Inverse Function: One to one function...Help needed! 15 pts for your help!

Answer:

Both legs would be 20

Step-by-step explanation:
In the image below, it shows the relationship between the legs and the hypotenuse in every 45 45 90 triangle. If we know that the hypotenuse is 20, then the 2 legs are both 20.

I am slightly confused with the problem since they asked for the "short" leg and the "long" leg. Both legs should be the same length because a 45 45 90 triangle is isosceles, with the two legs being the same length.

Answer:

The answers are=

The x-coordinate of the vertex is (38, 0) and the y-coordinate of the vertex is (19, 1768.9).

It is defined as the graph of a quadratic function that has something bowl-shaped.

(x - h)² = 4a(y - k)

(h, k) is the vertex of the parabola:

a = √[(c-h)² + (d-k²]

(c, d) is the focus of the parabola:

It is given that:

The graph of the parabolic path is shown in the picture.

From the graph:

The x-coordinate of the vertex is (38, 0)

The x-coordinate represents time in seconds

The y-coordinate of the vertex is (19, 1768.9)

The y-coordinate represents the height in meters

Thus, the x-coordinate of the vertex is (38, 0) and the y-coordinate of the vertex is (19, 1768.9).

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Answer: 110 degrees

Step-by-step explanation:

By the exterior angle theorem.

[tex]10x-10=100-2x+2x+10\\\\10x-10=110\\\\\therefore \angle ABC=110^{\circ}[/tex]

Answer:

3.036, 3.36, 3.3661 , 3.5

Step-by-step explanation:

Look at the first 2 numbers

3.3661, 3.5, 3.36, 3.036

We can order them as 3.0 , 3.3 , 3.3 . 3.5

So 3.036 is first one

Now we have 2 of the 3.3's

One is 3.3661 and the other one is 3.3600

Because if you add a number to the end it will always be a zero and it wont change the answer

So  3.36 is second and 3.3661 is third one

3.5  is bigger than 3.3

So 3.5 is last

The total amount due on the electricity bill is $55.64.

Here given that the last month's electricity consumption is 354 kWh

According to my contract with the electricity company, I agree to pay 11.3 cents per kWh.

So for 354 kWh of last month, I have to pay [tex]=11.3\times354=4000.2[/tex] cents

Now we know that 1 dollar = 100 cents

100 cents = $1

1 cent = [tex]\$\frac{1}{100}[/tex]

4000.2 cents [tex]=\$\frac{4000.2}{100}=\$40.002[/tex]

also, I have to pay a fixed charge of $15.63

So the total bill for last month will be [tex]=\$40.002+\$15.63=\$55.632\approx\$55.64[/tex]

Hence the total due amount on the electricity bill is $55.64 approximating the amount to the next two decimal place number.

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The diagram shows that ∠2 and ∠4 are the vertical angles.

Vertical angles are the angles that are opposite of each other when two lines cross.

The statements are:

1. < 2 & < 4 are vert. angles

2. Lines M & N intersect at P

3. < 2 & < 3 are a linear pair

4. m < 2 + m < 3 = 180

5. <3 and < 4 are a linear pair

6. m < 3 + m <4 =180

7. m < 2 + m < 3 = m < 3 + m < 4

8. m < 2 = m < 4

9. < 2 =~ <4

Here are the reasons:

1. Given

2. Def of vertical angles.

3. Def of. Linear pair

4. Angle addition postulate

5. Def of a linear pair

6. Angle addition postulate

7. Substitution property

8. Subtraction property

9. Def of =~ angles.

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Answer: View the picture below!

Step-by-step explanation: Just did the assignment!

Answer:

First Image: Choice B

Second Image: Choice B

Step-by-step explanation:

The equation of the line is written in the slope-intercept form,

y = mx + b

where m represents the slope

            b represents the y-intercept

First Image:

In our equation, y = 0.1x + 1,

we see that the y-intercept of the line is 1 and the slope is 0.1

We can simple plug in the x values to test if the table is true:

x = -1

y = 0.1x + 1 → y = 0.1(-1) + 1 → y = -0.1 + 1 → y = 0.9

This proves choices A and C are INCORRECT

The next point is at x = 10

y = 0.1x + 1 → y = 0.1(10) + 1 → y = 1 + 1 → y = 2

Making choice D INCORRECT

Hence, you've selected the correct choice (B)!

Second Image:

In our equation, y = 3x + 2,

we see that the y-intercept of the line is 2 and the slope is 3

Choice A is INCORRECT due to (0,0) not logical as the y-intercept is 2

Choice B is CORRECT due to (1/3, 3) not logical as that 3 = 3(1/3) + 2

6 = 3(4/3) + 2 → 6 = 4 + 2.     → 6 = 6

3 = 3(1/3) + 2 → → 3 = 1 + 2.   → 3 = 3

20 = 3(6) + 2 → 20 = 18 + 2.  → 20 = 20

Choice C is INCORRECT due to (-6, 20) not logical as that 20 = 3(-6) + 2

Choice D is INCORRECT due to (10, 4) not logical as that 10 = 3(4) + 2

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Answer:

Step-by-step explanation: 1. 5040 because 10x9x8x7

3. 10000 because 10^4=1000

1)There are 5040 possible codes are there if the digits cannot be repeated.

