For which values of A, B, and C will Ax + By = C be a vertical line through the point (7, 4)?

A. A = 1, B = 0, C = 4

B. A = 0, B = 1, C = 4

C. A = 0, B = 1, C = 7

D. A = 1, B = 0, C = 7

(a) tangent line to the graph of f(x) = x^3 at the point (4,2).

(b) equation of the tangent line to the graph of f(x) = x^2 - x at the point (4,12).

(a) To find the equation of the tangent line to the graph of f(x) = x^3 at the point (4,2), we need to find the slope of the tangent line at that point. We can do this by taking the derivative of f(x) with respect to x and evaluating it at x = 4. The derivative of f(x) = x^3 is f'(x) = 3x^2. Evaluating f'(x) at x = 4 gives us the slope of the tangent line. Once we have the slope, we can use the point-slope form of a linear equation to write the equation of the tangent line.

(b) Similarly, to find the equation of the tangent line to the graph of f(x) = x^2 - x at the point (4,12), we differentiate f(x) to find the derivative f'(x). The derivative of f(x) = x^2 - x is f'(x) = 2x - 1. Evaluating f'(x) at x = 4 gives us the slope of the tangent line. Using the point-slope form, we can write the equation of the tangent line.

In both cases, the equations of the tangent lines will be in the form y = mx + b, where m is the slope and b is the y-intercept.

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Answer:

Step-by-step explanation:

1.  Calculate the slope for the line with points (-6,-1) and (1,7).  Rise/Run, so take the difference between the two points for both x and y:

  Change in x (the run) is 1 - (-6) = 7

   Change in y (the rise) is 7 - (-1) = 8

The slope is rise/run so 8/7.

Any line of the form y=mx+b, where m is the slope, will be parallel to this line if it has the same slope:  y = (8/7)x + whatever.  

Any line in the same format with be perpendicular if the slope is the negative inverse of the reference line.  In this case the perpendicular slope would be (-7/8).  y = (-7/8)x + whomever.

cos B = \(\frac{BC}{BD}\) \(=\frac{4}{8}\) \(=\frac{1}{2}\)   c = [a2 + b2 - 2ab cos C] is the cosine formula used to determine the side of the triangle. a, b, and c are indeed the triangle's three sides. is that response accurate.

How do you calculate sin and cos B?

Formula: Sin (a,b) Cos

Sin a cos b = (1/2)[sin(a + b) + sin(a - b)] is the formula for sin a cos b. Whenever the composite angles (a + b) and (a - b) are available, as well as the quantities of degrees a and b, following equation for sin a cos b may be used.

How does the cosine rule work?

Every triangle that you would like to connect all 3 components to a single angle can benefit from the cosine rule. Knowing the other 2 aspects and indeed the opposing angle are necessary to determine the lengths of a side. It's edge a that you're looking for.

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Answer:

Step-by-step explanation:

1) c²+d² is not factorable

2) e²/25 - f²/36 = e²/5² - f²/6² = (e/5)² - (f/6)² = (e/5 + f/6) (e/5 - f/6)

3) \(\sqrt{x-4}\) nothing can be done

Answer:

2. If we plug in X = 0 into our problem ( Y = A(B)^X ) I would get Y = A which drastically changes the initial value, the Y-intercept, and the point on the graph. The point changes to (0,a) which becomes the new Y-intercept.

3. Cindy and Javier would be ln(x) and x^(1/2) as they will grow somewhat fast at first and then die out.

While Alison would be 1/(1+e^-x) representing an s curve showing a lot of growth and later evening out.

Step-by-step explanation:

The answer to part [2] and [3] are given above.

        y = A(B)ˣ

Given is the standard form of an exponential function -

y = a (b)^x

[2] - Changing the number outside the parenthesis will determine the amplitude scaling of the graph of (A)ˣ. For -

a > 1   (Magnitude will increase)

a < 1   (Magnitude will decrease)

a = 0  (Magnitude will become zero)

[3] - For Alison, we can write the expression as -

y{A} = 5000(1000)ˣ

For Cindy and Javier, we can write -

y{C} = (2)ˣ

y{J} = (3)ˣ

where -

[x] represents the number of posts.

Therefore, the answer to part [2] and [3] are given above.

