What is the inverse of the function f(x) = 2x+1

Answer:

with what

Step-by-step explanation:

I can't really see the question

Answer:

Step-by-step explanation:

Answering a comes from simplification, and answering b and c are done all in one step: completing the square on the quadratic that results from a.

(a)  If Martina has 240 m of fencing and is only utilizing one side for the length and 2 sides for the width, the perimeter formula is

240 = x + 2w where x is a length and w is the width. Solving this for w in terms of x:

240 - x = 2w so

\(w=120-.5x\) The area for a rectangle is L * W, so our area using the lengths we have is

A(x) = x(120 - .5x) and we simplify:

A(x) = 120x - .5x²  That's the answer to a.

Now for b and c, we will complete the square on this to get the vertex.

Begin by factoring out the -.5:

\(A(x)=-.5(x^2-240x)\) Now we take half the linear term, square it and add it both inside the parenthesis and outside the parenthesis. Our linear term is 240. Half of 240 is 120, and 120 squared is 14400:

\(A(x)=-.5(x^2-240x+14400)+7200\) (The 7200 comes from multiplying the 14400 times the -.5; -.5 times 14400 is -7200 so to balance things out, we have to add 7200).

The perfect square binomial that results from this is

A(x) = -.5(x - 120)² + 7200. From this we determine that our vertex is

(120, 7200). The 120 is the value of x, the length we are asked to find in b; the 7200 is the max area we are asked to find in c.

The required solutions are,,
(a) area = 240x - 2x²
(b) the side adjacent to the rivers gives the maximum length of the field.
(c) the maximum area could be 6400-meter square.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
length of the field is x,
The perimeter of the field, = 240
x + x + width = 240
width = 240 - 2x
now,
(a)
area of the field,
= length * width,

= x(240-2x)
= 240x - 2x²

Similarly,
(b) the side adjacent to the rivers gives the maximum area of the field.
(c) the maximum area could be 6400-meter square.

Thus, the required solutions are mentioned above.

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Answer:

Step-by-step explanation:

The domain and range of a linear function is always real numbers (T or F)

It is True. This is because of a couple of reasons.

    1.) You cannot divide by 0.

     2. A negative number cannot have its square root taken.

The range is determined by the domain in a linear function, and thus it must always consist of real numbers.

A 1-gigabyte flash drive has 1000 times more storage space than a 1-megabyte flash disk. The right response is thus "1,000 times greater."

We need to find the ratio between the two capacities.

Given that there are \(10^9\) bytes in a gigabyte and\(10^6\) bytes in a megabyte, we can calculate the ratio as follows:

Ratio = (1 GB) / (1 MB)

= \((10^9 bytes) / (10^6 bytes)\)

= \(10^(9 - 6)\)

=\(10^3\)

= 1000

Therefore, A 1-gigabyte flash drive has 1000 times more storage space than a 1-megabyte flash disk. The right response is thus "1,000 times greater."

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Answer:

2x^7

Step-by-step explanation:

add the exponents because they both are x

2x^4*x^3=2x^7

The correct answer for the intercept c'(100) is 0.04.

According to the question, the given expression for the cost function in terms of intercept is as written below:

\(c(q)=84+0.16q-0.0006q^{2} +0.00000q^{3}\)

Differentiate the given expression and it can be re-written as:

\(c'(q)=0+0.16-0.0006(2q) +0.00000(3q^{2})\)

Now, substituting the value of the variable 'q' as 100:

\(c'(100)=0+0.16-0.0006(2(100)) +0.00000(3(100)^{2})\\ c'(100)=0.16-0.0006(200) +0.00000(30000)\)

⇒c'(100) = 0.16 - 0.12 =

  c'(100) = 0.04

Hence, the correct answer for the intercept c'(100) is 0.04.

What is intercept?

The term intercept can be defined as the point on the y-axis. It is used to calculate the slope of the line. And it is that point from where straight line passes.

