1.5+r=3 show work and soultion​

Answer:

f(x) = x³ - 4x + 6

f'(x) = 3x² - 4

a) f'(2) = 3(2²) - 4 = 12 - 4 = 8

6 = 8(2) + b

6 = 16 + b

b = -10

y = 8x - 10

b) 3x² - 4 = 0

3x² = 4, so x = ±2/√3 = ±(2/3)√3

= ±1.1547

f(-(2/3)√3) = 9.0792

f((2/3)√3) = 2.9208

c) 3x² - 4 = 8

3x² = 12

x² = 4, so x = ±2

f(-2) = (-2)³ - 4(-2) + 6 = -8 + 8 + 6 = 6

6 = -2(8) + b

6 = -16 + b

b = 22

y = 8x + 22

f(2) = 6

y = 8x - 10

The equation perpendicular to the tangent is y = -1/8x + 25/4

-The smallest slope on the curve is 2.92

The curve has the smallest slope at the point (1.15, 2.92)

The equations at tangent points are y = 8x + 16 and  y = 8x - 16

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

y = x³ - 4x + 6

Differentiate

So, we have

f'(x) = 3x² - 4

The point is (2, 6)

So, we have

f'(2) = 3(2)² - 4

f'(2) = 8

The slope of the perpendicular line is

Slope = -1/8

So, we have

y = -1/8(x - 2) + 6

y = -1/8x + 25/4

We have

f'(x) = 3x² - 4

Set to 0

3x² - 4 = 0

Solve for x

x = √[4/3]

x = 1.15

So, we have

Smallest slope = (√[4/3])³ - 4(√[4/3]) + 6

Smallest slope = 2.92

So, the smallest slope is 2.92 at (1.15, 2.92)

Here, we set f'(x) to 8

3x² - 4 = 8

Solve for x

x = ±2

Calculate y at x = ±2

y = (-2)³ - 4(-2) + 6 = 6: (-2, 0)

y = (2)³ - 4(2) + 6 = 6: (2, 0)

The equations at these points are

y = 8x + 16

y = 8x - 16

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Answer:

1

Step-by-step explanation:

Answer:

Hello There!!

Step-by-step explanation:

The answer is 1 as that means its certain that the event will happen.

hope thus helps,have a great day!!

~Pinky~

Answer:

6.64

Step-by-step explanation:

The nearest hundredth is the second digit after the decimal point.

6.6428571 rounded to the nearest hundredth is 6.64

3172.97 joules is the value of x when the Richter scale rating is 3.2

The equation that relates earthquake magnitude (M) and energy (E) is:

M = 2/3 × log(E) - 1.8

We have to find the value of X when the richer scale rating is 3.1

If an earthquake with a rating of 3.2 is not usually felt, then we can assume that x corresponds to the energy released by an earthquake that is just barely felt.

According to the United States Geological Survey, an earthquake with a magnitude of 2.5 corresponds to an energy release of about 1.3 × 10⁸ joules.

Using this as a reference point, we can set up the following equation:

3.2 = 2/3 × log(x) - 1.8

Solving for x, we get:

2.3 = 2/3 × log(x)

log(x) = 3.45

x = 3172.97

Therefore, the value of x when the Richter scale rating is 3.2 is approximately 3172.97 joules.

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Answer:

The point-slope form is y - 2 = 1/2 (x - 3)

Step-by-step explanation:

The point-slope form is y - y1 = m (slope) (x - x1). All I did was plug the numbers in the correct locations to get my answer.

Answer:

  3.3 ft

Step-by-step explanation:

Side NO is opposite the angle M, so the applicable trig relation is ...

