inverse of f(x) =e^2x- 4

Answer:

g-1(x)=SQRT{(x-4)/2} + 4

Step-by-step explanation:

I assume that the 2 is the exponent so ^ represents exponent

We know your function is g(x)=2(x-3)^2+4

For inverse functions we swap x and y values, note g(x) is like the y value

Isolate for y

y=2(x-3)^2+4

x=2(y-3)^2+4

(x-4)/2 = (y-3)^2

SQRT{(x-4)/2} + 4 = y

Therefore g-1(x)=SQRT{(x-4)/2} + 4

Answer:

17% of the bill

Step-by-step explanation:

Well to find the answer to this question we first have to add 35 + 48 to get the total percent of the bill that Michelle and Lori paid.

35 + 48 = 83%

now that we know the percent of the bill that Lori and Michelle are paying we have to subtract that amount by 100% to get the percent of the bill that Patti is paying.

100% - 83% = 17%

So Patti is paying 17% of the bill

If we wanted to go even farther and find out what 17% of the bill was all we would have to do is multiply 45 by 17% or 45 x 0.17

45 x 0.17 = 7.65

So Patti is paying 7 dollars and 65 cents

Answer:

The answer is A

Step-by-step explanation:

Answer:

A. 136 stars

B. 340 stars

Answer:

At 10 pm he counted 136 stars and at 12 pm he counted 340

Step-by-step explanation:

for 10 pm:

68 x 2

for 12 pm:

68 x 5

Answer:

25m

Step-by-step explanation:

The perimeter of a square= 4L (L=length of the side)

so L=perimeter /4

=100/4=25m

Answer:

I would say Acute. The angle is definitely less than a right angle. Reflex angles are angles more than 180 degrees, but less than 360 degrees.

Answer:

2 seconds later

Step-by-step explanation:

Since the required equation is lacking, let the equation modeled by the height be expressed as y = -16t² + 64

The ball hits the ground at y =0. Substitute y = 0 into the expression and find t;

Since y = -16t² + 64

0 =  -16t² + 64

16t² = 64

t² = 64/16

t² = 4

t = ±√4

t = 2 and -2

Time cannot be negative, hence the ball hits the ground 2 seconds later.

Note that the equation used was assumed. Similar solution can be applied for any given equation.

Answer:

D

Step-by-step explanation:

Answer:

she should buy 3 quarts and keep the remainder which can possibly cover 30 square feet.

Answer:

1. 8,5a + 38

2.  5,5+b

Step-by-step explanation:

1. a) 9,5(a+4)-a= 9,5a + 38-a= 8,5a + 38

2. 8+b-2,5= 5,5+b

Answer:

[tex]y - 2x - 1 = 0[/tex]

Step-by-step explanation:

the slope is :

[tex] \tan( \alpha ) = 4 \div 2 = 2[/tex]

at a pt on graph , when

[tex]x = 1 \\ y = 3 \\ [/tex]

therefore, coordinates are (1,3)

The equation is :

[tex](y - 3) = slope \times (x - 1) \\ (y - 3) = 2 \times (x - 1) \\ y - 3 = 2x - 2 \\ y - 2x - 1 = 0[/tex]

Answer:

x = -2

Step-by-step explanation:

Answer:

x=3.2

Step-by-step explanation:

8*0.4=3.2

We have that for the Question "The figures are similar, and the ratio of the perimeters is 2 : 5. Find x." it can be said that  the perimeters of x is

x=3.2

From the question we are told

The figures are similar, and the ratio of the perimeters is 2 : 5. Find x.

Generally the equation for the the ratio is mathematically given as

2=x

and

5=8

Therefore

[tex]x=\frac{2*8}{5}[/tex]

x=3.2

Therefore

the perimeters of x is

x=3.2

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Answer:

0.57 inches was left

Step-by-step explanation:

Here, we start by calculating the total length of the yam they have

Mathematically, that will be 0.37 + 0.45 = 0.82 inch

Now, to get what is remaining, we subtract what was borrowed

Mathematically, that is 0.82-0.25 = 0.57 inches

Answer:  speed = 17m/s

              time taken = 3min = 3 x 60 = 180 seconds   (1min = 60sec)

distance = ST

               = speed x time

                = 17 x 180

= 3060m

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Answer:

41.68201 km=25.9 miles

Step-by-step explanation:

Answer:

Step-by-step explanation:

5m=8k

25.9m = ?k

25.9/5 = 5.18

5.18 X 9 = 46.62

Therefore 25.9 miles is 46.62 km

Answer:

Independent-samples t-test.

Step-by-step explanation:

We are looking for the appropriate design for testing the significance of the difference between the means.

Now, there is a parametric test known as the Independent Samples t Test and what this test does is that it compares the mean of two independent groups in order to find out whether there is statistical evidence that the related population mean is significantly different.

Thus, the test to be used here is Independent-samples t-test.

Answer:

[tex]\sqrt[3]{2y^3} * 7\sqrt{18y} = 21(y^{\frac{3}{2}})(2^{\frac{5}{6}})[/tex]

Step-by-step explanation:

The question is poorly formatted.