2)The probability that you will guess the correct code on your first try will be (1/5040).

3) Possible code = 10000 .

Given,

Numbers : 0 to 9

Here,

Total number of digit = 0,1,2,3,4,5,6,7,8,9

Given condition;

a)

Four digit card must be drawn;

The total possible ways there if the digits cannot be repeated will be;

⇒10×9×8×7

⇒5040

b)

The probability that you will guess the correct code on your first try is;

P(A) = n(A)/n(S)

Where,

n(A) is the event has the right code

n(S) is the total possible ways;

P(A) =1/5040

Hence the total possible ways there if the digits cannot be repeated and the probability that you will guess the correct code on your first try will be 5040 and (1/5040) respectively.

c)

If the gits can be repeated then we have 10 digits for each place :

Possible code = 10 * 10 * 10 *10

Possible code = 10000

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Answer:

[tex]y = \sin( \frac{2\pi}{3} x) [/tex]

Step-by-step explanation:

The equation of a sine function is y = a sin(bx), where a = amplitude (aka height) and b equals period (aka time). I'm assuming there isn't any information other than the graph shown, so let's assume that our amplitude is 1 and our period is 2pi/3. Plugging these values into the equation, we get:

[tex]y = (1) \sin(( \frac{2\pi}{3})x ) = \sin(\frac{2{\pi} }{3}x )[/tex]

Answer:

I think the best answer is 143

Answer:

The area for the trapezoid is

A=h/2(a+b)

A=8/2(10+15)

A=100 cm square

Hope it helps!

Answer:

[tex] \frac{dy}{dy} = \frac{x - 5}{3y + 6} [/tex]

The probability that both of them have the secret decoder ring will be 0.1356.

Its basic premise is that something will almost certainly happen. The percentage of favorable events to the total number of occurrences.

Inside the box of every cereal box contains a surprise gift.

The store manager assures employees that 18 of the 48 boxes on the shelf have a secret decoder ring.

And inside the other 30 boxes on the shelf contain a different gift.

If two cereal boxes are randomly selected from the shelf to purchase.

Then the probability that both of them have the secret decoder ring will be

The total events will be

Total event = ⁴⁸C₂

Total event = 1128

The favorable events will be

Favorable event = ¹⁸C₂

Favorable event = 153

Then the probability will be

P = 153 / 1128

P = 0.1356

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Answers:

x intercept = -4

y intercept = 16

The graph is shown below.

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

Explanation:

To determine the x intercept(s), we set the expression equal to zero and solve for x. In other words, we plug in y = 0 and solve for x.

y = x^2 +8x+16​

0 = x^2 +8x+16​

x^2 +8x+16​ = 0

(x+4)^2 = 0

x+4 = 0

x = -4

There's only one x intercept. It's located at the vertex of the parabola.

The location of the x intercept is the point (-4,0)

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

To find the y intercept, we plug in x = 0 and compute like so:

y = x^2 +8x+16​

y = (0)^2 +8(0)+16​

y = 16

The y intercept is 16 which is located at (0,16)

Check out the graph below. It was made using the free app Desmos.

Answer: -7

Step-by-step explanation:

[tex]f(-8)=-5\\\\g(4)=3\\\\\therefore -1 \cdot f(-8) -4\cdot g(4)=-1(-5)-4(3)=5-12=\boxed{-7}[/tex]

The maximum value of the objective function is 31.787

The given parameters are:

Objective function:

Max P = 4x + 5y + 21

Subject to:

y- x < 1

21x + 7y < 25

x>-2,  y>-4

Rewrite the inequalities as equation

y - x = 1

21x + 7y =  25

Add x to both sides in y - x = 1

y = x + 1

Substitute y = x + 1 in 21x + 7y =  25

21x + 7x + 7 =  25

Evaluate the like terms

28x = 18

Divide both sides by 28

x = 0.643

Substitute x = 0.643 in y = x + 1

y = 0.643 + 1

y = 1.643

So, we have:

Max P = 4x + 5y + 21

This gives

P = 4 * 0.643 + 5* 1.643 + 21

Evaluate

P = 31.787

Hence, the maximum value of the objective function is 31.787

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Using translation concepts, it is found that the equation that represents the graph of g(x) is:

[tex]g(x) = \sqrt[3]{x + 2}[/tex].

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

In this problem, we have that g(x) is a shift left of 2 units of f(x), hence:

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Answer:

The answer is B. On EDGE.2022

Step-by-step explanation:

Just did it

Answer:

27

Step-by-step explanation:

3.75/2.5x18=27

Answer:

5.9

Step-by-step explanation:

It's because area is 345

Among all the three ordered pairs no one lies on the graph of the function  f(x)=[tex]-25^{x} +1[/tex].