  Sin = Opposite/Hypotenuse

  Opposite = Hypotenuse×Sin

  NO = MN×sin(39°) = (5.3 ft)sin(39°)

  NO ≈ 3.3 ft

Answer: 2/90 = 1/45

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

i took test

The ordered pair (4, -5) satisfies the equation

3x- 2y= 22

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

We have ordered pair (4, -5)

First equation, 2x - 5 y= -30

So, 2(4)- 5(-5)= 8 + 25= 33

Second equation,7 x + 4 y = -19

So, 7(4)+4(-5)= 28 -20= 8

Third equation, 6x - y= -29

So, 6(4) +5= 24+ 5 = 29

Fourth equation, 8 x + 3 y= -37

So, 8(4) + 3(-5)= 32 - 15 = 17

Fifth equation, 3x- 2y= 22

3(4)- 2(-5)= 12 + 10 = 22

sixth equation, 2x+ 9y = -37

2(4) + 9(-5)= -37

seventh equation, 5x- 6y= 49

5(4) - 6(-5)= 20 + 30 = 50

eight equation, x+ 8y= -27

4+ 8(-5)= -36

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Answer:

3 (x + y) (x - y)

Step-by-step explanation:

3x²-3y²​

GCF is 3

3(x² - y²)

Since both terms are perfect squares, factor using the difference of squares formula, a² − b² = (a+b) (a−b) where a = x  and b = y.

So, the answer is 3 (x + y) (x - y)

Answer:

15

Step-by-step explanation:

Answer:

7k + 6

Steps:

Subtract the numbers 20+6k-14k+k

6+6k+k

Combine the terms:

6+6k+k

6+7k

Rearange terms:

6+7k

7k+6

Answer:

see explanation

Step-by-step explanation:

(1)

4(m + 7) = 4 ( divide both sides by 4 )

m + 7 = 1 ( subtract 7 from both sides )

m = - 6

(2)

let the number be n , then

\(\frac{3}{5}\) n - 2 = 40 ( multiply through by 5 to clear the fraction )

3n - 10 = 200 ( add 10 to both sides )

3n = 210 ( divide both sides by 3 )

n = 70

The required number is 70

(3)

The 4 sides of a square are congruent , then

length of side = 36 cm ÷ 4 = 9 cm

Answer:

Therefore, the solution to the equation -x + 3y = 11 is x = -34/11 and y = 29/11.

Step-by-step explanation:

The given equation is:

-x + 3y = 11

To solve this equation by elimination, we need to add or subtract one or both equations to eliminate one of the variables. In this case, we can eliminate the variable x by adding the equation with another equation that has x with the same coefficient, but opposite sign.

Let's suppose we have another equation with x, for example:

2x + 5y = 7

We can eliminate x by multiplying the first equation by 2 and the second equation by 1, so that the coefficients of x are opposite:

-2x + 6y = 22 (multiply the first equation by -2)

2x + 5y = 7 (the second equation)

Now we can add the two equations to eliminate x:

-2x + 2x + 6y + 5y = 22 + 7

Simplifying the equation, we get:

11y = 29

Dividing both sides by 11, we get:

y = 29/11

Now that we know the value of y, we can substitute it back into one of the original equations to find the value of x. Let's use the first equation:

-x + 3y = 11

Substituting y = 29/11, we get:

-x + 3(29/11) = 11

Simplifying the equation, we get:

-x + 87/11 = 11

Subtracting 87/11 from both sides, we get:

-x = 11 - 87/11

Multiplying both sides by -1, we get:

x = 87/11 - 11

Simplifying the equation, we get:

x = (87 - 121)/11

x = -34/11

Answer:

It spends 20 years asleep.

Step-by-step explanation:

5/6 of 24 is 20

Answer:

6.8

Step-by-step explanation:

To round 6.752 to the nearest tenth consider the hundredths’ value of 6.752, which is 5 and equal or more than 5. Therefore, the tenths value of 6.752 increases by 1 to 8.

The compound interest rate of the investment is 1.10%

The given parameters about the compound interest are

Principal, P = $11,000

Amount, A = $20,000

Time, t = 9

Number of times, n = 12 i.e. monthly interest

To calculate the amount, we have:

A = P(1 + R/n)^nt

Substitute the known values in the above equation, so, we have the following representation

20000 = 11000 * (1 + r/12)^(12 * 9)

This gives

1.82 = (1 + r/12)^108

Take the 108th root of both sides

1 + r/2 = 1.0055

Subtract 1 from both sides

r/2 = 0.0055

Multiply by 2

r = 0.011

Express as percentage

r = 1.10%

Hence, the value of the interest rate is 1.10%

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Answer:

6.66%

Step-by-step explanation:

Compounded Monthly:

�

=

�

(

1

+

�

�

)

�

�

A=P(1+

n

r

​

)

nt

Compound interest formula

�

=

20000

�

=

11000

�

=

9

�

=

12

A=20000P=11000t=9n=12

Given values

20000

=

20000=

11000

(

1

+

�

12

)

12

(

9

)

11000(1+

12

r

​

)

12(9)

Plug in values

20000

=

20000=

11000

(

1

+

�

12

)

108

11000(1+

12

r

​

)

108

Multiply

20000

11000

=

11000

20000

​

=

11000

(

1

+

�

12

)

108

11000

11000

11000(1+

12

r

​

)

108

​

Divide by 11000

1.8181818

=

1.8181818=

(

1

+

�

12

)

108

(1+

12

r

​

)

108

(

1.8181818

)

1

/

108

=

(1.8181818)

1/108

=

[

(

1

+

�

12

)

108

]

1

/

108

[(1+

12

r

​

)

108

]

1/108

Raise both sides to 1/108 power

1.0055509

=

1.0055509=

1

+

�

12

1+

12

r

​

−

1

−1=

−

1

−1

Subtract 1

0.0055509

=

0.0055509=

�

12

12

r

​

12

(

0.0055509

)

=

12(0.0055509)=

(

�

12

)

12

(

12

r

​

)12

Multiply by 12

0.0666108

=

0.0666108=

�

r

6.66108

%

=

6.66108%=

�

r

Convert to percent (multiply by 100)

�

≈

r≈

6.66

%

6.66%

Round to the nearest hundredth of a percent

The number of minutes that the players spend running bases during each hour of practice is the constant of proportionality of the proportional relationship.

A proportional relationship is defined as follows:

y = kx.

In which k is the constant of proportionality.

In the context of this problem, the variables x and y are given as follows:

The equation for the constant is given as follows:

k = y/x.

Representing the hourly time spent running times, you can calculate it taking any point (x,y) on the graph of the function.

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The ordered pair that represents the point plotted and labeled A include the following: (−1, 2).

In Mathematics and Geometry, the translation of a graph to the left simply means a digit would be subtracted from the numerical value on the x-coordinate of the pre-image:

g(x) = f(x - N)

Conversely, the translation of a graph upward means a digit would be added to the numerical value on the y-coordinate (y-axis) of the pre-image.

g(x) = f(x) + N

Note: "Point A is one unit left and two units up from the origin. "

Since point A is one unit left and two units up from the origin (0, 0), we can logically deduce the following:

(x, y)                   →           (x - 1, y + 2)

Origin (0, 0)        →           (0 - 1, 0 + 2) = point A (-1, 2).

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Answer:

A: -2 + 3i

B: -1 + -1i

C: 3 + -4i

D: 4 + 1i

Step-by-step explanation:

These are the answers, Basically just normal graphing. run/rise.

I hope this helps! :)))))

The bunch of roses costs $12/$3 = 4 times as much as a single rose.

What is arithmetic sequence?

An arithmetic sequence is a sequence of numbers in which each term after the first is found by adding a fixed constant number, called the common difference, to the preceding term.

The bunch of roses costs 4 times as much as a single rose.

To see why, we can divide the cost of the bunch of roses by the number of roses it contains. If a bunch of roses costs $12 and contains, say, 4 roses, then each rose in the bunch costs $3. On the other hand, a single rose costs $3 on its own.

Therefore, the bunch of roses costs $12/$3 = 4 times as much as a single rose.

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The solution of cosx=2x is given by the graph shown below:

As seen from the graph, the function has two solutions.

(0,0) and (0.450183,0.9003672)

Answer:

It would be 86/9 because you would need to make it improper

Step-by-step explanation:

Answer: its still going to get 9 5/9 or 86/9 theres no common divisor for them

Step-by-step explanation:

The solutions to the equation x² + 6x + 1 = 0 are x = -3 + 2√(2) or x = -3 - 2√(2)

What is a quadratic equation?

A quadratic equation is a second-degree polynomial equation of the form ax² + bx + c = 0 where a, b, and c are constants, and x is the variable. The solutions can be found using the quadratic formula x = (-b ± √(b² - 4ac)) / (2a) or by factoring the quadratic expression into two linear factors.

