pls help 100 pnts!!!!!!!!!!!!!!!!!!

Which graph represents the function of f(x) = the quantity of 4 x squared minus 4 x minus 8, all over 2 x plus 2?

The shape of y=x^2, but upside-down and vertically stretched by a factor of 9, is given by the equation y=-9x^2.

To describe the transformation of the function y=x^2 into the shape y=x^2, but upside-down and vertically stretched by a factor of 9, we can break it down into two components:

Upside-down reflection:

To flip the graph upside-down, we multiply the function by -1. So, the equation becomes y=-x^2.

Vertical stretching:

To vertically stretch the graph by a factor of 9, we multiply the function by 9. So, the equation becomes y=9(-x^2), which can be simplified to y=-9x^2.

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The shape of y=x^(2), but upside -down and vertically stretched by a factor of 9 .

9514 1404 393

Answer:

  D  y +5 = -2/7(x -4)

Step-by-step explanation:

The point-slope form is ...

  y -k = m(x -h) . . . . . . line with slope m through point (h, k)

You're given (h, k) = (4, -5), so the equation will be of the form ...

  y +5 = m(x -4) . . . . for some slope m

This form eliminates the first two choices.

__

The slope of the given line is the coefficient of x when solved for y:

  2y = 7x +14

  y = 7/2x +7  . . . .  slope is 7/2

The perpendicular line will have a slope that is the opposite reciprocal of this, ...

  -2/7 . . . . slope of perpendicular line

This is the slope shown in choice D:

  y +5 = -2/7(x -4)

D

Step-by-step explanation:

Answer:

1 solution

Step-by-step explanation:

The equation will be a horizontal parabola that has an x-intercept of (-5,0) therefore 1 solution

Answer:

vertex: (-5,0)

axis of symmetry: x=-5

some points: (-7,4)(-6,1)(-5,0)(-4,1)(-3,4)

Since the training set consists of 40 observations, you would need to fill in the counts for each category based on the actual classifications made by the model using the 0.5 cutoff value.

To construct the confusion matrix for a 40-observation training set, we need to use a cutoff value of 0.5 to classify each profile observation as either interested or not interested. The confusion matrix is a tool that shows the performance of a classification model.

Let's denote the four possible outcomes as follows:
- True Positive (TP): The model correctly classified an observation as interested.
- True Negative (TN): The model correctly classified an observation as not interested.
- False Positive (FP): The model incorrectly classified an observation as interested when it was actually not interested.
- False Negative (FN): The model incorrectly classified an observation as not interested when it was actually interested.

Since we have a cutoff value of 0.5, any observation with a prediction score above or equal to 0.5 will be classified as interested, while any observation with a prediction score below 0.5 will be classified as not interested.

Based on this information, we can construct the confusion matrix:

                   Predicted Interested   Predicted Not Interested
Actually Interested       TP                           FN
Actually Not Interested    FP                           TN

Note that the values TP, TN, FP, and FN are counts of observations falling into each category.

In your case, since the training set consists of 40 observations, you would need to fill in the counts for each category based on the actual classifications made by the model using the 0.5 cutoff value.

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Answer:

Step-by-step explanation:

To design a roller coaster and compute its thrill, we need to follow the given definitions and limitations. Here's a step-by-step approach:

Design the Roller Coaster Function:

We need to design a differentiable function that represents the shape of the roller coaster. Let's denote this function as r(x), where x is the horizontal distance.

The function should satisfy the given limitations: r(0) = 0 (start on the ground), r(x) ≤ 75 (maximum height), and r(x) ≥ -25 (above the underground).

The function should be differentiable over the interval [0, 200] to ensure a smooth ride.

Identify Drops:

Drops occur where the function is strictly decreasing. We can find these drops by analyzing the intervals where r'(x) < 0 (negative slope).

Each drop will be an interval with a start and end point.

Compute Angle of Descent:

To calculate the angle of descent at a point on the drop, we need to find the tangent line to the function at that point.

The angle of descent is the angle between the horizontal line and the tangent line.

We can use the derivative of the function, r'(x), to find the slope of the tangent line.

The angle can be calculated using trigonometry: angle = arctan(r'(x)).

Calculate Thrill of Each Drop:

The thrill of a drop is the product of the angle of steepest descent during the drop and the total vertical distance of the drop.

