which equation is equivalent to the given equation ? x ^ 2 - 10x = 14

The sequence a_n = -2 - 51n is an arithmetic sequence

The 11th term of the sequence is -563

The nth term of the sequence is given as:

a_n = -2 - 51n

Substitute 11 for n to calculate the 11th term of the sequence

a11 = -2 - 51 * 11

Evaluate the product

a11 = -2 - 561

Evaluate the difference

a11 = -563

Hence, the 11th term of the sequence is -563

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The equation of the graphed function is given as follows:

f(x) = x³ + 2x² - 5x - 6.

The equation of the function is obtained considering the Factor Theorem, as a product of the linear factors of the function.

From the graph, the zeros of the function are:

Hence the function is:

f(x) = a(x + 3)(x + 1)(x - 2).

In which a is the leading coefficient.

Expanding the product, we have that:

f(x) = a(x² + 4x + 3)(x - 2)

f(x) = a(x³ + 2x² - 5x - 6).

When x = 0, y = -6, hence the leading coefficient a is obtained as follows:

-6a = -6

a = 1.

Hence the function is:

f(x) = x³ + 2x² - 5x - 6.

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P(x, y) lies in the third quadrant.

To determine the quadrant in which the terminal point P(x, y) lies, we need to find the values of x and y based on the given information.

Starting at the point (1, 0) on a unit circle, we can use the angle measure to determine the coordinates of the terminal point P. Since we are moving a distance t = 5.5 along the circle, we can calculate the angle by dividing the distance traveled by the radius of the circle.

The circumference of a unit circle is 2π, and in this case, we are traveling a distance of 5.5, which is 5.5/2π times the circumference. Dividing 5.5 by 2π, we get approximately 0.8778.

To find the corresponding angle, we can multiply this value by 360 degrees (the number of degrees in a full circle) or 2π radians (the number of radians in a full circle). Let's calculate the angle in radians:

angle = 0.8778 * 2π ≈ 5.504 radians

Now, we can find the coordinates (x, y) using trigonometric functions. The x-coordinate is given by cos(angle), and the y-coordinate is given by sin(angle).

x = cos(5.504) ≈ -0.793

y = sin(5.504) ≈ -0.609

Since both x and y are negative, the terminal point P(x, y) lies in the third quadrant (Quadrant III).

In mathematics, specifically in the Cartesian coordinate system, the term "quadrants" refers to the four regions or sections into which the coordinate plane is divided.

These quadrants are numbered using Roman numerals from I to IV, starting from the positive x-axis and moving counterclockwise.

Each quadrant represents a different combination of positive and negative x and y coordinates. The quadrants are defined as follows:

- Quadrant I: This quadrant is located in the upper right-hand side of the coordinate plane. It contains points where both the x and y coordinates are positive.

- Quadrant II: This quadrant is located in the upper left-hand side of the coordinate plane. It contains points where the x coordinate is negative, but the y coordinate is positive.

- Quadrant III: This quadrant is located in the lower left-hand side of the coordinate plane. It contains points where both the x and y coordinates are negative.

- Quadrant IV: This quadrant is located in the lower right-hand side of the coordinate plane. It contains points where the x coordinate is positive, but the y coordinate is negative.

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Answer:

Height = 7

Step-by-step explanation:

35*2

70

70/10

7

Answer:

-5x=-50

x=-10

Step-by-step explanation:

The unit rate represented in the equation y = 3/5x is the value multiplying x, that is, the unit rate is 3/5.

In order to find the unit rate of each table, we just need to divide the y-values by the x-values.

So, the unit rate of the first table is:

The value 4/3 is greater than the value 3/5.

In the second table we have that:

The value 4/5 is greater than the value 3/5;

In the third table, we have that:

In order to compare this fraction with 3/5, we need to make them be in the same denominator, so we have to calculate the least common multiple of the denominators.

Since 5 and 31 are prime numbers, the LCM is the product of both numbers.

So we have that:

The number 90/155 is lesser than 93/155, therefore 18/31 is lesser than 3/5, so the answer is the third table.

Answer:

The first one

\( log_{11} \: (x)\)

Step-by-step explanation:

f(x) = 11^x

Here are the steps to find the inverse of a function:

1. Let f(x)=y

2. Make x the subject of formula.

3. Replace y by x.

\(11 {}^{x} = y \\ \: log(11 {}^{x} ) = log(y) \\ x log(11) = log(y) \\ x = \frac{ log(y) }{ log(11) } = log_{11}(y) \\ f {}^{ - 1} (x) = log_{11}(x) \)

Answer:

He will bike 312 miles in 8 days.

