(q4)Find the area of the region bounded by the graphs of
and x = y - 4.

We subtract the cost of wine when buying one bottle per week from the cost of wine when buying two bottles per weekend. Miranda saves $780 in one year by buying only one bottle of wine per week instead of two.

To calculate how much Miranda saves in one year by buying only one bottle of wine per week instead of two, we can follow these steps:

Determine the number of bottles of wine she buys in a year:

Miranda used to buy 2 bottles of wine per weekend, so in a week, she bought 2 bottles.

Since there are 52 weeks in a year, the number of bottles she bought in a year is 2 bottles/week * 52 weeks = 104 bottles.

Calculate the total cost of wine for the year:

Since each bottle costs $15, the total cost of wine for the year when buying 2 bottles per week would be 104 bottles * $15/bottle = $1560.

Calculate the cost of wine for one year when buying only one bottle per week:

With Miranda's decision to buy one bottle per week, the total number of bottles she buys in a year is 1 bottle/week * 52 weeks = 52 bottles.

Therefore, the cost of wine for one year when buying only one bottle per week would be 52 bottles * $15/bottle = $780.

Calculate the amount saved in one year:

To determine the amount saved, we subtract the cost of wine when buying one bottle per week from the cost of wine when buying two bottles per weekend.

Amount saved = $1560 - $780 = $780.

Therefore, Miranda saves $780 in one year by buying only one bottle of wine per week instead of two.

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The algebra 2 is a vast field that deals with various mathematical concepts, such as equations and inequalities.

Algebra 2 is a branch of mathematics that mainly deals with equations and inequalities. An equation is a mathematical statement that implies that two expressions are equal.

Similarly, an inequality implies that two expressions are not equal but are related by a certain operation.There are different types of equations that one may encounter in Algebra 2.

A linear equation is an equation that can be represented by a straight line on the coordinate plane. A quadratic equation is one that can be written in the form ax² + bx + c = 0.

There are also exponential, logarithmic, and trigonometric equations that one may come across.Inequalities are statements that two expressions are not equal. Inequalities can be represented graphically on a coordinate plane, just like equations.

There are different types of inequalities such as linear, quadratic, exponential, and logarithmic inequalities.In conclusion,  These concepts help in solving real-world problems by providing a framework to analyze them mathematically.

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In this  rectangle, there are two lines of symmetry.

A line of symmetry is a line that divides a shape into two equal halves, such that each half is a mirror image of the other. The lines of symmetry in a rectangle are vertical and horizontal.

Vertical Line of Symmetry:

A vertical line of symmetry runs from the top to the bottom of the rectangle, dividing it into two equal halves. Each half is a mirror image of the other. To identify the vertical line of symmetry in a rectangle, you can visualize folding the rectangle along a line from top to bottom. The left and right sides of the folded rectangle will match perfectly.

Horizontal Line of Symmetry:

A horizontal line of symmetry runs from one side of the rectangle to the other, dividing it into two equal halves. Each half is a mirror image of the other. To identify the horizontal line of symmetry in a rectangle, imagine folding the rectangle along a line from left to right. The top and bottom sides of the folded rectangle will align perfectly.

I find the lines of symmetry in a rectangle, you can also observe its properties. In a rectangle, opposite sides are parallel and equal in length, and all interior angles are right angles (90 degrees). By considering these characteristics, you can determine that the vertical and horizontal lines passing through the center of the rectangle will be the lines of symmetry.

Understanding the lines of symmetry in a rectangle is essential in various applications, such as geometry, design, and architecture. These lines allow for balanced and symmetrical arrangements, providing aesthetic appeal and structural stability.

Final answer:

In following  rectangle, there are two lines of symmetry.  

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The area of triangle ADE is,

⇒ A = 48 square units

We have to given that,

In the diagram , DE is a midsegment of triangle ABC.

And, The area of triangle ABC is 96 square units

Now, We know that,

Since DE is a midsegment of triangle ABC, it is parallel to AB and half the length of AB. Therefore, DE is half the length of AB.

Hence, the area of triangle ADE is half the area of triangle ABC,

That is,

A = 96 / 2

A = 48 square units

Thus, The area of triangle ADE is,

⇒ A = 48 square units

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The magnitude of the complex number -3 + 4i is 5.

