Graph 7/3≥z on a number line

A function f(x) is said to have a jump discontinuity at x = a if:

3. The left and right limits are not equal.

The function has a jump discontinuity at x = 6 because:

The different lateral limits are the reason given for the jump discontinuity, as shown in the graph presented at the end of the answer.

A function f(x) is continuous at x = a if it is defined at x = a, and the lateral limits are equal, that is:

[tex]\lim_{x \rightarrow a^-} f(x) = \lim_{x \rightarrow a^+} f(x) = f(a)[/tex]

If the lateral limits are different, the limit does not exist and the function is not continuous at x = a, being said to have a jump discontinuity.

The function has a jump discontinuity at x = 6 because:

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Answer:

y = 3[tex]x^{4[/tex]

Step-by-step explanation:

given y varies directly as [tex]x^{4}[/tex] then the equation relating them is

y = k[tex]x^{4}[/tex] ← k is the constant of variation

to find k use the condition when x = 3 , y = 243 , then

243 = k × [tex]3^{4}[/tex] = 81k ( divide both sides by 81 )

3 = k

y = 3[tex]x^{4}[/tex] ← equation of variation

In the figure the area of circle is obtained as option C: 144π cm².

What is area?

An object's area is how much space it takes up in two dimensions. It is the measurement of the quantity of unit squares that completely cover the surface of a closed figure.

The area of the square is = 144 cm².

The formula for area of square is - (side)²

The equation is -

Area = (side)²

Substitute the value into the equation -

144 = (side)²

side = √144

side = 12 cm

The side of the square is the radius of the circle.

The area of circle is given as -

Area = πr²

Substitute the value into the equation -

Area = π(12)²

Area = 144π cm²

Therefore, the area of circle is 144π cm².

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The value of the equation is A = 50 ( n ) , where n is the number of employees

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

Let the number of employees be n

So , A = product of 50 and the number of employees

A = 50 ( n )   be equation (1)

Therefore , the value of A is 50n

Hence , the equation is A = 50n

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Answer:this is a rational number

Step-by-step explanation:

The number zero can be written as 0 ÷ any non-zero integer. For example, the rational numbers 0/1 and 0/(-2) are equal to 0. This is in the form of p/q, where p and q are integers and q ≠ 0.

the following shaded-regions in the plane consists of all points whose polar coordinates satisfy the inequalities 0 ≤ r ≤ 3 and π/6 ≤ θ ≤ π/12.

It is referred to as a polar coordinate system when each point on a plane in a two-dimensional coordinate system is determined by a distance from a reference point and an angle measured from a reference direction. Pole: The object of comparison. The term "polar coordinates" refers to these new coordinates since you interpret the axes' intersection as a pole from which all other points radiate outward. change (degrees are measured in radians) (degrees are measured in radians).

Given that,

0 ≤ r ≤ 3

and π/6 ≤ θ ≤ π/12

In the given condition we can clearly see that the radius is not equal to 3 but it is less than 3. Thus graph number 1, 2, 4 and 6 do not match the given condition.

Now in the given condition 0 ≤ r ≤ 3 the angle is between 30° to 105°

In the graph number 3 radius varies from 0 ≤ r ≤ 3 but angle varies from 75° to 150°, so it is also incorrect.

Thus in the remaining graph number 5, the radius varies from 0  and angle also varies from 30° to 105°.

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The complete question is as follows:

Answer:

11.3

Step-by-step explanation:

13.3 - 2 = 11.3

Answer:

975

Step-by-step explanation:

The largest number of pages the book can have is 975 because the maximum number of times the digit 7 can appear in the page numbers is 25. The maximum number of pages is obtained when the page numbers range from 100 to 999, inclusive, which would result in the digit 7 appearing 25 times.

The average rate of change of the function in the interval [ 4 , 9 ] is given by the equation m = -67

The average amount that a function changed per unit during that time period is the rate of change of that function. It is calculated using the slope of the line connecting the interval's endpoints on the graph of the function.

Rate of change = f ( b ) - f ( a ) / ( b - a )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Let the first point be P ( 4 , -84 )

Let the second point be Q ( 9 , -419 )

Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

The rate of change of the function = slope

Slope m = ( -419 - ( -84 ) ) / ( 9 - 4 )

On simplifying the equation , we get

Slope m = ( -419 + 84 ) / 5

Slope m = -335/5

Slope m = -67

Hence , the rate of change of function is m = -67

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The intervals at which the parabolic equation from the graph is decreasing is (4, ∞).