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Answer:

the spent on food would be $23

And for clothes it would be = $23 + $24 = $47

Step-by-step explanation:

Let us assume the food be x

So for clothes it would be  x + $24

And, the total spent on food and clothes is $70

So the equation is

x + x + $24 - $70

2x = $70 - $24

2x = $46

x = $23

So, the spent on food would be $23

And for clothes it would be = $23 + $24 = $47

Answer:

324

Step-by-step explanation:

18 x 18 = 324

Answer:

324

Step by step explanation:

18² = 18 × 18

= 324

Answer:

Step-by-step explanation:

The factors of 96 are the integers that divide evenly into 96. To find the factors of 96, you can divide 96 by integers starting from 1 and increasing until you reach 96.

The factors of 96 are:

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, and 96.

These are all the integers that divide evenly into 96.

Answer:

A. 53.21

Step-by-step explanation:

72-6.19-12.6=53.21

The water is left in the bird bath is 53.21 ounces.

Option (A) is correct.

It is required to find how much water is left in the bird bath.

The branch of mathematics dealing with the properties and manipulation of numbers. a science that deals with the addition, subtraction, multiplication, and division of numbers. Fractions, decimals, percentages, fractions, square root, exponents, and other arithmetic operations are used to achieve mathematical simplifications.

Given :

Aaron filled the bird bath with 72 ounces of water.

Blue jays drank 6.19 ounces.

vulture drank twelve and three fifths ounces of the water.

According to question

72 - 6.19 = 65.81

water is left in the bird bath

=65.81 - 12 3/5

=65.81-12.5

= 53.21

Therefore, the water is left in the bird bath is 53.21 ounces.

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Answer:

Step-by-step explanation:

If the second angle's measure is based on the first angle's measure, and the third angle's measure is also based on the first angle's measure, then the first angle is the main angle. We will call that x.

1st angle: x

2nd angle: x + 20%

3rd angle: x - 20%

By the Triangle Angle-Sum Theorem, all those angles will add up to 180, so:

x + (x + 20%) + (x - 20%) = 180 and

3x = 180 so

x = 60. That means that

2nd angle: 60 + (.2*60) which is

60 + 12 = 72 and

3rd angle: 60 - (.2*60) which is

60 - 12 = 48. Let's check those angles. If

∠1 = 60

∠2 = 72

∠3 = 48,

then ∠1 + ∠2 + ∠3 = 180 and

60 + 72 + 48 does in fact equal 180, so you're done!

Answer:

The slopes of these two lines are different.

The statistical values of the data given are :

Given the data : 6, 6, 7, 10, 10, 10, 11, 13, 13, 16, 16, 18, 18, 18 6,6,7,10,10,10,11,13,13,16,16,18,18,18

The statistical values in the data can be calculated thus:

Sort values in a sending order : 6,6,6,6,7,7,10,10,10,10,10,10,11,11,13,13,13,13,16,16,16,16,18,18,18,18,18,18

Minimum = 6 (least value)

Maximum= 18 (highest value)

Median = (N+1)/2 th term

Median = (11 + 13)/2 = 12

First quartile: 1/4(N+1)th term

First quartile = 10

Third quartile = 3/4(N+1)th term

Third quartile = 16

Interquartile Range: (Third Quartile - First quartile)

Interquartile range = 16-10 = 6

Therefore, the statistical values of a box and whisker plot are those calculated above .

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Regular hexagon is a closed shape polygon having six equal sides and six equal angles.

A regular hexagon is defined as a closed 2D shape made up of six equal sides and six equal angles.

Each angle of the regular hexagon measures 120 degrees.

A hexagon has six angles and the sum of all six interior angles is 720 degrees. In a regular hexagon, each interior angle measures 120 degrees.

Polygon

A polygon can be defined as a flat or plane, two-dimensional closed shape bounded with straight sides. It does not have curved sides. The sides of a polygon are also called its edges. The points where two sides meet are the vertices of a polygon.

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Answer:

- 1 and -11

Step-by-step explanation:

-1 × -11 = 11

- 1 + - 11 = -12

A graph which best shows the combination of both functions, c(t) is plotted in the image attached below.

A graph can be defined as a type of chart that's commonly used to graphically represent data on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis.

A linear function can be defined as a type of function whose equation is graphically represented by a straight line on the cartesian coordinate.

This ultimately implies that, the data on a linear graph are directly proportional and as such, as the value on the x-axis increases or decreases, the values on the y-axis also increases or decreases.