Step-by-step explanation:

You divide total miles (117) by total time (3) which is 39, multiple that by 8 and you get your answer of 312.

Answer:

2x4=8+3=11

Step-by-step explanation:

first multiply 2 times 4 equals 8 and add 3 which equals 11.

Answer:

B = 60°

Since the measure of all sides of the given triangle are equal, it is an equilateral triangle.

An equilateral triangle have all sides and angles equal.

Therefore, each angle measures 60°.

Using the z-distribution, it is found that:

A. In both cases for the right-tailed test, the test statistic is greater than the critical values, hence the null hypothesis is rejected in both cases, that is, it can be concluded that the proportion is greater than 0.4.

B. For a 5% significance level, the test statistic is greater than the critical value, hence it can be concluded that the proportion is different of 0.4. For a 1% significance level, the test statistic is less than the critical value, hence it cannot be concluded that the proportion is different of 0.4.

Item a:

\(H_0: p = 0.4\)

\(H_1: p > 0.4\)

Using a z-distribution calculator, for a right-tailed test, as we are testing if the mean is greater than a value, we have that:

In both cases for the right-tailed test, the test statistic is greater than the critical values, hence the null hypothesis is rejected in both cases, that is, it can be concluded that the proportion is greater than 0.4.

Item b:

\(H_0: p = 0.4\)

\(H_1: p \neq 0.4\)

Using a z-distribution calculator, for a two-tailed test, as we are testing if the mean is different than a value, we have that:

For a 5% significance level, the test statistic is greater than the critical value, hence it can be concluded that the proportion is different of 0.4. For a 1% significance level, the test statistic is less than the critical value, hence it cannot be concluded that the proportion is different of 0.4.

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F(13) means x equals 13.

Replace x in the equation with 13 and solve:

-13 + 3 = -10

F(13) = -10

Answer:

-10

Step-by-step explanation:

if the x in f(x) is 13, then the x in the equation is 13 and there is a negative sign in front so it is negative 13 plus 3 which is negative 10

Suppose that triangles ABC and DFE are similar. Therefore, the ratio between their corresponding sides is constant. Let x and y be

Then,

Triangle DFE is impossible, the lengths of its sides are impossible to construct in such a manner that the result is a right triangle whose hypotenuse is 3. DFE is an impossible triangle, the hypotenuse of a right triangle is always its largest side.

However, we can algebraically find x and y, although it would not make any sense geometrically speaking.

Solving for x,

Similarly, solving for y,

Juan would have to make $20 in sales to earn the same amount as Rita in a two-hour shift.

Let's calculate the earnings for both Rita and Juan in a two-hour shift.

Rita's earnings:

Rita earns $7 per hour, so in a two-hour shift, she would earn:

Rita's earnings = $7/hour * 2 hours = $14

Juan's earnings:

Juan earns $6 per hour plus a 10% commission on sales. Let's assume his sales in dollars are S.

Juan's earnings = (hourly wage * hours worked) + (commission rate * sales)

Juan's earnings = ($6/hour * 2 hours) + (0.10 * S)

To earn the same amount as Rita, Juan's earnings should be equal to $14.

($6/hour * 2 hours) + (0.10 * S) = $14

Simplifying the equation:

$12 + 0.10S = $14

Subtracting $12 from both sides:

0.10S = $14 - $12

0.10S = $2

Dividing both sides by 0.10:

S = $2 / 0.10

S = $20

Therefore, Juan would have to make $20 in sales to earn the same amount as Rita in a two-hour shift.

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Answer:

No

Step-by-step explanation:

x=(b-5)/c≠(5-b)/c

supposedly

b=6

c=1

x=6-5/1=1

x=5-6/1= -1

1≠ -1

Answer:

No

Step-by-step explanation:

x = b - 5 / L equal to - (5 - b) / L

Answer:

Step-by-step explanation:

A

Answer:

The answer is Not Statistical.

Answer:

non-statistical

Step-by-step explanation:

because you are asking about one gorilla, if there were more, than that would be non statistical

The shaded part is of the figure will be

The shaded part is gotten using the instruction given in the problem. The expression are:

Point A and point B are approximately 7 cm apart

Counting from A

Less than 4 cm from A will be from 0 to almost 4

And closer to B than to A will be more than 3.5 units

3.5 units is halt the distance, hence the shaded part will be 3.5 < x < 4

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The standard form of the equation of a line perpendicular to the line (3x + 6y = 5) and passing through the point (1, 3) is (2x - y = -1)

To determine the equation of a line perpendicular to the line (3x + 6y = 5) and passing through the point (1, 3), we can follow these steps:

1. Obtain the slope of the provided line.

To do this, we rearrange the equation (3x + 6y = 5) into slope-intercept form (y = mx + b):

6y = -3x + 5

y =\(-\frac{1}{2}x + \frac{5}{6}\)

The slope of the line is the coefficient of x, which is \(\(-\frac{1}{2}\)\).