A parabolic equation is an equation of a curve usually in form of a U-shape when displayed on the graph. In the given diagram, we can use the standard form of a quadratic equation y = ax² + bx + c as the starting point for finding the equation through the three points of the curve.

Using the following points on the curve; (0,-2) (4,6), and (6,4), because these points pass along the x and y-axis of the curve.

Create a system of equations by substituting the x and y values of each point into the standard formula of a quadratic equation to create the three-equation system.

−2 = a(0)² + b(0) + c,

6 = a(4)² + b(4) + c,

4 = a(6)² + b(6) + c

Solve the system of equations to find the values of a, b, and c.

[tex]$$a= - \dfrac{1}{2}$$, b = 4, c = -2[/tex]

Substitute the actual values of a, b, and c into the formula for a quadratic equation to find the resulting equation.

[tex]y = - \dfrac{x^2}{2} + 4x - 2[/tex]

Since we know the resulting equation of the parabola, we can now deduce the intervals at which the parabola is decreasing. As such, the interval at which the parabolic equation is decreasing is (4, ∞)

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Answer:

564 inches is equivalent to 47 yards and 0 feet.

The graph of the function h is added as an attachment

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

Suppose that the function h is defined as follows.

h(x) = -1 if -2.5 < x ≤ -1.5

           0 if -1.5 < x ≤ -0.5

            1 if -0.5 < x ≤ 0.5

            2 if 0.5 ≤ x < 1.5

            3 if 1.5 ≤ x  < 2.5

The above function is a piecewise function

Next, we graph the individual functions in the function h according to their domain

See attachment for the graph of h

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Answer:

6 pints of lemonade. here you go

The total cost for the rental is calculated by subtracting the first 50 miles from the total miles driven (430 miles) and then multiplying it by the per mile rate ($0.35/mile).

Miles is a unit of distance measurement. It is used for measuring the distance between two places. It is equivalent to 1.609 kilometers. Miles are used for measuring the length of roads, flight distances, distances between cities, and other large distances. Miles can also be used to measure the length of running, swimming, and cycling events. Miles are also used in the United States to measure the speed of vehicles, such as cars and airplanes.

This gives us a total cost of $118.50 for the miles driven. To calculate the total cost for the rental, we add the cost for the miles driven ($118.50) to the daily rate for the 2 days ($46.90 x 2 days = $93.80). This gives us a total cost of $212.30 for the rental.

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A two-column table to prove that the triangles formed by the vertical support beam are congruent, (ΔAXB ≅ Δ(CXB) is presented as follows;

[tex]{}[/tex]  Statement                             Reasons

1. [tex]\overline{BX}[/tex] ⊥ [tex]\overline{AC}[/tex]; AB = CB    [tex]{}[/tex]                        Given

2. m∠BXA = m∠BXC = 90°[tex]{}[/tex]                   Definition of ⊥ segments

3. ΔABC is an isosceles triangle [tex]{}[/tex]         Definition

4. ∠BAC ≅ ∠BCA   [tex]{}[/tex]                               Base angles of an isosceles Δ

5. ΔAXB ≅ ΔCXB [tex]{}[/tex]                                 SAA congruence postulate

An indication that two triangles are congruent is if the corresponding sides on each of the triangles are congruent.

The details of the reasons used to prove that the triangles ΔAXB and ΔCXB are congruent, are presented as follows;

[tex]\overline{BX}[/tex] ⊥ [tex]\overline{AC}[/tex]; Perpendicular segments

Two segments are perpendicular if they intersect at right angles, such that the angles formed by the intersection of the segments are 90° angles

Isosceles triangles

An isosceles triangle is a triangle that has a pair of congruent sides (sides of the same length)

Base angles of an isosceles triangle are congruent

The sides of the same length in an isosceles triangle, according to the angle side relationship theorem, the angle opposite the congruent sides of an isosceles triangle which are the base angles of the triangle are congruent.

SAA congruence postulate

The Side-Angle-Angle, SAA, congruence postulate states that if in a triangle, two angles and a non included side are congruent to two angles and a non included side of another triangle, then the two triangles are congruent

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The expected number of flips to get a string of r heads in a row, given that the probability of getting heads in each flip is p.

