Y=4x^2;estimate dy/dx x=2

Answer:

Step-by-step explanation:

Ana's conjecture that Raul lost 2/5 of his baby teeth is true.

To see why, consider that Raul originally had 20 baby teeth. If he lost 8 of these teeth, that means he has 20 - 8 = 12 baby teeth remaining. To determine what fraction of his baby teeth he lost, we can calculate:

8 baby teeth lost / 20 baby teeth total = 2/5

So, Raul lost 2/5 of his baby teeth, which supports Ana's conjecture.

On the other hand, Raul's statement that he lost 4/10 of his baby teeth is not correct, since 4/10 can be simplified to 2/5, which is the same as Ana's conjecture that he lost 2/5 of his baby teeth.

The graph of the equation is added as an attachment

From the question, we have the following parameters that can be used in our computation:

y = 6x

The above expression is a linear equation that implies that

The product of 6 and x is equal to the the value of y

Note that:

A linear graph is a straight line on a two-dimensional coordinate plane that represents a linear equation

Where the equation is in the form y= mx + b, where m is the slope and b is the y-intercept.

This also means that

Next, we plot the graph

See attachment for the graph of the linear equation and few points on it

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Answer:

Step-by-step explanation:

We can start by setting up an equation to solve for x, the number of years it will take for the car to be worth $8,200:

8200 = 20000(0.8)^x

Dividing both sides by 20,000, we get:

0.41 = 0.8^x

Taking the logarithm of both sides (using any base, as long as we're consistent), we get:

log(0.41) = log(0.8^x)

Using the property of logarithms that allows us to bring down the exponent as a coefficient, we get:

log(0.41) = x log(0.8)

Dividing both sides by log(0.8), we get:

x = log(0.41) / log(0.8)

Using a calculator, we find:

x ≈ 5.92

Therefore, it will take about 5.92 years for the car to be worth $8,200.

The line's slope is [tex]\frac{1}{2}[/tex] and the distance increases by 1 mile every 2 hours.

What is a good example of a line's slope?

The proportion of the increase in the y-value to the increase in the x-value may also be used to determine slope. For instance: We can get the slope of a line given two locations, P = (0, -1) & Q = (4,1) on the line.

A. Since the line's slope is 2, it follows that the y-variable, which is most likely distance, grows by 2 units for every increment in the x-variable, which is most likely time. The accurate statement is thus: speed is increased by Two miles per hour.

B. Since the line's slope is 2, it follows that the y-variable will drop by 2 units for every unit rise in the x-variable, which is most likely time. The accurate description is thus: speed drops by Two miles per hour.

C. If the line's slope is 1/2, the y-variable will rise by 1/2 unit for every increment in the x-variable, which is probably time. The precise description is that the distance grows by a mile every two hours.

D. If indeed the line's slope is 1/2, the y-variable will drop by 1/2 unit for every unit rise in the x-variable, which is probably time. The precise description is: distance shrinks by a mile every two hours.

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The area of the composite figure is equal to 63.270 square feet.

In this problem we need to compute the area of a composite figure, which is the result of adding the areas of a semicircle and a right triangle. The area formulas of the figures mentioned above are introduced below:

Semicircle

A = 0.5 · r²

Right triangle

A = 0.5 · b · h

Where:

If we know that r = 5 ft, b = 8 ft and h = 6 ft, then the area of the composite figure is:

A = 0.5π · (5 ft)² + 0.5 · (8 ft) · (6 ft)

A = 12.5π + 24 ft²

A = 63.270 ft²

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Answer:

-1/3

Step-by-step explanation:

When adding or subtracting fractions, you don't add or subtract the denominators.

So, Start by subtracting the numerators

3/9 - 6/9 = -3/9

you can simplify this fraction by dividing both the numerator and denominator by 3

-3 ÷ 3 = -1

9 ÷ 3 = 3

So, the answer is:

-1/3

Hope this helps!

The gym fee increases by $6 for each additional class taken. The average rate of change in cost per class is equal to the slope of the linear function, which is $6 per class.

What is average rate ?

Average rate refers to the rate of change of a quantity over a given period of time. It is calculated by dividing the change in the quantity by the time period over which the change occurs.

