What is the average rate of change for this exponential function for the
interval from x = 2 to x = 4?
O A. -6
O B. -12
O C. 12
O 0.6

Answer:

The points of the image are;

E'(5, 1), D'(5, -1), C'(1, 0), E'(-2, -3)

Step-by-step explanation:

The coordinates of the preimage are E(-5, -1) D(-5, 1) C(-1, 0) B(-2, -3)

Rotation of a point 180° about the origin gives;

Coordinates of the point of the preimage before rotation = (x, y)

The coordinates of the image after rotation = (-x, -y)

Therefore, the coordinates of the points EDCB after 180° rotation about the origin are;

E(-5, -1) rotated 180° becomes E'(5, 1)

D(-5, 1) rotated 180° becomes D'(5, -1)

C(-1, 0) rotated 180° becomes C'(1, 0)

B(-2, -3) rotated 180° becomes E'(-2, -3).

Answer:

y= [tex]\sqrt{x}[/tex]

Step-by-step explanation:

Answer:

36 : 6 and -6

12 = [tex]2\sqrt{3} , -2\sqrt{3}[/tex]

1.96 =1.4 and -1.4

0.64 : 0.8 and -0.8

400 : 20 and -20

25/36 = 5/6 and -5/6

Step-by-step explanation:

we know that

(-x)^2 = x^2

ALSO

(x)^2 = x^2

thus, square of both negative and positive number is same positive number.

_________________________________________________

36 = 6*6

36 = -6*-6

hence

square roots of 36 is both -6 and 6

12 = 4*3 = [tex]2^2*\sqrt{3} *\sqrt{3}[/tex]

[tex]\sqrt{12} = 2\sqrt{3}[/tex]

also

12 = [tex]-2\sqrt{3} *-2\sqrt{3}[/tex]

[tex]\sqrt{12} = -2\sqrt{3}[/tex]

___________________________________

1.96 = 196/100 = (14/10)^2

1.96 = 196/100 = (-14/10)^2

hence

[tex]\sqrt{1.96} = 14/10 \ or -14/10[/tex]

_______________________________

0.64 = 64/100 = (8/10)^2 = 0.8^2

0.64 = 64/100 = (-8/10)^2 = (-0.8)^2

Thus, square root of  0.64 = 0.8 and -0.8

_________________________________

400 = 20^2

400 = (-20)^2

[tex]\sqrt{400} = 20\\\sqrt{400} = -20\\[/tex]

__________________________________

25/36 = (5/6)^2

25/36 = (-5/6)^2

[tex]\sqrt{ 25/36} = 5/6 \\\sqrt{ 25/36} = (-5/6[/tex]

Answer:

The probability that the next failure will not occur before 30 months have elapsed is 0.0454

Step-by-step explanation:

Using Poisson distribution  where

t= number of units of time

x= number of occurrences in t units of time

λ= average number of occurrences per unit of time

P(x;λt) = e raise to power (-λt)  multiplied by λtˣ divided by x!

here λt = 25

x= 30

P(x= 30) = 25³⁰e⁻²⁵/ 30!

P (x= 30) = 8.67 E41 * 1.3887 E-11/30!    (where E= exponent)

P (x=30) = 1.204 E31/30!

Solving it with a statistical calculator would give

P (x=30) = 0.0454

The probability that the next failure will not occur before 30 months have elapsed is 0.0454

Answer:

≈23.66

Step-by-step explanation:

Height ---> x

base ---> 5x

Formula for area of triangle: (base*height)/2

((5x)(x))/2 = 1400

[tex]5x^{2}[/tex]/2 = 1400

[tex]5x^{2}[/tex] = 1400 · 2 = 2800

[tex]x^2[/tex] = 2800/5 = 560

x= √560 ≈ 23.66

Hey there! I'm happy to help!

When talking about percents, the word "is" usually means equals. Let's use this to solve an equation! We will call our number n. Note that 30% is equal to 0.3 in decimal form because 0.3 is 30% of one! :D

0.3n=45

To solve, we need to isolate the n. To do this, we divide both sides by 0.3 because this cancels out the 0.3 that is being multiplied by n and it shows us what n will then equal.