The vertical distance of a drop is the difference between the function values at the start and end points of the drop.

Calculate the angle of steepest descent for each drop and multiply it by the vertical distance to obtain the thrill of that drop.

Compute Total Thrill of the Roller Coaster:

The total thrill of the roller coaster is the sum of the thrills of all the drops.

Add up the individual thrill values calculated for each drop to get the overall thrill of the roller coaster.

Please note that the actual implementation of these steps requires specific mathematical calculations and programming. If you need assistance with any particular step or have further questions, feel free to ask.

Answer:

If the prism length is L, trapezoid base width B, trapezoid top width A, and trapezoid height H, then the volume of the prism is given by the four-variable formula: V(L, B, A, H) = LH(A + B)/2. In other words, multiply together the length, height, and average of A and B.

Step-by-step explanation:

Answer:

-177.8 feet below sea level.

Step-by-step explanation:

First, we know that descend means to lower. Anything lower than 0 has to be negative. It says that she descends for 91 seconds at a speed of 2.2 feet per second. So first to find out how many feet she descended in those 91 seconds, you need to multiply 91*-2.2= -200.2. Then, it says that she ascends for 32 seconds at the speed of 0.7 feet per second. It's the same thing, but ascend means to go up. So, we multiply 32*0.7=22.4. Now we add the two numbers together to get -177.8.

Answer:

220.4 feet below sea level

Step-by-step explanation:

use the following formula:

rate x time = distance

(rate going down)(time going down) = distance going down.

so if she starts at 0 feet above sea level, and descends for 91 seconds at a speed of 2.2 ft/sec. you would plug that in as:

(2.2 ft/sec)(91 seconds) = distance of 198 feet.

she then ascends for 32 seconds at a speed of 0.7 feet/second.

so, substitute that;

(0.7 ft/sec)(32sec) = distance of 22.4 feet.

distance traveled downward + distance traveled upward = total distance of location.

198 + 22.4 feet = 220.4 feet

The solutions to the given equation on the interval 0≤x<2π. −8sin(5x)=−4√ 3 The solutions to the equation -8sin(5x) = -4√3 on the interval 0 ≤ x < 2π are:

x = π/3 and x = 2π/3.

To find the solutions to the equation -8sin(5x) = -4√3 on the interval 0 ≤ x < 2π, we can start by isolating the sine term.

Dividing both sides of the equation by -8, we have:

sin(5x) = √3/2

Now, we can find the angles whose sine is √3/2. These angles correspond to the angles in the unit circle where the y-coordinate is √3/2.

Using the special angles of the unit circle, we find that the solutions are:

x = π/3 + 2πn

x = 2π/3 + 2πn

where n is an integer.

Since we are given the interval 0 ≤ x < 2π, we need to check which of these solutions fall within that interval.

For n = 0:

x = π/3

For n = 1:

x = 2π/3

Both solutions, π/3 and 2π/3, fall within the interval 0 ≤ x < 2π.

Therefore, the solutions to the equation -8sin(5x) = -4√3 on the interval 0 ≤ x < 2π are:

x = π/3 and x = 2π/3.

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We can express this as:

x + 2x = £3.45

We can solve for x with no additional work.

x + 2x = £3.45
3x = £3.45
3x/3 = £3.45/3
x = £1.15

Im guessing you're British by the use of the £ symbol, and I don't understand what "dearer" means as in America we don't use that term. I'll just give you both values.

x = £1.15 (this is the first book)
2x = £2.30 (this is the second book, which costs twice as much as the first.)

Answer: B. 2 2/5

Step-by-step explanation: Hope this help :D

2 1/6 ft

Step-by-step explanation:

This problem bothers on subtraction of fraction

Given data

Total length of rope 3 1/2 feet

Let's convert mixed fraction to proper fraction = 7/2ft

First piece of rope = 1 1/3ft

= 4/3ft

Hence the second piece of the rope is = 7/2-4/3= 21-8/6= 13/6

Second piece = 2 1/6 ft

Answer:

Step-by-step explanation:

Let the 2 point questions = x

Let the 4 point questions = y

This first equation gives the total number of questions.

x + y = 40                 Multiply this question by 2

2x + 2y = 80

The second equation gives the point distribution. The value  of multiple choice answers = 2x. The value of the short answer questions = 4y.

