In a student council election Kyle receives 120 votes for president. If Kyle receives 60% of the votes, how many students vote in the election?

[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).

Answer:

  y = 250(0.96^n)

Step-by-step explanation:

You want an equation for the number of students in the senior class after n years, when it has 250 students now and decreases at 4% per year. You also want to know the number of years until the class is 100 students.

The exponential equation will have the form ...

  y = a·b^x

where 'a' is the initial value, 'b' is the growth factor, and x is the independent variable.

You have an initial value of 250, a growth factor of (1+(-4%)) = 0.96, and an independent variable of 'n', representing the number of years the population has been declining. The equation is ...

  y = 250(0.96^n)

The population will reach 100 students when n has the value that satisfies ...

  100 = 250·0.96^n

  0.4 = 0.96^n . . . . . . . . . divide by 250

  log(0.4) = n·log(0.96) . . . . . take logarithms

  n = log(0.4)/log(0.96) ≈ 22.45

The senior class will have about 100 students in 22.45 years.

__

Additional comment

The growth factor used in these exponential equations is (1 + growth rate), where the growth rate is the fractional change in the period of interest. The independent variable (x or n) is the number of such periods. Here, the fractional change is given as -4%, a 4% per year decrease. This tells us a period is 1 year. Of course -4% is the decimal fraction -0.04.

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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The exact solutions of an quadratic equation, 9x² - 4 is equals to the values of x, i.e., x = 2/3, - 2/3.

In algebra, a quadratic equation is any equation that can be written in standard form as ax² + bx + c = 0, where x represents an unknown variable, and a, b, and c are known constants, where a ≠ 0. The solutions of a quadratic equation represent x values, where values stratified the equation . Quadratic formula is used to find the solution of standard equation and it can be written as, x = (- b ±√b² - 4ac)/2a .

We have, an quadratic equation,9x²- 4=0

Comparing it with standard equation ax² + bx + c = 0, we get, a = 9 , b = 0 , c = - 4

Using the quadratic formula to determine the solution of it , x = (- b ±√b² - 4ac)/2a

=> x = { -0 ±√0 - 4×9×(-4)}/2×9

=> x = ±(√144/18)

=> x = ± 12/18 = ± 2/3

Hence, the required solution are x = ± 2/3.

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The measure of length PQ will be 22 units.

A triangle's third side is stated to be parallel to the line segment uniting its two midpoints, and it is also half as long as the third side.

Given:

PQ = 5x + 62, and MN = 6x-4

Now, using Mid- Point Theorem

PQ= 1/2 MN

-5x+ 62 = 1/2( 6x - 4)

-5x+ 62 = 3x - 2

-5x- 3x = -2 - 62

-8x = -64

x= 8

PQ= 5x+ 62 = -5(8) + 62 = -40 + 62 = 22

Hence, the measure of PQ is 22 units.

The missing image is attached below.

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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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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 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:

Below in bold.

Step-by-step explanation:

To do this we keep dividing by successive primes, using the lowest prime that divides exactly.

2) 12600

2) 6300

2) 3150

3) 1575

3) 525

5) 175

5) 35

7        <---we end up with a prime number so tha's the end of the process

So, 12,600 = 2*2*2*3*3*5*5*7 or 2^3*3^2*5^2*7.

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 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

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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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:

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

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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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

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 -

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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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.

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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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!

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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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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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:

D. y = 5x

Step-by-step explanation:

This graph shows a linear relationship between the number of sandwiches bought (x) and their cost (y). In this question, we are asked to define the relationship between x and y using an equation. Since this relationship is linear and thus has a constant of proportionality, we can represent it in the form: y = mx, where m is the ratio of the cost of sandwiches to the number of sandwiches. We can solve for m with the formula:

m = rise / run

So, the value m of the given line is:

m = 10 / 2

m = 5

Hence, the equation that displays the proportional relationship between the number of sandwiches bought (x) and their cost (y) is D. y = 5x.

Answer:

A

Step-by-step explanation:

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:

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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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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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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