The triangles below are similar. Identify the
appropriate similarity theorem that justifies the
similarity. Justify your reasoning.

Statement A is correct. The ratio of the number of gallons of red paint to the number of gallons of blue paint in shade B is 2:1.

What is the ratio?

Equivalent ratios are those that are the same when compared. Two or more ratios can be compared to determine whether or not they are equal. For example, the ratios 1:2 and 2:4 are equivalent.

Given that,

Shade A                                                                            Total

Number of Gallons of Blue Paint: 8   12  16   24             60

Number of Gallons of Red Paint   12  18  24   36            90

Shade B      

Number of Gallons of Blue Paint:  5     7   9   12             33

Number of Gallons of Red Paint   10    14  18   24          66

The ratio of the number of gallons of red paint to the number of gallons of blue paint in shade B is 66: 33 = 2:1.

It means for every 2 gallons of red paint for every 1 gallon of blue paint.

The ratio of the number of gallons of red paint to the number of gallons of blue paint in shade A is 90:60 = 3:2.

It means for every 3 gallons of red paint for every 2 gallons of blue paint.

The total gallon in shade A is (60 + 90) = 150.

If she adds 1 gallon of blue paint to 20 gallons of shade A.

Then she creates 150/20 = 7.5 gallons of blue paint in shade B.

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A reference point used to appropriately scale the dilation of a figure.

A dilation’s center is a fixed point in the plane around which all points expand or shrink. Under a dilation (k 1), the sole invariant (not changing) point is the center, which might be within, outside, or on a figure. Scale Factor: In a dilatation, the scale factor is the amount by which the figure is stretched or shrunk. Dilation Center: The center of dilation is a reference point used to scale the dilation of a figure suitably.

Dilation of the pupil allows more light into the eye, much as opening a door allows light into a dark room. Dilation allows your eye doctor to examine for a variety of common eye issues, including diabetic retinopathy.

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The scale factor of a similarity transformation is the ratio of the lengths of the corresponding sides of the two similar figures.

The scale factor is a ratio between two corresponding lengths, areas, or volumes of two similar figures. It is used to compare the size of one figure to another, as well as to enlarge or reduce the size of a figure. The scale factor is expressed as a ratio, such as 1:2, where the first number is the original size and the second is the new size.

It is usually represented as a decimal or fraction, and can be calculated by dividing the length of one of the sides of one figure by the length of the corresponding side of the other figure. For example, if we have two triangles with corresponding sides that measure 3 units and 6 units, then the scale factor of the dilation is 0.5 (3/6). This means that the second triangle is half the size of the first.

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On solving the provided question, we can say that - Since the two triangle are similar and each sides are 3 times the others, so x= 3 X 4 = 12 cm

A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.

Since the two triangle are similar

\and each sides are 3 times the other,

so x= 3 X 4 = 12 cm

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The substitution principle in math we substitute the value of one variable with another one and solve the equation.

By changing the value of another variable in an equation, the variable can be eliminated using this method. Thus, the elimination by substitution method is the name given to this technique.

As we are aware, the substitution approach entails solving the equation to determine the value of the variable, which is then substituted in the other equation. The elimination approach, in contrast, involves removing variables from the equation such that the equation's system can be reduced to being the function of a single variable.

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Answer:

x = 6 / sqrt(2)

Step-by-step explanation:

We are given the diagonal of a square

The side length is x

Using the Pythagorean theorem

x^2 + x^2 = h^2  where h is the length of the hypotenuse which is 6

x^2+x^2 = 6^2

2x^2 = 36

x^2 = 18

Taking the square root of each side

sqrt(x^2) = sqrt(18)

x = 3 sqrt(2)

This can be rewritten as

x = 3 sqrt(2) * sqrt(2)

    ------------------------

             sqrt(2)

x =    3*2  

        -------

          sqrt(2)

x = 6 / sqrt(2)

Area of a trapezoid is found with the formula, A=(a+b)/2 x h. so the answer is 9(w-3) / (w + 7) (w + 2).

What is meant by trapezoid ?

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Therefore , the solution to the given problem of probability comes out to be P =0.6.

Probability theory, a subfield of mathematics, calculates the likelihood that an event will occur or that a statement is true. The probability of an event is a number between 0 and 1, where 1 denotes certainty and around 0 denotes how probable the event is to occur. A likelihood is a numerical representation of the likelihood that a particular event will occur. Probabilities may alternatively be stated as percentages with a range of 0% to 100% or as a number between 0 and 1. the percentage of events over a wide range of comparably likely outcomes that happen in comparison to all other conceivable outcomes.

