A right triangle has side lengths measuring 5cm 12cm and 13 cm a similar triangle has a hypotenuse of 169cm what is the length of the shortest of the larger triangle

[tex] \bold{(x-6)(x+6)}[/tex]

To simplify this equation, quadratic factoring patterns should be used. These patterns are the following:

[tex] \bold{a^2-b^2=(a-b)(a+b)}[/tex]

This pattern works because if one distributes the terms in the parentheses by multiplying each term in one of the parentheses by each term in the other, the result is the original equation:

[tex]\bold{36=6^2}[/tex] so it can be applied to the given equation:

[tex]\begin{gathered} \bold{x^2-36}\end{gathered}[/tex]

[tex]\bold{(x-6)(x+6)}[/tex]

∴ The factored form of the expression is (x - 6) (x + 6).

There are major two formulas in arithmetic progression which is related to the nth term of A.P.

The difference between any two consecutive integers in an arithmetic progression (AP) sequence of numbers is always the same amount. It also goes by the name Arithmetic Sequence. For instance, the natural number sequence 1, 2, 3, 4, 5, 6,... is an example of an arithmetic progression. It has a common difference of 1 between two succeeding terms (let's say 1 and 2). (2 -1). We can see that the common difference between two subsequent words will be equal to 2 in both the case of odd and even numbers.

Definition 1: An acronym for a mathematical sequence where the difference between any two consecutive terms is always a constant.

Definition 2: An arithmetic sequence or progression is a series of numbers in which the second number in each pair of consecutive terms is obtained by adding a predetermined number to the first.

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Slope is  $0.15 of the equation of cost  C=$0.15t+$35.00.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

Given that A cell phone company uses the equation C=$0.15t+$35.00

C is the total cost for a month of service.

t is the number of text messages.

We have to find the slope of the equation.

slope is 0.15 and 35.00 is the y intercept of the equation given.

Hence, slope is  $0.15 of the equation of cost  C=$0.15t+$35.00.

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The slope of 2y = -3x + 1 is  -3/2.

Given straight line is 2y = -3x + 1.

Slope of a straight line is determined by how its y-coordinate changes in respect to how its x-coordinate changes.

A line's equation can be used to determine the slope of the line.

we know that standard slope form of straight line is y = mx + c.

Where m is the slope of straight line.

Now we transform given equation to standard slope form of straight line :

Comparing this equation to standard equation, we find m = -3/2.

Therefore, the slope of given line is -3/2.

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Answer: a. i. In this context, x represents the number of cups of water.

ii. In this context, y represents the number of cups of lemon juice.

iii. Yes, there is a proportional relationship between x and y. The recipe states that for every cup of water, there should be one cup of lemon juice. This means that as the amount of water increases, the amount of lemon juice also increases in the same proportion.

b. To plot the pairs in the table in a coordinate plane, we can use the values of x and y as the coordinates. For example, the first pair (x=1, y=4) would be plotted at the point (1, 4) on the coordinate plane. Similarly, the second pair (x=2, y=1) would be plotted at the point (2, 1), and so on.

Please note that the table provided with X, Y and ²14,1 is incorrect, it is not possible to plot these values in a coordinate plane as the values are not valid.

Step-by-step explanation:

The perimeter of the isosceles triangle is 128.8/(√35 +2) cm.

What is an isosceles triangle?

A triangle with two equal sides is said to be isosceles. Also equal are the two angles that face the two equal sides. In other terms, an isosceles triangle is a triangle with two sides that are the same length.

We are given that the base of an isosceles triangle is equal to 1/3 of the lateral side.

Also, the height of the base together with the height is 9.2 cm.