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The sampling method used by the restaurant manager allows for efficient data collection and a representative sample, it may introduce bias and lacks randomization.

Based on the information provided, we can identify the following statements that are true about the sampling method used by the restaurant manager to evaluate customer satisfaction with the new smoothie:

1. The manager uses systematic sampling: The manager surveys every other customer who orders the new smoothie. This systematic approach involves selecting every second customer, providing a consistent and organized sampling method.

2. The sample is representative: By surveying every other customer who orders the new smoothie, the manager ensures that the sample includes a variety of customers, reflecting the customer population as a whole.

3. The sample size may be smaller than the total customer base: Since the manager surveys every other customer, the sample size may be smaller compared to surveying every customer. This allows for efficient data collection and analysis.

4.The sampling method may introduce bias: The manager may inadvertently introduce bias by only surveying every other customer. Customers who are skipped in the survey may have different preferences or opinions, leading to a potential bias in the results.

5. The sampling method lacks randomization: Randomization is not employed in this sampling method, as the manager systematically selects customers. This could potentially introduce bias or exclude certain types of customers from the sample.

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Answer: its true

Step-by-step explanation:

i got it right

Answer:

true it is true relly it is

The length of line x in the figure of the cube given is 19.

Calculate the length of the base of the cube, which is the diagonal of the lower sides :

base length = √10² + 6²

base length = √136

The length of x is the diagonal of the cube

x = √(√136)² + 15²

x = √136 + 225

x = √361

x = 19

Therefore, the length of line x in the figure given is 19.

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Answer:

i think it's square foot of4

The system of linear equations and their solutions are:

1. (51, 26):  x - y = 25; 2x + 3y = 180

2. (-17, -36): x - y = 19; -2x + y/6 = 28

3. (47, 33): 2x - 3y = -5; x + y/11 = 50

4. (-31, -56): 2x - y = -6; x - 305/3 = 2y.

We can solve a system using the substitution method by finding the value of one of the variables, followed by substitution.

1. x - y = 25 -- eqn. 1

2x + 3y = 180 -- eqn. 2

Rewrite eqn. 1:

x = 25 + y

Substitute x = 25 + y into eqn. 2:

2(25 + y) + 3y = 180

50 + 2y + 3y = 180

5y = 180 - 50

5y = 130

y = 26

Substitute y = 26 into eqn. 1:

x - 26 = 25

x = 25 + 26

x = 51

The solution is: (51, 26).

2. x - y = 19 -- eqn. 1

-2x + y/6 = 28 -- eqn. 2

Rewrite eqn. 1:

x - y = 19

x = 19 + y

Substitute x = 19 + y into eqn. 2:

-2(19 + y) + y/6 = 28

-38 - 2y + y/6 = 28

-11y/6 = 28 + 38

-11y/6 = 66

-11y/6 (-6/11)= 66(-6/11)

y = -36

Substitute y = 36 into eqn. 1:

x - y = 19

x - (-36) = 19

x + 36 = 19

x = 19 - 36

x = -17

The solution is: (-17, -36).

3. 2x - 3y = -5 -- eqn. 1

x + y/11 = 50 -- eqn. 2

x + y/11 = 50

x = 50 - y/11

Substitute x = 50 - y/11 into eqn. 1

2(50 - y/11) - 3y = -5

100 - 2y/11 - 3y = -5

-35y/11 = -5 - 100

-35y/11 = -105

-35y/11(-11/35) = -105(-11/35) (multiplication property)

y = 33

Substitute y = 33 into eqn. 2:

x + 33/11 = 50

x + 3 = 50

x + 3 - 3 = 50 - 3

x = 47

The solution is (47, 33).

4. Solving the last one, we will definitely have the solution, (-31, -56).

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Answer:

$ 324.00

Step-by-step explanation:

Interest= principal x rate x time

First, converting R percent to r a decimal

r = R/100 = 12%/100 = 0.12 per year,

then, solving our equation

I = 2700 × 0.12 × 1 = 324

I = $ 324.00

The simple interest accumulated

on a principal of $ 2,700.00

at a rate of 12% per year

for 1 years is $ 324.00.

