Solve f(x) >0
F(x)= (x-1)(x+3)^2

Answer:

Step-by-step explanation:here is a example:Recall that the volume of a regular prism is given by the area of the base times the height.

Given that the base of the prism is a regular pentagon with an apothem of 2.8 centimeters.

The pentagon consist of 5 isosceles triangles with the apothem as the height and the side of the pentagon as the base.

Recall that the are of a triangle is given by 1/2 base times height.

Thus the area of of the pentagon base of the prism is given by

Therefore, the volume of the prism is given by volume=7x(2x+1)=14x2+7x

if angle m∠2 = 120°, then m∠7 is 120°.

An angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.

Supplementary angles are those angles that sum up to 180 degrees.

Given that  m∠2 = 120°.

We have to find the  m∠7.

m∠2  and m∠4 are supplementary angles.

120+m∠4=180

m∠4=60 degrees.

m∠4 is corresponding angle of m∠8.

m∠8 and m∠7 are again supplementary angles.

60+m∠7=180

m∠7=120 degrees.

Hence, if angle m∠2 = 120°, then m∠7 is 120°.

To learn more on Angles click:

brainly.com/question/28451077

#SPJ1

The system of equations for the given situation are 14=b-c ; 35=b+c and the speed of boat is 24.5 miles/hr and speed of current is 10.5 miles/hr.

Given,

Distance covered by boat in upstream in 3 hours = 42 miles

Distance covered by boat in downstream in 2 hours = 70 miles.

Let

speed of boat in still water be 'b'

speed of current of stream be 'c'

we know that distance=speed x time

If the boat is moving upstream, the current (which is 'c' miles per hour) will push against it, reducing the boat's speed by 'c' miles per hour. The boat's resulting speed (as it travels upstream) is 'b-c' miles per hour. If, on the other hand, the boat is travelling downstream, the current will push it faster, increasing the boat's speed by 'c' miles per hour. The boat's downstream speed is 'b+c' miles per hour as a result.

Then the system of equations will be

distance while going upstream ,

distance=speed x time

42=(b-c)(3)

14=b-c....i

distance while going downstream,

70=(b+c)(2)

35=b+c....ii

solving eq. i and eq. ii

14=b-c

35=b+c

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

49=2b

b=24.5

Substitute in eq. i,

14=24.5-c

c=24.5-14

c=10.5

Thus, the boat's speed is 24.5 miles per hour and the current's speed is 10.5 miles per hour.

To learn more about speed refer here

https://brainly.com/question/14354804

#SPJ4

we verified the intermidiate value theorem applies to the function f(x) = x^2 + 7x  + 1 . And the value of c is 2.

According to the given question.

We have a function.

f(x) = x^2 + 7x  + 1

As, we know that "the Intermediate Value Theorem (IVT) states that if f is a continuous function on [a,b] and f(a)<M<f(b), there exists some c∈[a,b] such that f(c)=M".

Now, we will apply the theorem for the given function f(x).

So,

f(0) = 0^2 +7(0) + 1 = 1

And,

f(9)=9² + 7(9) + 1 = 81 + 63 + 1 = 145

Here,  f(0) = 1< 19< 145 = f(9).

So, f is continous since it is a polynomial. Then the IVT applies, and such c exists.

To find, c,

We have to solve the quadratic equation f(c) =19.

This equation is

c² + 7c + 1 = 19.

Rearranging, c²+ 7c - 18=0.

Factor the expression to get

c² + 9c - 2c -18 = 0

⇒ c(c + 9) - 2( c + 9) = 0

⇒ (c - 2)(c + 9) = 0

⇒ c = 2 or -9

c = -9 is not possible beacuse it is not in the interval [0, 9].

So, the value of c is 2.

⇒ f(2) = 2^2 + 7(2) + 1 = 4 + 14 + 1 = 19

Hence, we verified the intermidiate value theorem applies to the function f(x) = x^2 + 7x  + 1 . And the value of c is 2.