To find the magnitude of a complex number, we use the formula:

Magnitude = √(real^2 + imaginary^2)

In this case, the complex number is -3 + 4i.

The real part is -3, and the imaginary part is 4.

Using the formula, we can calculate the magnitude:

Magnitude = √((-3)^2 + 4^2)

= √(9 + 16)

= √25

= 5

Therefore, the magnitude of the complex number -3 + 4i is 5.

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The equation of the circle graphed below is (x + 2)² + (y - 3)² = 16.

To determine the equation of the circle graphed below, we need to use the standard form equation of a circle.

The standard form of a circle equation is (x - h)² + (y - k)² = r², where (h, k) is the center of the circle and r is the radius.

Given the graph, we can see that the center is located at (-2, 3), and the radius is 4 units. Therefore, we can substitute these values into the standard form equation as follows:(x - (-2))² + (y - 3)² = 4²(x + 2)² + (y - 3)² = 16

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Answer:

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

Step-by-step explanation:

The equation of a circle in standard form is:

[tex]\boxed{\begin{minipage}{4 cm}\underline{Equation of a circle}\\\\$(x-h)^2+(y-k)^2=r^2$\\\\where:\\ \phantom{ww}$\bullet$ $(h, k)$ is the center. \\ \phantom{ww}$\bullet$ $r$ is the radius.\\\end{minipage}}[/tex]

To determine the equation of the graphed circle, we need to find its center and radius.

The center of the circle is a single point that lies at an equal distance from all points on the circumference of the circle.

From inspection of the graphed circle, we can see that its domain is [-5, -1] and its range is [0, 4].  The x-coordinate of the center is the midpoint of the domain, and the y-coordinate of the center is the midpoint of the range.

[tex]x_{\sf center}=\dfrac{-5+(-1)}{2}=-3[/tex]

[tex]y_{\sf center}=\dfrac{0+4}{2}=2[/tex]

Therefore, the center of the circle is (-3, 2).

The radius of the circle is the distance from the center to all points on the circumference of the circle.  From observation, we can see that the radius of the circle is r = 2.

To determine the equation of the circle, substitute the center and radius into the standard formula.

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

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

Therefore, the equation of the graphed circle is:

[tex]\boxed{(x +3)^2+(y-2)^2=4}[/tex]

T satisfies the homogeneity property.

To prove that T is a linear transformation, we need to show that it satisfies two properties: additivity and homogeneity.

Additivity:

Let's consider two arbitrary vectors z₁ = [x₁, y₁] and z₂ = [x₂, y₂] in R².

T(z₁ + z₂) = T([x₁ + x₂, y₁ + y₂])

= [-2(x₁ + x₂) - 1, -2(x₁ + x₂) + 2(y₁ + y₂)]

= [-2x₁ - 2x₂ - 1, -2x₁ - 2x₂ + 2y₁ + 2y₂]

= (-2x₁ - 1, -2x₁ + 2y₁) + (-2x₂ - 1, -2x₂ + 2y₂)

= T(z₁) + T(z₂)

Therefore, T satisfies the additivity property.

Homogeneity:

Let's consider an arbitrary vector z = [x, y] in R² and a scalar k.

T(kz) = T([kx, ky])

= [-2(kx) - 1, -2(kx) + 2(ky)]

= (-2kx - 1, -2kx + 2ky)

= k(-2x - 1, -2x + 2y)

= kT(z)

Since T satisfies both additivity and homogeneity, we can conclude that T is a linear transformation.

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Answer:

Step-by-step explanation:

Multiply −12y(9y − 7).

Answer:

$2,067.59

Step-by-step explanation:

To calculate the balance of the savings account, we can use the continuous compounding interest formula:

[tex]\boxed{\begin{minipage}{8.5 cm}\underline{Continuous Compounding Interest Formula}\\\\$ A=Pe^{rt}$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\\phantom{ww}$\bullet$ $P =$ principal amount \\\phantom{ww}$\bullet$ $e =$ Euler's number (constant) \\\phantom{ww}$\bullet$ $r =$ annual interest rate (in decimal form) \\\phantom{ww}$\bullet$ $t =$ time (in years) \\\end{minipage}}[/tex]

Given values:

Substitute the given values into the formula and solve for A:

[tex]\begin{aligned}A&=1727 \cdot e^{0.03 \cdot 6}\\&=1727 \cdot e^{0.18}\\&=1727 \cdot 1.19721736...\\&=2067.59438...\\&=2067.59\end{aligned}[/tex]

Therefore, the balance of the savings account 6 years from now is $2,067.59.