Part a: The data points appear to follow an exponential pattern. This is because the balance is increasing at a rate that is proportional to the current balance.

Part b: The equation of the best fit is y = 50(1.06)^x. This can be found using a variety of methods, including graphing the data points and fitting a curve to them, or using a statistical software package.

Part c: When x = 32, y = 50(1.06)^32 = $2,499.82.

Years since 1990, x 0 5 10 15 20 25 30

Balance, y $50 $62.31 $77.65 $96.76 $120.59 $150.27 $187.27 $2,499.82

The equation of the fitted curve is y = 50(1.06)^x.

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The total cost for X hours is the fixed cost of $15 plus the variable cost of $4 per hour which is equal to 4*X, so the total cost is 4*X + 15 

If Margie does not want to spend more than $27 then the inequality is 

4*X + 15 <= 27

4*X <= 12

X <= 3 

If Margie does not want to spend more than $27 then she cannot rent the bicycle for more than 3 hours 

Answer:

Step-by-step explanation:

let's every hour be x

first condition

therefore,

15

therefore

15+4x (as per our is x)

last condition

therefore,

15+4x≤27 (≤ is because as it says"does not want to spend more than $27"

few things about solving inequality

the direction of the inequality won't change

if

the direction of inequality will change

if

\(step - 1 \colon \: define\)

\(15 + 4x \leqslant 27\)

\(step - 2 \colon \: \\ subtract \:15 \: from \: both \: sides\)

\(15 - 15 + 4x \leqslant 27 - 15\)

\(4x \leqslant 12\)

\(step - 3 \colon \: \\ divide \: both \: sides \: by \: 4\)

\( \frac{4x}{4} \leqslant \frac{12}{4} \)

\(x \leqslant 3\)

\( \therefore \: she \: can \: rent \: the \: bicycle \: for \: 3 \: hours\)

Answer:

-45

Step-by-step explanation:

(-6)2+5(-6)-3=-45

Answer:

Solve the equation for  Y  by finding  a ,  b , and  c  of the quadratic then applying the quadratic formula. Y = − 5 − √ 97 + 24 y 12 Y = − 5 + √ 24 y + 97 12

Answer:

B hope this helped

Step-by-step explanation:

9514 1404 393

Answer:

Step-by-step explanation:

The 1-year interest is simply the invested amount times the interest rate.

Let r represent the lower interest rate. Then r+0.02 is the higher rate, and the total interest earned is ...

  1400r + 900(r +.02) = 202

  2300r +18 = 202 . . . . . . . . . .simplify

  2300r = 184 . . . . . . . . . .subtract 18

  r = 184/2300 = 0.08 = 8% . . . . . . divide by the coefficient of r

$1400 was invested at 8%.

$900 was invested at 10%.

Answer:

1 5/8

Step-by-step explanation:

Answer:

1 and 5/8

Step-by-step explanation:

8 goes into 13 once

that’s where we get the 1 which is basically (8/8)

then we subtract 8 from 13 and we get 5

so what we have left is 5/8

so the answer is 1 and 5/8

if we check our work

(8/8) + (5/8)

= 13/8

Answer: 128.5km

Step-by-step explanation:

Since we are given the information that the distance by road from town A to town B is 257 km. To get 50% of the distance, we simply have to multiply the distance given by 50%. This will be:

= 50% × 257km

= 50/100 × 257km

= 0.5 × 257km

= 128.5km

Therefore, 50% of the distance is 128.5km.

