as it reaches the point (1, 5), the y-coordinate is increasing at a rate of 4 cm/s. how fast is the x-coordinate of the point changing at that instant?

Answer:

B.   3,158

Step-by-step explanation:

h(x) = -49x − 125

Let x = -67

h(-67) = -49(-67) − 125

          =3283-125

          = 3158

Answer:

Answer B

Step-by-step explanation:

To find the value of h(-67) for the function h(x) = -49x - 125,

we substitute -67 for x in the function and evaluate it.

h ( - 67 ) = - 49 ( - 67 ) - 125

Now we can simplify the expression:

h ( -67 ) = 3283 - 125

h ( -67 ) = 3158

a. Using set notation, the number of students that played both football and volleyball is |F ∩ V| = 4

b. The venn diagram is attached below

b(i). The compliment of the set is 14

b(ii)  The complement of either not playing football or not playing volleyball is the intersection of the complements of F and V in set notation is (F') ∩ (V')

a) Presenting the above information in set notation:

Let F represent the set of students who played football.

Let V represent the set of students who played volleyball.

The number of elements in each set can be represented as follows:

|F| = 12 (12 students played football)

|V| = 28 (28 students played volleyball)

The number of students who played both football and volleyball is 4, which can be represented as the intersection of the two sets:

|F ∩ V| = 4

b) The venn diagram is attached below.

1) To determine the number of students who played neither football nor volleyball, we need to find the complement of the union of F and V (i.e., the complement of (F ∪ V)).

From the given information, we know that there are 50 students in total.

The number of students who played either football or volleyball (or both) can be calculated using the inclusion-exclusion principle:

|F ∪ V| = |F| + |V| - |F ∩ V|

|F ∪ V| = 12 + 28 - 4

|F ∪ V| = 36

Therefore, the number of students who played neither football nor volleyball can be calculated as:

|F ∪ V|' = 50 - |F ∪ V|

|F ∪ V|' = 50 - 36

|F ∪ V|' = 14

Hence, 14 students played neither football nor volleyball.

2) The complement of either not playing football or not playing volleyball is the intersection of the complements of F and V (i.e., (F') ∩ (V')).

In set notation, this can be written as:

(F') ∩ (V')

It represents the set of students who did not play football and did not play volleyball.

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Answer:

Slope of the line: 0

The admission fee does not change as time spend at the park increases.

Step-by-step explanation:

No change in amount of dollars, domain stays the same, slope of the line is then 0

The slope of the line will be 0.

The admission fee is $54.99, which is not change as time spend at the park increases.

What is Slope of line?

The slope of a line is a number that describe the both direction and the steepness of the line.

Given that;

The table shows the amount x (in hours) of time you spend at a theme park and the admission fee y (in dollars) to the park.

And, The points represented by the table lie on a line.

Now, The slope of the line with two points (x₁ , y₁) and (x₂, y₂) will be;

m =  (y₂ - y₁) / (x₂ - x₁)

So, The slope of the line with two points (6, 54.99) and (7, 54.99) is;

m =  (y₂ - y₁) / (x₂ - x₁)

m = (54.99 - 54.99) / 7 - 6

m = 0/1

m = 0

Thus, Slope of the line will be 0.

And, The admission fee is $54.99, which is not change as time spend at the park increases.

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Answer:

Chris = $25

Maria = $35

Justin = $75

Step-by-step explanation:

Chris's amount is x.

x + 3x + (x + 10) = 135

x = 25

Substitute 25 for x.

25 + 3(25) + (25 + 10) = 135

135 = 135

True

The correct statement regarding the transformation and the difference of functions f(x) and g(x) is given as follows:

A.

The graph of g(x) is the graph of f(x) vertically compressed by a factor of three.

The parent function for this problem is given as follows:

f(x) = 7^x.

The transformed function for this problem is given as follows:

g(x) = f(x)/3 = (1/3) x 7^x.

The only transformation is a multiplication by the constant 1/3. As the constant has an absolute value less than 1, the graph of g(x) is a vertical compression of the graph of f(x) by a factor of 3.