Probability is a scale between 0 and 1 that represents the possibility of an event happening. An event with probability 1 is guaranteed to happen, while an event with probability 0 is impossible. The number of favorable outcomes divided by the total number of potential outcomes in the sample space yields the probability of an event A, commonly denoted as P(A). The sample space, for a fair six-sided die, is the set of all potential outcomes, such as 1, 2, 3, 4, 5, and 6. The probability of rolling a 4 is 1/6. Numerous disciplines employ probability to make predictions, deduce conclusions, and make judgments in the face of uncertainty.

We can use a recursive formula to find the expected number of flips X.

Let X_i be the expected number of flips to get a string of r heads in a row, starting from the i-th flip. Then, X_i can be expressed in terms of X_{i+1}:

X_i = (1 - p) + p(1 + X_{i+1})

Here, (1 - p) represents the case where the i-th flip results in tails, and p(1 + X_{i+1}) represents the case where the i-th flip results in heads and we have to continue flipping until we get a string of r heads in a row.

To find the expected number of flips X, we need to sum over all X_i, starting from the first flip:

E[X] = X_1 = (1 - p) + p(1 + E[X])

Solving for E[X], we get:

E[X] = 1/(1 - p)

This formula gives us the expected number of flips to get a string of r heads in a row, given that the probability of getting heads in each flip is p.

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The two sets A = {x, j, a, m} and D = {x, a, b, y} are not equal.

What does the example set?

A set is a logically arranged group of items that can be represented in either set-builder form or roster form in mathematics.

                                 Sets are typically shown using curly brackets; for instance, A = 1, 2, 3, 4 is a set.

The given two sets are

            A = {x, j, a, m} and D = {x, a, b, y}

By definition,

The two sets A and B are equal sets if they contain the same elements.

Here,  j, m and b, y are different in two sets.

Thus, The set A and D does not contain the same elements.

Therefore, The two sets A = {x, j, a, m} and D = {x, a, b, y} are not equal.

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The height of the school is 13.27 m.

It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.

We have.

From the information given, we can draw the figure given below,

Now,

Triangle ABC and Triangle DCE are similar.

So,

x / 1.25 = 11.15 / 1.05

x = (11.15 x 1.25) / 1.05

x = 13.27 m

Thus,

The height of the school is 13.27 m.

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Answer:

hacunamatata

Step-by-step explanation:

it means no worrys

Answer:

6(f-2)

Step-by-step explanation:

is a factor of 6f & 12

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1.

to get factors

write 1 to 10

to see if any of the factor numbers can be divided by any of the numbers between 1 thru 10 or sometimes even up to 20

2.

write

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

so 6 & 12 can be divided by

1 2 3 4 6 12

Answer:

see below

Step-by-step explanation:

We need to solve the below two equations by graphing. We will plot the graph of the given equations and the point of intersection of line would be the solution to the equation.

[tex] 1. \begin{cases} y = -\dfrac{1}{2}x+2\\\\ y = -3x - 3 \end{cases}[/tex]

Firstly let's make a table;

[tex]\boxed{\begin{array}{c|c|c} x & 0 & 1 \\ y & 2 & 1.5 \end{array}}[/tex]

Now plot the points , (0,2) and (1,1.5) .

Similarly make another table for second equation [tex] y = -3x - 3[/tex] as ,

[tex]\boxed{\begin{array}{c|c|c} x & 0 & 1 \\ y & -3 & -6\end{array}}[/tex]

Now draw the lines joining the points. Hence from the graph the line intersects at (-2,3)

So the solution to equations are ,

_________________________________

Similarly we will solve the second set of equations as ,

[tex] 2. \begin{cases} x-4y=12\\\\ 7x-4y=12 \end{cases}[/tex]

make a table for plotting equation [tex] x-4y=-12[/tex]

[tex]\boxed{\begin{array}{c|c|c} x & 12 & 16 \\ y & 0 & 1\end{array}}[/tex]

make a table for plotting equation [tex] 7x-4y=12[/tex]

[tex]\boxed{\begin{array}{c|c|c} x & 0 & 2 \\ y & -3 & 0.5\end{array}}[/tex]

Now we see that the equations intersect at point (4,4) So the solution to the given equation is ,

________________________________

[tex] 3. \begin{cases} -8x-4y = 12 \dots (1)\\\\ x=y\dots(2)\end{cases}[/tex]

substitute value of equation 2 in 1

[tex]\longrightarrow -8x - 4x = 12 \\ [/tex]

simplify,

[tex]\longrightarrow -12x = 12[/tex]