Find dout more information about intermidiate value theorem here:

https://brainly.com/question/14456529

#SPJ4

Answer:

-5x+(- 15 ) = 20

x=-7

Step by Step

-5x+(-15)= 20 becomes

-5-15=20 add 15 tp (15 and 20)

-5x=35 ( divide by 51

x=-7

Answer:

sorry I didn't this answer

Answer:

see explanation

Step-by-step explanation:

The area (A) of a triangle is calculated as

A = \(\frac{1}{2}\) bh ( b is the base and h the perpendicular height )

(1)

b = 6 and h = 9 , then

A = \(\frac{1}{2}\) × 6 × 9 = 3 × 9 = 27 cm²

(2)

b = 3 and h = 5 , then

A = ×\(\frac{1}{2}\) × 3 × 5 = 1.5 × 5 = 7.5 cm²

(3)

b = 6 and h = 10 , then

A = \(\frac{1}{2}\) × 6 × 10 = 3 × 10 = 30 cm²

(4)

b = 8 and h = 14 , then

A = \(\frac{1}{2}\) × 8 × 14 = 4 × 14 = 56 cm²

(5)

b = 7 and h = 9 , then

A = \(\frac{1}{2}\) × 7 × 9 = 3.5 × 9 = 31.5 cm²

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

The figures are composed of a rectangle and a triangle

The area is the sum of the areas of the rectangle and the triangle

A = (5 × 4) + \(\frac{1}{2}\) × 5 × 4

   = 20 + 10

    = 30 cm²

(2)

A = (7 × 5) + \(\frac{1}{2}\) × 7 × 2

   = 35 + 7

    = 42 cm²

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

The area (A) of a trapezium is calculated as

A = \(\frac{1}{2}\) h (a + b)

where h is the perpendicular height and a, b the parallel bases

(1)

A = \(\frac{1}{2}\) × 5 × (7 + 11) = 2.5 × 18 = 45 cm²

(2)

A = \(\frac{1}{2}\) × 6 × (6.6 + 8.4) = 3 × 15 = 45 cm²

(3)

A = \(\frac{1}{2}\) × 4.3 × (9.1 + 7.1) = 2.15 × 16.2 = 34.83 cm²

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

The figure consists of a rectangle in the middle and 2 trapezium at the ends

A = \(\frac{1}{2}\) × 6 × (10 + 12) + (12 × 15) + \(\frac{1}{2}\) × 11 × (12 + 9)

    = 3 × 22 + 180 + 5.5 × 21

     = 66 + 180 + 115.5

     = 361.5 m²

Divide by 20 to find number of cans required

361.5 ÷ 20 = 18.075

Only whole tins can be bought , so 19 tins required

cost = 19 × £6 = £114

Answer: the opposite of 45 is......-45????

Step-by-step explanation: um your question is a little unclear, but the opposite of 45 is -45.

Answer:

the opposite of a number is just that number with a negative sign because it is flipped to the other side of zero

Step-by-step explanation:

i think that's what u wanted but the question was kind of unclear

Based on given details  i would say a reasonable expectation would be about 6 children .

Probability turned into added into arithmetic to are expecting the possibility of an occasion occurring. Probability essentially approach how in all likelihood it's miles that some thing will happen. This is the fundamental principle of possibility and is likewise utilized in possibility distributions to examine feasible consequences of random experiments.

For the question above, we will use probability.

after 4 children, there is 37.5% chance you have 2 boys/2 girls

after 5 children, there is 62.5% chance you have at least 2boys/2 girls

after 6 children, there is 78% chance you have at least 2boys/2 girls

after 8 children, there is 93% chance you have at least 2boys/2 girls ...

based on this i would say a reasonable expectation would be about 6 children

learn more about probability here :

brainly.com/question/11234923

#SPJ4

Answer: X = 6

Step-by-step explanation:

Answer:

The best way to decompose the composite figure to determine its area is as a semicircle, a trapezoid, and two rectangles. This way, we can use the following formulas to find the area of each part:

Area of a semicircle = 21​πr2, where r is the radius of the circle.

Area of a trapezoid = 21​(b1​+b2​)h, where b1​ and b2​ are the bases and h is the height of the trapezoid.

Area of a rectangle = l×w, where l is the length and w is the width of the rectangle.

