Question 1
Solve for x.
x(x + 6) = 0
Write your answers as integers or as proper or improper fractions in simplest form.
X =
|
X =

Therefore , the solution of the given problem of tractable problem comes out to be  the halting problem is undecidable for Turing machines.

a process that completes a manageable task in a polynomial amount of time. The polynomial upper bound is used. If an issue cannot be resolved in a polynomial amount of time, it is referred to as being intractable. The bound's minimum is exponential.

Here,

Alan Turing proved in 1936 that a general algorithm running on a Turing

machine that solves the halting problem for all possible program-input

pairs necessarily cannot exist.

the halting problem is undecidable for Turing machines.

Therefore , the solution of the given problem of probability comes out to be  the halting problem is undecidable for Turing machines.

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The coefficient of Y is 10 in  2y 5.

Any integer or symbol that multiplies the variable of a single term or the terms of a polynomial to represent a constant value is known as a coefficient in mathematics. In some phrases, a letter might be substituted for the usual number. For example, x is the variable and a and b are the coefficients in the formula: ax2 + bx + c.

What is a coefficient?

A coefficient is a quantity or number that is coupled with a variable. Frequently, an integer is multiplied by the variable and written next to it. The variables that don't have a corresponding number are presumed to have a coefficient of 1.

10 is the Y coefficient in 2y 5.

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Answer: Its B

Step-by-step explanation:

By simple algebra, Jane is 57 9/20 inches taller.

If one object or person's height exceeds that of another, the taller object or person is said to exist. There is a two-object or two-person limit. Taller is a relative term. For instance: Hoppy stands at 7 feet.

You can begin this issue by first figuring out Dwight's height. At 54 3/4 inches, he would be 1 1/2 inches taller than Chloe:

54 3/4 plus 1 1/2 equals 55 + (3/4 + 1/2) equals 55 + (3/4 + 2/4) equals 55 + 5/4 equals 56 1/4 inches.

Dwight stands at 56 1/4 inches.

Dwight is 1 1/5 inches shorter than Jane, so

56 1/4 plus 1 1/5 is 57 plus (1/4 plus 1/5) is 57 plus (5/20 plus 4/20) is 57 plus 9/20 is 57 9/20 inches.

Jane stands at 57 9/20 inches.

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The volume of the cake Lani is making is 314 inches³.

Volume is defined as the amount of space a figure occupies. The formula for the volume of a cone is given by:

V = πr²h/3

where V = volume

r = radius of the base of the cone

h = height of the cone

π = 3.14

If the cone shape mold has a diameter of 10 inches, then its radius is equal to half of 10 which is 5 inches.

Plug in the values to the formula and solve for the volume.

V = πr²h/3

V = (3.14)(5 inches)²(12 inches)/3

V = 314 inches³

Hence, the volume of the cake is 314 inches³.

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The student population in the school can be modeled using an exponential function of the form:

P(t) = 2,035 * 1.03^t

where P(t) is the student population t years from now, and 1.03 is the factor by which the population increases each year.

To predict the number of students in the school after five years, we can substitute t = 5 into the function:

P(5) = 2,035 * 1.03^5

= 2,035 * 1.1895

= 2,408.76

Thus, there will be approximately 2,408.76 students in the school after five years.

(a) Since cosθ = 7/12 and sinθ < 0, we can find the other four trigonometric functions as follows:

sinθ = √(1 - cos²θ) = √(1 - (7/12)²) = √(1 - 49/144) = -√(95/144)

tanθ = sinθ / cosθ = (-√(95/144)) / (7/12) = -4√(5/18)

cotθ = 1 / tanθ = -1 / (-4√(5/18)) = 1/(4√(5/18))

secθ = 1 / cosθ = 1 / (7/12) = 12/7

cscθ = 1 / sinθ = -1 / (-√(95/144)) = √(95/144)

(b) Since tanθ = 4/3 and θ is in Quadrant III, we can find the other five trigonometric functions as follows:

cosθ = √(1 / (tan²θ + 1)) = √(1 / (16/9 + 1)) = √(9 / 25) = 3/5

sinθ = cosθ * tanθ = (3/5) * (4/3) = 4/5

cotθ = 1 / tanθ = 1 / (4/3) = 3/4

secθ = 1 / cosθ = 1 / (3/5) = 5/3

cscθ = 1 / sinθ = 1 / (4/5) = 5/4

Trigonometric functions are a set of functions that relate the angles of a right triangle to the ratios of the sides of the triangle. The six most commonly used trigonometric functions are sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (csc).

The sine function, represented by sin, gives the ratio of the side opposite the angle to the hypotenuse. The cosine function, represented by cos, gives the ratio of the adjacent side to the hypotenuse. The tangent function, represented by tan, gives the ratio of the opposite side to the adjacent side.