The type of transformation shown is vertical translation.

Since, Transformation of geometrical figures or points is the manipulation of a given figure to some other way.

Different types of transformations are Rotation, Reflection, Glide reflection, Translation and Dilation.

Given a polygon EFGH.

It is transformed to another polygon with the same size E'F'G'H'.

Here the polygon EFGH is just moved downwards as it is and mark is as E'F'G'H'.

If it is rotation or reflection, the points will change it's correspondent place.

Translation is a type of transformation where the original figure is shifted from a place to another place without affecting it's size.

Therefore, here translation is done.

Since the shifting is done vertically, it is vertical translation.

Hence the transformation is vertical translation.

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Answer:

A) His estimate is incorrect, since he has increased a figure to the amount that each employee would receive.

B) Rounded to the nearest dollar, each employee would receive $ 209.

Step-by-step explanation:

Since a company has $ 6582 to give out in bonuses, and an amount is to be given out equally to each of the 32 employees, and A) a manager, Jake reasoned that since 32 goes into 64 twice, each employee will get about $ 2000 , to determine if his estimate is correct, and B) determine how much will each employee receive, rounded to the nearest whole dollar, the following calculations must be performed:

A)

2000 x 32 = 64000

200 x 32 = 6400

Therefore, his estimate is incorrect, since he has increased a figure to the amount that each employee would receive.

B)

6582/32 = X

208.68 = X

Therefore, rounded to the nearest dollar, each employee would receive $ 209.

The orientation change and the symmetry across the center of rotation confirm that it is a 180° clockwise rotation. Therefore, the correct answer is D. 180° clockwise rotation.

Based on the image provided, the type of transformation shown is a 180° clockwise rotation.

A 180° clockwise rotation occurs when each point in the original shape is rotated by 180° in a clockwise direction around a fixed point. In the given image, we can observe that the original shape has been rotated by half a complete revolution, resulting in the new shape being a mirror image of the original shape but in the opposite orientation.

This transformation is evident by comparing the positions of the vertices and sides of the original shape to those of the transformed shape. The orientation change and the symmetry across the center of rotation confirm that it is a 180° clockwise rotation.

Therefore, the correct answer is D. 180° clockwise rotation.

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The Wendy spent $27.78 on a silver necklace online.To calculate the total cost of the silver necklace, we need to add the cost of the necklace to the shipping and handling charges.

The cost of the necklace is given as $23.15.

Wendy bought a silver necklace online. It cost $23.15 plus 20% shipping and handling.

What was the total cost?When purchasing a silver necklace online, Wendy spent $23.15, but she had to pay for shipping and handling as well, which cost 20% of the total price of the item.

To find the total cost of the necklace, follow these steps:

1. Determine the cost of shipping and handling: $23.15 × 0.20 = $4.632

Add the cost of shipping and handling to the cost of the necklace:$23.15 + $4.63 = $27.78

The total cost of the necklace is $27.78.

It's important to consider the additional charges such as shipping and handling when calculating the total cost of an online purchase to have an accurate understanding of the amount spent.

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The total amount of meat bought is 46/4 or 11.5 kg (or 11.5 kilograms).

To express the total amount of meat bought in fraction and decimal form, we need to add up the quantities of each type of meat.

The given quantities are:

2 kg and a quarter of beef

5 kg and two quarters (or a half) of chicken

4 kg and three quarters of pork loin

To find the total amount of meat bought, we can add these quantities:

2 kg and 1/4 + 5 kg and 1/2 + 4 kg and 3/4

To add these mixed numbers and fractions, we need to find a common denominator. The common denominator here is 4.

2 kg and 1/4 can be converted to 9/4 by multiplying 2 by 4 and adding 1.

5 kg and 1/2 can be converted to 9/2 by multiplying 5 by 2 and adding 1.

4 kg and 3/4 remains the same.

Now we can add the fractions:

9/4 + 9/2 + 4 + 3/4

To add the fractions, we need to find a common denominator, which is 4.