Then, we can add up the areas of each part to find the total area of the composite figure. The other options are not as convenient because they either involve more parts or more complicated shapes. For example, option A would require finding the area of a triangle, which involves using trigonometry or the Pythagorean theorem. Option B would require finding the area of four triangles, which is more tedious than finding the area of two rectangles. Option C would require finding the area of a square, which is redundant because a square is a special case of a rectangle.

Step-by-step explanation:

The composite figure can be decomposed into a semicircle, a trapezoid, and two rectangles.

Option D is the correct answer.

It is a quadrilateral that has one pair of parallel sides and a height.

The area is calculated as: 1/2 x sum of the parallel sides x height.

Examples:

Area of a trapezium that has the parallel sides as 3 cm and 4 cm and a heght o 5 cm.

Area = 1/2 x (3 + 4) x 5

Area = 1/2 x 7 x 5

Area = 35/2 = 17.5 cm^2

We have,

The given figure can be decomposed into the following figure.

- Semicircle

- Trapezoid

- Two rectangles

Thus,

A semicircle, a trapezoid, and two rectangles.

Learn more about trapezium here:

https://brainly.com/question/22607187

#SPJ5

Answer:

3/4

Step-by-step explanation:

The approximate probability of exactly two people in a group of seven having a birthday on April 15 is (C) \(7.4 x 10^-^6\)

To calculate the probability of exactly two people in a group of seven having a birthday on April 15, we can use the binomial distribution formula:

\(P(X = k) = C(n, k) * p^k * (1 - p)^(^n^-^k^)\)

Where:

So, plugging in the values, we get:

\(P(X = 2) = C(7, 2) * (1/365)^2 * (1 - 1/365)^(7 - 2)\)

\(= 21 * (1/365)^2 * (364/365)^5\)

\(= 2.38 x 10^-5\)

The probability of exactly two people in a group of seven having a birthday on April 15 can be calculated using the binomial distribution formula.

The formula takes into account the number of trials, the probability of success in a single trial, and the number of successes desired.

In this case, we want to find the probability that exactly two people in a group of seven have a birthday on April 15, assuming that all days of the year are equally likely for a birthday.

Plugging in the values into the formula gives us an approximate probability of \(7.4 x 10^-^6\), which is the answer (C).

Learn more about Approximate probability

brainly.com/question/15696262

#SPJ11

The probability that it will snow at least once during the next three days is $\frac{26}{27}$.

To find the probability that it will snow at least once during the next three days, it is easier to first calculate the probability that it will NOT snow at all in those three days and then subtract that value from 1.

The probability of no snow for one day is 1 - $\frac{2}{3}$ = $\frac{1}{3}$.

For three days, the probability of no snow on all three days is the product of the individual probabilities:
($\frac{1}{3}$) * ($\frac{1}{3}$) * ($\frac{1}{3}$) = $\frac{1}{27}$.

Now, to find the probability of it snowing at least once during those three days, subtract the probability of no snow on all three days from 1:

1 - $\frac{1}{27}$ = $\frac{26}{27}$.

So, the probability that it will snow at least once during the next three days is $\frac{26}{27}$.

to learn more about probability click here:

brainly.com/question/29221515

#SPJ11

Answer:

The line segment that is a radius is FD.

Hope it will help:)❤

Descriptive statistics is a branch of statistics that deals with the collection, analysis, interpretation, and presentation of data. It focuses on summarizing and describing the characteristics of a sample or population. The purpose of descriptive statistics is to provide a clear and concise summary of the data, including measures of central tendency, variability, and distribution.

True,This information can be used to make inferences about the population as a whole. Therefore, descriptive statistics helps statisticians to better understand and interpret the population data.

False, Descriptive statistics is a branch of statistics that focuses on summarizing and organizing data from a sample or population. It provides insights into the basic features of the data, such as the mean, median, and standard deviation, but does not make inferences about the population.

To learn more about statistics : brainly.com/question/31577270

#SPJ11

Answer:

yes maam

Step-by-step explanation:

you know it

answer:

see explanation.

step-by-step explanation:

for all the x values, subtract 1 and for all y values, subtract 3. the end result should be more left and more down than the original shape. hope that helps!

Answer:

t-(-1,-3)     y-(-4,1)    m-(-4,-3)   q-(-3,-3)

Step-by-step explanation:

becuaes you subtrace on on each xvariable and you subtracte 3 on every y varibale

A number that represents the property of the sample is the statistics.