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There were two candidate A and B contesting for the municipal corporation election in a town. The total number of voter in the town were 80,000. If 90% of the voter had voted and 60% of vote polled were cat in favour of A, 28,800 the number of vote received by B.

A state-incorporated city, town, village, or county that has the power to manage local governmental matters, such as creating a police force. A municipal corporation is established by a state's legislature, which also determines its lifespan, privileges, and powers. likewise known as a municipality.

A local governing body, such as cities, counties, towns, townships, charter townships, villages, and boroughs, is referred to legally as a "municipal corporation." Municipally-owned companies can also be referred to as this

Regulation of building construction and land usage. Town planning is included in urban planning. preparing for social and economic progress. water supply for residential, commercial, and industrial uses.

Given that,

Total number voters = 80,000

Total number of votes polled = 90%

Thus,

= (90/100) × 80,000

= 72,000

So, total percent of votes received by B if A gets 60% of polled votes.

= 100% - 60%

= 40%

Hence, total number of votes received by B

= (40/100) × 72,000

= 28,800

Therefore, the number of votes received by B, out of total votes polled is 28,800 votes.

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Answer:

x = 6

Step-by-step explanation:

Solve for x:

-(7 x)/3 + 14 = 0

Put each term in -(7 x)/3 + 14 over the common denominator 3: -(7 x)/3 + 14 = -(7 x)/3 + 42/3:

(-(7 x)/3 + 42/3) = 0

-(7 x)/3 + 42/3 = (-7 x + 42)/3:

((-7 x + 42)/3) = 0

Multiply both sides of (-7 x + 42)/3 = 0 by 3:

(3 (-7 x + 42))/3 = 3×0

(3 (-7 x + 42))/3 = 3/3×(-7 x + 42) = -7 x + 42:

(-7 x + 42) = 3×0

0×3 = 0:

-7 x + 42 = 0

Subtract 42 from both sides:

(42 - 42) - 7 x = -42

42 - 42 = 0:

-7 x = -42

Divide both sides of -7 x = -42 by -7:

(-7 x)/(-7) = (-42)/(-7)

(-7)/(-7) = 1:

x = (-42)/(-7)

The gcd of 42 and -7 is 7, so (-42)/(-7) = (-(7×6))/(7 (-1)) = 7/7×(-6)/(-1) = (-6)/(-1):

x = (-6)/(-1)

(-6)/(-1) = (-1)/(-1)×6 = 6:

Answer:  x = 6

The quadratic equation 2a^2 = -6 + 8a has two solutions: a = 3 and a = 1.

To solve the quadratic equation 2a^2 = -6 + 8a, we need to rearrange it into standard quadratic form, which is ax^2 + bx + c = 0, where a, b, and c are coefficients.

Step 1: Move all the terms to one side of the equation to set it equal to zero:

2a^2 - 8a + 6 = 0

Step 2: The equation is now in standard quadratic form, so we can apply the quadratic formula to find the solutions for 'a':

a = (-b ± √(b^2 - 4ac))/(2a)

Comparing with our equation, we have:

a = (-(-8) ± √((-8)^2 - 4(2)(6)))/(2(2))

Simplifying further:

a = (8 ± √(64 - 48))/(4)

a = (8 ± √16)/(4)

a = (8 ± 4)/(4)

Now, we can calculate the two possible solutions:

a1 = (8 + 4)/(4) = 12/4 = 3

a2 = (8 - 4)/(4) = 4/4 = 1

Therefore, the quadratic equation 2a^2 = -6 + 8a has two solutions: a = 3 and a = 1.

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Answer:

.

Step-by-step explanation:

True. Recursion is often necessary to solve certain types of problems that exhibit a recursive structure or require repeated subproblem solving.

Recursion is a programming technique where a function calls itself in its own definition. It allows for the decomposition of complex problems into smaller, more manageable subproblems that can be solved recursively. Recursion is particularly useful when problems exhibit a recursive structure, such as tree traversal, backtracking, or divide-and-conquer algorithms.