To find the average rate of change in cost per class, we need to calculate the slope of the linear function that relates the gym fee to the number of classes taken.

Let x be the number of classes taken, and y be the gym fee. We can use the two data points given to find the equation of the line:

When x = 6, y = 43

When x = 11, y = 73

The slope of the line passing through these two points can be calculated as follows:

slope = (change in y) / (change in x)

slope = (73 - 43) / (11 - 6)

slope = 30 / 5

slope = 6

Therefore, the gym fee increases by $6 for each additional class taken.

The average rate of change in cost per class is equal to the slope of the linear function, which is $6 per class.

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Answer:

A. 10

Step-by-step explanation:

The 9 in 290,481 is in the ten thousands place (10⁴)

The 9 in  964,352 is in the hundred thousands place (10⁵)

10⁵/10⁴ = 10

Answer:
A. 10

The value of 9 in 964,352 is 10,000 times greater than the value of 9 in 290,481, because it is positioned in the hundreds of thousands place versus the tens place.

The value of a digit in a number is determined by its position or place value. In the number 964,352, the value of the 9 is 900,000, because it is in the hundreds of thousands of places. In the number 290,481, the value of the 9 is 90, because it is in the tens place. To find out how many times greater the value of the 9 in 964,352 is than the value of the 9 in 290,481, we divide 900,000 by 90, which gives us 10,000. Therefore, the answer is C. 10,000.

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So, it is proven that the area of triangle ABC is 1/2*a*b*sinC  .

A triangle is a 2D shape having three sides and the sum of all angles is 180°. A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC. In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane.

We have,

A ΔABC,

And,

AB = c

BC = a

CA = b

H = Altitude of the triangle,

Now,

Area of triangle = 1/2* base* height

i.e.

Area of triangle ABC =1/2*a*h     .....(i)

Now,

Using trigonometric ratios,

sinC = perpendicular/hypotenuse

i.e. sinC = h/b

We get,

h = b * SinC

Now,

putting this value in equation (i),

We get,

Area of triangle ABC=1/2*a*b*sinC

So, It is proved that area of triangle ABC =1/2*a*b*sinC   ,

Hence, we can say that it is proven that the area of triangle ABC is 1/2*a*b*sinC , using trigonometric ratios and the triangle's area formula.

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The second bar represents the price range from $2.51 to $5.00, so the data set includes the value of 4.53 and the value of 5.00 the correct answer is {0.50, 2.00, 2.52, 3.37, 4.53, 5.00, 8.99}

A histogram is a graph used to represent the frequency distribution of a few data points of one variable. Histograms often classify data into various “bins” or “range groups” and count how many data points belong to each of those bins.

The histogram shows the number of items sold at various price ranges, and the heights of the bars indicate the number of items sold within each price range.

The data set that is represented in the histogram is:

{0.50, 2.00, 2.52, 3.37, 4.53, 5.00, 8.99}

This is because the histogram has four bars with heights of 2, 4, 0, and 1, which correspond to the number of items sold in each of the four price ranges shown.

The values in the data set correspond to the boundaries of these price ranges. For example, the first bar represents the price range from $0.00 to $2.50, so the data set includes the value 2.00 (which is within this range) and the value 2.52 (which is just outside this range).

Similarly, the second bar represents the price range from $2.51 to $5.00, so the data set includes the value of 4.53 (which is within this range) and the value of 5.00 (which is the upper boundary of this range).

Therefore, the second bar represents the price range from $2.51 to $5.00, so the data set includes the value of 4.53 and the value of 5.00 the correct answer is {0.50, 2.00, 2.52, 3.37, 4.53, 5.00, 8.99}

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a. The six trigonometric functions of the angle β are:

sin β = 7/25

cos β = 24/25

tan β = 7/24

csc β = 25/7

sec β = 25/24

cot β = 24/7

b. Using trigonometric identity, cos X + (sin X)(tan X) = 1

We can use the given value of cos β = 24/25 to find the other trigonometric functions of the angle β.