Statistics refer to that number that describes a particular property of a sample set of numbers. It is the common property shared by all the numbers of the sample set. It involves the collection of data and information and then categorizing them according to their properties and inferences.

'Mean and proportion' is mathematical calculations that can be carried out on statistic number sets.

Mean refers to the average of the number set that is provided to us. It is calculated by adding the numbers and dividing them by the number of terms.

Proportion refers to the fraction of the number set according to some characteristics shared by the numbers.

To know more about mean and proportion,

https://brainly.com/question/24232216

#SPJ4

The derivative of the function is

A) dw/dz=z^5 (7z-18)

B) dh/dx=192x^11+36x^5-6x^2+19

C) dy/dx=24x^2-38x-15

In mathematics, the derivative of a function measures the sensitivity to change of the function value with respect to a change in its argument. It is the rate of change of a function with respect to a variable.

A) w = z^7 – 3z^6 + 14

dw/dz=7z^6-18z^5

dw/dz=z^5 (7z-18)

B) h(x) = 16x^12 + 6x^6 – 2x^3 + 19x – 7

dh/dx=192x^11+36x^5-6x^2+19

C) y = (8x + 5)(x^2 – 3x)

dy/dx=  d/dx  [8x+5]*〖(x〗^2-3x)+(8x+5)*d/dx[x^2-3x]

dy/dx=(8*  d/dx  [x}+d/dx[5])*〖(x〗^2-3x)+(8x+5)*(d/dx[x^2]-3 d/dx[x])

dy/dx=(8*1+0)(x^2-3x)+(8x+5)(2x-3*1)

dy/dx=8(x^2-3x)+(2x-3)(8x+5)

dy/dx=24x^2-38x-15

Note: The question is incomplete. The complete question probably is: Find the derivative of the following function: A) w = z^7 – 3z^6 + 14 B) h(x) = 16x^12 + 6x^6 – 2x^3 + 19x – 7 C) y = (8x + 5)(x^2 – 3x).

Learn more about Derivative:

https://brainly.com/question/23819325

#SPJ4

Answer:

24

Step-by-step explanation:

14 - (-10)

Subtracting a negative is like adding

14+10

24

Answer:

24

Step-by-step explanation:

14 - ( - 10 )

14 + 10

add the numbers

24

a) There are 27,405 solutions to the equation x₁ + x₂ + x₃ + x₄ + x₅ = 25 with no restrictions.

b) There are 1,001 solutions to the equation x₁ + x₂ + x₃ + x₄ + x₅ = 25, with xi ≥ 3 for i = 1, 2, 3, 4, 5.

c) There are 5,561 solutions to the equation x₁ + x₂ + x₃ + x₄ + x₅ = 25, where 3 ≤ x₁ ≤ 10.

d) There are 780 solutions to the equation x₁ + x₂ + x₃ + x₄ + x₅ = 25, where 3 ≤ x₁ ≤ 10 and 2 ≤ x₂ ≤ 7.

a) No Restrictions:

In this arrangement, the first urn contains 5 balls, the second urn contains 3 balls, the third urn contains 9 balls, and the fourth urn contains 8 balls.

By applying this method, we need to find the number of ways we can arrange the 25 balls and 4 separators. The total number of positions in this arrangement is 29 (25 balls + 4 separators). We choose 4 positions for the separators from the 29 available positions, which can be done in "29 choose 4" ways. Therefore, the number of solutions to the equation x₁ + x₂ + x₃ + x₄ + x₅ = 25 with no restrictions is:

C(29, 4) = 29! / (4! * (29 - 4)!) = 27,405.

b) xi ≥ 3 for i = 1, 2, 3, 4, 5:

In this case, each xi should be greater than or equal to 3. We can use a similar approach to the previous case but with a few modifications. To ensure that each variable is at least 3, we subtract 3 from each variable before distributing the balls. This effectively reduces the equation to x₁' + x₂' + x₃' + x₄' + x₅' = 10, where x₁' = x₁ - 3, x₂' = x₂ - 3, and so on.