For example, problems like computing the factorial of a number, calculating Fibonacci numbers, or traversing a binary tree can be elegantly and efficiently solved using recursion. These problems can be broken down into smaller instances of the same problem until a base case is reached, and then the solutions are combined to solve the original problem.

However, it's worth noting that not all problems require recursion for their solution. There are alternative approaches, such as iterative loops or dynamic programming, which can be used depending on the problem's characteristics and requirements.

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The real zeros of the polynomial function P(x) = x⁵ − 50x³ + 49x are -1, 0, and 1.

To find the zeros of this function, we can factor it by first factoring out an x to get P(x) = x(x⁴ − 50x² + 49). Then, we can factor the quadratic expression inside the parentheses using the difference of squares formula, which gives us P(x) = x(x² − 1)(x² − 49). Simplifying further, we have P(x) = x(x − 1)(x + 1)(x - 7)(x + 7).

Therefore, the zeros of P(x) are the values of x that make each factor equal to zero. This gives us x = -7, -1, 0, 1, and 7. Since all of these values are real, we conclude that the number of real zeros of P(x) is 5.

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Answer:

2

Step-by-step explanation:

You are trying to find (f' o f)(2).  This means that you need to put f(x) into f'(x) and solve for 2.

First, find f'(x).  To do this, take the original function and switch the x and y values.

y = 2x⁵ + 12

x = 2y⁵ + 12

x - 12 = 2y⁵

(x - 12)/(2) = y⁵

y = ⁵√(x - 12)/(2)

Now, you need to put f(x) into the inverse function through the x-value.  Simplify completely.

y = ⁵√((2x⁵ + 12) - 12)/(2)

y = ⁵√((2x⁵)/(2)

y = ⁵√x⁵

y = x

Now plug in the value given to you.

(f⁻¹ o f)(2) = 2

The answer is 2.

The length of the vertical pole is 24 feet.

The length between the pole and stake is 8 feet.

We are asked to find the length of the cable needed from the top of the pole and anchored to a stake.

Let us draw a sketch to better understand the problem.

Notice that it is a right-angled triangle, so we apply the Pythagorean theorem given by

Where c is the hypotenuse (length of the cable required)

a and b are the shorter legs (length of pole and the length between pole and stake)

a = 24 feet

b = 8 feet

Let us substitute these values into the above formula and solve for c

Therefore, the required length of the cable is 25 feet. (to the nearest foot)

Answer:

\( \huge \boxed {slope = - 3}\)

Step-by-step explanation:

\(m = \frac{rise}{run} \)

The slope is the change of y over the change of x.

\(m = \frac{12 - 3}{ - 1 - 2} \\ m = \frac{9}{ - 3} \\ m = - \frac{9}{3} \\ m = - 3\)

Therefore, the slope is -3.

Answer:

The answer should be C. 250 in^3

Answer:

C. 250 in^3

Step-by-step explanation:

An algebraic expression which models the given context would be written as s + 0.02s = 1.05s.

Price can be define as an amount of money which is primarily set by the seller of a good (product), and it must be paid by a buyer to the seller, so as to enable the acquisition of this good (product).

An algebraic expression can be defined as a mathematical equation which is used to show the relationship existing between two or more variables and numerical quantities.

Let s represent the price of a pair of shoes.

Therefore, an algebraic expression which models the given context would be written as follows:

s + 0.02s = 1.05s.

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To keep up with the inflation, Mario would have to earn $91,175.98 in 2014. To get the answer, follow these steps:Let's first find the inflation rate between 2011 and 2014.

Using the CPI formula, we get the inflation rate as follows:Inflation rate = [(CPI in 2014 - CPI in 2011)/CPI in 2011] x 100Inflation rate = [(125.2 - 119.9)/119.9] x 100Inflation rate = (5.3/119.9) x 100Inflation rate = 4.42%Since Mario needs to keep up with the inflation, he should earn an amount that is increased by 4.42%. Therefore, we need to calculate what amount Mario should have earned in 2014 to keep up with the inflation:Amount in 2014 = Amount in 2011 x (1 + Inflation rate)Amount in 2014 = $88,000 x (1 + 0.0442)Amount in 2014 = $88,000 x 1.0442Amount in 2014 = $91,175.98 (rounded to the nearest cent)Therefore, Mario would have to earn $91,175.98 in 2014 just to keep up with inflation.