Let the lateral side be 'x' and the height be 'h'

So, the base is x/3

Since the height of the triangle, divides it into two right angled triangles, therefore,

x^2= h^2 + (x/6)^2

⇒h^2 = x^2 - (x/6)^2

⇒h^2 = √[x^2 - (x/6)^2]

We are given h+b=9.2 cm

So,

⇒√[x^2 - (x/6)^2] + x/3 = 9.2

⇒x√35/6 + x/3 = 9.2

⇒(x√35 +2x)/6 = 9.2

⇒x√35 +2x = 55.2

⇒x(√35 +2) = 55.2

⇒x = 55.2/(√35 +2)

So, the base is 1/3*55.2/(√35 +2) = 18.4/(√35 +2)

Perimeter = 2*55.2/(√35 +2) + 18.4/(√35 +2)

= (110.4 + 18.4)/(√35 +2)

= 128.8/(√35 +2) cm

Hence, the perimeter of the isosceles triangle is 128.8/(√35 +2) cm.

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Answer:

x = 111°

Step-by-step explanation:

Sum of interior angle

(n - 2) 180°

=(7 - 2) 180

=(5) 180°

=900°.

The value of x

=139° + 141° + 120° + x + 136° + 118° + 135° = 900°

=400° + x + 389° = 900°

=789° + x = 900°

x = 900° - 789°

x = 111°.

Answer:

The correct answer is B.

The side-length of square C as required in the task content is; 5 ft.

It follows from the task content that the side length of square C is to be determined according to the given diameter.

Recall that the Area, A of a square in terms of its side length, s is; A = s².

Therefore, s = √A.

On this note, for each of the given squares their side lengths are as follows;

For square A; side length is; √9 = 3ft.

For square B; side length is; √16 = 4ft.

Hence, since sides A, B and C form a right triangle;

C² = A² + B²

C² = 3² + 4²

C² = 9 + 16

C² = 25

C = 5.

Ultimately, the side-length of square C is; 5 ft.

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Answer:

7

Step-by-step explanation:

v is is and e is 5

2v is 20 and e is 5 and plus 3

20 divided by 5 plus 3 will equal to 7

Answer:

[tex] \sf \: 2v ÷ e + 3 = 7[/tex]

Step-by-step explanation:

Given expression,

→ 2v ÷ e + 3

Now we have to use,

→ v = 10

→ e = 5

Let's solve the expression,

→ 2v ÷ e + 3

→ 2(10) ÷ (5) + 3

→ 20 ÷ 5 + 3

→ 4 + 3

→ 7 => final value

Therefore, the answer is 7.

Answer:

Step-by-step explanation:

Simplify the following:

(sqrt(48))/(sqrt(42))

Rationalize the denominator. (sqrt(48))/(sqrt(42)) = (sqrt(48))/(sqrt(42))×(42^(1 - 1/2))/(42^(1 - 1/2)) = (sqrt(48)×42^(1 - 1/2))/42:

(sqrt(48)×42^(1 - 1/2))/42

Combine powers. (sqrt(48)×42^(1 - 1/2))/42 = sqrt(48)×42^((1 - 1/2) - 1):

sqrt(48)×42^((1 - 1/2) - 1)

Put 1 - 1/2 over the common denominator 2. 1 - 1/2 = 2/2 - 1/2:

sqrt(48)×42^((2/2 - 1/2) - 1)

2/2 - 1/2 = (2 - 1)/2:

sqrt(48)×42^(((2 - 1)/2) - 1)

2 - 1 = 1:

sqrt(48)×42^(1/2 - 1)

Put 1/2 - 1 over the common denominator 2. 1/2 - 1 = 1/2 - 2/2:

sqrt(48)×42^(1/2 - 2/2)

1/2 - 2/2 = (1 - 2)/2:

sqrt(48)×42^((1 - 2)/2)

1 - 2 = -1:

sqrt(48)×42^((-1)/2)

sqrt(48) = sqrt(2^4×3) = 2^2 sqrt(3):

2^2 sqrt(3) 1/sqrt(42)

2^2 = 4:

4 sqrt(3) 1/sqrt(42)

Rationalize the denominator. (4 sqrt(3))/(sqrt(42)) = (4 sqrt(3))/(sqrt(42))×(sqrt(42))/(sqrt(42)) = (4 sqrt(3) sqrt(42))/42:

(4 sqrt(3) sqrt(42))/42

The gcd of 4 and 42 is 2, so (4 sqrt(3) sqrt(42))/42 = ((2×2) sqrt(3) sqrt(42))/(2×21) = 2/2×(2 sqrt(3) sqrt(42))/21 = (2 sqrt(3) sqrt(42))/21:

(2 sqrt(3) sqrt(42))/21

sqrt(3) sqrt(42) = sqrt(3×42):

2/21 sqrt(3×42)

3×42 = 126:

(2 sqrt(126))/21

sqrt(126) = sqrt(3^2×14) = 3 sqrt(14):

2/21 3 sqrt(14)

3/21 = 3/(3×7) = 1/7:

Answer: (2 sqrt(14))/7

To calculate std deviation in R you can create a list of values or import a CSV file to find the standard deviation.

