in the equation, 6 + 3y + 4y + 2 the variable y represents the same value is y = 2, 3, 4, or 5 the solution of this equation? explain

Answer:

x = 1 , x = 13

Step-by-step explanation:

(x - 7)² = 36 ( take square root of both sides )

x - 7 = ± [tex]\sqrt{36}[/tex] = ± 6 ( add 7 to both sides )

x = 7 ± 6 , then

x = 7 - 6 = 1

x = 7 + 6 = 13

Answer:Q1. The values of a and b cannot be determined from the given information. To find the values of a and b, additional information is needed to solve the equation √2+2√3 = (a + b√6)/(2√2+√3).

Q2. To find the length and breadth of a rectangle, you need to factor the polynomial expression 6x² - 29x + 30. Then, you need to identify two numbers that multiply to 30 and add up to -29. The expression 6x² - 29x + 30 can be factored as (2x - 5)(3x - 6). The length of the rectangle is 2x - 5, and the breadth is 3x - 6. The perimeter of the rectangle is (2 * length) + (2 * breadth) = 2(2x - 5) + 2(3x - 6) = 4x + 4.

Step-by-step explanation:

Q1. The values of a and b cannot be determined from the given information. To find the values of a and b, additional information is needed to solve the equation √2+2√3 = (a + b√6)/(2√2+√3).

Q2. To find the length and breadth of a rectangle, you need to factor the polynomial expression 6x² - 29x + 30. Then, you need to identify two numbers that multiply to 30 and add up to -29. The expression 6x² - 29x + 30 can be factored as (2x - 5)(3x - 6). The length of the rectangle is 2x - 5, and the breadth is 3x - 6. The perimeter of the rectangle is (2 * length) + (2 * breadth) = 2(2x - 5) + 2(3x - 6) = 4x + 4.

Answer:

D

Step-by-step explanation:

D.D.D..D.D.D.D.D.D.D.D D D. D.D.D.

Solving the provided question, we can say that area of parallelograms = 1/2[( a +b)/ 2 ] = 1/2[( AB+EF)/ 2 ]

A parallelogram is a straightforward quadrilateral in Euclidean geometry that has two sets of parallel sides. In a particular kind of quadrilateral known as a parallelogram, both sets of opposite sides are parallel and equal. There are four different kinds of parallelograms, including three unique kinds. Parallelograms, squares, rectangles, and rhombuses are the four different shapes. Having two sets of parallel sides makes a quadrilateral a parallelogram. In a parallelogram, the opposing sides and angles are both the same length. On the same side of the horizontal line, the interior angles are additional angles as well. 360 degrees is the total number of interior angles.

we have

area of parallelograms = 1/2[( a +b)/ 2 ]

a  = AB and b = EF

area of parallelograms = 1/2[( AB+EF)/ 2 ]

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Answer:     c is greater than 11

Step-by-step explanation:

Since Heather needs to spend more than $26 and she already spent $15, we can write this out as

      c + 15 is greater than 26

subtracting 15 from both sides;

     c is greater than 11

The required value of k will the system of linear equations has infinite number of solutions is 2.

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."

We know that

KX + 4y - 3 = 0 . ..........(1)

6x + 12y - 9=0 ..........(2)

Because there are infinity many solutions to linear equations.

[tex]\frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}=\frac{c_{1}}{c_{2}}[/tex]

⇒ k/6 = 4/12 = -3/-9

k/6 = 1/3

k = 2

Thus,required value of k is 2.

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The number of parakeets are there in 2006 are approximately equal to 4240 monk parakeets.

What is Algebraic expression ?

Algebraic expression can be defined as the combination of variables , constants and exponents.

Given, expressions

In 1992, 1219 monk parakeets were observed in the United States. For the next 11 years, about 12% more parakeets were observed each year.

The initial amount is 1219 . The percent growth is 12%.

So the growth factor is 1+0.12 = 1.12

Therefore,

The model us M = 1219 (1.12)^t

where M is the number of monk parakeets after t years.

M(11) = 1219(1.12)^11

M(11)=4240.35

There will be approximately 4240 monk parakeets in 2003.

M = 1219 (1.12)^t. In 2023, there will be approximately equal to 4240 monk packets.

Hence, The number of parakeets are there in 2006 are approximately equal to 4240 monk parakeets.

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If the first two selections were boys, the way that it affects the probability of the third candidate being a girl is; It increases the probability of a girl being the third candidate.

Conditional probability in mathematics is defined as the type of probability that depends on the occurrence or outcome of another event.