Here,

Given :

Twelve 16 GB and 18 32 GB pen drives are packaged together in a box.

To find the probability of 16gb pen drive is defective:

Thus,

Total pendrive = 30

Event = 16gb pen drive or defective:

The probability of it is 16gb pendrive = 12/30 = 0.4

The probability of it is defective pendrive = 6/30 = 0.2

thus,

total probability (16gb pen drive or defective) = 0.4 +0.2 =0.6

Therefore , the solution to the given problem of probability comes out to be P =0.6.

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Suppose that 60% of the people who inquire about investments at a certain brokerage firm end up investing in stocks. The probability that a person who inquires about investments at this firm will invest in stocks or bonds (or both) is 66%.

60% invest in stocks

50% invest in bonds

44% invest in both bonds and stocks

Percent (only stock) = 60% -44%

Percent (only stock) = 16%

Percent (only bond) = 50% - 44%

Percent (only bond) = 6%

Percent (both) = 44%

Total = 16% + 6% + 44%

Total = 66%

Therefore the probability is 66%.

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The equation for a horizontal line that passes through the points (a, b) is y = b, where b is constant because b is the y-intercept in the equation y = mx + b.

As a result of the fact that in the equation y = mx + b, where 'b' is the y-intercept, there is no change in the value of y on the horizontal line and the slope is zero, the equation of a horizontal line is y = b, where 'b' is constant.A horizontal line's points all share the same y-coordinate.

When two points share the same y-coordinate, b, the line's equation is y=b. The coordinates (0,b) are known as the y-intercept of a horizontal line y=b. Horizontal lines are consistently perpendicular to the x-axis. The formula for the lines is always y = a y= a y= a, where a stands for a real number.

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Answer:

BE = 24

Step-by-step explanation:

These triangles are similar because of AA (Angle, Angle)

The given gives us a pair of parallel sides, allowing us to see that angles C and B are congruent due to being alternate interior angles.

Furthermore, we see that <AEB = <CEB due to vertical <'s being =

Next, we must set up a proportion;

If we create a proportion between the triangles, we must divide corresponding sides;

52/26 = 5x -7 / 2x+2 because we divided both triangles by using the same corresponding sides divided by the same corresponding side.

Simplify 52/26 to 2 and we get that 2 = 5x-7 / 2x+2

Multiply both sides by 2x+2 to get 4x+4 = 5x-7

Subtract 4x from both sides and add 7 from the right side to isolate x and get x=11

Finally, substitute the value of 11 for x into BE 2(11) + 2 and get 22 + 2 =24

The law of exponential change states that when a quantity grows or decays at a rate proportional to its size, then the quantity changes exponentially over time. In other words, it follows an exponential function as opposed to a linear function.

The law of exponential change describes the phenomenon of a quantity changing exponentially over time. This means that the rate of change is proportional to the quantity itself. For example, if a quantity increases by 10% each minute, then the quantity will double every 7.2 minutes. This is because each time the quantity increases by 10%, it is multiplying by 1.1. This process is ongoing and the rate of growth or decay will continue to increase exponentially.

The law of exponential change is used in many areas of science and mathematics, such as population growth and radioactive decay. It is also an important concept in economics, as it can be used to measure the growth of money over time.

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A ratio or value that may be stated as a fraction of 100 is called a percentage.

A percentage is a figure or ratio that can be stated as a fraction of 100 in mathematics. If we need to determine a percentage of a number, multiply it by 100 and divide it by the total. So, a part per hundred is what the percentage refers to. Percent signifies for every 100. The sign "%" is used to denote it.

The value must be divided by the entire value, and the resulting number must then be multiplied by 100 to get the percentage.

The simplest way to use percentages is to compare two numbers, with the second number being rebased to 100.

Therefore, the answer is 25%.

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In the given word problem the Gunnar's car can travel 399.17 miles travel using 17.82 gallon of gas.

A math word problem is a question that is written as one or more sentences and asks students to use their mathematical understanding to solve an issue from "real world." In order for kids to understand the word problem, they must be familiar with the terminology that goes along with the mathematical symbols that they are used to.

Gunnar's car travel using per gallon of gas = 22.4 miles.

According to the given question,

Gunnar's car can hold 17.82 gallons of gas. Then number of miles does Gunnar's car can travel is ,

=> 22.4 × Car's total tank has hold

=> 22.4 × 17.82

=> 399.17 miles

Hence the Gunnar's car can travel 399.17 miles travel using 17.82 gallon of gas.