Now, we have 10 balls (representing the value of 10) and 4 urns (representing the variables x₁', x₂', x₃', and x₄'). Using the stars and bars method, we can determine the number of ways to arrange these balls and separators. The total number of positions is 14 (10 balls + 4 separators), and we need to choose 4 positions for the separators from the 14 available positions.

Therefore, the number of solutions to the equation x₁ + x₂ + x₃ + x₄ + x₅ = 25, where each xi is greater than or equal to 3, is:

C(14, 4) = 14! / (4! * (14 - 4)!) = 1001.

c) 3 ≤ x₁ ≤ 10:

Now, we have a specific restriction on the value of x₁, where 3 ≤ x₁ ≤ 10. This means x₁ can take any value from 3 to 10, inclusive. For each value of x₁, we can determine the number of solutions to the reduced equation x₂ + x₃ + x₄ + x₅ = 25 - x₁.

Using the stars and bars method as before, we have 25 - x₁ balls and 4 urns representing the variables x₂, x₃, x₄, and x₅. The total number of positions is 25 - x₁ + 4, and we need to choose 4 positions for the separators from the available positions.

By considering each value of x₁ from 3 to 10, we can calculate the number of solutions to the equation for each case and sum them up.

Therefore, the number of solutions to the equation x₁ + x₂ + x₃ + x₄ + x₅ = 25, where 3 ≤ x₁ ≤ 10, is:

∑(C(25 - x₁ + 4, 4)) for x₁ = 3 to 10.

By evaluating this sum, we find that there are 5,561 solutions.

d) 3 ≤ x₁ ≤ 10 and 2 ≤ x₂ ≤ 7:

In this case, we have restrictions on both x₁ and x₂. To count the number of solutions, we follow a similar approach as in the previous case. For each combination of x₁ and x₂ that satisfies their respective restrictions, we calculate the number of solutions to the reduced equation x₃ + x₄ + x₅ = 25 - x₁ - x₂.

By using the stars and bars method again, we have 25 - x₁ - x₂ balls and 3 urns representing the variables x₃, x₄, and x₅. The total number of positions is 25 - x₁ - x₂ + 3, and we choose 3 positions for the separators from the available positions.

We need to iterate over all valid combinations of x₁ and x₂, i.e., for each value of x₁ from 3 to 10, we choose x₂ from 2 to 7. For each combination, we calculate the number of solutions to the equation and sum them up.

Therefore, the number of solutions to the equation x₁ + x₂ + x₃ + x₄ + x₅ = 25, where 3 ≤ x₁ ≤ 10 and 2 ≤ x₂ ≤ 7, is:

∑(∑(C(25 - x₁ - x₂ + 3, 3))) for x₁ = 3 to 10 and x₂ = 2 to 7.

By evaluating this double sum, we find that there are 780 solutions.

To know more about equation here

https://brainly.com/question/21835898

#SPJ4

Answer:

10km

Step-by-step explanation:

20 - 10 = 10.

Answer: Reuben runs 10km

Step-by-step explanation: Amos' 20km - Amos' additional 10km = 10km

Step-by-step explanation:

Divide a percentage by 100% to convert it.

=> (1/20%) / 100% = 0.0005 or 1/2000.

The simplified form of expression 25a-5x is 5(a.5-1.x)

An algebraic expression is consists of variables, numbers with various mathematical operations,

The given expression is,

25a-5x

The expression can be written as,

5.5a-5x

Take 5 common from the expression,

5(5a-x)

To know more about Algebraic expression on:

https://brainly.com/question/19245500

#SPJ1

Answer:

120

Step-by-step explanation:

The value of x that makes the equation true is x = 16/9.

To solve for x in the equation 27=13(6x−9)+3x, we first simplify the right-hand side by distributing the 13:

27 = 78x - 117 + 3x

Then, we can combine like terms by adding 117 to both sides:

144 = 81x

Finally, we isolate x by dividing both sides by 81:

x = 144/81 = 16/9

This means that if we substitute x = 16/9 into the original equation, both sides will be equal.

In the context of the problem, this value of x represents the solution that satisfies the equation. It indicates that the given equation is consistent and has a unique solution for x.

To learn more about equation here:

https://brainly.com/question/29657983

#SPJ1

Answer:

student 3 i think yea

Step-by-step explanation:

Answer:

I have know idea what the answer is