Now write the first equation under this question.

2x + 4y = 100

2x + 2y = 80             Subtract.

2y = 20                     Divide by 2

2y/2 = 20/2            

y = 10

x + y = 40

x + 10 = 40

Subtract 10 from both sides

x = 30

Answer

Answer:

Step-by-step explanation:

IT is 0.5 and 10

answer:

0.5 and 10 are the answers

Answer:

Option D: (0,-5)

Step-by-step explanation:

Comparing the given points to the graph.

So, the point that will lie at the shaded area represent  solution to the linear inequality.

So, point (0,-5) is a solution to the linear inequality.

The answer is option D. (0,-5)

Note: the line y = 6x-4 is graphed using the table on the graph.

The simplified expression is 7x- 2.

A mathematical operation such as subtraction, addition, multiplication, or division is used to combine terms into an expression. In a mathematical expression, the following terms are used:

Given:

−4x−2y+6 from 3x−2y+4.

So, subtraction will be as follows

3x - 2y + 4-( -4x  -2y + 6 )

or, 3x - 2y + 4  + 4x + 2y -6

or, 7x - 2

Hence, the simplified expression is 7x- 2.

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The value of x that makes the expressions equivalent is 8

What is the solution to an equation?

In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.

4(x-5)= 32-20

Distribute the 4

4x-20=12

4x= 12+20 = 32

x= 32/4 = 8

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a) The circle crosses the y-axis at the points (0, 6) and (0, -2). b) the radius of the circle is 5. c) (i) The length of CP is √34. (ii) The length of PQ is 10.

(a) To find the y-coordinates of the points where the circle crosses the y-axis, we substitute x = 0 into the equation of the circle:

0² + y² + 6(0) - 4y = 12

y² - 4y = 12

y² - 4y - 12 = 0

To solve this quadratic equation, we can factor it:

(y - 6)(y + 2) = 0

Setting each factor to zero, we find two possible values for y:

y - 6 = 0 => y = 6

y + 2 = 0 => y = -2

Therefore, the circle crosses the y-axis at the points (0, 6) and (0, -2).

(b) To find the radius of the circle, we can complete the square to rewrite the equation of the circle in standard form:

x² + y² + 6x - 4y = 12

(x² + 6x) + (y² - 4y) = 12

(x² + 6x + 9) + (y² - 4y + 4) = 12 + 9 + 4

(x + 3)² + (y - 2)² = 25

Comparing this equation with the standard form of a circle, (x - h)² + (y - k)² = r², we can see that the center of the circle is at (-3, 2) and the radius is √25 = 5.

Therefore, the radius of the circle is 5.

(c) (i) To find the length of CP, we can use the distance formula between two points. The coordinates of C are (-3, 2), and the coordinates of P are (2, 5).

The distance formula is given by:

d = √((x₂ - x₁)² + (y₂ - y₁)²)

Substituting the coordinates into the formula, we have:

CP = √((2 - (-3))² + (5 - 2)²)

= √(5² + 3²)

= √(25 + 9)

= √34

Therefore, the length of CP is √34.

(ii) To find the length of PQ, we can use the fact that PQ is a tangent to the circle. The radius of the circle is 5, and the line segment CP is perpendicular to PQ.

Since CP is perpendicular to PQ, CP is the radius of the circle. Therefore, CP = 5.

Therefore, the length of PQ is equal to 2 times the length of CP:

PQ = 2 * CP

= 2 * 5

= 10

Therefore, the length of PQ is 10.

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The arc length and sector area of the sector with 280° at the center of a circle with radius 3 units are 14.66 units and 21.99 square units respectively.

We know that the arc length of the arc subtend angle A at the center of a circle with radius 'r' is given by,

L = 2πr*(A/360°)

and sector area is given by (S) = πr²*(A/360°)

and the value of π is = 3.14 (approx.)

Here given the radius of the circle is = 3 units.

So, r = 3 units.

And the angle subtend by the sector at the center of circle = 280°

So, the Arc length of the sector = 2π*3*(280°/360°) = 14.66 units (rounding off to two decimal places).

The sector area = π(3)²*(280°/360°) = π*9*(280°/360°) = 21.99 square units.