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Danielle earned a total of $1,058.25 last week.

A commission is a percentage of total sales as determined by the rate of commission. A commission is a profit paid due to making a sale.

commission=rate of commission⋅total sales.

To find the commission on a sale, multiply the rate of commission by the total sales.

commission = rate of commission⋅total sales.

commission = 7.75% x $4,300

commission = 0.0775 x $4,300

commission = $333.25

Danielle's earnings will be the addition of both her commission and base salary

Total = commission + base salary

Total = $333.25 + $725

Total = $1,058.25

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Part a: Future amount due on a compound interest loan is $12271.78.

Part b: The amount due on the loan would be $12033.64, if the compounding period is increased to monthly.

The formula for compounding is:

A = P(1 + r/100n)∧nt

P = $12,000

r = 0.07

Part a: compounded semiannually.

t = 4 years.

n = 2

A = 12000(1 + 0.07/100*2)∧2*4

A = 12000*1.00280

A = 12271.78

Thus, future amount due on a compound interest loan is $12271.78.

Part  b:

t = 4 years.

n = 12

A = 12000(1 + 0.07/100*12)∧12*4

A = 12000*1.0028038

A = 12033.64

Thus, if the compounding period is increased to monthly, the amount due on the loan would be $12033.64.

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Answer: $15,802

$15,865

Step-by-step explanation:

The inequality to represent the number of matinee tickets, x, and evening tickets, y, Aiden can buy is,

⇒ 5x + 10y ≤ 50

A relation by which we can compare two or more mathematical expression is called an inequality.

Given that;

Aidan is going to buy movie tickets for his friends. matinee tickets are $5 each and evening tickets are $10 each. Aidan can spend at most $50 dollars.

Now, Let the number of matinee tickets Aiden can buy = x

And, The number of evening tickets Aiden can buy = y

So, We can formulate;

The correct inequality is,

⇒ 5x + 10y ≤ 50

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The desktop computer cost $1750 before the finance charge, and the laptop cost $1900 before the finance charge.

The discipline of finance is the study of money, money systems, and capital assets. It is associated with economics, which is the study of the production, distribution, and consumption of money, assets, products, and services, but is not the same thing

Let x be the cost of the desktop computer before finance charges.

We know that the laptop cost 150 more than the desktop, so the cost of the laptop is x+150

We also know that the total finance charge for one year is $303 and the interest rate of the desktop is 7% and the interest rate of the laptop is 9.5%

So we can set up the following equations using the information provided:

(x*0.07) + ((x+150)*0.095) = 303

Simplifying and solving for x:

0.07x + 0.095x + 14.25 = 303

0.165x = 288.75

x = $1750

Therefore, the desktop computer cost $1750 before the finance charge, and the laptop cost $1900 before the finance charge.

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Answer:

A = 72 units²

Step-by-step explanation:

the area (A) of a trapezoid is calculated as

A = [tex]\frac{1}{2}[/tex] h (b₁ + b₂ )

where h is the perpendicular height between the bases b₁ and b₂

note that the middle section of the lower base = upper base = 6

here h = 8 , b₁ = 3 + 6 + 3 = 12 , b₂ = 6 , then

A = [tex]\frac{1}{2}[/tex] × 8 × (12 + 6) = 4 × 18 = 72 units²

We can write the linear equation:

y = x + 50

And evaluating it on the given values of x, we will get the table:

x        y

10     60

20    70

30    80

40    90

50    100

We know that there are x sparrows in a tree, and there are 50 sparrows on the ground beneath the tree.

y represents the total number of sparrows, then y is equal to the number of sparrows on the tree (x) plus the ones beneath (50) then we will get:

y = x + 50

B) Now we want to make a table. To make that table, we need to evaluate the linear equation in different values of x.

if x = 10

y = 10 + 50 = 60

if x = 20

y = 20 + 50 = 70

if x = 30

y = 30 + 50 = 80

if x = 40

y = 40 + 50 = 90

if x = 50

y = 50 + 50 = 100

Then the table will be:

x        y

10     60

20    70

30    80

40    90

50    100

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Rachel's personal loan of $4,500 with a 12% annual interest rate for 36 months will have a finance charge of $6,230.16, meaning that she will need to pay a total of $10,730.16 to pay off the loan amount.

The finance charge on Rachel's loan can be calculated by multiplying the loan amount by the interest rate and then multiplying by the loan term (in months).