Let's draw a right triangle with angle β, adjacent side of length 24, and hypotenuse of length 25 (since cos β = adjacent/hypotenuse):

Using the Pythagorean theorem, we can find the opposite side:

Opposite side = sqrt(hypotenuse^2 - adjacent^2) = sqrt(25^2 - 24^2) = sqrt(49) = 7

So the triangle is:

Now we can find the other trigonometric functions:

sin β = opposite/hypotenuse = 7/25

cos β = adjacent/hypotenuse = 24/25

tan β = opposite/adjacent = 7/24

csc β = hypotenuse/opposite = 25/7

sec β = hypotenuse/adjacent = 25/24

cot β = adjacent/opposite = 24/7

2. We can use the trigonometric identity for tangent:

tan X = sin X / cos X

to rewrite the expression as:

cos X + (sin X)(sin X / cos X)

Multiplying through by cos X, we get:

(cos X)(cos X) + (sin X)(sin X)

Using the Pythagorean identity:

(sin X)^2 + (cos X)^2 = 1

we can simplify further:

1 - (cos X)^2 + (cos X)^2 = 1

So the final simplified expression is equal to 1

3. We can start with the left-hand side of the equation and manipulate it using the definitions of the trigonometric functions and the Pythagorean identity until we arrive at the right-hand side:

tan²α(csc²α - 1)

= (sin²α/cos²α)((1/sin²α) - 1)

= (sin²α/cos²α - sin²α/cos²α)

= 0

Now, let's look at the right-hand side:

1

We see that the left-hand side simplifies to 0, while the right-hand side is 1. Therefore, the identity is not true for all values of α.

We can see this more clearly by picking a specific value of α and evaluating both sides of the equation. For example, let's take α = 45°:

tan²45°(csc²45° - 1) = (1/1)((2/1) - 1) = 1

1 = 1

So the identity holds for α = 45°, but we have already shown that it does not hold for all values of α. Therefore, the identity is not true for all values of α.

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The equations that represent the plants' height after any given number of days are as follows;

y = 2x + 5

y = 3x + 3

The height of the first plant is 33 cm.

The height of the second plant is 48 cm.

Based on the information provided above, the first plant is 5 cm high and the plant grows 2 cm per day. Therefore, the total height, y, can be represented by this equation:

y = 2x + 5

where:

x represents the number of days.

For the second plant, we have:

y = 3x + 3

After 15 days, the total height of each plant is given by;

First plant, y = 2x + 5 = 2(15) + 3 = 33 cm.

Second plant, y = 3x + 3 = 3(15) + 3 = 48 cm.

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Answer:

A is the correct answer

Step-by-step explanation:

The equation of line is y = ( -6/5 )x + 2 , where the slope is m = ( -6/5 )

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( -6/5 )

The y intercept of the line is b = 2

So , equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

On simplifying , we get

y = ( -6/5 )x + 2

Hence , the equation of line is y = ( -6/5 )x + 2 and the graph is plotted

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Answer:

the output is −16

Step-by-step explanation:

x=-1

9·x-7

9·-1-7

-9-7

-16

Answer: it is 4:2

Step-by-step explanation: because it is a ratio, both sides can be divided by the same number and still have the same meaning. btw in this case both divided by 2

The area of the composite figure is approximately 57.51 square centimeters.

By calculating the area of the triangle and the sector, and then adding them together, we may determine the area of the composite figure.

The following formula can be used to determine the sector's area:

Sector area is equal to (central angle / 360) x r2.

The sector's radius is 8 cm, and its central angle is 60°, resulting in:

Sector area equals (60/360) x 3.14 x 82

Sector size: 33.51

The following formula can be used to get the triangle's area:

Area of triangle Equals base x height x half.

The Pythagorean theorem can be used to determine the triangle's height given that its base is 8 cm:

a² + b² = c²

8² + h² = 10²

64 + h² = 100

h² = 36

h = 6

As a result, given that the triangle's height is 6 cm, we have:

Triangle's area equals 1/2 x 8 x 6.

Triangle has a 24 area.

By combining the areas of the triangle and the sector, we can determine the area of the composite figure.

33.51 + 24 times the composite figure's area

The composite figure's area is 57.51.

Hence, the composite figure has a surface area of roughly 57.51 square centimetres.

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A table that represents the function y = -3x/4 + 3 is: B. table B.

In order to use the given linear function to complete the table, we would have to substitute each of the values of x (x-values) into the linear function and then evaluate as follows;

When the value of x = -2, the linear function is given by;

y = -3x/4 + 3

y = -3(-2)/4 + 3

y = 9/2 (False).