Now, we are told that in the school;

Number of Girls = 7

Number of boys = 3

Since the staff is choosing the candidates at random, then it means everyone has an equal chance to be picked.

Now, since we are told that 2 boys are selected first, it means that there would be only 1 boy left and as such the probability of selecting a girl will increase because there would now be seven girls out of 8 people.

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Answer: 120 quarters

Step-by-step explanation:

There are 4 quarters in a dollar.

For 30 dollars, there are 3 * 40 = 120 quarters

120 quarters are in thirty dollars

Kinetic energy acquired by the body in 10 sec is 4000 J.

What is kinetic energy?

The energy that an object has as a result of motion is known as kinetic energy. It is described as the effort required to move a mass-determined body from rest to the indicated velocity. The body holds onto the kinetic energy it acquired during its acceleration until its speed changes.

Here. we ave

Given: A body of mass 5 kg initially at rest is subjected to a force of 20 N

Force = mass × acceleration

A= F/m

a= 4 m/s ².

We know that,

K.e = 1/2 mv²

To find v:-

V= u+at

V= 0+40

V= 40 m/s.

K.E = 1/2 ×5×40×40

K.E = 4000 J.

Hence, kinetic energy acquired by the body in 10 sec is 4000 J.

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Answer:

Solving the expression:

3−9/3+(2)(9)

=3−3+(2)(9)

=0+(2)(9)

=0+18

By the definition of the mode, we can say the mode of this data is 33.

What is the mode?

The mode in statistics refers to a number in a set of numbers that appears the most often. For example, if a set of numbers contained the following digits, 1, 1, 3, 5, 6, 6, 7, 7, 7, 8, the mode would be 7, as it appears the most out of all the numbers in the set.

We have given,

Data set 18 16 11 45 33 16 33 14 18 33.

To find what is the mode for this data set.

Solution: We have given

Data set 18 16 11 45 33 16 33 14 18 33.

Mode: The mode of a set of data values is the value that appears most often.

So,

We can see the most repeated number is 33. ( 3 times)

Hence, by the definition of the mode, we can say the mode of this data is 33.

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The value of constant p is 6. Polynomials are algebraic formulas with variables and coefficients. Variables are also known as indeterminates.

Remainder for f(2) = 20.

F(2)=2(23)+22−3(2)+p=20

16+4−6+p=20

14+p=20

P=6

To divide polynomials, divide each term independently by the monomial (as mentioned above), and sum the quotients of each division to get the result. Polynomial long division is a procedure in algebra for dividing a polynomial by another polynomial of the same or lower degree, which is an extended version of the well-known arithmetic approach known as long division. It is simple to accomplish by hand because it divides an otherwise difficult division problem into smaller ones.

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It will take 87.5 cm³ × 40 = 3500 cm³ volume of wax will it take to make 40 candles

The volume of a pyramid with a square base can be calculated using the formula V=13s2h, where s is the length of the base's sides. A polygonal base and an apex come together to form a polyhedron known as a pyramid. Volume = (1/3) base area height, where height is the height from the base to the apex, is the basic formula for a pyramid's volume.

Given,

side = 7cm

height = 15cm

Volume = 1/3 × h × 5/2 × s

⇒ volume = 15×7 ×5/6

⇒ volume = 87.5 cm³

It will take 87.5 cm³ × 40 = 3500 cm³ volume of wax will it take to make 40 candles

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Complete Question -

Ana makes wedding favors with candles in the shape of a quadrangular pyramid decorated with seeds. a) If one side of the base measures 7 cm and the height of the pyramid is 15 cm, what volume of wax will it take to make 40 candles?​

Answer: The Answer is D. Variability

Answer: D: Variability

Hope this helped!

The required required value of G is 1) 2.11 × 10^7 2) 2.06 × 10^7.

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the word percent means. The letter "%" stands for it.

We have,

1) m = 6. 1 x 10^-5, t = 1. 7 x 10^-6

G = m/t^2

G =6. 1 x 10^-5/(1. 7 x 10^-6)^2

G = 2.11 × 10^7

2)m is increased by 8%

New m = 6.59 x 10^-5,

t is increased by 5%

New t = 1.79  x 10^-6

So

G = m/t^2

G = 6.59 x 10^-5/(1.79  x 10^-6)^2

G = 2.06 × 10^7.

Thus, required value of G is 1) 2.11 × 10^7 2) 2.06 × 10^7.

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The equation of equilibrium states that the sum of the forces in the x-direction must be zero.

