Which of the following is a key property of the quadratic parent function?

Answer:

Step-by-step explanation:

Hello,

For any function f which has an inverse function we can write

[tex]x=(f^{-1}of)(x)=(fof^{-1})(x)=f(f^{-1}(x))[/tex]

This is why, in practice, to find the inverse of f we will consider f(x) = y and we will look for x as a function of y, so we switch x and y and solve for y. Let's do it.

Step 1 - The function f(x) can be written as a variable.  [tex]\boxed{y}=f(x)[/tex]

f(x) = y = 5x + 2

Step 2 - switch the variables x <-> y

x = 5y + 2

subtract 2 to both parts of the equation

<=> x - 2 =  5y + 2 - 2 = 5y

divide by 5 both parts of the equation

[tex]<=> y=\dfrac{x-2}{5}[/tex]

It means that the inverse of f is as below.

[tex]\boxed{ \ f^{-1}(x)=\dfrac{x-2}{5}\ }[/tex]

Step 3 - Find the inverse of g(x)

We already found that the inverse of f is g, so the inverse of g is f.

Let's do it again.

[tex]g(x)=y=\dfrac{x-2}{5} \ \ \text{ switch x and y } \\ \\ x= \dfrac{y-2}{5} \ \ \text{ solve for y }\\ \\ y-2=5x \ \ \text{ mulitply by 5 both parts of the equation } \\ \\ y = 5x+2 \ \ \text{ add 2 to both parts of the equation }[/tex]

And we found what we already known, meaning f is the inverse of g.

[tex](gof)(x)=(fog)(x)=x[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answers and Step-by-step explanation:

Step 1:

We want to find the variable that ff(x) represents. Well, we know it can't be x because we already have x on the other side of the equation: ff(x) = 5x + 2.

So, ff(x) must equal y.

Since ff(x) = y, we know then that ff(x) = y = 5x + 2. And our equation is:

y = 5x + 2

Step 2:

Let's switch the variables now. This means that what used to be y will be x and what used to be x will be y:

y = 5x + 2  ⇒  x = 5y + 2

Subtract 2 from both sides:

5y = x - 2

Divide by 5 from both sides:

y = (x - 2)/5

Step 3:

Let's find the inverse of g(x) by doing the exact same thing as we did with ff(x):

g(x) = y = (x - 2)/5

Switch the variables:

y = (x - 2)/5  ⇒      x = (y - 2)/5

Multiply by 5 on both sides:

5x = y - 2

Add 2 to both sides:

y = 5x + 2

Notice that this is the exact same as ff(x)! This means that ff(x) and g(x) are inverses.

Answer:

Step-by-step explanation:

[tex] - 3a( {a}^{2} - 10a + 25)[/tex]

Multiply each term in the parentheses by -3a

[tex] = - 3a \times {a}^{2} - 3a \times ( - 10a) - 3a \times 25[/tex]

Calculate the product

[tex] = - 3 {a}^{3} - 3a \times ( - 10a) - 3a \times 25[/tex]

Multiplying two negatives equals a positive [tex]( - ) \times ( - ) \ = ( + )[/tex]

[tex] = - 3 {a}^{3} + 3a \times 10a - 3a \times 25[/tex]

Calculate the product

[tex] = - 3 {a}^{2} + 30 {a}^{2} - 75a[/tex]

Hope this helps...

Best regards!!

Bro did you go in the next grade?

Answer:

Step-by-step explanation:

P = efe =4.8

f =0.26

substitute the value of P and f into the equation to obtain the value of e

4.8 = e*0.26*e

4.8 = 0.26*e^2

make e^2 the subject of the formula

e^2 =4.8/0.26 =18.62

find the square root of e

e =[tex]\sqrt{x} 18.46\\[/tex]

e = 4.3

Lower bound of P = 4.8 - 4.79 = 0.01

Answer:

∠y = 70º, ∠z = 60º, ∠w = 70º

Step-by-step explanation:

i believe the angle measures are the same for both triangles.

so ∠z = 60º, ∠x = 50º

to get ∠w, 180 - (50 + 60) = 70

∠w = 70º

∠w and ∠y would be equivalent

Answer:

9[tex]a^{4}[/tex]b³

Step-by-step explanation:

The 2 terms are like terms and can be combined, that is

[tex]a^{4}[/tex]b³ ( 1 + 8)

= 9[tex]a^{4}[/tex]b³

Answer:

9a^4b^3

Step-by-step explanation:

a^4b^3 + 8a^4b^3

These are like terms so we can add them together

Factor out a^4b^3

a^4b^3( 1+8)

a^4b^3 (9)

9a^4b^3

Answer:

Step-by-step explanation:

[tex]x^2+\frac bax+\frac ca=0\\\\ ax^2+bx+c=0\\\\x_1=\dfrac{-b-\sqrt{b^2-4ac}}{2a}\qquad\quad x_2=\dfrac{-b+\sqrt{b^2-4ac}}{2a}\\\\\\x_1+x_2=\dfrac{-b-\sqrt{b^2-4ac}}{2a}+\dfrac{-b+\sqrt{b^2-4ac}}{2a}=\dfrac{-2b}{2a}=\dfrac{-b}a\\\\\\x_1\cdot x_2=\dfrac{-b-\sqrt{b^2-4ac}}{2a}\cdot\dfrac{-b+\sqrt{b^2-4ac}}{2a}=\\\\{}\ \ =\dfrac{b^2-b\sqrt{b^2-4ac}+b\sqrt{b^2-4ac}-(\sqrt{b^2-4ac})^2}{2a}=\dfrac{b^2-(b^2-4ac)}{4a^2}=\\\\{}\ \ =\dfrac{b^2-b^2+4ac}{4a^2}=\dfrac{4ac}{4a^2}=\dfrac{c}{a}[/tex]

[tex]x_1-x_2=\frac{-b-\sqrt{b^2-4ac}}{2a}-\frac{-b+\sqrt{b^2-4ac}}{2a}=\frac{-2\sqrt{b^2-4ac}}{2a}=\frac{-\sqrt{b^2-4ac}}{a}\\\\\\x_1\div x_2=\frac{-b-\sqrt{b^2-4ac}}{2a}\div\frac{-b+\sqrt{b^2-4ac}}{2a}=\frac{-b-\sqrt{b^2-4ac}}{2a}\,\cdot\,\frac{2a}{-b+\sqrt{b^2-4ac}}=\\\\=\frac{-b-\sqrt{b^2-4ac}}{-b+\sqrt{b^2-4ac}}=\frac{b+\sqrt{b^2-4ac}}{b-\sqrt{b^2-4ac}}=\frac{b^2+2\sqrt{b^2-4ac}+b^2-4ac}{b^2-b^2+4ac}=\frac{2b^2+2\sqrt{b^2-4ac}-4ac}{4ac}=[/tex]

[tex]=\frac{b^2+\sqrt{b^2-4ac}-2ac}{2ac}[/tex]

Answer:

16a + 22t = 11826

Step-by-step explanation:

Cost of 1 (a) ticket = $16

Cost of 1 (t) ticket = $22

Total tickets sold = 648

Cost of 648 tickets = $11826

So eqn will be => 16a + 22t = 11826

This question is incomplete

Complete Question

The area of a sector of a circle is given by the equation A = πr²S/360 where r is the radius of the circle and S is the angle measure of the sector. If Mia solved this equation for S, which of the following equations did she write?

a) 360A+ πr²

b) 360A - πr²

c) 360 + A / πr²

d) 360A/ πr²

Answer:

d) 360A/ πr²

Step-by-step explanation:

In the above question,

Area of the sector (A) = πr²S/360

r = radius

We are also told that Mia solved for S = Angle measure of the sector.

In other to find the equation that Mia used to solve for S,

We would use the Subject of the formula method.

Area of the sector (A) = πr²S/360

We cross Multiply

360 × A = πr²S

Making S the subject of the formula, we divide both sides by πr²

360 × A / πr² = πr²S/ πr²

S = 360 × A/ πr²

S = 360A/ πr²

Therefore, the equation Mia wrote if she solve this equation ( A = πr²S/360) for S is :

S = 360A/ πr²

Option d is the correct option.

Answer:

It is C

Step-by-step explanation:

42.60=43.00

587.70=588.00

27.99=28.00

Answer:

d. (4) + (-5)

Step-by-step explanation:

We know that 4 is the positive value and 5 is the negative value, therefore if to be able to rewrite in it we will almost make a sum of these values without changing the meaning of each one of the values, therefore:

(+4) + (-5)

Which means that the correct option is the last option, that is, d. (4) + (-5). Furthermore, the representation is correct because the resulting arrow is the one corresponding to -1.