The cotangent function, represented by cot, gives the ratio of the adjacent side to the opposite side. The secant function, represented by sec, gives the ratio of the hypotenuse to the adjacent side, and the cosecant function, represented by csc, gives the ratio of the hypotenuse to the opposite side.

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Therefore , the solution of the given problem of linear equation comes out to be  it is not a linear equation in two variables.

A linear model is the one that satisfies the algebraic formula y=mx+b. m is the y-intercept, while B is the slope. The foregoing sentence is sometimes referred to as a "mathematical expression having two variables" both y and x are different factors. Bivariate linear equations are two-variable linear equations. There are several uses for linear equations: , all result in zero. An equation is said to be linear if its formula is y=mx+b, where m denotes the slope and b the y-intercept. Y=mx+b is the formula for an equation, where m stands for the slopes and b for the y-intercept.

Here,

Given : 2x + 3 =0

thus,

To find that it is linear equation in two variable is given  equation

As,

We can see there is only one variable that is x.

So , it is not a linear equation in two variables.

Therefore , the solution of the given problem of linear equation comes out to be  it is not a linear equation in two variables.

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Answer:

X ≥ 49.5

Step-by-step explanation:

X + 15 ≥ 64.5

Subtract 15 from both sides

X ≥ 49.5

So, the answer is X ≥ 49.5

Answer:

3/4

Step-by-step explanation:

Answer:

2/3 of a day

Step-by-step explanation:

3/4 : 1/2 = 1 : X

X=2/3

Therefore , the solution to the given problem of trigonometry comes out to be  angle of elevation : 62.3°.

The area of mathematics called trigonometry examines the correlation between triangle length l. The field first came into existence in the Classical world, presumably in the third-century BC, as a result of the integration of geometry with astronomy studies. Precise approaches mathematics deals with certain trigonometric equations and possible uses of them in calculations. There are six common trigonometric functions in trigonometry. They are known by their respective names and abbreviations sine, trigonometry, tangent, secant, etc. cosecant (csc). The studies of triangle aspects, particularly those right triangles, is known as trigonometry. However, studying geometry entails learning about all polygons' characteristics.

Here,

given  :

An aircraft is being followed by two radar stations, which are 4.3 miles apart.

Station A is 9.6 miles away from the plane in a straight line.

Thus,

To find the angle of elevation  from station A to plane :

Using Trigonometric ratios:

=> Sin A  = 8.5 / 9.6

=> Sin A = 85/96

=> A =  [tex]Sin^{-1}[/tex](85/96 )

=> A = 62.302840124651483 °

=> A = 62.3°

Therefore , the solution to the given problem of trigonometry comes out to be  angle of elevation : 62.3°.

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Answer:

1/2

Step-by-step explanation:

-3x+5x-2>-4x+1

first, you will combine like terms. -3x+5x=2x.

2x-2>-4x+1

you need to move the variable to one side. So you will add 4x on both sides.

6x-2>1

You need to add 2.

6x>3.

Now you will divide both sides by 6 to get x by itself.

x> .5 or 1/2

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The area of the figure is 51.63 m²

A composite figure is figure that is made up of two or more different shapes.

The composite figure in the given image is made up of a rectangle, semicircle and a triangle. Therefore, the area of the composite figure will be the sum of the areas of the shape it is made of. Thus:

Area of figure = area if rectangle + area of semicircle + area of triangle

Area of figure = LW + 1/2πr² + 1/2bh

Area of figure = (6 × 5) + (1/2 × 3.14 × 3²) + (1/2 × 3 × 5)

Area of figure = 30 + 14.13 + 7.5

Area of figure = 51.63 m²

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There are 24 ,5-digit palindromes with different neighboring .

A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.

No, it is always between 0 t0 1.

Such a palindromic number should be  abcba  

2a+2b+c=14

Thus  c has to be even and we need

a+b=14−c/2 and we can choose for  a any value from  1 to  (14−c)/2

Thus the number of such palindromic numbers is

7+6+5+4+3=25

starting from  c=0 up to  c=8

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Answer:

2

Step-by-step explanation:

look at where it intersects the line that goes straight up

Yes, if the value of y = 0 then it makes the horizontal line.

The term horizontal line is defined as one that goes from left to right.

And here we also know that they are parallel to the x –axis in the coordinate plane.

And the horizontal line has a slope of zero.

While we looking into the move along the right of the line, then it does not rise or fall at all.

Here we have to the that the following factors are also included in feature:

In as the horizontal line is parallel to the x-axis and it is parallel to the horizon.