2. Determine the slope of the line perpendicular to the provided line.

The slope of a line perpendicular to another line is the negative reciprocal of the slope of the provided line.

So, the slope of the perpendicular line is \(\(\frac{2}{1}\)\) or simply 2.

3. Use the slope and the provided point to obtain the equation of the perpendicular line.

We can use the point-slope form of a line to determine the equation:

y - y1 = m(x - x1)

where x1, y1 is the provided point and m is the slope.

Substituting the provided point (1, 3) and the slope 2 into the equation, we have:

y - 3 = 2(x - 1)

4. Convert the equation to standard form.

To convert the equation to standard form, we expand the expression:

y - 3 = 2x - 2

2x - y = -1

Rearranging the equation in the form (Ax + By = C), where A, B, and C are constants, we obtain the standard form:

2x - y = -1

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90-22.5=67.5

He has $67.5

The given table represents a discrete probability distribution.

To determine whether the table represents a discrete probability distribution, we need to check if it satisfies two conditions: the sum of probabilities equals 1 and all probabilities are non-negative.

In the given table, the sum of probabilities is 0.3 + 0.3 + 0.1 + 0.3 = 1, which satisfies the first condition.

Additionally, all probabilities in the table are non-negative, as each value of p(x) is greater than or equal to 0. This satisfies the second condition.

Therefore, since the table satisfies both conditions, it represents a discrete probability distribution. It provides the probabilities for each value of x, indicating the likelihood of each outcome occurring in a discrete random variable scenario.

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The following are the expressions for the perimeter and area for the rhombus:

9). perimeter = 4(x + 2) in

area = (x + 10)(x + 9)/2 in²

10). perimeter = 4(x - 3) mm

area = (x - 8)(x + 6)/2 mm²

A rhombus is a two-dimensional geometric shape with four equal sides and four equal angles, but the angles are not necessarily 90 degrees. It is a type of parallelogram.

Two same triangles make up the rhombus so we evaluate for the area expression of one triangle and multiply the result by 2 to get the areas. And multiply each side by 4 to get the expression for the perimeters

area of a triangle = 1/2 × base × height

9). base = (x + 10) and height = (x + 9)/2

area of one triangle = 1/2 × (x + 10) × (x + 9)/2

area of one triangle = (x + 10)(x + 9)/4

area of rhombus = 2 × (x + 10)(x + 9)/4

area of rhombus = (x + 10)(x + 9)/2 in²

perimeter of rhombus = 4(x + 2) in

10). base = (x - 8) and height = (x + 6)/2

area of one triangle = 1/2 × (x - 8) × (x + 6)/2

area of one triangle = (x - 8)(x + 6)/4

area of rhombus = 2 × (x - 8)(x + 6)/4

area of rhombus = (x - 8)(x + 6)/2 mm²

perimeter of rhombus = 4(x - 3) mm

Therefore, the rhombus have the expression for the perimeter and area as:

9). perimeter = 4(x + 2) in

area = (x + 10)(x + 9)/2 in²

10). perimeter = 4(x - 3) mm

area = (x - 8)(x + 6)/2 mm²

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This equation holds true for any value of x, which means that f(x) = ∑(n=0)(∞) xn/n! is indeed a solution of the differential equation f′(x) = f(x).

To show that the function f(x) = ∑(n=0)(∞) xn/n! is a solution of the differential equation f′(x) = f(x), we need to demonstrate that f′(x) = f(x) holds true for this function.

Let's first compute the derivative of f(x) using the power series representation:

f(x) = ∑(n=0)(∞) xn/n!

f'(x) = ∑(n=1)(∞) nxn-1/n!

Now we can substitute f(x) and f'(x) into the differential equation:

f′(x) = f(x)

∑(n=1)(∞) nxn-1/n! = ∑(n=0)(∞) xn/n!

We can rewrite the left-hand side of this equation by shifting the index of summation by 1:

∑(n=1)(∞) nxn-1/n! = ∑(n=0)(∞) (n+1)xn/n!

We can also factor out an x from each term in the series:

∑(n=0)(∞) (n+1)xn/n! = x∑(n=0)(∞) xn/n!