It is simple to compute an average and standard deviation in R. The mean() and sd() functions compute the average and standard deviation, respectively.

The positive square root of the variance is the standard deviation. One of the fundamental techniques used in statistical analysis is standard deviation. Standard deviation, also known as SD or indicated by the symbol "," indicates how far a value deviates from the mean value.

A low standard deviation indicates that the values are often within a few standard deviations of the mean, whereas a large standard deviation indicates that the values are much outside of the mean. Learn how to determine a random variable's standard deviation as well as the standard deviation of data that has been grouped and ungrouped.

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Yes, it is possible to find the HCF (highest common factor) of 7 and 9 without using the prime factorization method.

One way to find the HCF of two numbers without using prime factorization is to use the Euclidean algorithm.

The Euclidean algorithm for finding the HCF of two numbers is as follows:

Divide the larger number by the smaller number and get the remainder.

Divide the smaller number by the remainder obtained in step 1 and get the remainder.

Repeat step 2 until the remainder is 0.

The last non-zero remainder obtained is the HCF of the two numbers.

Using the Euclidean algorithm for 7 and 9:

9/7 = 1 remainder 2

7/2 = 3 remainder 1

2/1 = 2 remainder 0

So the last non-zero remainder obtained is 1.

Therefore, the HCF of 7 and 9 is 1.

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Answer:

A = 42

Step-by-step explanation:

If 6 / 7 = A / 49, then:
(multiply both sides of the equation by 49)
A = 49 * 6 / 7
A = 42

You can also solve by the rule of proportions (see picture):
7 * A = 6 * 49
A = 6 * 49 / 7
A = 6 * 7 = 42

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Answer:

A

Step-by-step explanation:

The five types of inequality in mathematics are greater than (>), less than (<), greater than or equal to (≥), less than or equal to (≤), and not equal to (≠). These are used to compare two values and determine if one is greater than, less than, equal to, or not equal to the other.

Greater than (>) - This type of inequality is used to compare two values and determine which one is greater than the other. For example, if we say x > y, this means that x is greater than y.

Less than (<) - This type of inequality is the opposite of the greater than inequality. If we say x < y, then this means that x is less than y.

Greater than or equal to (≥) - This type of inequality is used to compare two values and determine if one is greater than or equal to the other. This means that the two values are either equal to each other or one is greater than the other. For example, if we say x ≥ y, then this means that either x is equal to y, or x is greater than y.

Less than or equal to (≤) - This type of inequality is the opposite of the greater than or equal to inequality. If we say x ≤ y, then this means that either x is equal to y, or x is less than y.

Not equal to (≠) - This type of inequality is used to compare two values and determine if they are not equal to each other. For example, if we say x ≠ y, then this means that x is not equal to y.

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The asked quadratic equation is x²+6x+41/2 = 0

A quadratic equation is a second-order polynomial equation in a single variable x ax²+bx+c = 0. with a ≠ 0.

Given that, the roots of a quadratic equation are −6±5i

Since, -b±√(b²-4ac)/(2a) is the quadratic formula,

Therefore, we have,

b = 6, 2a = 1, a = 1/2

√(b²-4ac) = 5i

√(b²-4ac) = [tex]\sqrt{-5}[/tex]

Squaring both sides,

b²-4ac = -5

6²-4(1/2)c = -5

36-2c = -5

2c = 41

c = 41/2

Therefore, the equation = x²+6x+41/2 = 0

Hence, the asked quadratic equation is x²+6x+41/2 = 0

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Four red cells and eight blue cells make up the body. Then, C is the right answer.

