Given f(x) = 3x^3 + kx – 5, and x – 1 is a factor of f(x), then what is the value
of k?

The width of the parking lot is 78 m

We have been given the perimeter of a rectangular parking lot which is equal to 350 m.

We know the perimeter of a rectangular plot is 2 X (width of the plot ) + 2 X (length of the parking lot ).

And the length of the parking lot is given as 97 m.

2 X (width of the plot ) +2 X (length of the parking lot ) =350 m

2 X (width of plot ) + 2 X 97 =350

2 X (width of the plot ) =156 m

width of the plot = 78 m

Hence the width of the plot is 78 meters.

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The width of this rectangular parking lot is equal to 78 meters.

In Mathematics and Geometry, the perimeter of a rectangle can be calculated by using this mathematical equation (formula);

P = 2(L + W)

Where:

By substituting the given side lengths into the formula for the perimeter of a rectangle, we have the following:

P = 2(L + W)

350 = 2(97 + W)

175 = 97 + W

Width, W = 175 - 97

Width, W = 78 meters.

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Answer:

The constant is 7.7 . This is because the quantities are directly proportional so constant of proportionality is a/b or 46.2/6

Answer:

Step-by-step explanation:

Given the expression for the situation

\(10.50 = 0.50 a + 3\)

The variable "a" represents the time in minutes for late pick ups.

The expression is similar to the equation of a straight line

\(y=mx+c\)    

when compared to the given expression

we can state that

y= 10.5 which is the outcome of the situation

m= gradient which is 0.5

a= independent variable which is the time in minutes

c= 3 which is the constant term

Answer:

a or number of minutes of pickups

Step-by-step explanation:

khan

To evaluate the triple integral 5(\(x^3\)yx\(y^2\)) dv in cylindrical coordinates, we first need to express the equation of the paraboloid z = \(x^2\) + \(y^2\) in cylindrical coordinates.

Using the conversion formulae, we have:

x = r cos(theta)

y = r sin(theta)

z = z

Substituting these values in the equation of the paraboloid, we get:

z = \(r^2\)

The limits of integration for r, theta, and z are:

0 ≤ r ≤ √z

0 ≤ theta ≤ π/2

0 ≤ z ≤ 1

Thus, the triple integral becomes:

∫∫∫ 5(\(r^5\)\(cos^3\)(theta)\(sin^3x^{2}\)(theta)) r dz dr d(theta)

Simplifying this expression and evaluating the integral, we get:

5/32

Therefore, the value of the given triple integral in cylindrical coordinates is 5/32.

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1)The expression 4x^2-16x+12/x^2-9 is undefined when the denominator, x^2-9, equals zero because division by zero is undefined.

x^2-9 equals zero when x equals 3 or x equals -3. Therefore, the expression is undefined at x = 3 and x = -3. In all other cases, the expression is defined.

2) The given expression is:

(5-2x)/(x+2) + x^2/(x^2-4) - 5

To simplify this expression, we need to first find the LCD (least common denominator) of the two fractions. The denominator of the first fraction is x+2, and the denominator of the second fraction is x^2-4, which can be factored as (x+2)(x-2). So the LCD is (x+2)(x-2). Now we can rewrite the expression with this common denominator:

[(5-2x)(x-2) + x^2(x+2) - 5(x+2)(x-2)] / [(x+2)(x-2)]

Expanding the brackets and simplifying, we get:

(-x^3 - 3x^2 - 3x + 5) / [(x+2)(x-2)]

This expression is undefined when the denominator, (x+2)(x-2), equals zero because division by zero is undefined.

(x+2)(x-2) equals zero when x equals -2 or x equals 2. Therefore, the expression is undefined at x = -2 and x = 2. In all other cases, the expression is defined.

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−3/7×14/15×7/12×(−30/35)

=(−3/7×14/15)×(7/12×−30/35)

On further calculation, we get

=−2/5×−1/2

We get,

=1/5.

Property 1:

If a/b is a rational number and m is a non-zero integer then a/b =(a*m)/(b*m). In other words, we can say that the rational number remains unaltered if we multiply both the numerator and denominator with the same integer. Ex: 2/3 = 2*2/3*2 = 4/6, 2*3/3*3 = 6/9, 2*4/3*4 = 8/12.

Math Properties

Commutative Property.

Associative Property.

Distributive Property.

Identity Property.

Inverse Property.

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\(2x + 5 = 19 \\ 2 \times 7 + 5 = 19 \\ 14 + 5 = 19 \\ 19 = 19 \)

So, The first equation has the solution x = 7

In the theater, that have 1,464 seats.

1426 seats are in "regular" sections

38 seats are  "premium" front-row section

The seat arrangement is solved by division. In this case the 62 equal spaced is the divisor while the number of seats is the in each row is the quotient

The division is as follows

1464 / 62

= 23 19/31

The number of seats in the regular section is 23 * 62 = 1426

The remainder will be arranged in premium front row

using equivalent fractions

19 / 31 = 38 / 62

the remainder is 38 and this is the seat for the premium front row section

OR 1464 - 1426 = 38 seats

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Answer:

1/8" = 1'-0" Invert the fraction and multiply by 12

Step-by-step explanation:

i hope this help

Answer:

B

Step-by-step explanation:

Hope it’s correct

Answer:

0.6 cm

Step-by-step explanation:

she divided the the height of the tree 500, so the same factor has to be applied to everything else

3m * 1/500 = 0.6cm

The correct line of code that completes this operator which transforms a Point by dx and dy is shown below: Point operator+(int dx, int dy) { return Point(x_+dx,y_+dy);}Note that the function operator+ takes two arguments: an integer dx and an integer dy.

The function returns a point, which is created by adding dx to x and dy to y.The completed code is shown below:class Point { int x_{0}, y_{0};public: Point(int x, int y): x_{x}, y_{y} {} int x() const { return x_; } int y() const { return y_; }};Point operator+(int dx, int dy) { return Point(x_+dx,y_+dy);}Therefore, the correct answer is: `Point(x_+dx,y_+dy)`

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In this scenario, Marcos is planning to travel from Phoenix to Flagstaff, and we are using variables to represent different aspects of his journey.

The variable t represents the number of hours since Marcos left Phoenix, which serves as a measure of time elapsed since the start of the journey. It allows us to track the progress of Marcos over time and analyze various time-related aspects such as the duration of the journey or the rate at which he is traveling. On the other hand, the variable d represents the number of miles Marcos has traveled from Phoenix. It serves as a measure of distance covered, indicating how far Marcos has progressed on his route. By monitoring the value of d, we can determine the distance remaining to reach Flagstaff or calculate other distance-related parameters such as average speed or total distance traveled.

By using these variables, we can establish a relationship between time and distance traveled by Marcos. This relationship can be represented by a function or equation that describes Marcos' progress over time, such as a velocity equation or a distance-time equation. These variables and their relationship allow us to analyze and make predictions about Marcos' journey. We can determine when he is expected to reach certain milestones, calculate his average speed or rate of travel, and estimate the time required to complete the journey. Additionally, these variables provide a framework for solving various problems or making decisions related to Marcos' travel, such as optimizing his route or estimating fuel consumption based on distance traveled.

In summary, by using the variables t and d to represent time and distance traveled, respectively, we can effectively describe and analyze Marcos' journey from Phoenix to Flagstaff, enabling us to make informed decisions and predictions about his travel experience.

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Answer:

both plumbers charge $120 for 3 hours of work

Step-by-step explanation:

1) x=3 and x stands for hours.

2) 120=y and y stands for money charged

so the points (3, 120) show that the plumbers both charge 120 for 3 hrs.

Answer:

c

Step-by-step explanation:

The red line represents the critical value, and the shaded region on the right-hand side of the red line represents the rejection region. If the calculated test statistic is greater than the critical value of z, which is 1.88 in this case, we will reject the null hypothesis.

The critical value(s) and rejection region(s) for the type of z-test with a level of significance a = 0.03 and a right-tailed test are as follows :Step 1: Determine the critical value of  zThe critical value is calculated by using the normal distribution table and the level of significance. A right-tailed test will have a critical value of zα. For a level of significance of 0.03, we will look for the z-value that corresponds to 0.03 in the normal distribution table.Critical value for a = 0.03 is z = 1.88 (approx).Step 2: Determine the Rejection Region The rejection region for a right-tailed test is defined as any z-value that is greater than the critical value. That is, if the test statistic is greater than 1.88, we reject the null hypothesis at the 0.03 level of significance, and if it is less than or equal to 1.88, we fail to reject the null hypothesis.Therefore, the rejection region for a right-tailed test with a level of significance of 0.03 is as follows:Rejection Region: Z > 1.88  OR  Z ≤ -1.88Graph: The graph for the given values will be as follows:The red line represents the critical value, and the shaded region on the right-hand side of the red line represents the rejection region. If the calculated test statistic is greater than the critical value of z, which is 1.88 in this case, we will reject the null hypothesis.

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Answer:

No solution

Step-by-step explanation:

Any equations with the same slope are parallel, or will never intersect.

In a slope-intercept equation, this would mean the 'm' values are the same.

y = mx + b

Two equations:

y = 5x - 4

y = 5x - 5

Since the two equations given have the same slope, they will never intercept and therefore have no solution.

Answer:3x10^0 or 3x10 to the power of 0

Step-by-step explanation:

I did the same exact one with my teacher i hope this helps you

Using the definition of expected value, it is found that Ayo can be expected to make a profit of £55.8.

The expected value is given by the sum of each outcome multiplied by it's respective probability.

In this problem:

Hence, his expected profit for a single game is:

\(E(X) = -6\frac{1}{72} - 3\frac{17}{72} + 1.4\frac{54}{72} = \frac{-6 - 3(17) + 54(1.4)}{72} = 0.2583\)

For 216 games, the expected value is:

\(E = 216(0.2583) = 55.8\)

Ayo can be expected to make a profit of £55.8.

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Answer:

You would want to do the square root of 361 which is 19

Hope This Helps!

ps. no, I'm not stalking u I just clicked on the next question from your last one.

Answer:

The side length is 19.

Step-by-step explanation:

You need to find the number that makes 361 when squared, and that would be 19

Answer:

375

Step-by-step explanation:

Since they started at the same point and went in opposite directions, add the 2 distances.

162.5 + 212.5 = 375

Answer:

C!!!

Step-by-step explanation:

<3

a. The graph of the budget line would have hamburgers on the x-axis and bags of figs on the y-axis. b. the budget line equation represents Rachel's affordability based on her income and the prices of hamburgers and figs. Changes in prices, income, or additional resources can affect the slope, position, or rotation of the budget line on a graph.

a) Rachel's budget line equation can be written as follows:

Budget = (Price of Hamburger * Quantity of Hamburgers) + (Price of Figs * Quantity of Figs)

Since the price per hamburger is $3 and the price per bag of figs is $2, the equation becomes:

Budget = 3x + 2y

Where x represents the quantity of hamburgers and y represents the quantity of bags of figs. The graph of the budget line would have hamburgers on the x-axis and bags of figs on the y-axis.

b) If the price of figs increases to $3, the new budget line equation becomes:

Budget = 3x + 3y

The graph of the new budget line would show a steeper slope compared to the original budget line. This indicates that the relative price of figs has increased, making them relatively more expensive compared to hamburgers.

c) In this scenario, Rachel has an income of $50, the price per hamburger is $3, the price per bag of figs is $3, and she receives an additional $10 in cash from a friend. The new budget line equation can be written as:

Budget = (3x + 3y) + 10

The graph of the new budget line would shift upward parallel to the original budget line. The additional cash from Rachel's friend increases her purchasing power, allowing her to afford more hamburgers and/or bags of figs.

d) Now, Rachel's friend gives her a gift basket containing 3 free bags of figs. In this case, the budget line equation remains the same as in part c:

Budget = (3x + 3y) + 10

However, since Rachel receives 3 free bags of figs, she can allocate more of her budget towards purchasing hamburgers. This would cause the budget line to rotate outward from the y-intercept, resulting in a flatter slope. The new budget line would reflect Rachel's ability to purchase more hamburgers with the same income and price of figs.

In summary, the budget line equation represents Rachel's affordability based on her income and the prices of hamburgers and figs. Changes in prices, income, or additional resources can affect the slope, position, or rotation of the budget line on a graph.