Answer:

10b+10a

Step-by-step explanation:

Answer:

The answer is 10a

Step-by-step explanation:

(1)(0b+10a)

=(1)(0b)+(1)(10a)

=0+10a

=10a

Hope this helps :)

Answer:

below

Step-by-step explanation:

-14y = 28 - 10x

10x - 14y - 28 = 0.

a = 10

b = -14

c = -28

Answer:

a = 10

b = -14

c = 28

Step-by-step explanation:

Goal form: Standard form

ax + by = c

Given form: linear form (not fully simplified)

-14y = 28 - 10x

Add 10x on both sides (to move the x-value to the left-hand side of the equation)

-14y + 10x = 28 - 10x + 10x

-14y + 10x = 28

10x - 14y = 28

Determine [ a ], [ b ], [ c ]

ax + by = c

10x - 14y = 28

\(\Large\boxed{a=10}\)

\(\Large\boxed{b=-14}\)

\(\Large\boxed{c=28}\)

Hope this helps!! :)

Please let me know if you have any questions

At a temperature of 20°C, the mouse would burn approximately 1,567.44 calories each day.

According to the given model C = 0.37219T + 1,560, where C represents the number of calories an idle mouse burns each day and T represents the temperature of its environment in °C.

To find the most comfortable temperature for an idle mouse, we need to determine the temperature at which the mouse burns the least amount of calories per day.

To find this temperature, we can minimize the equation C = 0.37219T + 1,560. To do so, we take the derivative of C with respect to T and set it equal to zero:

dC/dT = 0.37219 = 0

Solving this equation, we find that the derivative is a constant value, indicating that the function C = 0.37219T + 1,560 is a linear equation with a slope of 0.37219. This means that the mouse burns the least calories at any temperature, as the slope is positive.

Therefore, there is no specific "most comfortable" temperature for an idle mouse in terms of minimizing calorie burn. However, if we consider the range of temperatures mice typically encounter, we can find a temperature where the calorie burn is relatively low.

For example, if we take a temperature of 20°C, we can calculate the calorie burn:

C = 0.37219 * 20 + 1,560

C = 7.4438 + 1,560

C ≈ 1,567.4438 calories per day

Therefore, at a temperature of 20°C, the mouse would burn approximately 1,567.44 calories each day.

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Answer:

Hey there!

0.5(8.4)(h)=69.3

4.2h=69.3

h=16.5

Hope this helps :)

Answer:

\( \boxed{\sf Height \ of \ the \ triangle = 16.5 \ mm} \)

Given:

Area of the triangle = 69.3 mm²

Base of the triangle = 8.4 mm

To Find:

Height of the triangle

Step-by-step explanation:

\(\sf \implies Area \ of \ the \ triangle = \frac{1}{2} \times Base \times Height \\ \\ \sf \implies 69.3 = \frac{1}{2} \times 8.4 \times Height \\ \\ \sf \implies 69.3 = \frac{1}{ \cancel{2}} \times \cancel{2} \times 4.2 \times Height \\ \\ \sf \implies 69.3 = 4.2 \times Height \\ \\ \sf \implies 4.2 \times Height = 69.3 \\ \\ \sf \implies Height \times \frac{ \cancel{4.2}}{ \cancel{4.2}} = \frac{69.3}{4.2} \\ \\ \sf \implies Height = \frac{16.5 \times \cancel{4.2}}{ \cancel{4.2}} \\ \\ \sf \implies Height = 16.5 \: mm\)

Answer:

Step-by-step explanation:

1/2 + 6/7 + 2/9 = 199/126

Answer:

2/14

Step-by-step explanation:

2/14

Answer:

2.2785 this is most likely to be the answer

Answer:

Step-by-step explanation:

To dilate the square by a factor of 1111 from the origin, we need to multiply each coordinate by 1111.

The coordinates of point C are (8,8). So, to find the coordinates of point C' after dilation, we can simply multiply each coordinate by 1111:

x-coordinate of C' = 1111 * 8 = 8888

y-coordinate of C' = 1111 * 8 = 8888

Therefore, the coordinates of point C' are (8888, 8888).

Answer:k

Step-by-step explanation:

h