Where as the horizontal line is a sleeping line and it is also defined as can be a sleeping, standing, or a slanting line.

Where the horizontal line is perpendicular to the y-axis.

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The expression (1/4)(s + 24.80) is used to determine the discount when you buy shoes with a retail price of s dollars and hats with a total retail price of $24.80. The expression calculates the discount as a quarter of the total retail price of the shoes and hats. So another expression is 0.25s + 6.20.

Another expression that can be used to determine the discount would be to calculate the discount as a percentage of the total retail price of the shoes and hats. For example, if the discount is 25%, the expression would be:

Discount = 0.25 × (s + 24.80)

This expression calculates the discount as 25% of the total retail price of the shoes and hats.

Another expression can be :

Discount = 0.25×s + 6.2

This expression calculates the discount as 25% of the shoes price and $6.2 for hats.

It is important to note that the specific expression used to determine the discount will depend on the details of the sale and how the discount is being offered. The above expressions are just examples of how the discount can be calculated using different methods.

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One side of the square has a length of 10 cm.

The triangle $ABC$ is a right triangle and it has one leg of length 6 cm and one leg of length 8 cm. Using the Pythagorean theorem, we can find the length of the hypotenuse:

c^2 = a^2 + b^2

c = √(a^2 + b^2)

c = √(6^2 + 8^2)

c = √(36 + 64)

c = √(100)

c = 10

So the hypotenuse of triangle $ABC$ has a length of 10 cm.

The square has one side on the hypotenuse of the triangle $ABC$ and a vertex on each of the two legs of the triangle $ABC$. Since the square is on the hypotenuse of the triangle, one side of the square has the same length as the hypotenuse of the triangle, which is 10 cm.

Therefore, one side of the square has a length of 10 cm.

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Answer: A ratio is a comparison of two or more values. To compare the ratios of orange juice to yogurt, we want to ensure that the proportion of orange juice to yogurt is the same in each ratio.

Option A is 40:30. To compare this ratio to the original ratio, we can convert the amounts in cups to tablespoons. 40 cups is equal to 320 tablespoons and 30 tablespoons of yogurt. The proportion of orange juice to yogurt is not the same as the original ratio since 320 is not equivalent to 3.

Option B is 19:9. To compare this ratio, we convert the amount in cups to tablespoons. 19 cups is equal to 152 tablespoons of orange juice and 9 tablespoons of yogurt. The proportion of orange juice to yogurt is not the same as the original ratio since 4 cups of orange juice is not equal to 19 cups.

Option C is 15:20. To compare this ratio, we convert the amount in cups to tablespoons. 15 cups is equal to 120 tablespoons of orange juice and 20 tablespoons of yogurt. The proportion of orange juice to yogurt is not the same as the original ratio since 4 cups of orange juice is not equal to 15 cups.

Option D is 8:6. To compare this ratio, we convert the amount in cups to tablespoons. 8 cups is equal to 64

Step-by-step explanation:

Rational and Irrational numbers can be depicted as the number that can be communicated as p/q are reasonable and which can't be communicated are called Unreasonable Numbers.

Rational Numbers are characterized as a number that can be addressed as p/q where q isn't equivalent to zero.

We can likewise, say that the part where the denominator and the numerator are whole numbers and the denominator isn't equivalent to zero is called Reasonable Numbers.

For Instance: 2/3, 3/9, addresses  Rational numbers.

Irrational Numbers are characterized as genuine numbers that can't be communicated as a proportion of whole numbers.

For Instance: [tex]\sqrt{2}[/tex], [tex]\sqrt{3}[/tex] addresses an Irrational number.

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The value of a is -1 When we put the value of x as zero all the terms which include x become zero then only constant terms are remaining.

The given question is in the form of an equation.

let's try to understand what is an equation.

There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance,

the equation 4x + 56 = 14 consists of the two equations 4x + 56 and 14, which are separated by the 'equal' sign. Mathematical algebraic equations typically have one or more variables.

There are so many types of equations present linear equations, quadratic equations, and cubic equations.

According to the degree of the equation so many different types of equations.

2x^2 + x -a + 4  = 5 put x = 0.

2*0 + 0 - a + 4  = 5

-a + 4 = 5

-a = 5 - 4

-a  = 1

a  = -1.

So the value of a is -1.

Given Question is incomplete complete question here

What should be the value of a if the value of  2x^2 + x -a + 4  equals to  5 when x =0.

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The value of x in 2(5x)=14 is 1 2/5.

A mixed fraction is one that is represented by both its quotient and remainder. A mixed fraction is, for instance, 2 1/3, where 2 is the quotient and 1 is the remainder. An amalgam of a whole number and a legal fraction is a mixed fraction.