In conclusion, a graph which best shows the combination of both functions, c(t) is plotted in the image attached below.

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It is difficult to determine which graph would best represent the combination of the functions without knowing the details of those functions.

The sum of the two functions h(t) and s(t), which model the rise in pool temperature, can be written as follows:

c(t) = h(t) + s (t)

The specific functions h(t) and s(t) and their values at various times t would affect the graph of c(t).

Both the function h(t) and the function s(t) model the rise in temperature brought on by the sun and the heater, respectively.

The resulting function, c(t), provides the overall increase in temperature caused by the heater and the sun at any given time t. The specific functions h(t) and s(t) and their corresponding rates of change at various periods t, as well as other elements that might have an impact on the pool's temperature, would determine the shape of the graph of c(t).

Which graph would best depict their combination is difficult to answer without knowing the precise functions.

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The system of equations that matches the given graph is:

A. 3x - 6y = 12

9x - 18y = 36

To determine which system of equations matches a given graph, we need to analyze the slope and intercepts of the lines in the graph.

Looking at the options provided:

A. 3x - 6y = 12

9x - 18y = 36

B. 3x + 6y = 12

9x + 18y = 36

Let's analyze the equations in each option:

For option A:

The first equation, 3x - 6y = 12, can be rearranged to slope-intercept form: y = (1/2)x - 2.

The second equation, 9x - 18y = 36, can be simplified to 3x - 6y = 12, which is the same as the first equation.

In option A, both equations represent the same line, as they are equivalent. Therefore, option A does not match the given graph.

For option B:

The first equation, 3x + 6y = 12, can be rearranged to slope-intercept form: y = (-1/2)x + 2.

The second equation, 9x + 18y = 36, can be simplified to 3x + 6y = 12, which is the same as the first equation.

In option B, both equations also represent the same line, as they are equivalent. Therefore, option B does not match the given graph.

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The correct statement is: The rate of change from 2 years to 4 years on the graph is 1.5 inches per year.

The rate of change in a linear function represents how the dependent variable (in this case, height) changes with respect to the independent variable (time). To find the rate of change in this scenario, we can calculate the slope of the line that goes through the given points (2, 3) and (4, 6).

The slope of a line is determined by the change in the y-values divided by the change in the x-values. In this case, the change in y is 6 - 3 = 3 inches, and the change in x is 4 - 2 = 2 years.

Therefore, the rate of change is 3 inches / 2 years = 1.5 inches per year. This means that for every additional year of growth, the plant's height increases by an average of 1.5 inches.

Now, let's analyze the given statements:

1. The rate of change of a linear function is always the same.

  This statement is true. In a linear function, the rate of change (slope) remains constant throughout the entire graph.

2. The rate of change of a linear function always increases as the input increases.

  This statement is not necessarily true. The rate of change can be positive or negative, depending on whether the line slopes upward or downward.

3. The rate of change from 2 years to 4 years on the graph is 1.5 inches per year.

  This statement is true. We calculated the rate of change to be 1.5 inches per year.

4. The rate of change from 0 years to 6 years on the graph is 1.5 inches per year.

  This statement is not necessarily true. The rate of change may vary depending on the specific section of the graph being considered. However, we only calculated the rate of change between 2 and 4 years, so we cannot determine the rate of change over a larger time frame based on this information.

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Answer:

7 - 3x

Step-by-step explanation:

Product would cause the 3 and x to combine.

Answer:

7 - 3x

Step-by-step explanation:

the product , multiplication of 3 and x = 3 × x = 3x

now subtract this product from 7 to obtain

7 - 3x

he required solution is \(y=c_1e^{2x}+c_2e^{-2x}+c_3\sqrt2\cos(\sqrt2x)+c_4\sqrt2\sin(\sqrt2x)\)

where \(c_1,c_2,c_3\) and \(c_4\) are constants.

Let’s assume the general solution of the given differential equation is,

y=e^{mx}

By taking the derivative of this equation, we get

\(\frac{dy}{dx} = me^{mx}\\\frac{d^2y}{dx^2} = m^2e^{mx}\\\frac{d^3y}{dx^3} = m^3e^{mx}\\\frac{d^4y}{dx^4} = m^4e^{mx}\\\)

Now substitute these values in the given differential equation.

