comparing two amounts of the same unit and calculating the ratio allows us to determine how much of one quantity is included in the other. Two categories of ratios exist. The part to whole ratio is one, and the part-to-part ratio is another. The part-to-part ratio illustrates the relationship between two separate entities or groupings.

In the question given,

Ratio between birth weight and adult weight of a bear is 3:1000.

The average birth weight as given here is = 12 ounces.

Now let the average adult weight be = x

According to the ratio,

12/x = 3/1000

⇒ 3x = 12000

⇒ x = 4000 ounces.

Now 16 ounces = 1 pounds

4000 ounces

= 4000/16

= 250 pounds.

The angles are in the ratio 2:15:19

Now we know all the angles sum up to 180°

Let the angle be = x.

The equation is as follows:

2x + 15x + 19x = 180

⇒ 36x = 180

⇒ x = 180/36

⇒ x = 5

So, all the angles of the triangles are, 10°, 75° and 95°.

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Answer:

X = 61,  Angle 57 and 123

Step-by-step explanation:

If you could provide the exact question that would be great, but from the information given what we know is that the entirety of half of a circle is 180 degrees so the angle at x-4 and the angle and 2x+1 must be equal to 180 degrees.

Therefore:

x-4  +  2x+1 = 180 degrees

X = 61,    Therefore:

x-4 -->  61 -4 = 57 degrees

2x+1 ---> 2(61) +1  = 123 degrees

So:

The angles are 57 degrees for x-4 and 123 for 2x+1 .

Answer:

To determine which statements are true, we can use the standard form of the equation of a circle:

(x - h)^2 + (y - k)^2 = r^2

where (h, k) is the center of the circle and r is the radius.

Using this form, we can rewrite the given equation as:

(x - 1)^2 + y^2 = 3^2 + 1^2 = 10

Comparing this to the standard form, we can see that the center of the circle is (1, 0), so the statement "The center of the circle lies on the x-axis" is true. However, the statement "The center of the circle lies on the y-axis" is false.

To find the radius, we can rearrange the equation as follows:

x^2 - 2x + y^2 = 8

Completing the square for x, we get:

(x - 1)^2 + y^2 = 9

This shows that the radius of the circle is 3, so the statement "The radius of the circle is 3 units" is true, as well as the statement "The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9."

Therefore, the three true statements are:

1.The radius of the circle is 3 units.

2.The center of the circle lies on the x-axis.

3.The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.

Step-by-step explanation:

hope its help <:

Given:-

To find:-

Answer:-

In the given right angled triangle, we may use the trigonometric ratios. We can see that the measure of the longest side is 5 which is hypotenuse and the measure of perpendicular needs to be find out .

We may use the ratio of sine here as , we know that in any right angled triangle,

[tex]\implies\sin\theta =\dfrac{p}{h} \\[/tex]

And here , p = 5 and h = x , so on substituting the respective values, we have;

[tex]\implies \sin\theta = \dfrac{x}{5} \\[/tex]

Again here angle is 45° . So , we have;

[tex]\implies \sin45^o =\dfrac{x}{5} \\[/tex]

The measure of sin45° is 1/√2 . so on substituting this we have;

[tex]\implies \dfrac{1}{\sqrt2}=\dfrac{x}{5} \\[/tex]

[tex]\implies x =\dfrac{5}{\sqrt2}\\[/tex]

Value of √2 is approximately 1.414 . So we have;

[tex]\implies x =\dfrac{5}{1.414} \\[/tex]

[tex]\implies \underline{\underline{\red{\quad x = 3.53\quad }}}\\[/tex]

Hence the value of x is 3.53 .

and we are done!

Answer:

The length of side x to the nearest tenth is 3.5.

Step-by-step explanation:

From inspection of the given right triangle, we can see that the interior angles are 45°, 45° and 90°. Therefore, this triangle is a 45-45-90 triangle.

A 45-45-90 triangle is a special right triangle where the measures of its sides are in the ratio  1 : 1 : √2.  Therefore, the formula for the ratio of the sides is b: b : b√2 where:

We have been given the hypotenuse, so:

[tex]\implies b\sqrt{2}=5[/tex]

Solve for b:

[tex]\implies \dfrac{b\sqrt{2}}{\sqrt{2}}=\dfrac{5}{\sqrt{2}}[/tex]

[tex]\implies b=\dfrac{5}{\sqrt{2}}[/tex]

The side labelled "x" is one of the sides opposite the 45° angles, so:

[tex]\implies x=b[/tex]

Substitute the found value of b into the equation for x:

[tex]\implies x=\dfrac{5}{\sqrt{2}}[/tex]

[tex]\implies x=3.5355339...[/tex]

[tex]\implies x=3.5\;\sf(nearest\;tenth)[/tex]

Therefore, the length of side x to the nearest tenth is 3.5.