When the value of x = -4, the linear function is given by;

y = -3x/4 + 3

y = -3(-4)/4 + 3

y = 6 (True).

When the value of x = 0, the linear function is given by;

y = -3x/4 + 3

y = -3(0)/4 + 3

y = 3 (True).

When the value of x = 4, the linear function is given by;

y = -3x/4 + 3

y = -3(4)/4 + 3

y = 0 (True).

When the value of x = 8, the linear function is given by;

y = -3x/4 + 3

y = -3(8)/4 + 3

y = -3 (True).

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All the central angles are,

Red= 100°

blue= 150°

green= 50°

purple= 60°

The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.

Given that;

The data below shows the colors preferred by a group of people.

Cooler          Number of people

Red=                 20

blue=                 30

green=               10

purple=              12

Now, Total number of Peoples is,

⇒ 20 + 30 + 10 + 12

⇒ 72

Hence, We get;

Proportion of Red = 20/72 = 5/18 = 10/36

Central angle = 5/18 x 360 = 100°

Proportion of Blue = 30/72 = 15/36

Central angle = 15/36 x 360 = 150°

Proportion of Green = 10/72 = 5/36

Central angle = 5/36 x 360 = 50°

Proportion of Purple = 12/72 = 1/6 = 6/36

Central angle = 1/6 x 360 = 60°

Thus, All the central angles are,

Red= 100°

blue= 150°

green= 50°

purple= 60°

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The maximum and minimum of the given function are 22 and -2, respectively

The system of inequalities is given as

y ≥ -x - 2

y ≥ 3x + 2

y ≤ x + 4

See attachment for the graph

From the graph, we have the following coordinates

(-1, -1), (-3, 1) and (1, 5)

Substitute (-1, -1), (-3, 1) and (1, 5) in f(x, y) = -3x + 5y

So, we have

f(-1, -1) = -3(-1) + 5(-1) = -2

f(-3, 1) = -3(-3) + 5(1) = 14

f(1, 5) = -3(1) + 5(5) = 22

Hence, the maximum is 22 and the minimum is -2

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The logical form of this argument is -

Denying the Antecedent.

Denying the antecedent, sometimes also called inverse error or fallacy of the inverse, is a formal fallacy of inferring the inverse from the original statement.

It is committed by reasoning in the form :

If P, then Q. Therefore, if not P, then not Q.

Given is the argument as -

"If seven clowns are squeezed into a small car, we are at the circus. Seven clowns are not squeezed into a small car. So, we are not at the circus"

The logical form of this argument is -

Denying the Antecedent

Therefore, the logical form of this argument is -

Denying the Antecedent.

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The equation that represents the graph will be x = (1/12) y². Then the correct option is A.

It's the locus of a moving point that keeps the same distance between a stationary point and a specified line. The focus is a non-movable point, while the directrix is a non-movable line.

The equation of the upward parabola is written as,

y = 4ax²

The equation of the downward parabola is written as,

y = - 4ax²

The equation of the rightward parabola is written as,

x = 4ay²

The equation of the leftward parabola is written as,

x = - 4ay²

From the graph, the parabola opens rightward, then the equation is written as,

x = (1/12) y²

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Answer:

1. 6/18 = 1/3

  9/21 = 3/7

2. 4/6 = 2/3

   2/4 = 1/2

3. 6/12 = 1/2

   8/12 = 2/3

4. 2/8 = 1/4

   3/6 = 1/2

5. 7/21 = 1/3

   8/10 = 4/5

6. 9/12 = 3/4

   12/20 = 3/5

7. 8/16 = 1/2

   10/25 = 2/5

Answer:[tex]3x^{5} \sqrt{x}[/tex]

Step-by-step explanation:

The price per pound of the carrots Dora bought is $0.80.

What is the unit rate?

Unit rate is a ratio that compares the amount of one unit of measure to the corresponding amount of another unit of measure. It is a special case of a ratio, in which the second term is always one. For example, if a car travels 120 miles in 2 hours, the unit rate of speed is 60 miles per hour, which means that the car travels 60 miles for every hour of driving.

Unit rate is commonly used in everyday life, such as in shopping (price per unit) or in cooking (ingredients per serving).

To find the price per pound of the carrots, we need to divide the total cost by the total weight.

First, we need to convert the mixed number 4 1/2 to an improper fraction:

4 1/2 = (4 x 2 + 1) / 2 = 9/2

Next, we divide the total cost by the total weight in pounds:

Price per pound = Total cost / Total weight

Price per pound = $3.60 / 4.5 pounds

Price per pound = $0.80

Therefore, the price per pound of the carrots Dora bought is $0.80.

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(a) Commutative property of addition , (b) Distributive Property , (c) Associative Property of Multiplication , (d) Commutative property of multiplication and (e) Associative property of addition.

What is Associative Property ?

The associative property is a mathematical principle that states that the way in which factors are grouped in a multiplication or addition expression does not affect the final result. In other words, when using the associative property, we can add or multiply a group of numbers in any order we want, as long as we keep the order of the individual numbers the same.

(7 + 3) + 2 = 2 + (7 + 3)      Commutative property of addition

3(2x +4) = 6x + 12              Distributive Property

(9 * x) * 3 = 9 * (x * 3)         Associative Property of Multiplication

(8 * x * 2) = (8 * 2* x)          Commutative property of multiplication

(4 + 5) + 1 = 4 + (5 + 1)        Associative property of addition

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Answer:

Step-by-step explanation:

Square pyramid (since the base is a square)

Area base [tex]= 8^2=64mm^2[/tex]              (area of square)

Area each side [tex]= \frac{1}{2} base[/tex]×[tex]height[/tex]    (area triangle formula)

                          = [tex]\frac{1}{2}[/tex]×[tex]8[/tex]×[tex]10[/tex]

                          = [tex]40 mm^2[/tex]

Total area [tex]= 4triangles + square base[/tex]

                 [tex]=4[/tex]×[tex]40+64[/tex]

                 [tex]=224 mm^2[/tex]

"The graph of f(x) has exactly two x-intercepts" -  For a linear function whose domain is the set of all real numbers, this assertion cannot be accurate.

Any function with the formula f(x) = mx + b is referred to as linear.

Setting f(x) = 0, we get:

mx + b = 0

Solving for x, we get:

x = -b/m

Depending on the slope m and y-intercept b values, there are an unlimited number of x-intercepts.

A linear function in mathematics is one that has either one or two variables and no exponents. It is a function with a straight line as its graph. If the function has more variables, they should all be constants or known variables in order for the function to continue to function as a linear function. A linear function is a function that, when plotted, creates a straight line. Typically, it is a polynomial function with a maximum degree of 1 or 0. Nonetheless, calculus and linear algebra are also used to represent linear functions. The function notation is the only distinction. It is also important to understand an ordered pair written in function notation.

from the questions:

A function with the formula f(x) = mx + b, where m and b are constants, is referred to as a linear function. When f(x) = 0, the point where a linear function intersects the x-axis is known as the x-intercept.

Setting f(x) = 0, we get:

mx + b = 0

Solving for x, we get:

x = -b/m

As a result, the x-intercept of a linear function is a single point, (-b/m, 0), and depending on the slope m and y-intercept b values, there may only be zero, one, or infinitely many x-intercepts.

As a result, for a linear function whose domain is the set of all real numbers, it is not possible for the statement "The graph of f(x) has precisely two x-intercepts" to be true.

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The graph of the rational equation is solved and f ( x ) = 1/ ( x + 2 ) ( x - 5 )

Given data ,

Let the function be represented as f ( x )

Now , the value of f ( x ) is

f ( x ) = 1/ ( x + 2 ) ( x - 5 )

The function will have increasingly large values as the denominator approaches zero. When x -2, the denominator is positive and the function tends to the upside. When x -2 x 5, the function is negative. When x 5, the function becomes positive once more.

Hence , the rational function is f ( x ) = 1/ ( x + 2 ) ( x - 5 )

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The complete question is attached below :

Which of the following rational functions is graphed below?

A. F(x) =(x-2)/(x+5)

B. F(x) =1/(x-2)(x + 5)

C. F(x) =1/(2x + 5)

D. F(x)= 1/(x+2)(x-5)