A ratio is a group of sequentially ordered numbers a and b expressed as a/b, where b is never equal to zero. When two objects are equal, a statement is said to be proportional. A ratio that connects a part to a whole is a percentage. For instance, there are 100 students in the class with 20 men and 80 women. The percentage of men is 20/100, or 20%. 80 out of 100, or 80%, are women.

There are 12 square boxes in the grids.

Let R stand for red and B for blue.

R + B = 12                                    ...1

R / B = 1/2                                    ...2

We have by resolving equations 1 and 2

R + 2R = 12

3R = 12

R = 4

Then

4 + B = 12

B = 8

Then, C is the right answer.

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Complete Question -

Answer:

x = 9

Step-by-step explanation:

first step, multiply both sides by 6. This is going to get rid of that fraction-looking situation on the left.

3x+9 / 6 = x - 3

6• 3x+9 /6 = 6(x-3)

On the left the 6s cancel (cancel is not a technical math term, but 6/6 is 1, so you are left with only the 3x+9)

3x + 9 = 6(x - 3)

Next, use distributive property on the right side.

3x + 9 = 6x - 18

Subtract 3x from both sides.

9 = 3x - 18

Add 18 to both sides.

27 = 3x

Divide both sides by 3.

27/3 = x

9 = x

x = 9

1: Convert the mixed number into an improper fraction.

2: Rewrite the whole number as a fraction with the denominator 1.

3: Multiply two fractions by multiplying the numerators and denominators separately.

4: Convert it into simplified form if required.

Now, According to the question:

A mixed number is a whole number and a proper fraction represented together.  It generally represents a number between any two whole numbers.

To multiply a mixed number with a fraction, first, convert the mixed number to a fraction and then multiply the two fractions. Two fractions can be multiplied by multiplying the numerators and denominators separately to get a fraction as an answer. The fraction can be written in its simplest form by removing any common factors between the numerator and denominator.

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The pizza pie cost  $16.50.

We have the following information. An equation is a mathematical statement that asserts the equality of two expressions. It is written in the form of "left-hand side = right-hand side," where both sides are expressions that are made up of numbers, variables, and mathematical operations.

Gentiana spent $10 on her entrance fee, so she has $40 - $10 = $30 left.

25% of $30 is $30 x 0.25 = $7.50.

She spent $7.50 on a Movie.

20% of $30 is $30 x 0.20 = $6.

She spent $6 on popcorn.

So, the total amount spent on Movie and popcorn is $7.50 + $6 = $13.50.

Therefore, the pizza pie cost $30 - $13.50 = $16.50

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25% of $30 is $30 x 0.25 = $7.50.

She spent $7.50 on a Movie.

20% of $30 is $30 x 0.20 = $6.

She spent $6 on popcorn.

So, the total amount spent on Movie and popcorn is $7.50 + $6 = $13.50.

Therefore, the pizza pie cost $30 - $13.50 = $16.50

Answer:

Step-by-step explanation:

Hello! You know that the price of a new car is $29,990 and the sales tax rate is 6.5%.  To calculate the tax you will have to pay, you have to multiply 0.065 by 29,990.  You have to move the decimal space two spaces to the left to get rid of the percentage.  29,990 x 0.065 = 1949.35.  The sales tax being charged for the car is $1949.35.  The total cost of the car including tax is $29,990 + $1949.35, which equals $31939.35. Hope this helps!

The angle of the refracted ray is 15°.

When an incident light ray strikes the surface of the water at an angle of 20 degrees, it will be refracted, or bent, as it enters the water. The refracted ray will continue to travel through the water at a different angle than the incident ray.

In order to determine the angle of the refracted ray, we may apply Snell's law, which states that the ratio of the sines of the angles of incidence and refraction is constant for a given wave when it passes through two different media. Mathematically, this is:

n₁sin(θ₁) = n₂sin(θ₂)

Where n is the refractive index. Substituting the values given into the equation:

1.0003 * sin(20°) = 1.33 * sin(θ)

θ = 14.91

The angle of the refracted ray is 15°.

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The value of side x for the right-angle triangle is 8.6 cm.

