Ron chose 45 square units as his answer. Why is this answer incorrect?

The slope of the line that divides the region bounded by the parabola \(y=5x-3x^2\)and the x-axis into two regions with equal area is 5.

To find the slope of the line that divides the region into two equal areas, we need to determine the point of intersection between the parabola and the x-axis. Since the line passes through the origin, its equation will be y = mx, where m represents the slope.

Setting the equation of the parabola equal to zero, we find the x-values where the parabola intersects the x-axis. By solving the equation\(5x - 3x^2 = 0\), we get x = 0 and x = 5/3.

To divide the region into two equal areas, the line must pass through the midpoint between these x-values, which is x = 5/6. Plugging this value into the equation of the line, we have y = (5/6)m.

Since the areas on both sides of the line need to be equal, we can set up an equation using definite integrals. By integrating the equation of the parabola from 0 to 5/6 and setting it equal to the integral of the line from 0 to 5/6, we can solve for m. After performing the integration, we find that m = 5.

Therefore, the slope of the line that divides the region into two equal areas is 5.

Learn more about: Parabola

brainly.com/question/11911877

#SPJ11

The angle between the vectors can be found using the dot product. The formula is θ= |A| =√(x12 + y12 + z12) The angle between the vectors -2i + 3j + k and i + 2j - 4k is approximately 137.8 degrees.

v1 • v2 = (-2i + 3j + k) • (i + 2j - 4k)

= -2 - 6 + 1 = -7

|v1| = \(\sqrt{((-2)^2 + 3^2 + 1^2)}\)

=\(\sqrt{(4 + 9 + 1)}\)

=\(\sqrt{14}\)

|v2| = \(\sqrt{((1)^2 + 2^2 + (-4)^2)}\)

= \(\sqrt{(1 + 4 + 16) }\)

= (\(\sqrt{21}\)

θ= |A| (-7/\(\sqrt{14}\)\(\sqrt{21}\))

=  |A| (-7/21*14)

=  |A|(-7/294)

= 137.8 degrees

The angle between two vectors can be found using the dot product formula. This formula isθ= |A| =√(x12 + y12 + z12). In the case of the vectors -2i + 3j + k and i + 2j - 4k, this formula can be used to find the angle between them. The dot product of the two vectors is -2 - 6 + 1 = -7. The magnitude of the first vector, |v1|, can be found using the Pythagorean theorem, which is

\(\sqrt{((-2)^2 + 3^2 + 1^2)}\)

= \(\sqrt{(4 + 9 + 1)}\)

= \(\sqrt{14}\).

The magnitude of the second vector, |v2|, can be found using the Pythagorean theorem, which is

\(\sqrt{((1)^2 + 2^2 + (-4)^2)}\)

= \(\sqrt{(1 + 4 + 16)}\)

= \(\sqrt{21}\)

Once the dot product and magnitudes are known, the angle between the two vectors can be found using the formula .Therefore, the angle between the two vectors is approximately 137.8 degrees.

Learn more about vector here

https://brainly.com/question/15709504

#SPJ4

Answer:

x = 17

Step-by-step explanation:

Answer:

X=35

Step-by-step explanation:

all angles on a straight line equal 180 degrees

there fore the equation for x will be,

180= 40+(2X+30)+40

180=40+ 2X +30+40

180 =2X+110

180-110=2X

70=2X

70/2=X

35=X

Answer:

sorry I can't understand this question

Step-by-step explanation:

im busy sorry

Answer:

∠2 = 80°

Step-by-step explanation:

∠1 and ∠2 are supplementary angles (their sum is 180°)

Add the 3 ratios together: 1 + 3 + 2 = 6

Divide perimeter by total:

30/6 = 5

Multiply each ratio by 5:

1 x 5 = 5

3 x 5 = 15

2 x 5 = 10

The greatest side is 15 cm

Answer:

The slope of this linear equation is -5/2x.

Answer:

(25x * 4y * 2z) + (15x * 2y^3)

10xy(20z + 3y^2)

(if you want working, just comment [too much effort lol])

The relationship between the distance S and time t is:2t^2 = (1/2)a1t^2 + v2t + (1/2)a2t^2.

Let the velocity and acceleration of the first car be v1 and a1 respectively.The velocity of the second car be v2 and acceleration be a2.Let the distance between the two cars at any time after t=0 be given by S.If the initial distance between them is 50 feet, then S=S0+50ft where S0 is the distance between them at time t=0.

From the given conditions, we can set up the following relationships for the two cars.1) For the first car:S=ut+(1/2)at^2 where u is the initial velocity.