0.3n÷0.3=45÷0.3

n=150

Therefore, 30% of 150 is 45. Try multiplying 0.3 by 150 and you will get 45!

Have a wonderful day! :D

Answer:  y = -2

Step-by-step explanation:

f(x) = A cos (Bx - C) + D

                                  ↓

                                center line (aka midline)

f(x) = 2 cos (3x - 5π/6) - 2

                                      ↓

                                  midline = -2

The midline of the cos function f(x) = 2cos(3x − 5π/6) − 2 is y = -2 after comparing with standard cos function f(x) = Acos(Bx - C) + D

It is defined as a function that is sin-cos wave in nature, and it has a domain of all real numbers and lies between the [a, a] where is the amplitude of the function.

It is given that the cos function is:

f(x) = 2cos(3x - 5π/6) - 2

As we know, the standard form of the cos function is:

f(x) = Acos(Bx - C) + D

Here, A is the amplitude

B is the period of the cos function

C is the phase shift of the cos function

D is the vertical shift of the cos function/midline

On comparing:

D = -2

The midline:

y = -2

Thus, the midline of the cos function f(x) = 2cos(3x − 5π/6) − 2 is y = -2 after comparing with standard cos function f(x) = Acos(Bx - C) + D

Learn more about the cos function here:

https://brainly.com/question/14397255

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Answer:

22 units.

Step-by-step explanation:

In 45- 45- 90 triangles, there is a 1 to 1 to the square root of 2 formula. Each side length measures 1x, while the hypotenuse measures x times the square root of 2.

In this case, the hypotenuse measures 22 and the square root of 2 units. To find the value of x, simply divide that by the square root of 2 units, and you get x = 22 units. Multiply that by 1, and you get 22 units, which is the length of the leg of the triangle.

Hope this helps!

Answer:

Step-by-step explanation:

In triangle DEF, we have:

Given:

<EDF=56

<EFD=84

So, <DEF =180 - 56 - 84 =40 (sum of triangle angles is 180)

____________

DE is a midsegment of triangle ACB

( since CD=DA(given)=>D is midpoint of [CD]

and BE = EA => E midpoint of [BA] )

According to midsegment Theorem,

(DE) // (CB) "//"means parallel

and DE = CB/2 = FB =CF

___________

DEBF is a parm /parallelogram.

Proof: (DE) // (FB) ( (DE) // (CB))

AND DE = FB

Then, <EBF = <EDF = 56

___________

DEFC is parm.

Proof: (DE) // (CF) ((DE) // (CB))

And DE = CF

Therefore, <DCF = <DEF =40

___________

In triangle ACB, we have:

<CAB =180 - <ACB - <ABC =180 - 40 - 56 =84(sum of triangle angles is 180)

[tex]HOPE \: THIS \: HELPS.. GOOD \: LUCK! [/tex]

Answer:

The axis of symmetry of parabola is the equation where it cuts the middle of the graph.

So the axis of symmetry is x = 2 .

==================================================

Work Shown:

T(2) = 20 means the second term is 20

T(1) = 26 because we go backwards from what the rule says (subtract 6) to step back one term. Going forward, 26-6 = 20.

Since a = 26 is the first term and d = -6 is the common difference, the nth term is

T(n) = a + d*(n-1)

T(n) = 26 + (-6)(n-1)

T(n) = 26 - 6n + 6

T(n) = -6n + 32

Plugging n = 1 into the equation above leads to T(1) = 26. Using n = 2 leads to T(2) = 20.

Plug in n = 10 to find the tenth term

T(n) = -6n + 32

T(10) = -6(10) + 32

T(10) = -60+32

T(10) = -28

Answer:

-28.

Step-by-step explanation:

T(1) = 20 + 6 = 26.

This is an arithmetic series  with:

nth term T(n) =  26 - 6(n - 1).

