Match each of the equations with their corresponding graph

Answer:

I think it’s  28.3

Step-by-step explanation:

Sorry If I’m wrong

Answer:

Answer:

no expression is equal to -20

The approximate probability of drawing one orange marble and one green marble from a bag containing five red marbles, four orange marbles, one yellow marble, and three green marbles is approximately 0.154.

To find the approximate probability of drawing marbles, we can use the following formula

probability = (number of favorable outcomes) / (total number of outcomes)

We need to find the number of favorable outcomes where one marble is orange and the other is green. We can choose one orange marble from four orange marbles in the bag in 4 ways, and one green marble from three green marbles in 3 ways. So, the number of favorable outcomes is 4 x 3 = 12.

The total number of ways of choosing two marbles from the bag is 13C2, which is the number of combinations of 2 marbles that can be drawn from the 13 marbles in the bag. Therefore, the total number of outcomes is

13C2 = (13 x 12) / (2 x 1) = 78

Thus, the approximate probability of drawing one orange marble and one green marble is

probability = number of favorable outcomes / total number of outcomes = 12/78 ≈ 0.154

Therefore, the approximate probability of drawing one orange marble and one green marble from the bag is approximately 0.154.

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Answer:

−4x + 10 < 26

Step 1: Subtract 10 from both sides.

−4x + 10 − 10 < 26 − 10

−4x < 16

Step 2: Divide both sides by -4.

-4x/−4  <  16 /−4

x > −4

Answer:

x > −4

assuming you're solving for x:

solve using pemdas backwards, so basically sadmep :)

first subtract 10, and you end up with the equation -4x < 16.

Next is dividing the -4. Remember dividing by a negative number switches the sign direction, so the < becomes a >. So, your answer would be x > -4

Answer:

Uhdhdb

Step-by-step explanation:

Jsjddj hdhdhhdb

Answer: each belt is $15

Step-by-step explanation:

An equation of the tangent line to the graph of f at the point (1, 3) is y = 2x - 1.

To find the equation of the tangent line to the graph of f at a given point, we need to find the slope of the tangent line at that point. The slope of the tangent line is equal to the derivative of the function evaluated at the given point.

First, we find the derivative of f(x) by taking the derivative of each term separately. The derivative of x^2 is 2x, the derivative of 4x is 4, and the derivative of -2 is 0. Combining these derivatives, we get f'(x) = 2x + 4.

Next, we substitute the x-coordinate of the given point into the derivative to find the slope. At x = 1, the slope is f'(1) = 2(1) + 4 = 6.

Finally, using the slope-intercept form of a line (y = mx + b), we can substitute the given point (1, 3) and the slope (m = 6) to find the y-intercept (b). Solving for b, we get b = 3 - 6(1) = -3. Therefore, the equation of the tangent line is y = 2x - 1.

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Three types of rigid transformations are Reflection, Rotation, and Translation. Rigid transformation, also called isometry.

A rigid transformation, also called isometry,  is a transformation that doesn't change the size or shape of a geometric figure. The following are 3 types of rigid transformation:

1. Reflection

→  is the act of shifting an object's coordinates that flip it across a line without changing its shape or size. Horizontal (draw a figure to the left or right) or vertical (draw a figure to the up or down) reflections are possible. The result of reflection is a mirror image of the figure itself.  

The figure is reflected across \(x-\) or \(y-\) axis, and then change \(x-\) or \(y-\) coordinate.

2. Rotation

→ is the non-modification of an object's size or shape by rotating it around an fixed point. A center of rotation is required to rotate an object. And the rotation did by using a degree.

The figure is rotated by a degree (ex: 90°), and then change \(x-\) or \(y-\) coordinate. Meanwhile, a point's center rotation stays at the same.

3. Translation

→ is sliding a figure in any direction without changing its size, shape, or orientation. Translation could be horizontal (make a figure left or right),  or vertical reflections (make a figure up or down).

Vertical translation is shifting the graph along  \(y-\) axis

Horizontal translation is shifting the graph along  \(x-\) axis.

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The x-values on the graph of f(x) = -3sin(x)cos(x) where the tangent line is horizontal are given by x = π/4 + n(π/2), where n is an integer. To find the x-values on the graph of the function f(x) = -3sin(x)cos(x) where the tangent line is horizontal, we need to determine where the derivative of the function is equal to zero.

The derivative of f(x) can be found using the product rule:

f'(x) = (-3)(cos(x))(-cos(x)) + (-3sin(x))(-sin(x))

= 3\(cos^2(x) - 3sin^2(x)\)

= 3(\(cos^2(x) - sin^2(x))\)

Now, to find the x-values where the tangent line is horizontal, we set f'(x) = 0 and solve for x:

3(\(cos^2(x) - sin^2(x)) = 0\)

Since \(cos^2(x) - sin^2(x)\) can be rewritten using the trigonometric identity cos(2x), we have:

3cos(2x) = 0

Now we solve for x by considering the values of cos(2x):

cos(2x) = 0

This equation is satisfied when 2x is equal to π/2, 3π/2, 5π/2, etc. These values of 2x correspond to x-values of π/4, 3π/4, 5π/4, etc.

Therefore, the x-values on the graph of f(x) = -3sin(x)cos(x) where the tangent line is horizontal are π/4, 3π/4, 5π/4, etc.

In summary, the x-values on the graph of f(x) = -3sin(x)cos(x) where the tangent line is horizontal are given by x = π/4 + n(π/2), where n is an integer.

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Answer:

Ykjhcgighgy7vgygoohgvg

Answer:

1,099.6

Step-by-step explanation:

if the radius is 5 and height is 14

you do

V=(pi)r squared × height

Incomplete question. However, let's assume this are feasible regions to consider:

Points:

- (0, 100)

- (0, 125)

- (0, 325)

- (1, 200)

Answer:

Maximum value occurs at 325 at the point (0, 325)

Step-by-step explanation:

Remember, we substitute the points value for x, y in the objective function P = 2x + 1.5y.

- For point (0, 100): P= 2(0) + 1.5 (100) =150

- For point (0, 125): P= 2(0) + 1.5 (125) =187.5

For point (0, 325): P= 2(0) + 1.5 (325) = 487.5

For point (1, 200): P= 2(1) + 1.5 (200) = 302

Therefore, we could notice from the above solutions that at point (0,325) we attain the maximum value of P.

Negative numbers get smaller the more they move away from 0.

Answer:

-15

Step-by-step explanation:

The greater the number after the minus sign, the smaller it is.

For example, -5 is smaller than -1.

the two points are

A(4,56) and B(5,70)

so, the linear equation is

thus, the equation is

y = 14x + 0

so we can put 14 in first place and 0 in second

A Gantt chart is a graphical representation of a project that shows each task as a horizontal bar whose length is proportional to its time for completion.

A Gantt chart is a popular project management tool that visually displays the schedule of a project. It consists of a horizontal timeline where each task or activity is represented by a horizontal bar. The length of the bar corresponds to the duration or time required to complete the task.

The horizontal bars in a Gantt chart are arranged sequentially along the timeline, and they can be color-coded or labeled to represent different tasks or phases of the project. The chart allows project managers and team members to visualize the project schedule, understand the dependencies between tasks, and track progress over time.

By using a Gantt chart, project stakeholders can easily identify the duration of each task, the order in which tasks should be performed, and the overall timeline of the project. It provides a clear overview of the project's progress and helps in planning and coordinating activities efficiently.

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       A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."

         A domain's discreteness or continuousness can be determined by examining the function's graph. The domain is continuous if the graph is a line. The domain is discrete if the graph consists of a collection of points.

Private Domain

      The values that will be effective for the function are distinct from one another. The maximum number of children you can have, for instance, has a defined answer. You can have 0 children, 1, 2, 3, etc., but not 2,34.

      Discrete graphs are those in which no lines connect the points. Start by locating all the x-coordinates in order to determine the domain and range of a discrete graph. The graph's entire set of x-coordinates makes up the domain. The graph's entire range of y-coordinates is considered to be the range.

        The domain is the collection of all possible inputs for a function. The codomain is the collection of all permitted outputs.

     Graphs, logical assertions, and combinations are a few examples of discrete structures. Infinite or finite discrete structures are both possible. Contrary to continuous mathematics, which works with structures whose values can span the real numbers or have other non-separable qualities, discrete mathematics deals with discrete objects.

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The inverse of the functions are f⁻¹(x) = 1/2(x + 3), f⁻¹(x) = 1/2√(x + 5) and A⁻¹(r) = 1/2√(r/pi)

Function (a)

This function is given as

f(x)=1/(2x)-3

The function needs to be represented as an equation

So, we have

y = 1/(2x) - 3

Swap the positions of x and y

x = 1/(2y) - 3

So, we have

1/(2y) = x + 3

Take the inverse of both sides

2y = 1/(x + 3)

Divide by 2

y = 1/2(x + 3)

So, the inverse function is

f⁻¹(x) = 1/2(x + 3)

Function (b)

This function is given as

f(x)=4x²-5

The function needs to be represented as an equation

So, we have

y = 4x²-5

Swap the positions of x and y

x = 4y² - 5

So, we have

4y²= x + 5

Divide both sides by 4

y²= 1/4(x + 5)

Take the square roots

y= 1/2√(x + 5)

So, the inverse function is

f⁻¹(x) = 1/2√(x + 5)

Function (c)

This function is given as

A(r) = 4(pi)r²

The function needs to be represented as an equation

So, we have

y = 4(pi)r²

Swap the positions of r and y

r = 4(pi)y²

So, we have

y²= r/(4pi)

Take the square roots

y = 1/2√(r/pi)

So, the inverse function is

A⁻¹(r) = 1/2√(r/pi)

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Answer:

\(y=x-1\)

Step-by-step explanation:

The line of symmetry of an isosceles triangle is perpendicular to its base.

Given vertices of the isosceles triangle:

By sketching the triangle with the given points, we can see that AB is its base.  (See attached graph).

To find the equation for the line of symmetry, first find the slope of the line AB.  To do this, use the coordinates of points A and B and the slope formula.

Define the points:

\(\implies \textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{6-2}{3-7}=-1\)

As the line of symmetry is perpendicular to line AB, its slope is the negative reciprocal of the slope of line AB.

Therefore, the slope of the line of symmetry = 1.

The line of symmetry will pass through point C (4, 3).

Therefore, substitute the found slope and the coordinates of point C into the point-slope formula:

\(\implies y-y_1=m(x-x_1)\)

\(\implies y-3=1(x-4)\)

\(\implies y-3=x-4\)

\(\implies y=x-1\)

Therefore, the equation of the given isosceles triangle's axis of symmetry is:

\(y = x - 1\)

If we graph the points

then we will get AC=CB

That means C is the point from where the axis of symmetry passes

Foot of perpendicular is midpoint of AB

Midpoint of AB

Find equation of C and foot of perpendicular

Slope

Equation

Answer:

multiples of 14

Step-by-step explanation:

we multiply 7×2

Answer:

357=10.5*4*x

8.5x

Step-by-step explanation:

357=10.5*4*x

357=42*x

8.5=x

Answer:

36. \(\frac{a^{7} }{b^{8} }\)  | 37. 1 ( anything raise to 0 equal 1 ) | 38. \(g^{4}\)

Step-by-step explanation: Just flip the exponent degree to negative when you move it down and positive when you move it up. You will be able to solve the rest. :)

Answer:

-8

Step-by-step explanation:

m∠3 + m∠5 = 180 (interior angles are supplementary)

-4x + 5 + (-13x + 39) = 180

-4x + 5 -13x +39 = 180

-17x = 180 - 5 - 39

-17x = 136

x = 136/(-17) = -8

Answer:

D

Step-by-step explanation:

This uses the Altitude- on- Hypotenuse theorem

An altitude drawn to the hypotenuse of a right triangle.

The 2 triangles formed are similar to the given triangle and each other, thus

Δ BAC ~ Δ BDA

The ratios of corresponding sides are equal, that is

\(\frac{BA}{BD}\) = \(\frac{BC}{BA}\) , substitute values

\(\frac{14}{x}\) = \(\frac{30}{14}\) ( cross- multiply )

30x = 196 ( divide both sides by 30 )

x ≈ 6.5 ( to the nearest tenth ) → D

The expression is simplified to F⁸. Option C

To determine the value, we have that;

Index forms are described as forms used in the representation of numbers that are too small or large.

Other names for index forms are scientific notation and standard forms.

From the information given, we have that

F² by the power of 4

This is represented as;

(F²)⁴

To simply the index form, we need to expand the bracket by multiplying the exponential values, we get;

F⁸

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Answer:

Step-by-step explanation:

You want equations of lines parallel and perpendicular to y = 2x -1 through the point (-7, 2).