2) For the second car:S=vt+(1/2)at^2 where v is the initial velocity.In the first equation, we can substitute u=0 (since it started from rest) and a=a1.

In the second equation, we can substitute v=50ft (since it is 50ft behind) and a=a2.

Substituting the above values in the above two equations, we get:S= (1/2)a1t^2 and

S= 50ft + v2t + (1/2)a2t^2

From the problem statement, we are also given that the lead car is accelerating in such a way that the distance S in feet between the two cars at any time t after t=0 seconds is 50 more than twice the square of t.

Therefore,S = 2t^2 + 50ft

We can now equate the above two expressions for S, and solve for t, to get the relationship between the distance S and time t:

S = 2t^2 + 50ft = (1/2)a1t^2 + 50ft + v2t + (1/2)a2t^2

Simplifying the above expression, we get:2t^2 = (1/2)a1t^2 + v2t + (1/2)a2t^2

Therefore, the relationship between the distance S and time t is:2t^2 = (1/2)a1t^2 + v2t + (1/2)a2t^2.

Know more about acceleration here,

https://brainly.com/question/2303856

#SPJ11

Initially, only one person had heard the rumor.

The answer is b.

We have the following information available from the question is:

The function  \(N(t) =\frac{300}{1+299e^ \\,0.36t}\) describes the spread of a rumor among a group of people in an enclosed space.

Where,

N represents the number of people who have heard the rumor,

and t is measured in minutes since the rumor was started.

Now, According to the question:

The function is:

\(N(t) =\frac{300}{1+299e^ \\,0.36t}\)

And, we put t = 0 we get :

\(N(0) =\frac{300}{1+299e^ \\,0.36(0)}\)

\(N(t) =\frac{300}{1+299e^ \\0}\)

\(N(t) =\frac{300}{1+299}\\\\N(t) =\frac{300}{300} = 1\)

Hence, Initially, only one person had heard the rumor.

The answer is b.

Learn more about Function at:

https://brainly.com/question/30721594

#SPJ4

Complete question is:

The function N(t)=300/(1+299e^-0.36t) describes the spread of a rumor among a group of people who have heard the rumor, and (t) is measured in minutes since the rumor was started. Which of the following statements are true?

a. The rate at which the rumor spreads speeds up over time.

b. Initially, only one person had heard the rumor.

c. It will take approx. 14 mins for 100 people to hear the rumor.

d. There are 299 people in the enclosed space.

Answer:

D, 23

Step-by-step explanation:

In order to find b use sin

Sin (30) = b/46

Sin (30) = b/46b = sin (30) × 46

Sin (30) = b/46b = sin (30) × 46b = 1/2 × 46

Sin (30) = b/46b = sin (30) × 46b = 1/2 × 46b = 23

Answer:

8 in or .67

Step-by-step explanation:

Answer:

1 foot

Step-by-step explanation:

he used up 3/4 of it so 16x0.75=12 to find remaining length subtract 16-12=4

so there is a 4 foot board left then he gives 1/4 of that to his brother 4x0.25=1

so he gave his brother 1 foot of wood

The probability that at least one bulb out of 12 will stop working during holiday season making all of lights go out on string is given by 0.2153.

Number of bulbs working throughout the holiday season = 12

Chance of each bulb working throughout the holiday season = 98%

Let A be the event that at least one bulb stops working during the holiday season, .

Making all of the lights go out, and let B be the event that all bulbs work throughout the holiday season.

Find P(A), the probability of event A.

Use the complement rule to find P(A),

P(A) = 1 - P(B)

To find P(B), we need to calculate the probability that each of the twelve bulbs works throughout the holiday season,

0.98¹² = 0.7847

So, the probability that all bulbs work throughout the holiday season is 0.7847.

This implies,

P(A) = 1 - P(B)

       = 1 - 0.7847

       = 0.2153

Therefore, probability that at least one bulb will stop working during  holiday season, making all of the lights go out on the string is 0.2153.

learn more about probability here

brainly.com/question/13369746

#SPJ4

By applying interior angles of triangles concept, it can be calculated that:

Triangle is a 2D shape that is bounded by three sides and has three vertices.

The three interior angles of triangles will always have a sum of 180°.