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The question is incomplete. The complete question will be -

Answer:

YES

Step-by-step explanation:

Answer:

D. (3,-2)

Step-by-step explanation:

When we rotate a point 180 degrees about the origin, the rule is:

(x,y) -> (-x,-y)

So let's use this rule with our point.

(-3,2) -> (3,-2)

The answer is D (3,-2)

Answer:

x=32

Step-by-step explanation:

27=x-5

+5   +5

32=x

Answer:

  A = C²/(4π)

Step-by-step explanation:

You want a formula for the area of a circle, given its circumference.

Relevant relations for a circle are ...

  A = πr² . . . . . . . . A = area, r = radius

  C = 2πr . . . . . . . . C = circumference

Solving the circumference equation for r, we find ...

  r = C/(2π)

Substituting that into the area equation, we have ...

  A = π(C/(2π))²

  A = C²/(4π)

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The function that models the area A of a circle in terms of its circumference C is A = C²/(4π).

The formula for the circumference of a circle is C = 2πr or C = πd, where r is the radius and d is the diameter. To find a function that models the area A of a circle in terms of its circumference C, we can rearrange the formula for the circumference to solve for the radius: r = C/(2π). Substituting this value of r into the formula for the area, we get A = π(C/(2π))² = C²/(4π).

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It cannot be determined. At least one other point on the line is needed to determine if x is proportional to y

Given data ,

A point on a straight line has an x-coordinate of 3 and a y-coordinate of 6

Now , A single point on a straight line does not define the connection between x and y. We must evaluate the connection between x and y for several places on the line in order to establish if x is proportional to y.

As a result, the relationship between x and y cannot be inferred only from the supplied location (3, 6). To establish the proportionality between x and y, at least one more point on the line is required

Hence , the equation of line is solved

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The Proportion of exam results between 82 and 89.2 points is 0.3330.

What is standard deviation?

A measurement of a data set's deviation from the mean is referred to as "standard deviation" (or ""). A low standard deviation means that the data are grouped around the mean, whereas a large standard deviation says that the data are more spread out..

For instance, the mean of the two integers 2, 7, 14, 22, 30 and 15, 15, 15, 14, 16 is the same. But the second is clearly more diffused.

Given:

Mean is 83.2 points, and

8 points is the standard deviation.

Consequently, the proportion is

P(82 ≤ x ≤ 89.2)

=P( 82- 83.2 / 8 ≤ z ≤ 89.2 - 83.2/8)

=P (0.75) - P(-0.15)

=0.7734 -(0.4404)

= 0.3330

So, the Proportion of exam results between 82 and 89.2 points is 0.3330.

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Answer:

let the points be P (m,2m) and Q(4m,4m)

Step-by-step explanation:

The distance between the point PQ is given by :

or ,(√13)^2 = 9m^2 +4m^2

therefore x = 1 ( solve the equation)

Answer:

The equation for this problem would be:

z = n * 1.58

This equation shows that the amount of money needed to buy the popcorn is equal to the number of bags purchased, multiplied by the price for each bag.

Answer:

0.5625

Step-by-step explanation:

The continuous proportional change in y when years of service increases from three years to five years is:Δy/y = (y_5 - y_3) / y_3= e^(ln(y_5) - ln(y_3)) / y_3= e^(-0.2Δt) = e^(-0.2*2)= e^(-0.4)≈ 0.6703The proportional change in y when years of service increases from three years to five years is approximately 0.6703.

A. Using non-linear equation (1), we are to calculate the market value y after three years of service (t=3) and after five years of service. Further, calculate the simple (discrete) proportional change in y when the vehicles go from three years of service to five years of service (i.e., the market value with three years of service is the base for the calculation).Given equation is y = 40e^(-0.025-0.2t)Where t = 3, the market value y is:y = 40e^(-0.025-0.2(3))= 40e^(-0.625)= 22.13 thousand dollarsWhere t = 5, the market value y is:y = 40e^(-0.025-0.2(5))= 40e^(-1.025)= 14.09 thousand dollarsSo, the discrete proportional change in y when the vehicles go from three years of service to five years of service is:proportional change in y = (y_5 - y_3) / y_3 * 100%= (14.09 - 22.13) / 22.13 * 100%= -36.28%B. We need to apply the natural log transformation to equation (1).