When converting a mixed fraction to an improper fraction, the denominator and the whole number are multiplied, the product is added to the numerator, and the sum is written as the numerator and denominator.

2(5x) = 14

10x = 14

x = 14/10

Simplify the fraction, by turning it into a mixed number.

x = 1 4/10

Simplify the equation by dividing it by 2, so that it is in simplest form.

x = 1 2/5

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Answer:

152°

Step-by-step explanation:

2x + 48 = 3x - 4 (the measure of an exterior angle of a triangle = the sum of the measures of the two non-adjacent interior angles of the triangle)
=> 4 + 48 = 3x - 2x (on transposing)
=> 52 = x
Substituting the vale of x in the m∠JKM,
m∠JKM = 3x - 4 = 3(52) - 4 = 152°

Hope you understood!!

The distribution has the greatest spread is

The term standard deviation refers to a measurement of the data's dispersion or spread from the mean.

A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed or spread out.

In the given problem the distribution that has a higher value of standard deviation is the one that has the highest spread spread

This is distribution 3 with a standard deviation of 7.2

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The factored form of quadratic equation 2x² + 7x + 3 is 2(x + 1/2) (x + 3)

A quadratic equation can be expressed in:

- Standard form: y = ax² + bx + c

- factored form: y = a(x - x₁) (x - x₂)

Here, x₁ and x₂ are the roots of the given function.

Suppose we are given a quadratic equation:

y = ax² + bx + c

To find the factored form, use the following properties:

x₁ . x₂ = c/a

x₁ + x₂ = - b/a

In this case, the quadratic function is:

y = 2x² + 7x + 3

We have to find x₁ and x₂ such that:

x₁ . x₂ = 3/2

x₁ + x₂ = - 7/2

Hence,

x₁ = - 1/2

x₂ = - 3

Therefore the factored form is:

y = 2(x + 1/2) (x + 3)

Your question is incomplete, but most probably your question was:

Which expression is the factored form of 2x² + 7x + 3?

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The solution of the inequality is,

⇒ x > - 5

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

Given that;

The inequality is,

⇒ - 4x + 3 < 23

Now,

Since, The inequality is,

⇒ - 4x + 3 < 23

Solve as;

⇒ - 4x < 23 - 3

⇒ - 4x < 20

⇒ - x < 5

⇒ x > - 5

Thus, The solution is,

⇒ x > - 5

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Answer:

4.472135955

Step-by-step explanation:

If a line is drawn so that it passes through the point [tex](2,-1)[/tex] and [tex](0,5)[/tex] , then  slope of line is -3 .

What is Slope ?

The slope of a line is defined as measure of steepness and direction of  line. The slope of line in a plane help in predicting whether lines are parallel, perpendicular, or none without using a compass.

The slope of line passes through points [tex](x_{1} ,y_{1} )[/tex] and [tex](x_{2} ,y_{2} )[/tex] is calculated by formula ⇒ [tex]Slope = \frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex] ;

the points are given as  [tex](2,-1)[/tex] and [tex](0,5)[/tex]  ;

So , on substituting the values in the slope formula ,

we get ;

[tex]Slope = \frac{5 -(-1) }{0 -2 }[/tex] ;

= [tex]\frac{6}{-2}[/tex]

= -3 .

Therefore , the required slope of the line is -3 .

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In 100 students, Science was rated favorably by 25 students, while math received ratings from 41 students. 19 of the students polled indicated that they approved of both. 16 students are the complement of math.

The phrase "complement" is typically used to describe a subset of a set that does not include another subset. The entire original set is obtained by adding the complement and its taking. The complement of a set is typically represented by the notations. The complement of a set is the set that includes all the elements of the universal set that are not present in the given set.

The Total number of students were 100

Students who like maths were 41

Students who like science were 25

Students who like both maths and science were 19

Students who does not like maths are 41-25 = 16.

So the students who are the complement of math are 16.

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Perfect squares NEVER be irrational numbers.

Repeating decimals will ALWAYS be rational numbers.

Irrational numbers will NEVER be able to be written as fractions.

A square number, also known as a perfect square, is an integer that is the square of another integer, or the result of multiplying another integer by itself. For instance, 9 is a square number since it equals 3² and is represented by the symbols 3 × 3.

A number whose decimal representation eventually becomes periodic is known as a repeating decimal, also known as a recurring decimal.

All real numbers that are not rational are considered irrational numbers. In other words, it is impossible to express an irrational number as the ratio of two integers.

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Complete question

Fill in the following statements with either "sometimes ", "always ", or "never " in order to make it a true statement.

Perfect squares _______be irrational numbers

Repeating decimals will_____be rational numbers

Irrational numbers will____ be able to be written as fractions