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Mario earned $88,000 in 2011. If the Consumer Price Index in 2011 was 119.9 and in 2014 it was 125.2, what did Mario have to earn in 2014 just to keep up with inflation?To calculate the inflation rate from 2011 to 2014, we will use the following formula:Inflation rate = ((CPI in 2014 - CPI in 2011) / CPI in 2011)) * 100Substituting the values, we get,

Inflation rate = ((125.2 - 119.9) / 119.9) * 100 = 4.43%Therefore, to maintain the same purchasing power, Mario needs to earn 4.43% more in 2014 than he earned in 2011.Using the following formula, we will calculate how much Mario has to earn in 2014.

Earnings in 2014 = Earnings in 2011 + (Inflation rate × Earnings in 2011)Earnings in 2014 = $88,000 + (4.43% × $88,000)Earnings in 2014 = $91,846.40Therefore, Mario would have to earn $91,846.40 in 2014 just to keep up with inflation.Answer: $91,846.40

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The measures of angles m∠ABC = 36° and m∠CBD = 84°.

Geometry is a branch of mathematics that deals with shapes, sizes, angles, and dimensions of objects.

The angle m∠ABD = 120° is the result for the sum of the two angles m∠ABC and m∠CBD so;

m∠ABC + m∠CBD = m∠ABD

2x + 5x - 6 = 120°

7x - 6 = 120° {add 6 to both sides}

7x = 120° + 6°

7x = 126° {divide through by 7}

x = 126°/7

x = 18

2x = 2(18) = 36°

5x - 6 = 5(18) - 6 = 84°

Therefore, the geometry question have the measure of angles m∠ABC = 36° and m∠CBD = 84°.

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Possible Question:

Find m∠ABC and m∠CBD if m∠ABD =120°, m∠ABC = 2x, m∠CBD = (5x - 6)°, and the angle m∠ABD is the sum of m∠ABC and m∠CBD.

Given the following question:

432cm^2

There are no real values for X and Y that satisfy the given equations X + Y = 17 and XY = 164.

To find the values of X and Y in the given equations, we can use a system of equations approach.

Let's start by solving the first equation, X + Y = 17, for one variable in terms of the other. We can choose to solve for X:

X = 17 - Y

Now, substitute this expression for X in the second equation, XY = 164:

(17 - Y)Y = 164

Expanding the equation gives us:

17Y - Y^2 = 164

Rearranging the equation to a quadratic form, we have:

Y^2 - 17Y + 164 = 0

To solve this quadratic equation, we can use factoring, completing the square, or the quadratic formula. Let's use the quadratic formula:

Y = (-(-17) ± √((-17)^2 - 4(1)(164))) / (2(1))

Simplifying further:

Y = (17 ± √(289 - 656)) / 2

Y = (17 ± √(-367)) / 2

Since the expression under the square root is negative, there are no real solutions for Y. This means that there are no real values for X and Y that satisfy both equations simultaneously.

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The maximum profit if the profits per acre are $75 for corn and $40 for soybeans is $371,255.83. Therefore, the correct option is c.

To find the maximum profit from planting corn and soybeans, we can use linear programming. Let's first define the variables and write the constraints.

Let x be the number of acres of corn and y be the number of acres of soybeans.

1. Total acre constraint: x + y ≤ 6,000

2. Fertilizer/herbicide constraint: 9x + 3y ≤ 40,501

3. Labor constraint: 0.75x + y ≤ 5,250

The objective function to maximize is the profit function: P(x,y) = 75x + 40y

Now, we will use the Solver to find the maximum profit:

Step 1: Set up a spreadsheet with the constraints and the objective function.

Step 2: Go to the Data tab and click on Solver. If Solver is not available, you may need to add it in Excel Options.