So T(10) = 26 - 6(10-1)

= 26 -54

= -28.

Answer:

About 11 (10.9955742876...)

Step-by-step explanation:

Circumference=(pi) (diameter) or C=πd

Hope this helps!

The circumference of the circle is about 11 inches.

We are given that the diameter of a circle is 3.5 inches.

Noted that the circumference of the circle that has a radius of r is defined as the product of diameter to the pie value.

Therefore circumference of the circle = 2πr

Circumference=(2πr)

The diameter or C = πd

diameter = 3.5 inches

Circumference=(3.5 x 3.14)

Circumference = (10.99) inches

Learn more about circumference here;

brainly.com/question/12512221

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Answer:

[tex]y = \frac{5x}{2} - 5[/tex]

Step-by-step explanation:

Given the equation 5x - 2y = 10, to write the equation in slope-intercept form, we need to write it in the standard format y = mx+c where m is the slope/gradient and c is the intercept.

From the equation given  5x - 2y = 10, we will make y the subject of the formula as shown;

[tex]5x - 2y = 10\\\\subtract \ 5x \ from \ both \ sides\\\\5x - 2y - 5x = 10 - 5x\\\\-2y = 10-5x\\\\Dividing \ both \ sides\ by \ -2;\\\\\frac{-2y}{-2} = \frac{10-5x}{-2}\\ \\[/tex]

[tex]y = \frac{10}{-2} - \frac{5x}{-2} \\\\y = -5 + \frac{5x}{2}\\\\y = \frac{5x}{2} - 5[/tex]

Hence the equation that represents the first equation written in slope-intercept form is [tex]y = \frac{5x}{2} - 5[/tex]

Answer:

Option B.

Step-by-step explanation:

According to the question, the data provided is as follows

[tex]H_o : p_1 - p_2 = 0\ (p_1 = p_2)\\\\ H_\alpha : p_1 - p_2 < 0\ (p_1 < p_2)[/tex]

Based on the above information,

The type ii error is the error in which there is an acceptance of a non rejection with respect to the wrong null hypothesis. The type I error refers to the error in which there is a rejection of a correct null hypothesis and the type II refers that error in which it explains the failure of rejection with respect to null hypothesis that in real also it is wrong  

So , the type II error is option B as we dont create any difference also the proportion is very less

Answer:

2(a - 3). = 4

_______

3

Cross multiply.

2(a- 3) = 12

2a - 6 = 12

2a = 12 + 6

2a = 18

a = 18 ÷ 2

a = 9

Answer:

a = 9

Step-by-step explanation:

Given

[tex]\frac{2(a-3)}{3}[/tex] = 4 ( multiply both sides by 3 to clear the fraction

2(a - 3) = 12 ( divide both sides by 2 )

a - 3 = 6 ( add 3 to both sides )

a = 9

As a check substitute a = 9 into the left side of the equation and if equal to the right side then it is the solution.

[tex]\frac{2(9-3)}{3}[/tex] = [tex]\frac{2(6)}{3}[/tex] = [tex]\frac{12}{3}[/tex] = 4 = right side

Thus solution is a = 9

Answer:

420

Step-by-step explanation:

To find 63% of 6000, we can do 0.63 * 6000 = 3780 because 63% = 0.63.

1/9th of that is 1/9 * 3780 = 420.

Answer:

420

Step-by-step explanation:

Let's first start by finding 63% of 6000 so we can later find 1/9 of that number.

We can set up a percentage proportion.

[tex]\frac{x}{6000} = \frac{63}{100}[/tex]

[tex]6000\cdot63=378000\\378000\div100 = 3780[/tex]

Now to find 1/9 of 3780.

[tex]\frac{1}{9} \cdot \frac{3780}{1}\\\\\frac{3780}{9} = 420[/tex]

So, the answer is 420.

Hope this helped!

Answer:

the first one has one solution because eventually they will cross

Answer:

0.15x + 0.20y = 1.80

Step-by-step explanation:

Here, we are interested in writing an equation for the total cost of the apples and bananas

before we write , kindly understand that 100p = £1

So the cost of apple which is 15p will be 15/100 =£ 0.15

The cost of bananas which is 20p will be 20/100 = £0.2

Thus, the total cost of the apples bought will be number of apples bought * price of apple bought = 0.15 * x = £0.15x

The cost of bananas = number of bananas bought * price of bananas = 0.2 * y = £0.2y

So the total cost of the apples and bananas will be;

0.15x + 0.20y = 1.80

Answer:

The fence must have:

220 meters

Step-by-step explanation:

The perimeter of the field is equal to the long of the fence round the field.

then:

perimeter = 2(long + wide)

perimeter = 2(85 + 25)

perimeter = 2*110

perimeter = 220m

Answer: The area of land =108 m²

Step-by-step explanation:

In the given piece of land is in the shape of a parallelogram.

Diagonals divide it into 2 equal parts.

So, area of parallelogram = 2 x (Area of triangle with sides 12m and 9 m and  15 m)

Heron's formula :

Area of triangle = [tex]\sqrt{s(s-a)(s-b)(s-c)}[/tex], where [tex]s=\dfrac{a+b+c}{2}[/tex]

Let a= 12 , b= 9 and c = 15

[tex]s=\dfrac{12+9+15}{2}=18[/tex]

Area of triangle = [tex]\sqrt{18(18-12)(18-9)(18-15)}[/tex]

[tex]=\sqrt{18\times6\times9\times3}=\sqrt{2916}=54\ m^2[/tex]

Then, area of parallelogram= 2 x 54 = 108 m²

Hence, the area of land =108 m²

Answer:

prime

Step-by-step explanation:

x^2 - 2x + 3

What two numbers multiply to 3 and add to -2

There are none so this cannot be factored in the real numbers

Answer:

a. 4r² b. 2r c. 6 cm

Step-by-step explanation:

The surface area A of the cube is A = 24r². We know that the surface area, A of a cube also equals A = 6L² where L is the length of its side.

Now, equating both expressions, 6L² = 24r²

dividing both sides by 6, we have

6L²/6 = 24r²/6

L² = 4r². Since the area of one face is L², the polynomial that determines the area of one face is A' = 4r².

b.  Since L² = 4r² the rea of one face of the cube, taking square roots of both sides, we have

√L² = √4r²

L = 2r

So, the polynomial that represents the length of an edge of the cube is L = 2r

c. The length of an edge of the cube is L = 2r. When r = 3 cm.

L = 2r = 2 × 3 cm = 6 cm

So, the length of an edge of the cube is 6 cm.

Answer:

38

Step-by-step explanation:

f(-9) is the value of f(x) when x = -9. Therefore, f(-9) = 4 from the graph. Doing the same with g(6), we can see that g(6) = 6. Our expression becomes:

-1 * 4 + 7 * 6

= -4 + 42

= 38

Answer:

(2, −1) and (−4, 17)

Step-by-step explanation:

I used a graphing tool to graph the systems of equations. The parabola and line pass at points (2, -1) and (-4, 17).

Answer:(2, −1) and (−4, 17) Its C on Edge 2023

Step-by-step explanation: Its (C) after an extensive research

Answer:

36°

Step-by-step explanation:

<U + < V + <W = 180° (sum of angles in a triangle)

<W = 54°

The tangent is always perpendicular to the radius drawn to the point of tangency...

therefore,

<U = 90°

90° + <V + 54° = 180°

144° + <V = 180°

<V = 180° - 144°

<V = 36°

Answer:

V=36

Step-by-step explanation:

tangent makes rigt angle with radius angle U=90

W+V+U=180

V=180-90-54

V=36

Answer:

I think that it should be

[tex] {(a - b)}^{3} + {(b - c)}^{3} + {(c - a)}^{3} = 3(a - b)(b - c)(c - a)[/tex]

Step-by-step explanation:

Here,

we take , a - b = A,b-c = B , c - a= C

A+B+C = 0

we know that,

[tex] {a}^{3} + {b}^{3} + {c}^{3} - 3abc = (a + b + c)( {a}^{2} + {b}^{2} + {c}^{2} - ab - bc - ca)[/tex]

Here , A+B+C = 0

so,

A^3 +B^3 + C^3 = 3 ABC

now we put the values

[tex]{(a - b)}^{3} + {(b - c)}^{3} + {(c - a)}^{3} = 3(a - b)(b - c)(c - a)[/tex]

I am done .