Equation of equilibrium:

F_x = 0 = mgsinθ - mgsinϕ

mgsinθ = mgsinϕ

sinθ = sinϕ

θ = ϕ

The equation of equilibrium states that the sum of the forces in the x-direction must be zero. This means that the force due to gravity in the x-direction, mgsinθ, must be equal to the force due to gravity in the x-direction, mgsinϕ. This can be rearranged to sinθ = sinϕ, which means that the angles θ and ϕ must be equal. Thus, the relationship between angles θ and ϕ is that they are equal.

The equation of equilibrium states that the sum of the forces in the x-direction must be zero.

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The equation of a line that passes through the point (0,3) and has a gradient of 2 is: y = 2x + 3

We know that the point-slope form of equation of line is:

(y - y₁) = m(x - x₁)

where m is the slope (also called as gradient)

Here, we have been given a point (0, 3) and the slope of the line is 2.

Let us assume that (x₁, y₁) = (0, 3)

and slope (m) = 2

Using point-slope form of equation of line,

(y - y₁) = m(x - x₁)

(y - 3) = 2(x - 0)

y - 3 = 2x

y - 3 + 3 = 2x + 3

y = 2x + 3

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If a  rhombus with a base of 18 inches and a height of 16 inches has an area of 288 square inches

a polygon is a plane figure that is described by a finite number of straight line segments connected to form a closed polygonal chain.

A rhombus is a quadrilateral whose four sides all have the same length.

Given that  rhombus with a base of 18 inches and a height of 16 inches.

Height = 16 inches

Base = 18 inches

Area of the rhombus = Base × Height

=16×18

288 square inches.

Hence, if a  rhombus with a base of 18 inches and a height of 16 inches has an area of 288 square inches.

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Answer:

288

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The solution for the inequality -4x-3>-5x+8 is x>11.

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

1) -11+x≥-3

Move all terms not containing x to the right side of the inequality.

x≥8

2) -x/4 <7

Move all terms not containing x to the right side of the inequality.

-x<28

x>-28

3) The highest waterfall in the world is Angel falls in Venezuela at 1000 meters.

So, the inequality represent the height of waterfall is h≤1000.

4) -4x-3>-5x+8

Add 5x on both the sides of an inequality, we get

x-3>8

Add 3 on both the sides of an inequality, we get

x>11

5) Given that, Area≤48

Here, 1/2 ×8×x≤48

4x≤48

x≤12

6) -2x-9<-x-4

Add x on both the sides of an inequality, we get

-x-9<-4

Add 9 on both the sides of an inequality, we get

-x<5

x>-5

7) 1/2 x-8>-3

Move all terms not containing x to the right side of the inequality.

Here x>10

Therefore, the solution for the inequality -4x-3>-5x+8 is x>11.

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220 cm serves as the door's maximum height allowance.

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Answer:

  (c)  15 units

Step-by-step explanation:

Given a right triangle with hypotenuse 17 and one leg 8, you want the measure of the other leg.

The Pythagorean theorem tells you the relationship between the sides of a right triangle:

  a² +b² = c² . . . . . . where c is the hypotenuse

  a² +8² = 17² . . . . . . using given values of b, c

  a² = 289 -64 = 225 . . . . subtract 8²

  a = √225 = 15

The length of segment BC is 15 units.

__

Additional comment

These side lengths {8, 15, 17} can be considered to be a "Pythagorean triple." It is one of a few that often appear in algebra and geometry problems. Others include {3, 4, 5}, {5, 12, 13}, {7, 24, 25}. Multiples of these are also commonly seen, such as 2×{3, 4, 5} = {6, 8, 10}.

The given options (i), (ii) and (iv) are all solutions of the equation. Option (iii) is not a solution of the equation since x=-1/2 does not equal 3 or -2.

The given equation is 2x2 - 5x - 3 = 0. The solutions of a quadratic equation are found by setting the equation equal to zero and solving for x. The solutions of this equation can be found by using the Quadratic Formula:

x = [-b ± (√b2 – 4ac)] / 2a

Using this formula:

x = [-(-5) ± (√(-5)2 – 4(2)(-3))] / 2(2)

x = [5 ± (√25 + 24)] / 4

x = [5 ± (√49)] / 4

x = [5 ± 7] / 4

Therefore, the solutions are x = 3 and x = -2.

The given options (i), (ii) and (iv) are all solutions of the equation. Option (iii) is not a solution of the equation since x=-1/2 does not equal 3 or -2.