Finance Charge = (Loan Amount x Interest Rate x Loan Term)

Finance Charge = ($4,500 x 0.12 x 36 months)

Finance Charge = $6,230.16

The finance charge on Rachel's loan can be calculated by multiplying the loan amount by the interest rate and then multiplying by the loan term (in months). In this case, Rachel took out a $4,500 loan with a 12% annual interest rate for 36 months. The total finance charge for this loan can be calculated as follows: Finance Charge = ($4,500 x 0.12 x 36 months) = $6,230.16. This means Rachel will need to pay a total of $10,730.16 to pay off the loan, including the finance charge. This also means that Rachel's monthly payments of $173.06 will go towards the principle balance of the loan and the interest accrued during each month.

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The number of bags of oranges did Shannon use on Tuesday will be 3 bags.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

Shannon operates an orange juice stand. On Monday she used 1 1/2 bags of oranges. On Tuesday she used 2 times as many oranges as on Monday.

The number of oranges will be calculated as,

⇒  2 × (1 ¹/₂)

⇒  2 × (1 + ¹/₂)

⇒  2 + 2 × ¹/₂

⇒  2 + 1

⇒  3 bags

The number of bags of oranges did Shannon use on Tuesday will be 3 bags.

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The sum of the additive inverse of 29 and 61 is equal to -90.

The sum of the additive inverse of two numbers is equal to zero. The additive inverse of a number is the (opposite) number which when added to the original number yields zero. The formula for calculating the additive inverse of a number is additive inverse (x) = - x. The additive inverse of 29 and 61 can be calculated using the formula, additive inverse (29) = -29 and additive inverse (61) = -61.

Therefore, the sum of the additive inverse of 29 and 61 will be -29 + -61 = -90. This can be confirmed by adding 29 and 61 which will yield 90 and then subtracting 90 from zero to yield -90. In other words, the sum of the additive inverse of 29 and 61 is equal to -90.

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Answer:

-300

just do inverse operation, and multiply both sides of the equation by -15 to cancel out the -15 from the denominator and you get V=20(-15)

solve for 20(-15) and you get -300

Third triangle is congruent to triangle PQR.

Triangle congruence: If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent. Slide, twist, flip, and turn these triangles to create an identical appearance. They are in alignment with one another when moved.

For triangles, there are five primary congruency rules:

Side-Side-Side is an SSS criterion.

The side-angle-side SAS criterion.

Angle, Side, Angle is an ASA criterion.

Angle-Angle-Side is an AAS criterion.

Right Angle Hypotenuse Side (RHS) Criteria

As Height of the triangle PQ is similar to triangle third

Angle 90° ≈ Angle 90° of third triangle

Angle 67° ≈ Angle 67° of third degree

So, By ASA, both the triangles are congruent.

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a. 5 + 7n is the algebraic expression for 7 more than the product of 5 and n

The expression needed to indicate the value of 5 added to the product of 7 and n is "5 greater than the product of 7 and n."

The equation 7n represents the product of 7 and n, and the expression 5 + 7n is obtained by adding 5 to 7n.

This is the proper algebraic expression for the phrase that was given.

It follows that 5 + 7n = 5 + 21 = 26, which is 5 more than the sum of the products of 7 and 3. As an illustration, if we substitute a value of 3 for n, the expression 7n would equal 21.

Because option b is a product of 5 and (7+n), which is not equivalent to 5 greater than the product of 7 and n, the other choices are incorrect.

The product of option c and (5+n) is 7, but it also does not equal 5 greater than the product of 7 and n.

A sum of 5, 7, and n makes up option d, which also does not equal 5 greater than the result of the product of 7 and n.

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When t = 3, the exponential function has a value of 809.0.

The exponential function is a mathematical function denoted by f(x)=\exp or e^{x}. Unless otherwise indicated, the word refers to a positive-valued function of a real variable, however it can be extended to complex numbers or applied to other mathematical objects such as matrices or Lie algebras. A mathematical function of the following type is an exponential function: f (x) = an x, where x is a variable and an is a constant known as the function's basis. The transcendental number e, which is about 2.71828, is the most often encountered exponential-function base.

Here,

Given the exponential function h (t) = 1250(0.865)^t

When t = 3

h(3) = 1250(0.865)^3

h(3) = 1250 (0.6472)

h(3) = 809.0

The exponential function when the value of t is 3 is 809.0.

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In Q1, The equation k = y² + a is correct,

To make y the subject of the formula, √k = y + a is incorrect, it should be √k = y + √a

√k - √a = y

In Q2, t = v/4 + 1 is correct

t - 1 + v/4 is incorrect, it should be t - 1 = v/4

t - 1/4 = v

so the correct answer is t-1/4=v