ΔABC:

            ∠A + ∠B + ∠C = 180°

4x + (7x - 2) + (5x - 10) = 180°

                       16x - 12 = 180°

                              16x = 192°

                                  x = 12°

Thus, ∠A = 4x = 4*12 = 48°

∠B = 7x - 2 = 7*12 - 2 = 82°

∠C = 5x - 10 = 5*12 - 10 = 50°

ΔDEF:

     ∠D + ∠E + ∠F = 180°

3x + 18x + (5x - 2) = 180°

                26x - 2 = 180°

                      26x = 182°

                           x = 7°

Thus, ∠D = 3x = 3*7 = 21°

∠E = 18x = 18*7 = 126°

∠F = 5x - 2 = 5*7 - 2 = 33°

ΔGHI:

 ∠G + ∠H + ∠I = 180°

16x + 16x + 13x = 180°

                 45x = 180°

                      x = 4°

Thus, ∠G = 16x = 16*4 = 64°

∠H = 16x = 16*4 = 64°

∠I = 13x = 13*4 = 52°

ΔJKL:

                  ∠J + ∠K + ∠L = 180°

(x + 8) + (6x - 5) + (2x - 3) = 180°

                                    9x = 180°

                                      x = 20°

Thus, ∠J = x + 8 = 20 + 8 = 28°

∠K = 6x + 5 = 6*20 - 5 = 115°

∠L = 2x - 3 = 2*20 - 3 = 37°

ΔMNO:

∠M + ∠N + ∠O = 180°, if ∠M = x, then:

     x + 5x + 4x = 180°

                  10x = 180°

                      x = 18°

Thus, ∠M = x = 18°

∠N = 5x = 5*18 = 90°

∠O = 4x = 4*18 = 72°

To learn more about interior angles of triangles, click here: https://brainly.com/question/7888180

#SPJ1

Solution of the equation 6∧²ˣ+2.6∧³ˣ=1x

here;

2x+3x = 1x

5x = 1 x

x= -1 / 5

By isolating the variable on one side, the equation with one variable may be solved.

A linear equation in one variable is one that contains just one variable of order 1. It has the formula axe + b = 0, where x is a variable.

There is just one solution to this equation. Here are a few examples:

3x = 1\s22x-1=0

4x+9=-11

Linear Equations in One Variable Standard Form

The conventional form of a linear equation in one variable is:

Where, axe + b = 0,

The letters 'a' and 'b' are genuine numerals.

'a' and 'b' are both greater than zero.

Thus, the linear equation formula in one variable is axe + b = 0.

Linear Equations in a Single Variable

The procedures below are used to solve an equation with only one variable.

Step 1: Using LCM, clear the fractions if necessary.

any.

Step 2: Reduce the complexity of both sides of the equation.

Step 3: Identify the variable.

Step 4: Double-check your solution.

Learn more about one variable from here;

https://brainly.com/question/11934411

#SPJ1

Answer:

Parallelogram formula- 1/2 x base xheight

Step-by-step explanation:

The failure of beta cells to function can result in a condition called diabetes mellitus.

Beta cells are specialized cells located in the pancreas that produce and release insulin. A hormone responsible for regulating blood sugar levels. When beta cells fail to function properly, it can lead to two main types of diabetes:

1. Type 1 Diabetes: In this autoimmune disease, the immune system mistakenly attacks and destroys the beta cells in the pancreas, resulting in little to no insulin production.

Without sufficient insulin, glucose (sugar) cannot enter the body's cells for energy, leading to high blood sugar levels.

2. Type 2 Diabetes: This form of diabetes is characterized by insulin resistance, where the body's cells become less responsive to the effects of insulin.

Over time, the beta cells may also fail to produce enough insulin to compensate for the increased demand. Type 2 diabetes is often associated with factors such as obesity, sedentary lifestyle, and genetic predisposition.

The failure of beta cells to function properly disrupts the normal regulation of blood sugar, leading to elevated glucose levels and potential complications associated with diabetes.

To know more about beta cells refer here:

https://brainly.com/question/6380474

#SPJ11

Answer:

perimeter = 96.8 m

Step-by-step explanation:

the sides of a square are congruent , then perimeter (P) is calculated as

P = 4s ( s is the side length )

the area (A ) of a square is calculated as

A = s²

given A = 585.64 , then

s² = 585.64 ( take square root of both sides )

s = \(\sqrt{585.64}\) = 24.2

Then

P = 4 × 24.2 = 96.8 m

Answer:

= 96.8 m

Step-by-step explanation:

Area of a square = side²

Perimter of a square = 4*side

Then:

585.64 = side²

√585,64 = √side²

it is a geometric figure, therefore, only the positive value will be obtained

24.2m = side

Perimeter = 4*side

Perimeter = 4*24.2

Answer:

-8 can be added to 2 to give us -6

Step-by-step explanation:

hopefully this helps :)

Answer:

37.25

Step-by-step explanation:

I THINK

Answer:

Arithmetic sequence

Step-by-step explanation:

An list of numbers whereby the difference between each consecutive number is constant is called an arithmetic sequence. Given thelistvif numbers:

–8, –4, 0, 4, 8, 12 ;

We can see that each consecutive number in the list has a constant difference of 4. Hence x this is called an arithmetic sequence.

