please show work clearly ! thanks
Option 2: Let F'(x) for f(x)=x3-2 find f'(x) using the Limit Definition.

Answer:

-30

Step-by-step explanation:

10(√81 - 12)

√81= 9 so

10(9-12)

9-12= -3

so

10(-3)

10*-3= 30

Answer: -30

Step-by-step explanation:

Factor and rewrite the radicand in exponential form: 10 (√9^2 - 12)

Simplify the radical expression: 10 x (9 - 12)

Calculate the sum or difference: 10 x (-3)

Remove the parentheses: -10 x 3

Calculate the product or quotient: -30

Answer: -30

Let's call the greater number "x" and the lesser number "y". According to the problem, we know that:

x - y = 48  (since the difference between the two numbers is 48)

y = (1/3)x   (since the lesser number is one third of the greater number)

Now we can substitute the second equation into the first equation:

x - (1/3)x = 48

Simplifying this equation, we get:

(2/3)x = 48

Multiplying both sides by 3/2, we get:

x = 72

Now that we know x, we can use the second equation to find y:

y = (1/3)x = (1/3)(72) = 24

So the two positive numbers are 72 and 24.

Learn more about Numbers here:- brainly.com/question/26856218

#SPJ11

Here is the ans of this ques. Hope it helps

Answer:

Step-by-step explanation:

The expression gives the number of centimeters in a mile 5,280 • 12 • (2.54). Option B

There are 2.54 cm in an inch, so we multiply by 2.54 to convert inches to centimeters.

There are 12 inches in a foot, so we multiply by 12 to convert feet to inches.

Finally, there are 5,280 feet in a mile, so we multiply by 5,280 to convert miles to feet.

Multiplying these three conversion factors together, we get:

5,280 • 12 • (2.54) = 63,360 cm.  Option B

Learn more about expression at https://brainly.com/question/30350742

#SPJ3

Answer

Second option is correct.

Option G is correct.

Area of the figure = (6.8/2) + (10.8)

Explanation

We can see that the figure is a combination of a triangle and a rectangle

Area of a rectangle = Length × Width

For the rectangular part,

Length = 10

Width = 8

Area of the rectangle = 10 × 8 = (10.8)

Area of a triangle = ½ × Base × Height

For this triangle,

Base = 16 - 10 = 6

Height = 8

Area of the triangle = ½ × Base × Height

Area of the triangle = ½ × 6 × 8 = (6.8/2)

Area of the figure = Area of the triangle + Area of the rectangle

Area of the figure = (6.8/2) + (10.8)

Hope this Helps!!!

the equation for the parabola is:

f(x) = 2*(x + 4)*(x - 5)

We know that if a parabola has x-intercepts a and b, and a leading coefficient A, then the equation is:

f(x) = A*(x - a)*(x - b)

In this case the x-intercepts are x = -4 and x = 5, then we have:

f(x) = A*(x + 4)*(x - 5)

Now we use the fact that the parabola passes through the point (1, -40), then we have that:

f(1) = -40 =  A*(1 + 4)*(1 - 5)

        -40 = A*(5)*(-4) = A*-20

       -40/-20 = A = 2

Then the equation for the parabola is:

f(x) = 2*(x + 4)*(x - 5)

If you want to learn more about parabolas:

https://brainly.com/question/4061870

#SPJ1

Answer:

b=   -1/2 a + 15

Step-by-step explanation:

isolate 2B, Take A to the other side and it will become negative. divide all by 2 because of 2B so we can get rid of 2. and that's all

The equation of the path of the parabola is y = a(x - 13)² + 27

Given data ,

To represent the path of Al's toss, we can assume that the path is a parabolic trajectory.

The equation of a parabola in vertex form is given by:

y = a(x - h)² + k

where (h, k) represents the vertex of the parabola

Now , the balloon was released from the 10-yard line and landed at the 16-yard line, we can determine the x-values for the vertex of the parabola.

The x-coordinate of the vertex is the average of the two x-values (10 and 16) where the balloon was released and landed:

h = (10 + 16) / 2 = 13

Since the height of the balloon reached 27 yards, we have the vertex point (13, 27)

Now, let's substitute the vertex coordinates (h, k) into the general equation:

y = a(x - 13)² + k

Substituting the vertex coordinates (13, 27)

y = a(x - 13)² + 27

To determine the value of 'a', we need another point on the parabolic path. Let's assume that the highest point reached by the balloon is the vertex (13, 27).

This means that the highest point (13, 27) lies on the parabola

Substituting the vertex coordinates (13, 27) into the equation

27 = a(13 - 13)² + 27

27 = a(0) + 27

27 = 27

Hence , the equation representing the path of Al's toss is y = a(x - 13)² + 27, where 'a' can be any real number

To learn more about parabola click :

https://brainly.com/question/24042022

#SPJ1

Answer:

The answer would be the 3rd option. 4^21/5^6.

Step-by-step explanation:

the rule in the image applys here. x is 4 and y is 5. a and b is the exponents so a is 7 and b is 2. c is your 3. a times c. b times c.

The coordinates of the point D that partitions the segment in ration 1:2 is D = (4. 3).

The line segment is divided into two pieces by a point, which may or may not be equal. If we know the coordinates of the point, we may calculate the ratio by which the supplied line segment is divided. Also, if we are aware of the ratio that the line segment connecting two places has produced, we may locate the point of division. The two may be accomplished using a section formula from coordinate geometry.

The position of a point that splits a line segment connecting two points into two portions with a length ratio of m:n is found using the section formula.

The coordinates of the point A and B from the given figure is:

A = (1, 3) and B = (10, 3)

The section formula is given as:

(x, y) = (mx2 + nx1 / m+n , my2 + ny1 / m+n)

Substitute the values of m = 1 and n = 2, and the coordinates of the point A and B.

(x, y) = ((1)(10) + (2)(1)/ 3 , (1)(3) + (2)(3) 3)

D(x,y) = (4, 3)

Hence, the coordinates of the point D that partitions the segment in ration 1:2 is D = (4. 3).

Learn more about section formula here:

https://brainly.com/question/30242641

#SPJ1

Answer:

how are you supposed to solve that??? I'm confused ://

The sum of the remainders is 10. This result is independent of the value of x and holds true for any five consecutive positive integers.

Arbitrary positive integer is any positive integer that is chosen without any particular reasoning or pattern. This can also refer to any number that is randomly chosen or assigned.

Let the original numbers be x, x+1, x+2, x+3, and x+4, where x is an arbitrary positive integer.

Then, their modulo 5 values are x mod 5, (x+1) mod 5, (x+2) mod 5, (x+3) mod 5, and (x+4) mod 5.

Now, let's calculate the sum of these modulo 5 values.

x mod 5 + (x+1) mod 5 + (x+2) mod 5 + (x+3) mod 5 + (x+4) mod 5

= x mod 5 + x mod 5 + 1 + x mod 5 + 2 + x mod 5 + 3 + x mod 5 + 4

= 5x mod 5 + 10

= 0 + 10

= 10

Hence, the sum of the remainders is 10.

This result is independent of the value of x and holds true for any five consecutive positive integers.

This is because when modulo 5 is applied to any set of five consecutive numbers, each number in the set will have an entry in the modulo 5 table, and the sum of the entries in the table is 10.

For more questions related to modulo

https://brainly.com/question/29262253

#SPJ1

Answer:

a=30 degrees

Step-by-step explanation:

the rule is that all 3 angles of a triangle added together equal 180

We know 2 of them the one clearly marked is 60 degrees

The one with the square as an angle means that it is a right angle meaning it’s 90 degrees

Add them together to get 90+60=150

Then subtract it from 180 to get 180-150=30

So a is 30 degrees

Hopes this helps please mark brainliest

Answer:

Step-by-step explanation:

f(x)= 12x2+5 should be written as  f(x) = 12x^2 + 5; the " ^ " symbol signifies exponentiation and is mandatory.

Here's how we find the inverse function.

1.  Apply the horizontal line test.  if a horizontal line intersects the graph in more than one place, the function is not one-to-one and does not have an inverse for all x.  However, if we focus on only [0, infinity), this part of the graph does have an inverse, which we can find as follows:

2.  Replace 'f(x)' with 'y:  y = 12x^2 + 5

3.  Interchange x and y:  x = 12y^2 + 5

                                                              x - 5

4.  Solve for y:  12y^2 = x - 5;   y^2 = ------------

                                                                12

                          x - 5

               y = √(----------)

                             12

Answer:

v = -15

Step-by-step explanation:

-25 = v - 10    (add 25 to both sides)

0 = v - 10 + 25

0 = v + 15   (subtract 15 from both sides)

0 - 15 = v + 15 - 15

-15 = v

v = -15

Hope this helps.

Answer:

if you're finding v it's (-15)

Step-by-step explanation:

you do the reverse. so first you add 10 to each side and cancel out -10 then you add -25+positive 10and get -15=v

The length of a truck is an example of a continuous data set, and 20 feet is just one possible value within that range.

The given value, "a truck with a length of 20 feet," is an example of a continuous data set.

Continuous data refers to values that can take on any numerical value within a range, with no gaps or interruptions. In this case, the length of a truck can take on any value between 0 and some maximum length, with no gaps or interruptions in between.

In contrast, discrete data refers to values that can only take on certain specific values, usually integers. For example, the number of tires on a truck is a discrete data set because it can only take on integer values (e.g. 4, 6, 8).

For more such questions on continuous data

https://brainly.com/question/17141874

#SPJ4  

When the weight of the child changes, the amount of medication they receive will also change in proportion to their weight. For example, if the child's weight increases from 20 lbs to 40 lbs, they would need twice as many teaspoons of medicine; if their weight decreases from 20lbs to 10lbs, they would require one half as much medicine.

Answer:

You will need to find the ratio of how much medication to every 1 pound then you will see how much the child weighs then the number of teaspoons will change once the child has gained another 20 pounds.

Step-by-step explanation:

The range for the scores is 1.0 (from 9.9 to 8.9). The range is the difference between the highest and lowest numbers in a set of numbers. In this case, the highest score is 9.9 and the lowest score is 8.9, so the range is 1.0.

In mathematics, the range of a function can refer to one of two similar terms:

the common area of ​​the function

The image of the function

Given two groups X and Y, the binary relation f between X and Y is a (exact) function (X to Y), if there is a y in Y for every x in X, so f is associated with y. The sets X and Y are called the area of ​​f and the common domain, respectively.

The range is a measure of dispersion in a set of numbers. To find the range, you need to subtract the lowest score from the highest score. In this case, the scores for the Olympic gymnast are: 9.9, 9.8, 9.6, 9.5, 9.7, 9.1, 8.9, and 9.8.

First, identify the highest and lowest scores:
Highest score: 9.9
Lowest score: 8.9

Next, subtract the lowest score from the highest score:
Range = 9.9 - 8.9

The range for the scores is 1.0 (9.9 to 8.9).

Your answer: 1.0 (9.9 to 8.9)

Learn more about Range:

brainly.com/question/28135761

#SPJ11

Answer:

1. X-intercept

Step-by-step explanation:

Answer:

quadranttwo

linear

Step-by-step explanation:

1 across

quadranttwo

14 across

linear

Answer:

m+8n

Step-by-step explanation:

-(-m-8n)

When there is a - in front of an expression in parentheses, change the sign of each term in the expression

m + 8n

Answer:

m + 8n

Step-by-step Explanation

\( -(-m-8n) \\ = - \times ( - m) - \times (- 8n) \\ = m + 8n\)

The indicated probability of X is 0.99534. if the specified mean is 18 and the standard deviation is 5.

The given data is as follows:

Let normal distribution = X

specified mean = μ = 18

standard deviation = σ = 5

Probability = p(x ≥ 5)

To calculate the Z value, the following formula is used,

Z =(X - μ)/σ

The Value of X is given in the probability that is greater than or equal to 5. Let us assume that the value of X is 5. By substituting the above value in the Z formula, we get,

Z = ( 5 - 18)/5

Z = 2.6

By using a Z-scores table, the Value of Z at 2.6 is 0.99534. (The table is attached in figure).

Therefore we can conclude that the indicated probability is 0.99534

To learn more about indicated probabilities problems

brainly.com/question/20731887

#SPJ4

The measure of the amount of random sampling error in a survey's result is known as margin of error.