Therefore, we take the natural log of both sides of the equation.y = 40e^(-0.025-0.2t)ln(y) = ln(40e^(-0.025-0.2t))= ln(40) + ln(e^(-0.025-0.2t))= ln(40) - 0.025 - 0.2tSo, we get the transformed equation as:ln(y) = -0.025 - 0.2t + ln(40)Now, let's take the derivative of both sides of this transformed equation, with respect to t. We get:1 / y * dy/dt = -0.2This equation doesn't exhibit constant marginal effect because dy/dt depends on y. Therefore, we can't say that a one unit increase in x would always lead to the same proportional change in y.C. (i) Use the slope term from your transformed equation from part B to directly calculate the continuous proportional change in y when years of service increases from three years to five years. Given transformed equation is:ln(y) = -0.025 - 0.2t + ln(40)When years of service increases from three years to five years, then change in t is:Δt = 5 - 3 = 2

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A perfect square trinomial is a trinomial expression that can be factored into the square of a binomial. In a perfect square trinomial, the first and last terms are perfect squares, and the middle term is twice the product of the square roots of the first and last terms.

To make this equation a perfect square trinomial, we need to take a few steps.

i. Determine the square root of the first term.

ii. Square the second term and divide it by 4.

iii. Add this result to both sides of the equation. This will ensure that the left-hand side is a perfect square trinomial.

iv. Write the left-hand side of the equation as a square of a binomial.

v. Solve the equation for x.

Let's implement these steps to get the value of k in the given equation.

x² − kx + 121 = 0

i. Determine the square root of the first term.

x² = (x)²

ii. Square the second term and divide it by 4.

(-k/2)² = k²/4

iii. Add this result to both sides of the equation. This will ensure that the left-hand side is a perfect square trinomial.

x² − kx + k²/4 + 121 = k²/4 + 121i

v. Write the left-hand side of the equation as a square of a binomial.

(x − k/2)² = k²/4 + 121

v. Solve the equation for x.

x − k/2 = ±sqrt(k²/4 + 121)x = (k/2) ±sqrt(k²/4 + 121)

Since this equation has no real roots, the expression under the radical must be negative. This can be written as

k²/4 + 121 < 0k²/4 < −121

This is a contradiction since the left-hand side is always positive. Therefore, there is no value of k that would make the left side of the given equation a perfect square trinomial.

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Since k²/4 + 121 is already a perfect square, we don't need to find a specific value for k.

Any value of k will make the left side of the equation a perfect square trinomial.

To make the left side of the equation a perfect square trinomial, we need to find the value of k that would complete the square.
In this equation, we have x² - kx + 121 = 0.
To complete the square, we want to rewrite the equation as a perfect square trinomial of the form (x - a)² = b.

Let's go step by step:
Step 1: Identify the coefficient of x, which is -k.
Step 2: Take half of the coefficient of x and square it. In this case, we have (-k/2)² = (k/2)² = k²/4.
Step 3: Add the result from step 2 to both sides of the equation. This ensures that the left side remains unchanged.
By adding k²/4 to both sides of the equation, we get x² - kx + k²/4 + 121 = k²/4.
Step 4: Simplify the equation on the left side by factoring it into a perfect square trinomial.
We can rewrite the left side as (x - k/2)² = k²/4 + 121.
Step 5: Now we want the right side of the equation to be a perfect square. In this case, k²/4 + 121 is already a perfect square.
The value of k that makes the left side a perfect square trinomial is any value that satisfies k²/4 + 121 = b², where b is a real number.

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The equation Y=-3x-1 represents a linear relationship between x and y, and can be used to model real-world situations such as distance vs. time or cost vs. quantity.

The equation Y=-3x-1 represents a straight line on a coordinate plane. The "slope-intercept" form of the equation is y=mx+b, where m is the slope and b is the y-intercept.

In this case, the slope is -3 and the y-intercept is -1. This means that the line goes downwards at a rate of 3 units for every 1 unit to the right, and intersects the y-axis at -1.

To find the solution to this equation, you would need to have a specific value for either x or y.

If you were given a value for x, you could plug it into the equation to find the corresponding value for y. If you were given a value for y, you could solve for x by rearranging the equation.

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