Now we can see that the right-hand side of this equation is just f(x) multiplied by x, so we can substitute f(x) = ∑(n=0)(∞) xn/n! to get:

x ∑(n=0)(∞) xn/n! = ∑(n=0)(∞) xn/n!

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To show that the function f(x) = ∑(n=0 to infinity) xn/n! is a solution to the differential equation f′(x) = f(x), we need to show that f′(x) = f(x).

First, we find the derivative of f(x):

f′(x) = d/dx [ ∑(n=0 to infinity) xn/n! ]

= ∑(n=1 to infinity) xn-1/n! · d/dx (x)

= ∑(n=1 to infinity) xn-1/n!

Now, we need to show that f′(x) = f(x):

f′(x) = f(x)

∑(n=1 to infinity) xn-1/n! = ∑(n=0 to infinity) xn/n!

To do this, we can write out the first few terms of each series:

f′(x) = ∑(n=1 to infinity) xn-1/n! = x^0/0! + x^1/1! + x^2/2! + x^3/3! + ...

f(x) = ∑(n=0 to infinity) xn/n! = x^0/0! + x^1/1! + x^2/2! + x^3/3! + ...

Notice that the only difference between the two series is the first term. In the f′(x) series, the first term is x^0/0! = 1, while in the f(x) series, the first term is also x^0/0! = 1. Therefore, the two series are identical, and we have shown that f′(x) = f(x).

Therefore, f(x) = ∑(n=0 to infinity) xn/n! is indeed a solution to the differential equation f′(x) = f(x).

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Answer:

second option

Step-by-step explanation:

The x- intercepts are the values on the x- axis where the graph crosses.

These are

x = - 3, x = - 1 and x = 3

Answer:

Step-by-step explanation:

9*9*3.14=254.34

Area=pi*radius suqare

Solving a system of equations we will see that they sold 184 adult tickets.

We know that the theater sells two types of tickets:

adult tickets for $8 and child tickets for $4.

The variables that we will use are:

x = number of adult tickets sold.

y = number of child tickets sold.

Then we can write the cost revenue equation as:

8x + 4y = 1900

And the total number of tickets sold is 291, then:

x + y = 291

Then we have a system of equations:

8x + 4y = 1900

x + y = 291

We can isolate y on the second equation to get:

y = 291 - x

Replacing that on the other equation we will get:

8x + 4*(291 - x) =1900

4x + 1164 = 1900

4x = 1900 - 1164 =736

x = 736/4 = 184

They sold 184 adult tickets.

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Answer: The person above me is correct. Here is a picture if you still dont get it..

Step-by-step explanation:

The distance between David's home and the airport is 210 miles.

let the distance traveled after first 1 hour = y

distance/speed = time

after 1 hour his speed = (35 + 15) = 50 mph

total time after 1 hour and 30 mins = 1.5 hr

y/50 + 1.5 = y/35

multiply through by 350

7y + 525 = 10y

3y = 525

y = 525/3

y = 175 miles

In the first 1 hour, at 35 mph, distance covered = 35 miles

Distance from his home to airport = 175 miles + 35 miles = 210 miles

Thus, the distance between David's home and the airport is 210 miles.

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The exact expression for the electrostatic potential at a point P in the x, y plane at a distance r from the center of the quadrupole is given by V(r) = k [Q/(r2 + D2)1/2 – Q/[(r2 + 2d + D2)1/2]] + k [-2Q/D].

Let's consider that three charges are placed in a straight line along the z-axis, and the charges are +Q on z=+D, -Q on z=-D, and -2Q at z=0.

To find the electrostatic potential at a point P in the x, y plane at a distance r from the center of the quadrupole, let's proceed with the following steps:

To find the electrostatic potential at a point P in the x-axis, we need to consider that the distance from the charges that are on the axis is r, and the distance from the charges that are on the axis and are at +D and -D is d.

The distance from the charges on the axis and at 0 is x. Now we can write,

V(x) = k [Q/(x2 + D2)1/2 – Q/[(x + d)2 + D2]1/2] + k [-2Q/D].

Now, we can substitute the values in the above expression and obtain,

V(x) = k [Q/(x2 + D2)1/2 – Q/[(x + d)2 + D2]1/2] + k [-2Q/D] .

Now, we need to use symmetry to argue that we can switch from x to r, which is given by r2 = x2 + y2.

Thus, the exact expression for the electrostatic potential at a point P in the x, y plane at a distance r from the center of the quadrupole is given by V(r) = k [Q/(r2 + D2)1/2 – Q/[(r2 + 2d + D2)1/2]] + k [-2Q/D].

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