9/4 + 9/2 + 16/4 + 3/4

Now we can add the numerators and keep the denominator:

(9 + 18 + 16 + 3) / 4

The numerator becomes 46, so the total amount of meat bought is 46/4.

To express this as a decimal, we can divide the numerator by the denominator:

46 ÷ 4 = 11.5

Therefore, the total amount of meat bought is 46/4 or 11.5 kg (or 11.5 kilograms).

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The solution set to the given system of inequalities is represented by the shaded region under the curve of f(x) = x^2 – 3 (including the points on the curve) and above the curve of g(x) = –x^2 + 2 (excluding the points on the curve). The overlapping region between these shaded areas represents the solution set to the system.

To graph the solution set to the system of inequalities y ≤ x^2 – 3 and y > –x^2 + 2, we can modify the graphs of f(x) = x^2 – 3 and g(x) = –x^2 + 2 accordingly. Here's how:

For the inequality y ≤ x^2 – 3:

The original graph of f(x) = x^2 – 3 is an upward-opening parabola with a vertex at (0, -3).

To graph y ≤ x^2 – 3, we need to shade the region below or on the parabola. This includes all points on the parabola itself.

Therefore, we shade the area under the curve of the original graph of f(x) and include the points on the curve.

For the inequality y > –x^2 + 2:

The original graph of g(x) = –x^2 + 2 is a downward-opening parabola with a vertex at (0, 2).

To graph y > –x^2 + 2, we need to shade the region above the parabola. This excludes all points on the parabola itself.

Therefore, we shade the area above the curve of the original graph of g(x) but exclude the points on the curve.

By modifying the graphs of f(x) and g(x) according to these shading instructions, we can graphically represent the solution set to the system of inequalities.

The solution set can be identified by observing the overlapping region or the intersection between the shaded area under the curve of f(x) and the shaded area above the curve of g(x). The points within this overlapping region satisfy both inequalities simultaneously.

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(a) √2 · √8. The simplified surd expression is 4.

(b) √80. The simplified surd expression is  4√5.

(c) √5/√20. The simplified surd expression is  1/2.

(d) √20. The simplified surd expression is  2√5.

The given surd expression is simplified as follows;

(a) √2 · √8

we can simplify it as;

√2 · √8 = √(2 x 8) = √16 = 4

(b) √80

we can simplify it as;

√80 = √ (16 x 5) = √16  x √5 = 4√5

(c) √5/√20

we can simplify it as;

√5/√20  x  √20 / √20

= (√5  x √20 ) /(20)

= √100 / 20

= 10/20

= 1/2

(d) √20

we can simplify it as;

√20 = √4  x √5 = 2√5

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Given statement Sale Pricing Confusion solution is :- You should have been charged $2.88, not $9.

Let's break down the costs:

Ice Cream: $0.73

Sprinkles: $0.15

Water bottle: $2.00

The total cost of these three items would be:

$0.73 + $0.15 + $2.00 = $2.88

According to the prices you mentioned, you should have been charged $2.88, not $9. If the cashier told you that you owed $9, it's possible that there was an error in their calculations or that they included other items in your bill. It's best to clarify the discrepancy with the cashier and ask for an explanation or correction.

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c) Mode: 15 (appears 6 times)

Mean: 15.25

Median: 15

d) Probability of being 13 years old: 2/20 = 0.1 or 10%

e) Probability of being 14 or 16 years old: 6/20 = 0.3 or 30%

f) Probability of not having 15 years old: 1 - (6/20) = 14/20 = 0.7 or 70%

a) To create a table and calculate the absolute frequency, relative frequency, and percentual frequency, we organize the given ages in ascending order:

13 13 14 14 15 15 15 15 15 16 16 17 17 17 18 18

Age Absolute Frequency Relative Frequency Percentual Frequency

13 2 2/16 12.5%

14 2 2/16 12.5%

15 5 5/16 31.25%

16 2 2/16 12.5%

17 3 3/16 18.75%

18 2 2/16 12.5%

b) To represent the data graphically with a histogram, we plot the ages on the x-axis and the absolute frequency on the y-axis:

c) To calculate the mode, mean, and median:

Mode: The mode is the most frequently occurring age in the dataset. In this case, the mode is 15, as it appears 5 times.