Divide both sides by 12 ,

[tex]\longrightarrow\underline{\underline{ x = -1}} [/tex]

Substitute this value in equation 2 as ,

[tex]\longrightarrow x = y \\ [/tex]

[tex]\longrightarrow\underline{\underline{ y = -1}} [/tex]

Hence our required solution is ,

___________________________________

[tex] 4. \begin{cases} 2x + 4y = -10 \dots (1)\\\\ -7x -y = 22(2)\end{cases}[/tex]

Taking equation 2 ,

[tex]\longrightarrow y = -7x -22 [/tex]

substitute this value in equation 1,

[tex]\longrightarrow 2x + 4(-7x-22)=-10\\[/tex]

[tex]\longrightarrow 2x -28x -88 = -10\\ [/tex]

[tex]\longrightarrow -26x = 78\\[/tex]

divide both sides by 26,

[tex]\longrightarrow\underline{\underline{ x = -3}} [/tex]

Again, substitute this value in equation 2 , as ;

[tex]\longrightarrow y = -7(-3) -22\\ [/tex]

[tex]\longrightarrow y = 21 -22\\ [/tex]

[tex]\longrightarrow\underline{\underline{ y = -1}} [/tex]

hence our required solution is ,

And we are done!

Answer:frequency

Step-by-step explanation:

The consistent state lattice x is equivalent to (0.6, 0.9), and the stochastic matrix P is normal.

To decide if a stochastic grid P is standard, we should initially compute the consistent state matrix x of the Markov chain with a matrix of change probabilities P. To do this, we set up the situation Px = x and address for x.

We can communicate the components of x as far as a boundary t as follows:

x1= 0.5t + 0.1

x2= 0.5t + 0.9

We can then settle for t in view of the amount of x1 and x2. The amount of x1 and x2 ought to be equivalent to 1, so:

0.5t + 0.1 + 0.5t + 0.9 = 1

t = 1

Therefore, The consistent state lattice x is equivalent to (0.6, 0.9).

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X+1, R2 is the synthetic division of (x²+3)+(x-1) by In the divisor x + 5, change the constant's sign from 5 to -5 and bring it down.

The number is said to be in variables its simplest form being divided in it's smallest equivalent fraction. When or how to find the most basic form. Look for common factors throughout the denominator and numerators. Verify a fractional integer to verify if it qualifies as a prime number. A statement having two orthogonal axes and even an equal sign in the middle is called an equation in mathematics. The general form of any equation provides the degrees of all the  in descending order. The conventional form of a linear equation is an x + b = 0. The general form of a linear equation with two variables is an x + b y + c = 0. (or something similar). Equations can be categorized as assumptions or conditional equation.

given

(x²+3)+(x-1)

2x+3 / x = 1

X+1, R2 is the synthetic division of (x²+3)+(x-1) by In the divisor x + 5, change the constant's sign from 5 to -5 and bring it down.

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As per the intersecting point, the length of AC is 4x + 10.

The diagonals of a rectangle are two lines that intersect at the midpoint of the rectangle. In this case, the diagonals of rectangle ABCD intersect at point E.

If AE = 2x + 5 and BD = 5x + 2, then we can calculate the length of AC. We know that AC is the sum of AE and ED, so AC = AE + ED.

Since the diagonals of a rectangle intersect at the midpoint of the rectangle, AE and ED are equal. Therefore, AC = 2x + 5 + (2x + 5) = 4x + 10.

Therefore, the length of AC is 4x + 10. Knowing the lengths of the diagonals can help us find the length of the sides of the rectangle, and can also be useful in finding the area of the rectangle

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First triangle x = 30

Second triangle N = 55

The average atomic mass of the element in the data table is 39.95 amu.

The average atomic mass of the element in the data table is calculated by applying the following formula.

average atomic mass = ( 0.3365 / 100  x 35.97 amu ) + ( 0.0632 / 100  x 37.96 amu ) + ( 99.6 / 100  x 39.96 amu )

average atomic mass = ( 0.121 amu ) + ( 0.024 amu ) + ( 39.8 amu )

average atomic mass = 39.95 amu

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Answer:

Carlos deposited $140 into his savings account, which can be represented by the signed number +140.

Step-by-step explanation:

This indicates an increase in his account balance of $140.