The branch of mathematics that sets up a relationship between the sides and the angles of the right-angle triangle is termed trigonometry.

The trigonometric functions, also known as a circular, angle, or goniometric functions in mathematics, are real functions that link the angle of a right-angled triangle to the ratios of its two side lengths.

Given that the sides are Hypotenuse H = 15 cm, perpendicular = x, and the base is y.

The value will be calculated as,

x = [ sin(35) x 15 ]

x = 8.6 cm

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30 : 15 : 15, cookies in total, we say that y is directly proportional to x when two variables, x and y, are such that the ratio yx remains constant.

We say that y is directly proportional to x when two variables, x and y, are such that the ratio yx remains constant. If k is used to denote the constant, we can obtain the equations y = kx or y = k, where k 0.

When added to your sugar cookie batter, a teaspoon or two of extracts will significantly enhance flavor. The obvious option is vanilla. Add both vanilla and almond extracts for a more interesting flavor. Other wonderful options to think about are rum, maple, and anise.

1/30 : 2/30 : 2/30.

30 : 15 : 15.

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To find the total number of revolutions the 32 windmills complete in 1 minute, you would use the operation of multiplication.

Multiplication is a mathematical operation used to find the total number of items in a group when the number of items in each group and the number of groups are known.

In this case, we know that there are 32 windmills and each windmill completes 120 revolutions per minute. To find the total number of revolutions completed by all 32 windmills, we need to multiply the number of windmills by the number of revolutions each windmill completes per minute.

So, the calculation would be: 32 * 120 = 3840. This calculation is read as "32 multiplied by 120 equals 3840." The result, 3840, represents the total number of revolutions completed by all 32 windmills in 1 minute.

In short, the operation of multiplication is used to find the total number of revolutions completed by all 32 windmills in 1 minute because it allows you to find the total number of items in a group when the number of items in each group and the number of groups are known.

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The company's monthly revenue rises by 8% on a monthly basis.

The mathematical formula f (x) = an x denotes an exponential function. a constant known as the function's base and a variable called x are present.

Any function whose constant is raised to the power of an input is said to be exponential.

An exponential function looks like this:

[tex]$y=a b^x$[/tex]

Where:

A stands for the starting point.

B is equal to 1 plus the rate r.

The following ordered pair can be seen in the table.

(x,y) = {(0,72000) (3,90000)}

The result is:

[tex]$90000=72000 \times b^3$[/tex]

Subtract 72000 from both sides.

[tex]$1.25=b^3$[/tex]

Take the cube's two side roots.

[tex]$b=\sqrt[3]{1.25}$$b=1.08$[/tex]

Observe that:

[tex]$b=1+r$[/tex]

The result is:

[tex]$1+r=1.08$[/tex]

Take 1 away from each side.

r= 0.08

Describe as a percentage

r= 8%

As a result, the company's monthly revenue increases by 8%.

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The simplified exponential expression for this problem is given as follows:

-9h^7g^5.

The exponential expression for this problem is defined as follows:

2h²g^4h^5g - 7hg²h^6g³ - 4g²h³h^4g³.

When two terms with the same base and different exponents are multiplied, the bases are kept while the exponents are added.

Hence the terms are simplified as follows:

Hence the simplified expression is given as follows:

2h^7g^5 - 7h^7g^5 - 4h^7g^5.

(2 - 7 - 4)h^7g^5.

-9h^7g^5.

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Answer:

1.

-x² + 2x

Step-by-step explanation:

x² + x - 2.

=x³ - x² + 2x - 2.

1

=-x² + 2x.

note: x³ cancel x² and x, and -2 cancel -2.

The area of the right triangle is equal to 1.5√187 square meters.

Right triangles are triangles with a right angle, whose side relationship is described by Pythagorean relationship:

r = √(x² + y²)

Where:

And the area of the triangle (A), in square meters, is determined by the following formula:

A = 0.5 · x · y

First, determine the length of the missing leg by Pythagorean theorem:

x = √(14² - 3²)

x = √187

Second, calculate the area of the triangle:

A = 0.5 · (3 m) · (√187 m)

A = 1.5√187 m²

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