Given The value of a  function f(x)=[tex]-25^{x} +1[/tex]

If we want to check whether it will lie on the graph of a function or not then we have to just put those points in the function ,if the function satisfies means they lie on that graph otherwise not.

Taking first ordered pair :(1,625)

value of x is 1 and  value of y is 625.

we have to put in the function so

625=-[tex]25^{1}+1[/tex]

625 is not equal to -24 so it does not satisfy.

Taking second ordered pair :(0,-25)

-25=-25 raise to power 0 +1

-25  is not equal to 1 so it does not satisfy.

Taking third ordered pair: (-1,-1)

-1=-1/25+1

-1 is not equal to 24/25 so it does not satisfy.

Hence among all the ordered pairs none will lie on line of the given function.

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To simplify the equation, we have y = [tex]\frac{3}{4x^2 + 24x} + 8[/tex]

Given the expression

y-8 = 3/4x [x-(-6)]

First, expand the bracket

[tex]y - 8[/tex]= [tex]\frac{3}{4x^2 + 24x}[/tex]

Make 'y' the subject of formula

y = [tex]\frac{3}{4x^2 + 24x} + 8[/tex]

Thus, to simplify the equation, we have y = [tex]\frac{3}{4x^2 + 24x} + 8[/tex]

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If the function f(x) is shifted right by one unit and upward by 5 units, then the function f(x) will be equal to the function g(x). Then the parent function is f(x) = |x|.

The absolute function is also known as the mode function. The value of the absolute function is always positive.

The absolute function is given as

f(x) = | x – h | + k

The function g is related to one of the parent functions g(x) = |x − 1| + 5.

Then the parent function f(x) will be

f(x) = |x|

If the function f(x) is shifted right by one unit and upward by 5 units, then the function f(x) will be equal to the function g(x).

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Answer:

h^24

Step-by-step explanation:

hope that helpssndbfbsb

Answer:

{x | x = -6, -1, 0, 3}

(first option listed)

Step-by-step explanation:

The domain of a function is all possible x-values for that function

So, we can see (from the x-value portion of our table) that the possible x-values are:

-6 , -1, 0, and 3

We write domain and range in lowest - highest number value order, so we write our domain as such:

{x | x = -6, -1, 0, 3}

{range is all possible y-values, and this would include -7 , 1, 9, and -2}

hope this helps!!

Answer:

Step-by-step explanation:

x×4=2x²(x-1)

2x³-2x²-4x=0

2x(x²-x-2)=0

x≠0

x²-x-2=0

x²-2x+x-2=0

x(x-2)+1(x-2)=0

(x-2)(x+1)=0

x=2

or

x=-1 (rejected)

Answer:

Step-by-step explanation:

Formula

The following relationship exists between the parts of each chord.

(x - 1)(2x^2) = 4*x

Solution

The easiest way to start is to divide both sides of the equation by x.

(x - 1)(2x^2)/x = 4x / x                  Divide by x    

( x-1)(2x) = 4                                 Remove the brackets

2x^2 - 2x = 4                              Subtract 4 from both sides

2x^2 - 2x - 4 = 4 - 4                    Combine

2x^2 - 2x - 4 = 0                         Pull out the common factor

2(x^2 - x - 2) = 0                         Divide by 2

x^2 - x - 2 = 0                              Factor

(x - 2)(x + 1)

Answer:

x can be 2 or x can be - 1 on paper. The x on the upper right prohibits that. A line can't have a length of - 1. So - 1 is called an extraneous solution.

The answer is x = 2

Answer:

x = 2

y = 4

Step-by-step explanation:

Let's start with the 7 in the middle. Subtract the 1 on its upper left to get 6.

Add the 3 on its lower left to get 10.

so, 3 - x = 1. x = 2

17 - y = 13. y = 4

Answer: B(1, 3) and D(1, −2)

Step-by-step explanation:

The distance from A to C is 5, meaning we need the length to be 4.

If they lie to the right, we need to add 4 to the x coordinates, so the x coordinates should be 1, and the y coordinates should be 3 and -2.

The locations of B and D are given by (A) B(1,3) and D(1,-2).

The area of rectangle is given by the product of the length and width of that rectangle.

Area = Length*Width

Distance between two points (a,b) and (c,d) is given by,

[tex]d=\sqrt{(c-a)^2+(d-b)^2}[/tex]

Here in the given question it is mentioned that AC forms width of a rectangle and A is at (-3,3) and C is at (-3,-2)

Now the width is [tex]=\sqrt{(-3-(-3))^2+(-2-3)^2}=\sqrt{0^2+(-5)^2}=\sqrt{25}=5[/tex] unit.

Also it is given that, the area of the rectangle is 20 square units.

So the length is = 20/5 = 4 units

B and D lie to the right of points A and C respectively.

We have to go 4 units right to the A to find B and 4 units right to C to find D.

A is at (-3,3)

then B is at (-3+4,3) = (1,3)

C is at (-3,-2)

So D is at (-3+4,-2) = (1,-2)

Hence correct option is (A) B(1,3) and D(1,-2)

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