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Given that the signal gets larger than 210 microvolts, there is a 2.335 % chance that it is also larger than 240 microvolts.

As, per the given question.

Gaussian random variable n (200, 256)

Part a: Probability that signal will exceed 240 micro volts.

P(x > 240) = 1 - P(x ≤ 240)

P(x > 240) = 1 - P(240 - 200)/16

P(x > 240) = 1 - P(2.5)

See p value for z = 2.5

P(x > 240) = 0.00621

Thus, Probability that signal will exceed 240 micro volts is 0.00621.

Part b:  larger than 210 micro volts.

P(x ≥ 240) | x ≥ 210) = P(x ≥ 240) / P(x ≥ 210)

P(x ≥ 240) | x ≥ 210) = 1 - P(240 - 200)/16 /  1 - P(210 - 200)/16

P(x ≥ 240) | x ≥ 210) = 0.00621 / 0.26599

P(x ≥ 240) | x ≥ 210) = 0.02335

Thus, for the signal gets larger than 210 microvolts, there is a 0.02335 percent chance that it is also larger than 240 microvolts.

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Answer:

x>5/2

Step-by-step explanation:

4x>10

x>10/4

x>5/2

Answer:

\(a_n=4n-11\)

Step-by-step explanation:

The common difference is \(d=4\) with the first term being \(a_1=-7\), so we can generate an explicit formula for this arithmetic sequence:

\(a_n=a_1+(n-1)d\\a_n=-7+(n-1)(4)\\a_n=-7+4n-4\\a_n=4n-11\)

Therefore, it will take the car 1.5 seconds to come to a complete stop.

To determine the time it will take for the car to come to a complete stop, you can use the formula:

vf = vi + at, where

vf = final velocity,

vi = initial velocity,

a = acceleration

t = time

To use this formula, first, you need to determine the initial velocity and the final velocity.

Since the car is coming to a complete stop, the final velocity will be 0.

Therefore:

vf = 0The initial velocity is given as 30 feet per second.

vi = 30 feet per second

You also know that the car is decelerating at a rate of 20 feet per second per second.

Therefore:

a = -20 feet per second per second

Note that acceleration is negative because it is a deceleration.

Substituting the known values into the formula, you have:0 = 30 - 20tt = 30/20t = 1.5 seconds

Therefore, it will take the car 1.5 seconds to come to a complete stop.

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Answer:

Step-by-step explanation:

Given Equation:

x^3- 4x^2 + 2x+ 10 = x^2 - 5x-3

which simplifies to

x^3- 5x^2 + 7x+ 13 = 0

Given one of the roots is x = 3x+2i, the conjugate is therefore x = 3-2i.

The product is real, (x-3+2i)(x-3-2i) = x^2-6x+13

The other root can therefore be obtained by long division

(x^3- 5x^2 + 7x+ 13)/(x^2-6x+13) = x+1, or x=-1

Therefore the three roots are:

{x=3-2i, x=3+2i, x=-1 }

Answer:

Step-by-step explanation:

The given points (6,4), (12,6), and (16,-6) do not form the vertices of a right triangle.

To determine if the given points form a right triangle, we can calculate the distances between the points and check if the squares of the distances satisfy the Pythagorean theorem. Let's calculate the distances between the points:

Distance between (6,4) and (12,6):

d₁ = √((12-6)² + (6-4)²) = √(36 + 4) = √40 ≈ 6.32

Distance between (12,6) and (16,-6):

d₂ = √((16-12)² + (-6-6)²) = √(16 + 144) = √160 ≈ 12.65

Distance between (16,-6) and (6,4):

d₃ = √((6-16)² + (4-(-6))²) = √((-10)² + (4+6)²) = √(100 + 100) = √200 ≈ 14.14

According to the Pythagorean theorem, if the points form a right triangle, then one of the distances squared should be equal to the sum of the squares of the other two distances. However, in this case, d₁² + d₂² ≠ d₃², d₁² + d₃² ≠ d₂², and d₂² + d₃² ≠ d₁². Therefore, the given points (6,4), (12,6), and (16,-6) do not form the vertices of a right triangle.

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