Answer:

Option C would likely produce the most representative sample of the population of smartphones made by the company. By testing every 500th smartphone off the production line, the manufacturer can ensure that they are selecting a random sample of smartphones from throughout the production process. This can help to account for any variations or changes that may occur in the manufacturing process over time.

Option A, testing the first smartphone off the production line each day, may not be representative of the entire production run since the first smartphone may not be representative of the rest of the batch. Similarly, option B, testing the last 1000 smartphones produced each month, may not be representative of the entire production run as there may be variations in quality and safety standards throughout the month.

Option D, testing every smartphone made on Wednesday, would likely not produce a representative sample as it may not account for any variations or changes that occur during other days of the week.

The tangent ratio for angle F is [tex]\frac{4}{3}[/tex] . The solution has been obtained by using trigonometry.

What is trigonometry?

In the area of mathematics known as trigonometry, right-angled triangles, including their sides, angles, and connections, are studied.

We are given a right angled triangle. The sides of the triangle are given as DF is 6, DE is 8 and EF is 10.

This means that the perpendicular is 8 and base is 6.

We know by trigonometry that tan θ is the ratio of triangle's perpendicular and base.

So, from this we get

⇒ tan F = [tex]\frac{8}{6}[/tex]

⇒ tan F = [tex]\frac{4}{3}[/tex]

Hence, the tangent ratio for angle F is [tex]\frac{4}{3}[/tex] .

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Question: What is the tangent ratio for angle F, if DF is 6, DE is 8 and EF is 10?

The domain of the function R(x) is (-∞, -4) U (-4, 3) U (3, ∞).

The vertical asymptote is x = -4 and x = 3

The horizontal asymptote is y = 1.

In Mathematics, a domain refers to the set of all real numbers (x-values) for which a particular function is defined.

In Mathematics, the horizontal portion of any graph is used to represent all domain values and they are both read and written from smaller to larger numerical values, which simply means from the left of any graph to the right.

By critically observing the graph shown in the image attached below, we can logically deduce the following domain:

Domain = {0, ∞}.

In conclusion, an asymptote is a line which the graph of any given function approaches but would never cross or touch;

Vertical asymptote is x = -4 and x = 3

Horizontal asymptote is y = 1.

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Complete Question:

Analyze the graph of the function.

[tex]R(x)=\frac{x^2}{x^2+x-12}[/tex]

a. What is the domain of R(x)?

b. What is the vertical and horizontal asymptote?

To be able to determine the size of the space for the photograph from the frame area, we need to know the area of the frame and the dimensions of the photo frame (length and width). The given information is insufficient.

Most ideally, we determine the size of an object using different measurements and units of measurement. The most common measurement used for size is length or distance, which refers to the distance between two points on an object.

The other measurements used for size include area, volume, mass, weight, and density, which provide additional information about the object's characteristics. In order to determine the size of an object mathematically, we must understand the units of measurement being used and the appropriate formulas or equations for calculating size.

Translated question "Patricia designed the photo frame on the right. She makes frames of different measurements, but keeping its thickness, which is 4 cm, as shown in the drawing. How can you determine the size of the space for the photograph from the frame area?

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The length of the base is 6 inches.

What is triangle?

A triangle is a three-sided polygon, which is a flat shape with straight sides. It is a basic shape in geometry and has many interesting properties that are useful in mathematics and other fields.

The formula for the area of a triangle is A = 1/2 * b * h, where A is the area, b is the length of the base, and h is the height of the triangle.

In this case, we know that the area of the triangle is 21 in² and the height is 7 in. So we can substitute these values into the formula and solve for the base:

21 = 1/2 * b * 7

Multiplying both sides by 2:

42 = b * 7

Dividing both sides by 7:

6 = b

Therefore, the length of the base is 6 inches.

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Complete question : The area of the triangle is 21 in² ad the height is 7 in. what is the length of the base?