Answer:

52

Step-by-step explanation:

42, 45, 58, 63

The mean is the sum divided by the number of terms

(42+ 45+ 58+ 63)/4

208/4

52

Answer:

Step-by-step explanation:

42 + 45 + 58 +631 + 422 + 473 + 52 = 1723

then divide by 7 to get 246.142857

hope this helps :)

1. Yes a circle is a two-dimensional figure. It lies in the plane, which is basically a flat piece of paper that doesn't bend or curve, and the paper extends infinitely in all directions.

2. A circle is not a polygon. A polygon has finitely many straight line segments that glue together to form an enclosed figure. Think of fencing in an area with straight fence portions.

3. Yes this is what makes a circle. Every point on the circle is the same distance from the center. We say these points on the circle are equidistant from the center.

Answer:

Is a circle a two d figure?

YES. It is a flat figure.

Is a circle a polygon?

NO, because it does not have 4 straight sides.

Is every point in a circle the same distance from the center?

YES. All points in a circle are equidistant from the center (they are all equal)

Answer:  approximately 24 square units in the shaded areas

Step-by-step explanation:  

The area of the entire dark circles will be for each πr², then divided by 2 to get the area of the semicircles created on the sides of the triangles:

16π + 9π = 25π   Half that times value for pi

≈ 39.2699  is the area of the dark semicircles. Round to 39.27

Now the fun! Find the area of the parts subtracted by the light semicircle:

The area of the entire circle is 25π  or about 78.54. The triangle is half of an inscribed rectangle, 6×8, so 48.  Subtracted from the circle leaves about 30.54 in the four slices between the arcs of the circumference and the perimeter of the rectangle. We are concerned with only half of the slices, so we will subtract 15.27

Area of the dark semicircles minus the area of the light slices will leave the area of the shaded crescents:

Answer:

The answer is option B.

Explanation:

A rule that uniquely associates elements of one set A with the elements of another set B and each element in set A maps to only one element in set B.

Each element from X is related to only one element in Y. But it is okay for two different elements in X to be related to the same element in Y. So its  still a function. Let suppose

{ (1,a) , (2, b) , (2, c) , (3, d) }

This relation is not a function from X to Y because the element 2 in X is related to two different elements, b and c.

Step-by-step explanation:

Check the attachment... Hope it helps:)

Good luck!!

Answer:

  see the attachment

Step-by-step explanation:

The graph of the inverse function is the reflection of the function across the line y=x. It can also be found by swapping the x- and y-coordinates of every point.

The endpoints of the inverse function segment are (-2, -6) and (4, -1). These are the endpoint coordinates of the given relation, with the elements of the ordered pair reversed.

Answer:

To determine the number of real number solutions of as system of equations in which one equation is linear and the other is quadratic

1) Given that there are two variables, x and y as an example, we make y the subject of the equation of the linear equation and substitute the the expression for y in x into the quadratic equation

We simplify and check the number of real roots with the quadratic formula, [tex]x = \dfrac{-b\pm \sqrt{b^{2}-4\cdot a\cdot c}}{2\cdot a}[/tex] for quadratic equations  the form 0 = a·x² - b·x + c

Where b² > 4·a·c there are two possible solutions and when b² = 4·a·c equation there is only one solution.

Step-by-step explanation:

Answer:

Isolate one variable in the system of equations. Use substitution to create a one-variable equation. Then, set the quadratic equation equal to zero and find the discriminant. If the discriminant is negative, then there are no real number solutions. If the discriminant is zero, then there is one real number solution. If the discriminant is positive, then there are two real number solutions.

Step-by-step explanation:

I just took the test on Edge 2020

Answer:

10 times 16 = C

Step-by-step explanation:

c2 = a2 + b2 − 2ab cos C = 162 + 102 − 2(10)(16) cos 22°

Answer:

The height of the totem tree is approximately 172.8ft

Step-by-step explanation:

Hello,

To find the height of the totem pole, we need to use our date to make a pictorial representation so that we can know if the pole and base makes a right angle triangle with the angle of elevation.

See attached document for better illustration.

Let T represent the height of the pole.

Using trigonometric ratio,

SOHCAHTOA, we can use tangent since we have our adjacent and we're to solve for the opposite.