\(\frac{d^4y}{dx^4}-2\frac{d^2y}{dx^2}-8y\\=0m^4e^{mx}-2m^2e^{mx}-8e^{mx}\\=0e^{mx}(m^4-2m^2-8)=0\)

Therefore, \(m^4-2m^2-8=0\)

\((m^2-4)(m^2+2)=0\)

Therefore, the roots are, \(m = ±\sqrt{2} and m=±2\)

By applying the formula for the general solution of a differential equation, we get

General solution is, \(y=c_1e^{2x}+c_2e^{-2x}+c_3\sqrt2\cos(\sqrt2x)+c_4\sqrt2\sin(\sqrt2x)\)

Hence, the required solution is \(y=c_1e^{2x}+c_2e^{-2x}+c_3\sqrt2\cos(\sqrt2x)+c_4\sqrt2\sin(\sqrt2x)\)

where \(c_1,c_2,c_3\) and \(c_4\) are constants.

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Answer:

391.5 in²

Step-by-step explanation:

SA = 2(9)(10) + 9(10) + 13.5(9)

SA = 180 + 90 + 121.5

SA = 391.5

Answer:

-----------------

Find each area and then find their difference.

The difference is:

Answer:

Answer choices?

Step-by-step explanation:

Answer: is there a graph

Step-by-step explanation:

Answer : One of the following statements is not always true: uX (vtw) =uXv+uXw, (vtw) Xu =vXu+wXu.

The statement, "one of the following is not always true: points a. uX (vtw) =uXv+uXw b. (vtw) Xu =vXu+wXu c. v X u=uXv d. 0 X u = 0," is correct. The first statement, "uX (vtw) =uXv+uXw," is false because in general, the distributive law does not apply to vector multiplication. This means that the left-hand side of the equation, "uX (vtw)," cannot be rearranged to "uXv+uXw."

The second statement, "(vtw) Xu =vXu+wXu," is also false because vector multiplication is not commutative; the order of the vectors in a multiplication equation matters. Therefore, "(vtw) Xu" is not equal to "vXu+wXu." The third statement, "v X u=uXv," is true because vector multiplication is commutative. This means that the order of the vectors in a multiplication equation does not matter.

The fourth statement, "0 X u = 0," is also true. The zero vector is a special type of vector whose components all equal 0. When any vector is multiplied by the zero vector, the result is always the zero vector.

In conclusion, one of the following statements is not always true: uX (vtw) =uXv+uXw, (vtw) Xu =vXu+wXu.

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Arithmetic expressions can be used as control expressions in programming languages when a control structure, such as an if statement or a loop, expects a condition to determine the flow of execution

Arithmetic expressions can be used as control expressions in certain programming languages or contexts where a control structure expects a conditional expression to determine the flow of execution.

Typically, control expressions are used in decision-making structures such as if statements, while loops, for loops, and switch statements.

In most programming languages, the control expression must evaluate to a boolean value (true or false) in order to determine the execution path. However, some languages allow arithmetic expressions to be used in control structures, considering a value of zero as false and any non-zero value as true.

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Answer:

48

Step-by-step explanation:

The area of a triangle is base \(b\) times height \(h\) divided by \(2\). You can use the first triangle to solve for the height: \(9\cdot h/2=27\) means that \(h=6\). The larger triangle is proportional to the smaller one. In fact, it is \(1.\bar3\) times larger. This means that the height of the larger triangle is \(6\cdot1.\bar3=8\). Putting all of this together, you can then calculate the area: \(12\cdot8/2=48\).

Answer:

Step-by-step explanation:

a) sum of angle on the straight line TRW is 180.

Given <TRS = 2x+10

<SRW = x-10

<TRS+<SRW = 180

2x+10+x-10 = 180

3x = 180

x = 180/3

x = 60°

<TRV = 180°-(2x+10)

Substitute x = 60° into the expression

<TRV = 180-(2(60)+10)

<TRV = 180-(120+10)

<TRV = 180-130

<TRV = 50°

2) From the diagram attached <MHJ= <LHK (oppositely directed angle)

Given

<MHJ= x+15

<LHK = 2x-20

Substitute the given data into the formula to get x

x+15= 2x-20

x-2x = -15-20

-x = -35

x = 35°

Next is to get the measure of <MHJ

<MHJ = x+15

<MHJ = 35+15

<MHJ = 50°