The given equation is written in slope-intercept form:

  y = mx + b

where m = 2, and b = -1.

The slope of the line is m, the x-coefficient. For the given line, the slope is 2.

A parallel line will have the same slope: 2.

A perpendicular line will have the opposite reciprocal slope: -1/2.

When you have a point and slope, it is useful to use the point-slope form of the equation for a line:

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

For both of the desired lines, the point is (h, k) = (-7, 2). Using this point and the above slopes, we have ...

The approximate probability that the mean number of siblings in the sample of size 50 is at most 2 is 0.1562 or 15.62%.

What is probability?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.

To answer this question, we need to use the central limit theorem, which states that the sample mean of a large enough sample from any population with a finite mean and variance will follow a normal distribution with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.

In this case, we have a sample size of 50, which is considered large enough for the central limit theorem to apply. Therefore, the mean of the sample means will be equal to the population mean, which is 2.2, and the standard deviation of the sample means will be equal to the population standard deviation divided by the square root of the sample size, which is 1.4/sqrt(50) = 0.198.

To find the probability that the mean number of siblings in the sample of size 50 is at most 2, we need to calculate the z-score and use the standard normal distribution table or calculator. The z-score can be calculated as:

z = (2 - 2.2) / 0.198 = -1.01

Using the standard normal distribution table or calculator, we can find that the probability of getting a z-score of -1.01 or less is approximately 0.1562.

Therefore, the approximate probability that the mean number of siblings in the sample of size 50 is at most 2 is 0.1562 or 15.62%.

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The function \(f(x) = \frac{x}{x^2+14}\) does not have any inflection points.

To find the inflection point(s) of a function, we need to determine where the concavity changes. An inflection point occurs when the second derivative of a function changes sign. Let's calculate the second derivative of \(f(x)\) to see if it changes sign.

The first step is to find the first derivative of \(f(x)\). Applying the quotient rule, we get:

\(f'(x) = \frac{(x^2+14)(1) - (x)(2x)}{(x^2+14)^2} = \frac{x^2 + 14 - 2x^2}{(x^2+14)^2} = \frac{-x^2 + 14}{(x^2+14)^2}\).

Next, we find the second derivative by differentiating \(f'(x)\):

\(f''(x) = \frac{(2x)(x^2+14)^2 - (-x^2+14)(2)(2x)(x^2+14)}{(x^2+14)^4} = \frac{2x(x^2+14) + 4x^2(-x^2+14)}{(x^2+14)^3}\).

Simplifying further, we get:

\(f''(x) = \frac{2x^3 + 28x + 4x^4 - 56x^2}{(x^2+14)^3} = \frac{4x^4 - 56x^2 + 2x^3 + 28x}{(x^2+14)^3}\).

To find the potential inflection points, we need to solve the equation \(f''(x) = 0\). However, after simplification, it becomes apparent that the numerator of \(f''(x)\) cannot be equal to zero, as it is a quartic polynomial. Therefore, there are no solutions to \(f''(x) = 0\), indicating that the function \(f(x)\) does not have any inflection points.

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Answer:

1. x < -8

2. y + 2 > -5

3. Yes, because -16 is less than -3

4. No, because -6 is less than -4

5. a > 6

6. k < -11

7. y  > -6

8. b < -3/7

9. x > -2.8

10. r < -0.9

Blake should invest $6,000 at 4% interest and the remaining $5,000 (11000 - 6000) at 5% interest to earn exactly $490 at the end of 1 year.

Let's denote the amount of money Blake invests at 4% interest as "x" (in dollars) and the amount he invests at 5% interest as "11000 - x" (since the total investment is $11,000).

To earn interest, we can use the formula: Interest = Principal × Rate × Time

For the 4% interest account, the interest earned is:

0.04x × 1 (1 year) = 0.04x

For the 5% interest account, the interest earned is:

0.05(11000 - x) × 1 (1 year) = 550 - 0.05x

According to the problem, the total interest earned is $490. Therefore, we can set up the equation:

0.04x + (550 - 0.05x) = 490

Simplifying the equation:

0.04x + 550 - 0.05x = 490

-0.01x + 550 = 490

-0.01x = -60

x = 6000

Blake should invest $6,000 at 4% interest and the remaining $5,000 (11000 - 6000) at 5% interest to earn exactly $490 at the end of 1 year.

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