Given

[tex]\sqrt[3]{2y^3} * 7\sqrt{18y}[/tex]

Required

Derive an equivalent expression

[tex]\sqrt[3]{2y^3} * 7\sqrt{18y}[/tex]

Express 18 as 9 * 2

[tex]\sqrt[3]{2y^3} * 7\sqrt{9 * 2y}[/tex]

Split the expression as follows:

[tex]\sqrt[3]{2y^3} * 7\sqrt{9} * \sqrt{2y}[/tex]

Take positive square root of 9

[tex]\sqrt[3]{2y^3} * 7*3 * \sqrt{2y}[/tex]

[tex]\sqrt[3]{2y^3} * 21 * \sqrt{2y}[/tex]

[tex]21*\sqrt[3]{2y^3} * \sqrt{2y}[/tex]

The cube root can be rewritten to give:

[tex]21*\sqrt[3]{2}*\sqrt[3]{y^3} * \sqrt{2y}[/tex]

[tex]\sqrt[3]{y^3} = y^{3*\frac{1}{3}} = y[/tex]

So, we have:

[tex]21*\sqrt[3]{2} * y * \sqrt{2y}[/tex]

Rewrite as:

[tex]21y *\sqrt[3]{2} * \sqrt{2y}[/tex]

Split [tex]\sqrt{2y[/tex]

[tex]21y *\sqrt[3]{2} * \sqrt{2} * \sqrt{y}[/tex]

Collect Like Terms

[tex]21y*\sqrt{y} *\sqrt[3]{2} * \sqrt{2}[/tex]

Represent in index form

[tex]21y*y^{\frac{1}{2}} *2^\frac{1}{3} *2^\frac{1}{2}[/tex]

Apply law of indices

[tex]21*y^{1+\frac{1}{2}} *2^{\frac{1}{3} +\frac{1}{2} }[/tex]

[tex]21*y^{\frac{2+1}{2}} *2^{\frac{2+3}{6}}[/tex]

[tex]21*y^{\frac{3}{2}} *2^{\frac{5}{6}}[/tex]

[tex]21(y^{\frac{3}{2}})(2^{\frac{5}{6}})[/tex]

Hence:

[tex]\sqrt[3]{2y^3} * 7\sqrt{18y} = 21(y^{\frac{3}{2}})(2^{\frac{5}{6}})[/tex]

Answer:

Despite the stereotype of the Mongols, yes they were "savage ruthless barbarians."

Step-by-step explanation:

You need to write the rest yourself.

Answer:

16.4

Step-by-step explanation:

4(5.5 + 6) - 3(6 + 4)

4(11.6) - 3(10)

46.4 - 30

16.4

Answer:

The answer is 16.

Step-by-step explanation:

4(x+6)−3(y+4)

=4x+24-3y-12

=4(5.5)+24-3(6)-12

=22+24-18-12

=46-30

=16

Step-by-step explanation:

The domain of the function is the range of x-values, which is -5 <= x <= 5. (D)

Given :

A road 2 m broad surrounds a square park 4225 m² in area.

Size of marble is 25 cm by 8 cm.

Price of each marble is Rs 50.

To Find :

Total cost.

Solution :

Side of square road is :

[tex]A^2 = 4225\ m^2\\\\A = 65\ m[/tex]

Area of road = [tex]4\times 65\times 2 \ m^2=520\ m^2[/tex]

Number of marbles required is :

[tex]N = \dfrac{A}{a}\\\\N = \dfrac{520\times 10^4\ cm^2}{200\ cm^2}\\\\N = 26000[/tex]

It is given that price per marble is Rs 50.

So, total price required is :

[tex]P = Rs \ 50\times 26000 \\\\P = Rs \ 13,00,000[/tex]

Hence, this is the required solution.

Answer:

DE ≅ XY and XY ≅ YZ, then DE ≅ YZ

Thus, this statement is illustrated or validated by the 'Transitive Property of Segment Congruence'.

Step-by-step explanation:

We know that if two segments are congruent to the third segment, then they will be congruent to each other. This is called Transitive Property of Segment Congruence.

For example, Let suppose

LM ≅ AB and AB ≅ BC, then LM ≅ BC

30  ≅ 30 and  30  ≅ 30, then 30  ≅ 30

Thus, this validates the 'Transitive Property of Segment Congruence'.

Now Given

DE ≅ XY and XY ≅ YZ, then DE ≅ YZ

Thus, according to the above discussion, this statement is illustrated or validated by the 'Transitive Property of Segment Congruence'.

Answer:

40 metres

Step-by-step explanation:

Pythagoras = [tex]\sqrt{41^{2} -9^{2} } =\sqrt{1600} =40[/tex]

Answer: She can buy 6 shirts

Step-by-step explanation: You subtract 95 from 240, which gives you 145 so you do 145/22.5 which will give you 6.4444 but you can't buy .44 of a shirt so you round down and you get 6.