To solve the quadratic equation x² + 6x + 1 = 0, we can use the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

where a, b, and c are the coefficients of the quadratic equation. Substituting the values from our equation, we get:

x = (-6 ± √(6²- 4(1)(1))) / (2(1))

Simplifying inside the square root, we get:

x = (-6 ± √(32)) / 2

We can simplify the square root further by factoring out a 4:

x = (-6 ± 4√(2)) / 2

Simplifying the fraction, we get:

x = -3 ± 2√(2)

Therefore, the solutions to the equation x² + 6x + 1 = 0 are:

x = -3 + 2√(2) or x = -3 - 2√(2)

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The scale factor of Figure A to Figure B is; 5/9

The scale factor of the figure A to the Figure B, will be given by the ratio of the side of the figure A to the given corresponding side of the Figure B.

Now, we see that the corresponding longest sides of the Figures A and B are given as 36 and 20 respectively

The corresponding shortest sides of the Figures A and B are given as 25.2 and 14 respectively

Therefore, we can conclude that the scale factor of the Figure A to the Figure B = 20/36 = 14/25.2 = 5/9

Finally, in order to get the dimension of Figure 'B' we multiply the dimension of Figure 'A' by 5/9

The  scale factor of Figure A to Figure B = 5/9

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Answer:

4. 145

5. 35

Step-by-step explanation:

F is 180 - 35 as angles in straight line are equal to 180. So H is diagonally opposite to F, so it'll be equal to F which is  145.

E will be 180 - H as angles in straight line are equal to 180. So that will be 180 - 145 = 35

2916 ft³

Volume helps describe the amount of space that a shape takes up.

Volume of a Sphere

Volume describes the 3-dimensional size of a shape. Since volume is a 3-D measurement, the units should be cubed; this explains why the answer is given in feet cubed. In order to find the volume, we need to use the radius. The radius of a sphere is the distance from the center to the outside. In this case, we are told that the radius is 9 ft.

Volume Formula

Every regular shape has its own volume formula. For a sphere, the formula is:

So, to find the volume, all we need to do is plug in the radius. For this sphere, r = 9.

When using 3 for pi, the volume of the sphere is 2916 ft³.

Answer:

The number of planes that land in a given time period follows a Poisson distribution with parameter lambda equal to the average rate of landing per unit time. In this case, lambda is equal to 0.1 planes per minute.

The probability that between 2 and 6 planes will land in 10 minutes is given by the cumulative distribution function of the Poisson distribution:

P(2 <= X <= 6) = P(X <= 6) - P(X <= 1)

Where X is the number of planes that land in 10 minutes.

Using the cumulative distribution function for the Poisson distribution, we have:

P(X <= 6) = 1 - e^(-0.1 * 10) * (1 + 0.1 * 10 + (0.1 * 10)^2 / 2! + ... + (0.1 * 10)^6 / 6!)

P(X <= 1) = 1 - e^(-0.1 * 10) * (1 + 0.1 * 10)

Therefore,

P(2 <= X <= 6) = (1 - e^(-0.1 * 10) * (1 + 0.1 * 10 + (0.1 * 10)^2 / 2! + ... + (0.1 * 10)^6 / 6!)) - (1 - e^(-0.1 * 10) * (1 + 0.1 * 10))

The exact value of this probability can be calculated using a calculator or computer software.

Answer:

0.3

Step-by-step explanation:

Answer:

225 calories

Step-by-step explanation:

1 recipe makes

12 standard sized pancakes

2 pancakes are 1/6 of the recipe

1/6 of the recipe has 150 calories

6 × 150 calories = 900 calories

The full recipe of 12 pancakes has 900 calories

1/2 recipe was made

1/2 recipe has 1/2 × 900 calories = 450 calories

1/2 recipe made 8 pancakes

4 pancakes are half of the half recipe or 1/4 recipe

1/4 × 900 calories = 225 calories

Answer:

310 hamburgers

Step-by-step explanation:

240 hm

240 cb

240-70= 170

480- 170= 310

Answer:

310 hamburgers

Step-by-step explanation: