Last week, Juliet ran 22 kilometers. ​ ​This week, she plans to run 2\frac{2}{5}2 5 2 ​ times as far as last week. ​ ​How many kilometers does Juliet plan to run this week?

Answer:

A.)  g (x) = f (x) - 2

Step-by-step explanation:

The first thing we are going to do in this case is to take into account the following definition.

Translations are transformations that change the position of the graph of a function.

The general shape of the graph of a function is moved up, down, to the right or to the left.

The translations are considered rigid transformations. Now we will see how these are performed.

Vertical translations:

Suppose that k> 0

To graph y = f (x) + k, move the graph of k units up.

To graph y = f (x) -k, move the graph of k units down.

Using the definition we conclude that:

g (x) = f (x) - 4

Two exponential functions, fand g, are shown in the figure, where g is a transformation of f, g (x) = f (x) - 4 equation shows transformation of f. The correct option is A.

A mathematical function of the form [tex]f(x) = a^x[/tex], where an is a positive constant and x is the input variable, is an exponential function.

The characteristic curve of exponential functions rises or falls rapidly depending on whether an is greater or less than 1.

To determine the transformation of f which gives g, we need to examine how f has been transformed to obtain g.

Looking at the graph, we can see that g is a vertical shift of f. Specifically, g is obtained by shifting f downward by 2 units. Therefore, we need a rule that subtracts 2 from f (x) to get g (x).

Out of the given options, the only one that matches this description is:

g (x) = f (x) - 4

Option A subtracts 4 from f (x), which is not what we observe in the graph. Option B uses an incorrect format and is also subtracting 4 from  f (x).

Option C adds 4 to x, which would result in a horizontal shift, not a vertical shift.

Therefore, the correct answer is A g (x) = f (x) - 2.

For more details regarding exponential function, visit:

https://brainly.com/question/14355665

#SPJ7

Given:

[tex]h(1)=9[/tex]

[tex]h(n)=h(n-1)\cdot (-3)[/tex]

To find:

The explicit formula for h(n).

Solution:

We have,

[tex]h(n)=h(n-1)\cdot (-3)[/tex]         ...(i)

It is the recursive formula of a geometric sequence. It is of the form

[tex]a(n)=a(n-1)\cdot r[/tex]         ...(ii)

where r is the common ratio.

On comparing (i) and (ii), we get

[tex]r=-3[/tex]

We have, [tex]h(1)=9[/tex] so the first term of the geometric sequence is [tex]a=9[/tex].

The explicit formula for a geometric sequence is:

[tex]h(n)=ar^{n-1}[/tex]

Substitute a=9 and r=-3 to get the explicit formula for the given sequence.

[tex]h(n)=9(-3)^{n-1}[/tex]

Therefore, the required explicit formula is [tex]h(n)=9(-3)^{n-1}[/tex].

The solutions to the given quadratic equation are (3+√5)/2 and (3-√5)/2.

Quadratic formula is the simplest way to find the roots of a quadratic equation.

The roots of a quadratic equation ax² + bx + c = 0 are given by x = [-b ± √(b² - 4ac)]/2a.

The given quadratic equation is x²-3x+1=0.

By comparing x²-3x+1=0 with ax²+bx+c=0, we get a=1, b=-3 and c=1.

Now, x= [3±√((-3)² - 4×1×1)]/2×1

= [3±√(9-4)]/2

= (3±√5)/2

So, the solutions to the given equation are (3+√5)/2 and (3-√5)/2.

Therefore, the solutions to the equation are (3+√5)/2 and (3-√5)/2.

To learn more about the quadratic formula visit:

https://brainly.com/question/11540485.

#SPJ5

Answer: The angle is 35 is specifically 34.85

Step-by-step explanation:

[tex]sin^{-1}[/tex]([tex]\frac{8}{14}[/tex])=34.85

Answer:

B. Will the particles of ice absorb heat from the water and begin to move faster?

Step-by-step explanation:

Answer:

200 shows

Step-by-step explanation:

subtract the total ($40) from how much he pays a month ($20) to get the total of how much he paid in shows total ($20)

40-20=20

divide the total bill of shows ($20) by how much it costs per show ($0.10) to get how many shows he has watched (200)

20/0.10=200

Hope this helps!!

Answer:

The answer has many ongoing 3's so just shorten it to

8.3 or 8.33

Answer:

$0.11 approx

Step-by-step explanation:

If 4 jalapenos cost $0.45, how much is 1 jalapeno?

Given data

We are told that  4 jalapenos cost $0.45

If  4 jalapenos cost $0.45

the 1 jalapenos cost x

cross multiply

x= 0.45/4

x= 0.1125

Hence the cost of 1 jalapenos is $0.11 approx

Answer: slope -1; y-intercept is 13, (0,13)

Step-by-step explanation:

We rewrite the function as y = -x + 13

y = mx + b; m is the slope, b is the intercept, by comparison, we found that the slope is -1, and the y-intercept is 13.

sample response: The pre-image is the point you start with. To check the transformation rule, substitute the values of the coordinates (4, 5) into the rule. You get (4, 5) → (4+4, 5+7). Simplify to get (4, 5) → (8, 12). This is the image. Instead the rule was applied to the image. This is the source of the error.

Answer:

The transformation rule should be applied to the pre-image.  The application of the rule results in the point (8, 12).  The transformation rule was applied to the wrong point.

Step-by-step explanation:

Answer:

4:6

Step-by-step explanation:

Answer:

oh snap

Step-by-step explanation:

at least it isn't due in 10 mins right? that happened to me.... luckily I saved 1st draft

Answer: I feel bad to you

Step-by-step explanation:lol

Answer:

The answer is A. Straight angle

Answer:

31 , 59

Step-by-step explanation:

a = b +28

a + b = 90 {Complementary}

b + 28 + b = 90    {Combine like terms}

2b + 28 = 90       {Subtract 28 form both sides}

       2b  = 90 - 28

       2b = 62      {Divide both sides by 2}

        b = 62/2

       b = 31

a = 31 + 28

a = 59

Answer:

b po

Step-by-step explanation:

sana po matulong po ako

Answer:

32°

Step-by-step explanation:

90 - 58 = 32

b = 32°

Answer:

x= 21/15

if you need to reduce it would be x=7/5

Step-by-step explanation:

12x-15 =6-3x

add 3x to both sides

15x- 15 = 6

now add 15 to both sides

15x = 21

lastly divide both sides by 15

x= 21/15

if you need to reduce it would be x=7/5

Answer:

x = 7/5 or 1.4

Step-by-step explanation:

12x - 15 = 6 - 3x             Need to move one variable term to the other side to

+3x              + 3x         isolate it on one side

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

15x - 15 = 6                   need to +15 to isolate the variable term

     +15   +15

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

15/15x = 21/15 (simplify 21/15 = 7/5)   need to divide by 15 to isolate x

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

x = 7/5 or 1.4

Answer:

-4

Step-by-step explanation:

Plug in -4 for x, so the absolute value of -4 is 4. However, there's a minus sign out in front still, so it gets tacked on to the 4. So, g(-4)=-4

Answer:

225.

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

Answer: 2

Step-by-step explanation: 1 2 3 so 1 + 1 is 2

Answer:

x = 18 , y = 15

Step-by-step explanation:

Given the 2 equations

3x - 2y = 24 → (1)

x + 2y = 48 → (2)

Adding the 2 equations term by term will eliminate the y- term

4x + 0 = 72

4x = 72 ( divide both sides by 4 )

x = 18

Substitute x = 18 into either of the 2 equations and solve for y

Substituting into (2)

18 + 2y = 48 ( subtract 18 from both sides )

2y = 30 ( divide both sides by 2 )

y = 15

Answer:

i^198 is -1

hope I helped :)

Answer:

-8?

Step-by-step explanation:

Answer:

15x +10y =400

All divide by 5

3x +2y =80

2y=80 - 3x

y=80-3x/2

Answer:

x = -2

Step-by-step explanation:

2(3x - 5) + 4 = -18

Distribute the 2

6x - 10 + 4 = -18

6x - 6 = -18

Add 6 to both sides

6x = -12

Divide both sides by 6

x = -2

Check:

2(3x - 5) + 4 = -18

substitute x = -2 into the original equation

2(3(-2) - 5) + 4 = -18

2(-6 - 5) + 4 = -18

2(-11) + 4 = -18

-22 + 4 = -18

-18 = -18

So x = -2 is true.

Answer:

x=-2

Step-by-step explanation:

2(3x-5)+4=-18

We move all terms to the left:

2(3x-5)+4-(-18)=0

We add all the numbers together, and all the variables

2(3x-5)+22=0

We multiply parentheses

6x-10+22=0

We add all the numbers together, and all the variables

6x+12=0

We move all terms containing x to the left, all other terms to the right

6x=-12

x=-12/6

x=-2