Mean: The mean is the average of all the ages. To calculate it, we sum up all the ages and divide by the total number of ages:

(13 + 13 + 14 + 14 + 15 + 15 + 15 + 15 + 15 + 16 + 16 + 17 + 17 + 17 + 18 + 18) / 20 = 306 / 20 = 15.3

Median: The median is the middle value in the dataset when arranged in ascending order. In this case, the median is 15 since it falls in the middle.

d) To calculate the probability of having 13 years old, we divide the absolute frequency of 13 (2) by the total number of ages (20):

Probability of 13 years old = 2/20 = 0.1 or 10%

e) To calculate the probability of having 14 or 16 years old, we add the absolute frequencies of 14 and 16 (2 + 2 = 4) and divide by the total number of ages (20):

Probability of 14 or 16 years old = 4/20 = 0.2 or 20%

f) To calculate the probability of not having 15 years old, we subtract the absolute frequency of 15 (5) from the total number of ages (20):

Probability of not having 15 years old = (20 - 5)/20 = 0.75 or 75%

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The lower z-score in scenario B suggests that the score of 40 on the exam with a mean of 50 and a standard deviation of 20 should lead to a better grade compared to the score of 55 on the exam with a mean of 60 and a standard deviation of 5. Option B.

To determine which exam score should lead to the better grade, we need to compare the scores relative to their respective mean and standard deviation.

In scenario A, we have a score of X = 55 on an exam with a mean of 60 and a standard deviation of 5.

In scenario B, we have a score of X = 40 on an exam with a mean of 50 and a standard deviation of 20.

To compare the scores, we can use a statistical measure known as the z-score, which indicates how many standard deviations a particular value is from the mean. The z-score formula is calculated as:

z = (X - mean) / standard deviation

Calculating the z-scores for each scenario:

For scenario A:

z = (55 - 60) / 5

z = -1

For scenario B:

z = (40 - 50) / 20

z = -0.5

The z-score represents the number of standard deviations below or above the mean a score is. In this case, a lower z-score indicates a better performance relative to the mean.

Comparing the z-scores, we can see that scenario A has a z-score of -1, while scenario B has a z-score of -0.5. Therefore, scenario B with a score of X = 40 leads to the better grade.

In scenario B, the score of 40 is closer to the mean of 50 and has a smaller deviation from the mean compared to scenario A. This indicates that the score in scenario B is relatively better than the score in scenario A when compared to their respective distributions. Option B is correct.

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Answer: 42.5%, 7.5%, Independent and Dependent

Step-by-step explanation:

A: The chance that both FDA will approve and double the value is 50%*85% or 0.50*0.85, or 85*1/2 which is 42.5%

B: 50%*(100-85)%=50%*15%=15%*1/2=7.5%

C: FDA approval is independent because nothing can effect it. However, the stock doubling is dependent, because if FDA does not approve, it will definitely not double.

Answer:

See explanation

Step-by-step explanation:

A: 50% * 85% = 42.5%

B: 50% * 15% = 7.5%

C: Dependent, because the stock price has a 0% chance of doubling if the GDA does not approve of the medicine.

To find out how many of the 39 practice trials would be faster than 62 seconds, we need to calculate the proportion of trials that fall within the range of more than 62 seconds.

We can use the z-score formula to standardize the values and then use the standard normal distribution table (also known as the z-table) to find the proportion.

The z-score formula is:

z = (x - μ) / σ

Where:

x = value (62 seconds)

μ = mean (61 seconds)

σ = standard deviation (1.5 seconds)

Calculating the z-score:

z = (62 - 61) / 1.5

z ≈ 0.6667

Now, we need to find the proportion of values greater than 0.6667 in the standard normal distribution table.

Looking up the z-score of 0.6667 in the table, we find the corresponding proportion is approximately 0.7461.

To find the number of trials faster than 62 seconds, we multiply the proportion by the total number of trials:

Number of trials = Proportion * Total number of trials

Number of trials = 0.7461 * 39

Number of trials ≈ 29.08

Rounding to the nearest whole number, approximately 29 of the 39 practice trials would be faster than 62 seconds.

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The simplified exponential function is determined as x⁴.

An exponential function is a mathematical function used to calculate the exponential growth or decay of a given set of data.

To simplify an exponential function, we will apply the rules of exponent as shown below;

The given exponential function;

= (∛ x² )⁶

The given expression is simplified as follows;

= [tex](x^2) ^{\frac{1}{3} \times 6}[/tex]

= ( x² )²

= x⁴

Thus, the simplified exponential function is determined by applying the rules of multiplication of powers.

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The correct statement is: On a coordinate plane, an absolute value graph has a vertex at (0, 1).

The function p(x) = |x - 1| represents an absolute value function. The vertex of an absolute value function in the form f(x) = |x - h| + k is given by the point (h, k). In this case, the function p(x) = |x - 1| has a vertex at (1, 0).

Therefore, none of the provided options accurately represents the vertex of the function p(x) = |x - 1|. The correct vertex for this function is (1, 0), which means the vertex is at x = 1 and y = 0 on the coordinate plane. It is important to note that the vertex is located at (h, k) where h represents the x-coordinate and k represents the y-coordinate.

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[tex]-2x+6=12\\2x=-6\\x=-3[/tex]

Daniela is 11 years old.

An equation means the formula that expresses the equality of two expressions by connecting them with the equals sign =.

Let us assume Daniela's age as x.

According to the given information, Santiago is 3 years older than Daniela, so Santiago's age would be x + 3.

The sum of their ages is 25.

We will set up the equation:

x + (x + 3) = 25.

Simplifying the equation, we get:

2x + 3 = 25.

2x = 22.

x = 22/2

x = 11.

Translated question:

Santiago is 3 years older than his cousin Daniela and the sum of their ages is 25. How old is Daniela?

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Answer:

S = π(12)(20) + π(12^2) - (π(3)(5) + π(3^2))

= π(240 + 144 - (15 + 9))

= 360π = about 1,130.97 cm^2

The Coordinates of the terminal point determined by `t = 1177` are approximately `(-0.17101, -0.98526)`.Thus, the correct option is B (-0.17101, -0.98526).

The following trigonometric function represents a point P on the unit circle as a function of the angle θ in standard position: `(cos θ, sin θ)`.

Here, we have to determine the coordinates of the terminal point determined by `t = 1177`.Terminal Point on a unit circle:The terminal point is a point on a circle that lies on the terminal side of an angle. The angles that end on the same terminal side of the x-axis are called coterminal angles. The angle between the positive x-axis and the line segment connecting the origin of the circle and the point on the circle is called the angle in the standard position.

So, the angle measure `t = 1177` may be too large or too small to locate the corresponding point P on the unit circle. To find an equivalent angle between 0 and 360 degrees, we may subtract or add an integral number of revolutions: `1177 - 360 × 3 = 97`.That is, an angle of `t = 1177` degrees is coterminal with an angle of `t = 97` degrees. The terminal point determined by `t = 1177` is the same as the terminal point determined by `t = 97`.

The point on the unit circle with `t = 97` degrees lies in the fourth quadrant because the standard angle of 97 degrees is obtained by rotating a ray 97 degrees counterclockwise from the positive x-axis.So, `P = (cos 97°, sin 97°)`.We can approximate the values of `cos 97°` and `sin 97°` using a calculator or computer software as: `cos 97° ≈ -0.17101` and `sin 97° ≈ -0.98526`.

Therefore, the coordinates of the terminal point determined by `t = 1177` are approximately `(-0.17101, -0.98526)`.Thus, the correct option is B (-0.17101, -0.98526).

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The percent decrease in total principal and interest paid between a 30-year term mortgage and a 15-year mortgage with a principal balance of $484,500.00 and a 6.5% APR is 31.0%. (Option A)

To calculate the  percent decrease, we can use the following formula.

Percent decrease = ( (30-year factor -   15-year factor) / 30-year factor) x 100

Substituting the values from the chart.  

= (($ 6.65 - $8.71) / $6.65) x 100

= ( -$ 2.06 / $6.65) * 100

= -0.309 *  100

Percent decrease ≈ - 30.9 %

Since the question asks for the percent decrease as a positive value, we take the absolute value of the result which is

Percent decrease ≈ 31%

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#SPJ1

Check the picture below.

[tex]\stackrel{ \textit{\LARGE S} }{\cfrac{8}{4}}~~ = ~~\stackrel{ \textit{\LARGE S} }{\cfrac{12}{6}}~~ = ~~\stackrel{ \textit{\LARGE S} }{\cfrac{4}{2}}\implies \text{\LARGE 2}\qquad \textit{similar triangles by SSS}[/tex]