The equation of the regression line for the given data can be determined by performing linear regression analysis.

The regression line represents the best-fit straight line that describes the relationship between the independent variable (number of years studied) and the dependent variable (proficiency exam grades). The equation of the regression line can be expressed as y = a + bx, where y is the predicted value of the dependent variable, x is the independent variable, a is the y-intercept, and b is the slope of the line.

To find the equation of the regression line, we first need to calculate the slope and y-intercept using the given data. We can use statistical software or a calculator to perform the regression analysis and obtain the values of a and b. Once we have these values, we can plug them into the equation of the regression line to get the final equation.

Learn more about regression analysis here:

https://brainly.com/question/31873297

#SPJ11

Answer:

Step-by-step explanation:

d = 96 inches

\(T_{max}=\dfrac{2*96}{3}+5\\\\\\=2*32 + 5\\\\= 64 + 5 \\\\T_{max} =69 \ inches\\\\\\\\T_{min}=\dfrac{96}{3}-2\\\\\\=32-2\\\\T_{min}= 30 \ inches\)

Answer:

The answer is, cool balls 420

Answer: A

Step-by-step explanation:

If they are similar, that means the proportions for corresponding sides will be the same.

          I personally ignore the picture and use the labels of "triangle RST and triangle XYZ" that the problem gives because the XYZ picture is not lined up with the similarity it has with RST.

(A) says that side ST is corresponding with side YZ,

          [] Triangle RST and triangle XYZ

          -> Correct

(A) also says that side RT is corresponding with size XZ,

          [] Triangle RST and triangle XYZ

          -> Correct

               This means that option A is the correct answer.

correct answer is option C, i.e. vertical shrink by a factor of 1/6.

Given:

Two graphs are given, one is of f(x) = x^4 and other is of b(x)=6x^4.

Find:

we have to find the correct option.

Explanation:

when we transformed the graph

The first part is half of the second part. The first part is 16 and the second part is 8.

Simplifying means making something easier to do or comprehend, as well as making something less difficult.

Let the first part is x, y os the second part, and the no of half times is z then the equation is;

x × y = z

16×(1/2) = 8

Hence,the first part is half of the second part. The first part is 16 and the second part is 8.

To learn more about the simplification, refer to:

https://brainly.com/question/23509407

#SPJ1

a) Number of bit string = 220

b)  Number of bit string = 299

c)  Number of bit string = 4017

d)  Number of bit string = 924

Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of the selection is irrelevant.

Given:

a) n= 12, r= 3

\(^{12}C_3\) = 12! / 3! 9 !

      = 12 x 11 x 10 x 9! / 3 x 2 x 9!

      = 220

b)  n= 12, r ≤ 3

\(^{12}C_3\) = 12! / 3! 9 !

      = 12 x 11 x 10 x 9! / 3 x 2 x 9!

      = 220

\(^{12}C_2\) = 12! / 2! 10 !

      = 12 x 11 x 10! / 2 x 10!

      = 66

\(^{12}C_1\) = 12! / 1! 11!

      = 12

\(^{12}C_0\) = 12! / 0! 12 !

      = 12 x 11 x 10 x 9! / 3 x 2 x 9!

      = 1

So, total number of bit strings = 220 +66 + 12 +1 =299

c)  n= 12, r ≥ 3

\(^{12}C_3\) = 12! / 3! 9 !

      = 12 x 11 x 10 x 9! / 3 x 2 x 9!

      = 220

\(^{12}C_4\) = 495

\(^{12}C_5\) = 792

\(^{12}C_6\) = 924

\(^{12}C_7\) = 792

\(^{12}C_8\) = 495

\(^{12}C_9\) = 220

\(^{12}C_{10\) = 66

\(^{12}C_{12\) = 12

\(^{12}C_{12\) = 1

So, total String= 4017

d)  n= 12 and r= 6

\(^{12}C_6\) = 12!/ 6! 6!

       = 12 x 11 x 10 x 9 x 8 x 7 x 6! / 6! 6!

       = 924

Learn more about Combination here:

https://brainly.com/question/28720645

#SPJ1