Step 3: Set the objective function by selecting the cell with the profit function.

Step 4: Choose "Max" for the objective.

Step 5: Add the constraints by selecting the corresponding cells.

Step 6: Click on "Solve" and the Solver will find the optimal values for x and y.

After using Solver, we find that the optimal values are x = 4,363.89 (corn) and y = 1,636.11 (soybeans), which yields a maximum profit of $371,255.83. Therefore, the correct answer is c: $371,255.83

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To find the equilibria of autonomous differential equations, set the derivative equal to zero and solve for the variable. Equilibria are fixed points where the rate of change is zero, and can be classified as stable or unstable based on the behavior of the solution trajectories near the equilibrium point.

To find the equilibria of autonomous differential equations, follow these steps:

1. Identify the autonomous differential equation, which is an equation in the form dx/dt = f(x), where f(x) is a function of x only.
2. Set the right-hand side of the equation (f(x)) equal to zero, as equilibria occur when dx/dt = 0.
3. Solve the resulting equation for x to find the equilibrium points.

These equilibrium points represent the constant solutions where the system remains unchanged over time.

To find the equilibria of autonomous differential equations, we first set the derivative equal to zero and solve for the variable. In other words, we find the values of the variable where the rate of change is zero. These values are called equilibria or fixed points.

For example, if we have an autonomous differential equation of the form dx/dt = f(x), where f(x) is a function of x, then we set f(x) equal to zero and solve for x. The resulting values of x are the equilibria.

It is important to note that equilibria can be classified as stable or unstable based on the behavior of the solution trajectories near the equilibrium point. If nearby solutions move towards the equilibrium point as time progresses, it is a stable equilibrium. If nearby solutions move away from the equilibrium point, it is an unstable equilibrium. The classification of the equilibrium can be determined by analyzing the sign of the derivative of f(x) near the equilibrium point.

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Answer:

y = 8.7

Step-by-step explanation:

Assuming we can use decimal places, y is equal to 8.7.

In programming, += is often used as a substitute for y = y + x (example)

Therefore, y = y + 3.7, and since y = 5, y = 5 + 3.7, y = 8.7

Answer:

B-

point s

Step-by-step explanation:

I just did the quiz, this is the correct answer

Point S is the endpoint of the rays.

Option B is the correct answer.

In geometry, a ray is a straight line that starts from a specific point (called the endpoint) and extends infinitely in one direction.

A ray can be thought of as a part of a line that has one endpoint and continues indefinitely in one direction.

We have,

A ray is a line that starts from a specific point and extends infinitely in one direction.

The starting point of the ray is called the endpoint, and the other end of the ray extends indefinitely.

Therefore, a ray does not have an endpoint in the direction it extends, but only at its starting point.

From the figure,

The ray SR, SU, and ST have one common starting point.

i.e Point S.

Thus,

Point S is the endpoint of the rays.

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Answer:

√78,9,10

Step-by-step explanation:

we know \(9^{2}\) is 81

so √78 is less than √81(9) and 10 is obviously more than 9

Please mark as brainliest

Answer:

x = 13.86

y = 6.93

Step-by-step explanation:

tan 30° = y/12

0.5774 = y/12

y = 12(0.5774) = 6.93

cos 30° = 12/x

0.8660 = 12/x

x = 13.86

Linear equations are equations with two variables that when plotted form a straight line on a coordinate plane. We have the following system of linear equations given below. 3x1+4x2+5x3=66--(1)7x1+4x2+3x3=74--(2)8x1+8x2+9x3=136--(3) To solve the linear system of equations.

we use the Gaussian elimination method.We convert the given system of linear equations into an augmented matrix by placing the coefficients of the variables in the corresponding rows as shown below.

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take for granted 1. Consider as true or real, anticipate correctly, as in I took it for granted that they'd offer to pay for their share but I was wrong. [c. 1600] 2. Underestimate the value of, become used to, as in The editors felt that the publisher was taking them for granted.

Answer:

$357

Step-by-step explanation:

Answer:

5p

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