I think that it should be

{(a - b)}^{3}  +  {(b - c)}^{3}  +  {(c - a)}^{3}  = 3(a - b)(b - c)(c - a)

Step-by-step explanation:

Here,

we take , a - b = A,b-c = B , c - a= C

A+B+C = 0

we know that,

{a}^{3}  +  {b}^{3}  +  {c}^{3}   - 3abc = (a + b + c)(  {a}^{2}  +  {b}^{2}  +  {c}^{2}  - ab - bc - ca)

Here , A+B+C = 0

so,

A^3 +B^3 + C^3 = 3 ABC

now we put the values

{(a - b)}^{3}  +  {(b - c)}^{3}  +  {(c - a)}^{3}  = 3(a - b)(b - c)(c - a)

I am done .

Answer:

11

Step-by-step explanation:

1650/15/10 = 11

Answer:

T = - 3.2e + 80

Step-by-step explanation:

Given the following :

e = elevation in thousands of feets

T = temperature (°F)

e1 = 5 ; e2 = 10 (in thousands of feet)

T1 = 64° ; T2 = 48°

y = mx + c ; T = me + c

y = ; m = slope, c = intercept

64 = m5 + c - - - - (1)

48 = m10 + c - - - - (2)

From (1)

c = 64 - m5

Substitute c = 64 - m5 into (2)

48 = m10 + c - - - - (2)

48 = m10 + 64 - m5

48 - 64 = 10m - 5m

-16 = 5m

m = - 16 / 5

m = - 3.2

Substitute the value of m into c = 64 - m5

c = 64 - 5(-3.2)

c = 64 - (-16)

c = 64 + 16

c = 80

Inserting our c and m values into T = me + c

T = - 3.2e + 80

Where e is in thousands of feet

T is in °F

Answer:

La magnitud del desplazamiento resultante es 2045.463 kilómetros. La dirección absoluta del desplazamiento resultante es 151.055º, el cual corresponde al sentido noroeste.

Step-by-step explanation:

En primer lugar, se construye el triángulo. La figura resultante se encuentra incluida como archivo adjunto. La magnitud del desplazamiento resultante se determina mediante la Ley del Coseno:

[tex]r = \sqrt{(800\,km)^{2}+(1400\,km)^{2}-2\cdot (800\,km)\cdot (1400\,km)\cdot \cos 135^{\circ}}[/tex]

[tex]r \approx 2045.463\,km[/tex]

La magnitud del desplazamiento resultante es 2045.463 kilómetros.

La dirección del desplazamiento resultante es hallada por medio de la Ley del Seno, sabiendo que el ángulo del desplazamiento resultante a la recta de 1400 kilómetros:

[tex]\frac{1400\,km}{\sin \alpha} = \frac{2045.463\,km}{\sin 135^{\circ}}[/tex]

Se despeja el ángulo correspondiente:

[tex]\alpha = \sin^{-1}\left(\frac{1400\,km}{2045.463\,km}\times \sin 135^{\circ} \right)[/tex]

[tex]\alpha \approx 28.945^{\circ}[/tex]

La dirección absoluta del desplazamiento resultante es:

[tex]\alpha' = 180^{\circ}-\alpha[/tex]

[tex]\alpha' = 180^{\circ}-28.945^{\circ}[/tex]

[tex]\alpha' = 151.055^{\circ}[/tex]

La dirección absoluta del desplazamiento resultante es 151.055º, el cual corresponde al sentido noroeste.