what does it mean by give your answer in 'terms of pi' ??
please help me and thanks

The inequality that represents the greatest distance that can be driven while staying within the daily budget is:

0.18x + 40 ≤ 67

Solving for x, we get:

0.18x ≤ 27

x ≤ 150

Therefore, the greatest distance that can be driven in a day while staying within the daily budget is 150 miles.

Two other two-step inequalities with the same solutions are:

0.18x ≤ 28

x ≤ 155

The indicated function values are If x = 0, then f(0) = 2,
If f(x) = 0, then x = - 1

To evaluate f(0), locate the point on the graph where x will be equal to '0' then find out the y-coordinate of that point where the value of f(0) will be equal to f(0).

Similarly, to find the x at f(x) = 0, take the y-coordinate as 0 and find the corresponding x - coordinate.  

Here we have

A graph that shows the function f(x)  

Given  x = 0  then f(0) will be equal to the y - coordinate at x = 1  

=> If x = 0 then f(0) = 2        

Given f(x) = 0 then x will be equal to the x - coordinate at y = 0

=> If f(x) = 0 then x = - 1    

Therefore,

The indicated function values are If x = 0, then f(0) = 2,
If f(x) = 0, then x = - 1

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Answer:

1. 2.25

2. -1

Step-by-step explanation:

right on edge

Answer:

[tex]2x^{2}[/tex] + [tex]2x[/tex] + [tex]2[/tex]

Step-by-step explanation:

1. In the expression: C - 3D, we plug in the values of C and D

2. So we get the expression: [tex](2x^{2} + 5x -1) - 3(x - 1)[/tex]

3. Then we simplify this even more: [tex](2x^{2} + 5x -1) - (3x + 1)[/tex] by multiplying 3 to the numbers in the parentheses

4. Now we can remove the parentheses: [tex]2x^{2} + 5x - 1 - 3x + 3[/tex]

5. Now we can put the like terms next to each other: [tex]2x^{2} + 5x - 3x + 3 - 1[/tex]

6. FINALLY we simplify: [tex]2x^{2} + 2x + 2[/tex]

Hope this helps! <3

The length of 164 centimeter after conversion to feet is equivalent to 5.38 feet .

The Units such as centimeter , meter , feet , inches , feet , are used to measure the distance between the two points .

We have to convert the length of 164 cm to feet ;

For conversion , we multiply the given length in centimeter by the conversion factor ;

The conversion factor to convert the length is 0.0328 ;

So , on multiplication ,

We get ;

⇒ 164 centimeter = 164 × 0.0328 feet ;

⇒ 164 centimeter = 5.3792 feet ≈ 5.38 feet .

Therefore , 164 centimeter is approximately equal to 5.38 feet .

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c=25.1327

Step-by-step explanation:

c=2pir

r=1/2 d

r=4

2pi*4= 25.1327

The options that are not polynomials are:

A, B, C, and E.

A general polynomial on a variable x can be written as:

P(x) = aₙ*xⁿ + ... + a₁*x + a₀

The coefficients a are all real numbers, and all the exponents on the variable x must be integer numbers.

So:

We can't have square roots of the variable.

We can't have negative exponents on the variable.

With that in mind, the options that aren't polynomials are:

A: because there is an exponent of 2/3

B: There is an exponent of -3

C: there is an exponent of -2

E: There is an exponent of -2

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The shape Miss Hodgman is describing a parallelogram.

A parallelogram is a two-dimensional flat shape with four sides. It has two pairs of opposite sides that are parallel and congruent, meaning they have the same length. Each pair of opposite sides is also parallel and has equal distance between them. The four interior angles of a parallelogram are all right angles or 90-degree angles.

The opposite angles of a parallelogram are also congruent, which means they have the same measure. The adjacent angles of a parallelogram are supplementary, which means they add up to 180 degrees. Therefore, each angle of a parallelogram measures 180 degrees divided by two, or 90 degrees.

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The system of equation is 100x + 72y = 1760 and 97x + 72y = 1718. The special price is $14 for hardcover books and $5 for paperback books.

Equations are declarations of equality between two mathematical expressions containing one or more variables. A linear equation is one in which the maximum power of the variable is one. Any arithmetic equation can be solved using linear equations, which can also be used to find the precise value or root of the variable that answers the question.

Let us suppose the price of hardback covers = x.

Let us suppose the price of paperback covers = y.

Given that, Mr. Howard purchased 100 new hardcover books and 72 new paperback books, which cost a total of $1,760.

100x + 72y = 1760........(1)

He also purchased 97 new hardcover books and 72 new paperback books for the adult fiction section, spending a total of $1,718.

97x + 72y = 1718.........(2)

The system of equation to describe the situation is:

100x + 72y = 1760.

97x + 72y = 1718

To find the solution subtract the two equations:

100x + 72y = 1760.

- (97x + 72y = 1718)

Thus,

3x = 42

x = 14

Substitute the value of x in equation 1:

100(14) + 72y = 1760

1400 + 72y = 1760

72y = 360

y = 5

Hence, the special price is $14 for hardcover books and $5 for paperback books.

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For the given rectangle, the angles are:

1 = 72°

2 = 36°

3 = 18°

4 = 144°

What is a rectangle?

The internal angles of a rectangle, which has four sides, are all exactly 90 degrees. At each corner or vertex, the two sides come together at a straight angle. The rectangle differs from a square because its two opposite sides are of equal length. A quadrilateral with parallel sides that are equal to one another and four equal vertices is known as a rectangle. It is also known as an equiangular quadrilateral for this reason.

Rectangles can also be referred to as parallelograms because their opposite sides are equal and parallel.

The given figure is a rectangle.

The angle 3 = 18°

This is because they are alternate angles.

In triangle ADC,

 ∠DAC = 180 - ( 18 + 90) = 72°

The angles  ∠DAC and  ∠BCE are alternate angles.

∠BCE and 1 are congruent angles.

1 = 72°

2 = 180 - ( 72+72) = 36°

From triangle BDC,

∠CDE = 180 - (72+90) = 18

So 4 = 180 - ( 3+∠CDE ) = 180 - (18+18) = 144°

Therefore for the given rectangle, the angles are:

1 = 72°

2 = 36°

3 = 18°

4 = 144°

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The Taylor series for sin(x) is an infinite series expansion that represents the trigonometric function sin(x) as a sum of infinite terms involving the powers of x.

The Taylor series for sin(x) can be written as:

where n! represents the factorial of n.

The series converges for all values of x, which means that it can be used to calculate the value of sin(x) to any desired degree of accuracy. The series is based on the idea that any continuous function can be represented as an infinite sum of terms involving the function's derivatives at a particular point, in this case, x=0.

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No es posible determinar si lo que dice Luis es correcto sin conocer el porcentaje de descuento aplicado en la compra de la casaca.

Si el precio original de la casaca es de $80 y después de aplicar un descuento el precio final es de $55, entonces se puede determinar el porcentaje de descuento utilizando la fórmula:

descuento = (precio original - precio final) / precio original

descuento = (80 - 55) / 80 = 0.3125 = 31.25%

Si el porcentaje de descuento es del 31.25%, entonces Luis tiene razón en su afirmación de que está comprando la casaca con un descuento. Sin embargo, si el porcentaje de descuento es diferente, entonces su afirmación podría ser incorrecta.

Por lo tanto, es importante conocer el porcentaje de descuento para determinar si lo que dice Luis es correcto o no.

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Answer:

Option 2

 x     y

−3     0

−1      3

 0     4

 3     0

4 3

Step-by-step explanation:

For a relation x →  y to be a function, there can be one and only one value of y for a value of x

Looking at the tables we see that option 1 is out since all x values are 2 andthere are multiple values of y

The last option is out because for x = 0 there are two values of y=-2 and y = 2

Correct choice is the second option which has a unique y value for each value of x

Answer:

option 2 im doing it rn

Step-by-step explanation:

So, the product of two irrational numbers may be rational or irrational, depending on the specific irrational numbers being multiplied.

A real number is said to be irrational if it cannot be expressed as the quotient of two integers, p/q, where p and q are both integers. The square root of two, for example, cannot be stated as an integer or a fraction.

No, that statement is not always correct.

In general, the product of two irrational numbers is not necessarily irrational. For example, consider the square roots of 2 and 8:

sqrt(2) * sqrt(8) = sqrt(2) * 2 * sqrt(2) = 2 * 2 = 4,

which is a rational number.

However, there are some cases where the product of two irrational numbers is irrational. For example, the product of the square root of 2 and the square root of 3 is irrational:

sqrt(2) * sqrt(3) = sqrt(6),

which is irrational.

So, the product of two irrational numbers may be rational or irrational, depending on the specific irrational numbers being multiplied.

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Answer:  x= 155 degrees

Step-by-step explanation:

All angles in a triangle add up to 180. That is how we find angle a

a + b = 120 degrees as 60 degrees is taken for a straight angle or 180 degrees.

Use Algebra to find angle b

To find c we do the same thing as for a.

x is everything remaining from 180 degrees after c is taken from it.

x =  155 degrees

Answer:

6,16

Step-by-step explanation:

The probability of A given B is 0, and P(A | B) is not equal to P(A). Events A and B are mutually exclusive, meaning that they cannot both occur at the same time, and thus they are not independent. Mutually exclusive events are not necessarily independent and independent events may or may not be mutually exclusive.

P(A) = 0.30 and P(B) = 0.40, so P(A and B) = 0 because the events A and B are mutually exclusive. This means that the probability of A given B is 0, and P(A | B) = 0. P(A | B) is not equal to P(A).Events A and B are mutually exclusive, meaning that they cannot both occur at the same time, and thus they are not independent.The statement that mutually exclusive events and independent events are the same is not accurate. Mutually exclusive events are not necessarily independent and vice versa.Given the results of this problem, we can conclude that mutually exclusive events are not independent, and independent events may or may not be mutually exclusive. The two concepts are not necessarily related as mutually exclusive events do not necessarily need to be independent and independent events do not necessarily need to be mutually exclusive.

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The value of the coefficient of the product is equal to - 30. (Correct choice: A)

The expanded form of a quadratic equation includes three real coefficients, whose definition is shown below:

(a · x + b)² = a · x² + 2 · a · b · x  + b · x²

The coefficient of the product is the element 2 · a · b of the expanded form. If we know that a = 5 and b = - 3, then the coefficient of thre product is:

2 · a · b = 2 · 5 · (- 3)

2 · a · b = - 30

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The missing side length is 22.6.

From the given figure, We can observe that it is a right-angled triangle.

We are provided with two angles in the triangles,

So, We can evaluate the third angle by the sum of the angles property of

a triangle.

∠ABC + ∠BAC + ∠ACB = 180°

90° + 37° + ∠ACB = 180°

∠ACB = 180° - 127°

∠ACB = 53°

By the property of the triangle,

tanα = Perpendicular/Base of the triangle

tanα = AB/BC

tan53° = x/17

x = tan53°×17

x = 22.6

Therefore, The missing side length is 22.6.

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The missing side length of right angled triangle is 22.6.

Given,

Right angled triangle

Here

Two angles in the triangles : 37 and 90 degrees .

So, We can evaluate the third angle by the sum of the angles property of a triangle.

∠ABC + ∠BAC + ∠ACB = 180°

90° + 37° + ∠ACB = 180°

∠ACB = 180° - 127°

∠ACB = 53°

By the property of the triangle,

tanα = Perpendicular/Base of the triangle

tanα = AB/BC

tan53° = x/17

x = tan53°×17

x = 22.6

Therefore, The missing side length is 22.6.

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If x is a rational number, then x = ab and x³ = a³b³, so both x and x³ are rational numbers. Considering the objection to this statement, we conclude that if x is irrational, then x³ is also irrational number.

This question is in the form p → q. Based on the Definition of a rational number is a ∈ Z, b ∈ Z ≥0, and  (a ≠ b) then a/b

Irrational Number:

All irrational numbers are real numbers that are not rational numbers. That is, an irrational number cannot be expressed as a ratio of two integers. A line segment is also said to be incommensurable if the ratio of the lengths of the two segments is irrational. That means there is no common "scale". That is, it can be used to express the length of two given segments as an integer multiple of itself.

Proof by inverse:

Inverse (q → p)

¬q≡ x is rational, and ¬p≡ x³ is rational.

∀x ∈ R:(x2∉Q)⇒(x∉Q) .

Using the method of proof by contradiction, let's try to prove that

∃x ∈ R: (x2∉Q) ∧(x∈ Q).

If  x is irrational, then we can represent it the next way:

x= pq, p∈ Z, q ∈N.

Let's raise  x to the 2nd power:

x³= (pq)³ = p³q³.

But  p³ is an integer and q³ is natural:

m = p³∈Z, n= q³∈N.

So we can say that

x³ =mn, m∈ Z, q∈ N,

which means that  x³ is irrational by definition

If x is a rational number, then x = ab and x³ = a³b³, so both x and x³ are rational numbers.

Considering the objection to this statement, we conclude that if x is irrational, then x³ is also irrational.

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Answer:

(D.) [tex]5x^{5} -5x^{3} +4[/tex]

Step-by-step explanation:

Adding Polynomials:

To add both of these two polynomials together, all we need to do is add like terms. All of the other options are wrong, since we do not add the exponents.

[tex]5x^{5} -5x^{3} +4[/tex]

Answer:

360 degrees

Step-by-step explanation:

I remember learning this in Math class. The rhombus angle sum will make 360 degrees.

The number of solutions in the equation is One solution

From the question, we have the following parameters that can be used in our computation:

The graph

On the graph, we have two lines that intersect at a point

This means that the number of solutions is one

Here, the skills needed are:

The strategy to solve the problem is to use the graph method to solve the system of linear equations and check if the resulting solution satisfies all the equations in the system.

If it does, then the system has one unique solution.

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If the recipe calls for 1 5/6 cups of flour, and Finn triples the recipe, he will need 3 times the amount of flour.

To find the total amount of flour Finn will need, we can first convert the mixed number 1 5/6 to an improper fraction:

Next, we can multiply this fraction by 3 to find the total amount of flour needed:

We can simplify this fraction by dividing both the numerator and the denominator by 3:

Therefore, Finn will need 11/2 cups of flour in total.

~ Zeph

The required number of pallets used to build one step of the mansion is 1/8 of a pallet of pavers.

In mathematics, the operation and interpretation of a function to make it simple or easier to grasp is known as simplifying, and the process is known as simplification.

Given:

Total number of pallets used = 3/4,

Number of steps = 6

pallet used to build one step = [3/4] / 6 = 3 / 24

                                               = 1 / 8

As a result, 1/8 of a paver pallet is what is needed to construct one step of the palace.

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Work Shown:

a = change in distance = 492-300 = 192 miles

b = change in time = 12 weeks

c = a/b = rate of change of distance over time = speed of growth

c = (192 miles)/(12 weeks)

c = (192/12) miles per week

c = 16 miles per week

In other words, each time a week goes by, Ryan has walked another 16 miles.

For a related math concept, check out the slope formula. The slope represents the rate of change. It's useful for graphing linear equations.

The coordinates of the figure are  A''(-3, 1),B''(2,2), C''(-2, -1).

What is the transformation of a point?

The transformation, or f: X →X, is the name given to a function, f, that maps to itself. After the transformation, the pre-image X becomes the image X. Any operation, or a combination of operations, such as translation, rotation, reflection, and dilation, can be used in this transformation. A function can be moved in one direction or another using translation, rotation, reflection, and dilation. A function can also be scaled using rotation around a point. Two-dimensional mathematical figures move about a coordinate plane according to transformations.

Given that the coordinates of the points A, B, C are A(-6,-3), B(-1,-4), C(-5,-1).

The rule of a reflection across the x-axis is (x,y)→(x,-y).

After reflection across the x-axis,

A(-6,-3)→ A'(-6,3)

B(-1,-4)→B'(-1,4)

C(-5,-1)→C'(-5,1)

A rule of translation of 3 units right and 2 units down is (x,y)→(x+3,y-2).

Thus the new coordinates are:

A'(-6,3)→ A''(-6+3,3-2)=A''(-3,1)

B'(-1,4)→ B''(-1+3,4-2)=B''(2,2)

C'(-5,1)→ C''(-5+3,1-2)=C''(-2,-1)

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The rate of change of a circle's diameter with respect to its radius is a constant value of 2.

The diameter (d) of a circle is twice the radius (r), so we can write:

d = 2r

To find the rate of change of diameter with respect to radius, we can take the derivative of both sides of this equation with respect to r using the chain rule:

d/dx [d] = d/dx [2r]

d' = 2r'

Here, d' is the derivative of diameter with respect to radius, and r' is the derivative of radius with respect to some independent variable (e.g. time).

Since r' is simply equal to 1 (because the derivative of a variable with respect to itself is always 1), we have:

d' = 2

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The surface area of the triangular prism is, 178 cm²

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

The triangular prism is shown in figure.

Now, We know that;

The surface area of the triangular prism is,

⇒ S.A = 2B + ph

Where, B stands for the area of the base, p represents the perimeter of the base, and h stands for the height of the prism.

Here, We have;

Height = 3 cm

Area of Base is,

⇒ B = 11 × 4

       = 44 cm²

Perimeter of base is,

⇒ p = 2 (11 + 4)

      = 2 × 15

      = 30

Hence, The surface area of the triangular prism is,

⇒ S.A = 2B + ph

          = 2 × 44 + 30 × 3

          = 88 + 90

          = 178 cm²

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s(x) represents the value of s(x) depending on the value of x since s is a function of x.

The first thing you should be aware of in this situation is that the following is contained in the provided expression:

S: stands for a function whose value we are interested in.

In order to understand the function s, we must use the term (numerical value) represented by x.

S is therefore dependent on X.

So, we have:

As s is a function of x, its value depends on the value of x.

As s is a function of x, the value of s (x) depends on the value of x.

Consider the provided notation.

Since s is a function of x. The s(x) value depends on the x value.

For any function f(x); The independent variable is x.

i.e. it depends on the variable x.

Similarly, here s(x) is the dependent variable. which is defined for the corresponding variable x.

Hence, s(x) represents the value of s(x) depending on the value of x, since s is a function of x.

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With the provided scale, the driveway's true length is 7/6 feet, and 1 and 1/6 feet.

The height of any unit can be converted to inches using the free online tool known as an inch calculator. Both inches and centimetres are units used to measure length; inches are abbreviated as "in" and centimeters as "cm".

To determine the real length of the driveway, we can use the provided scale.

The scale indicates that 5 inches just on illustration corresponds to 6 feet in everyday life.

Now, let's change 35 inches just on picture to feet:

35 inches / 5 inches for every 6 feet equals 7/6 feet.

The driveway is therefore 7/6 feet in length in actuality. We can condense.

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