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Steps which are required to solve quadratic equation by factoring are as follow :

1. Convert the equation into standard form.

2. calculate the factors of the equation by splitting or formula method.

3. Equate the factors to zero and get the value.

Example : Factors of x² + 4x + 4 = 0 are x = -2.

As given in the question,

Steps required to solve quadratic equation by factoring are given by :

Standard quadratic equation is : ax + by + c = 0

Two methods to solve quadratic equations are:

a. Splitting method

b. Formula  : x = ( - b ± √b² -4ac ) / 2a.

Consider a example:

x² + 4x = -4

1. Convert into standard from

x² + 4x + 4 = 0

solve it by splitting method :

x² + 2x + 2x + 4 = 0

⇒ x(x + 2 ) + 2 ( x + 2 ) =0

⇒ ( x + 2 ) ( x+ 2 ) = 0

⇒ x + 2 = 0

⇒ x = -2

Therefore, the steps required to solve quadratic equation are :

1. Convert the equation into standard form.

2. calculate the factors of the equation by splitting or formula method.

3. Equate the factors to zero and get the value.

Example : Factors of x² + 4x + 4 = 0 are x = -2.

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Simplifying 1/(1/4x -1/x+5) gives 4x²+20x)/5-3x

Simplifying an expression is just another way to say solving a math problem. When you simplify an expression, you're basically trying to write it in the simplest way possible. At the end, there shouldn't be any more adding, subtracting, multiplying, or dividing left to do.

1/(1/4x -1/x+5) = 1 ÷ 1/4x -1/x+5

= 1÷ (x+5 -4x)/4x²+20x

= 1× 4x²+20x/5-3x

= (4x²+20x)/5-3x

therefore the simplification of 1/(1/4x -1/x+5) is (4x²+20x)/5-3x

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There are 9 or 10 distinct ways to arrange 6 beads of distinct colors in a 2x3 grid if reflections and rotations are considered the same. We can solve this problem using Burnside's Lemma.

Burnside's Lemma states that for a group action on a set, the number of fixed points is given by the average over the group of the number of fixed points under a particular group element, where the average is taken over all group elements.

In this case, the group action is the action of rotating and reflecting the grid, and the set is the set of all possible bead arrangements in the grid. To use Burnside's Lemma, we need to find the number of fixed points (i.e., bead arrangements that are unchanged) under each group element, and then take the average over all group elements.

There are a total of $4$ rotations and $2$ reflections possible for a 2x3 grid.

The identity transformation keeps the grid in its original position, and thus there are

6!/(2!3!) = 60

The $90 rotation keeps $3 beads in the same place and switches the other $3, and similarly $180 and $270 rotation also keeps $3 beads in the same place and switches the other $3$, thus there are

3! = 6

The reflection on the horizontal axis keeps $3 beads in the same place and switches the other $3, and similarly the reflection on the vertical axis also keeps $3 beads in the same place and switches the other $3, thus there are

3! = 6

So the average number of fixed points is $(6+6+6+60)/8 = [tex]\frac{78}{8}[/tex] = 9.75$

So, there are 9 or 10 distinct ways to arrange 6 beads of distinct colors in a 2x3 grid if reflections and rotations are considered the same.

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The binary logarithm, sometimes referred to as log base 2, is the inverse function of the power of two functions.

According to the generic logarithm, can be represented in exponential form as for every real number n.

n = [tex]a^x[/tex]

The logarithm form is expressed as Log base 2 is the power to which the number 2 must be raised to acquire the value of n.

[tex]log_a n[/tex] = x

In this case, "a" is a positive real integer that is used as a base and "x" is an exponent. The formulas for log base 2 functions are given for any real value x as

x = [tex]log_{2}n[/tex]

Which is equal to

[tex]2^x[/tex] = n

The real number system does not specify the logarithm of base 0 or logarithms of negative values.

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The family would use: 6000 gallons of water per month on showering.

In each day, the family would use;

    4 showers/day * 10 minutes/shower

         = 40 minutes of shower time per day.

In a month with 30 days, the family would use

             40 minutes/day * 30 days

                  = 1200 minutes of shower time per month.

If each shower head delivers 5 gallons/minute, then the family would use 1200 minutes * 5 gallons/minute = 6000 gallons of water per month on showering.

The amount of water used by this family just on showering is more than half of the total amount of water used by the average family in a month.

Additionally, using standard flow shower heads can help to reduce water usage. Many cities have adopted regulations that require new shower heads to have a maximum flow rate of 2.5 gallons per minute or less. By using low-flow shower heads, this family could potentially reduce their water usage by half.

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