The margin of error is a statistical concept that quantifies the degree of uncertainty or sampling error associated with survey results. It provides an estimate of the range within which the true population parameter is likely to fall. The margin of error is typically expressed as a percentage and is based on the sample size and the level of confidence desired.

In survey research, random sampling error refers to the natural variability that occurs when a subset of individuals, known as the sample, is selected to represent a larger population. It arises because the sample is not an exact replica of the entire population. The margin of error takes into account this inherent variability and provides a measure of how much the survey results might deviate from the true population values.

A larger sample size generally leads to a smaller margin of error, as it reduces the random variability associated with sampling. Similarly, a higher level of confidence, such as 95% confidence level, results in a larger margin of error to account for a wider range of potential values.

By considering the margin of error, survey researchers can assess the reliability and precision of their findings, providing a range of values within which the true population parameter is likely to reside.

Learn more about subset here: https://brainly.com/question/31739353

#SPJ11

Meter, kilogram and time units of measure.

Everything around us has a measurement value, from the amount of sugar you put in a cake to the size of a football field. Each thing is measured differently based on its length, weight, volume, or duration. With these measurements, the idea of "Metric System" is introduced.

The Metric system has 3 main units namely, meter to measure the length, kilogram to measure the mass, and seconds to measure time.

Therefore, meter, kilogram and time units of measure.

Learn more about the Metric System here:

https://brainly.com/question/25966695.

#SPJ1

Answer:

?

Step-by-step explanation:

The given eqation is:

Notice that the slope of the line is 4

Recall that the slopes of parallel lines are equal

Hence the slope of the required line is 4.

Since the line passes through the point (5,1)

The equation is:

This is simplified to give:

Therefore the equation of the line is:

Answer:

8

Step-by-step explanation:

If it is proportional 3/3=1

And 24/3=8

Answer: go up the origin maybe that would help

Step-by-step explanation:

Answer:

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

The total cost of repair is expressed by the function:

As we see,

Therefore the answer is option A.

A hyperbolic model can be used to determine the position of a ship with the help of a hyperbola that describes the path of the ship with two stations acting as foci. When the center of the hyperbola is at the origin, and the stations are 340 miles apart, the equation of the hyperbola can be found.

If the ship is 154 miles west of the origin, the equation can be modified to obtain the location of the ship. Let the x-axis be the east-west direction with the origin at the center of the hyperbola. The y-axis will be the north-south direction with the center of the hyperbola as the origin. The distance between the stations is 340 miles; therefore, the distance between each focus and the center is equal to 170 miles.

The standard equation of a hyperbola is given by: `(x−h)²/a²−(y−k)²/b²=1`where (h,k) is the center of the hyperbola.  Since the center is at (0,0), a = 170. The distance from the center to the focus is c, and we know that 2a = 340, so a = 170, c = √(c² − a²) = √(340² − 170²) = 295.50. Therefore, the value of b is obtained using `c² = a² + b²`, which yields `b² = c² − a² = 295.50² − 170² = 17850.25. Solving for y, we get y = ±√(154²*17850.25/28900-17850.25) = ±128.53.Therefore, the ship's position is either 128.53 miles north or south of the origin.

To know more about hyperbola visit:

https://brainly.com/question/19989302

#SPJ11

The required line segment lengths are  AB = 8√2 units and BD= 8 units

In the given question, ΔABC, ΔABD, and ΔDBC are right-angled triangles.

It is also given that DC=AD = 8 units

AC=DC+AD

=8+8

=16 units

In ΔABC, from Trigonometry,

sin(∠BAC) =AB/AC

sin 45 = AB/16

1/√2 = AB/16

AB=16/√2 = 8√2

Again in ΔABC, from Trigonometry,

sin(∠BCA) =BC/AC

⇒ sin(45°) =BC/16

BC= 8√2

In ΔBCD, from Pythagoras theorem,

BC² = CD² + BD²

8√2² - 8² = BD²

BD²= 64×2 -64

BD=8 units.

To learn more on trigonometry click:

https://brainly.com/question/25122835

#SPJ4