Tanθ = opposite/ adjacent

Opposite = T

Adjacent = 20ft

θ = 83.4°

Tan83.4 = T / 20

T = 20Tan83.4

T = 20 × 8.64

T = 172.8ft

The height of the totem tree is approximately 172.8ft

Answer:

Below

Step-by-step explanation:

●(xy)^(-1)

● x^(-1) * y^(-1)

● (1/x)*(1/y)

● 1/xy

Answer:

70 +60muinte= 13

Step-by-step explanation:

so that the ans

In h hours you will go 70h far from the original position and domain of the function is the amount of hours you drive option (C) is correct.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

The question is incomplete.

The complete question is:

Driving on the highway, you can safely drive 70 miles per hour. “How far can you drive in ‘h’ hours?” What is the domain of the function which defines this situation?

A.)The amount of gas you use.

B.) 70.

C.) The amount of hours you drive.

D.)The distance you drive

We have:

Driving on the highway, you can safely drive 70 miles per hour.

The speed of the vehicle = 70 miles per hour

As we know,

Distance = speed×time

1 hour → 70 miles

h hour → D miles

D(t) = 70h

The above expression represents the situation.

Thus, in h hours you will go 70h far from the original position and domain of the function is the amount of hours you drive option (C) is correct.

Learn more about the function here:

brainly.com/question/5245372

#SPJ5

Answer:

The answer is 21.25cm

Step-by-step explanation:

Hope i am marked as brainliest

Answer:

(1,0) and (3,0)

Step-by-step explanation:

y=x^2-4x+3

To factor we need to know what numbers add up to -4 and multiply will equal to 3.

y=(x-3)(x-1)

The zeroes would be 3 and 1.

x=3  so y=0 for (x-3)

x=1 so y=0 for (x-1)

If right pls give me brainliest thank you.

Answer:

(1, 0) and (3, 0)

Step-by-step explanation:

[tex]y=x^2-4x+3[/tex]

Plug y as 0 to find the x-intercepts.

[tex]0=x^2-4x+3[/tex]

Factor right side.

[tex]0=x^2-1x-3x+3[/tex]

[tex]0=x(x-1)-3(x-1)[/tex]

[tex]0=(x-1)(x-3)[/tex]

Set factors equal to 0.

[tex]x-1=0\\x=1\\x-3=0\\x=3[/tex]

x=1 or x=3 when y=0

Answer:

1) A rectangular shape

2) Point  (30, 50)

3) (x - 30)² + (y - 50)² = 10²

4) Yes, the swimming pool will touch the flower beds

5) Point (45, 25)

Step-by-step explanation:

1) Given the number of shapes that are rectangles (4) and the number of circular shapes (1) to conserve more space Kylee should drw the swimming pool with a rectangular shape

2)  So as to avoid touching the flowerbeds which are 20 feet apart, the center of the swimming pool will be moved slightly up to (30, 50)

3) The equation that will draw the swimming pool is the equation of a circle, given as follows

(x - h)² + (y - k)² = r²

Where (h, k) is the coordinate of the center of the circle, and r is the radius of the circle,

Given that the diameter, D, of the circle = 20 feet, the radius, r = D/2 = 20/2 = 10 feet

The equation of the circle is therefore;

(x - 30)² + (y - 50)² = 10²

4) The coordinates of the center of the flower bed is (30, 45) which gives

(x - 30)² + (y - 45)² = 10²

Where the coordinates of the side of the flower pot is (20, 45), we have;

(20 - 30)² + (45 - 45)² = 10²

(-10)² = 10² = r²

Hence, point (20, 45) is on the circle

The other flower bed side has coordinates (40, 45) which gives

(40 - 30)² + (45 - 45)² = 10²

10² = r² = 10²

Point (40, 45) is also on the circle

Therefore, the swimming pool will touch the flower beds

5) At point (45, 25), we have;

(x - 45)² + (y - 25)² = 10²

The closest point is the patio with coordinates (40, 15) which gives;

(40 - 45)² + (15 - 25)² = 10² = 100

(-5)² + (-10)² = 125 > 100

Therefore, point (40, 15), is not on the circle.

Answer:

Final velocity, v = 21.75 m/s

Step-by-step explanation:

Given that the relation between final velocity, initial velocity, acceleration and distance traveled is expressed as:

[tex]v^2=u^2+2as[/tex]

Also, given that:

Initial velocity, u = 9 m/s

Acceleration, a = 7 m/[tex]s^2[/tex]

Distance, s = 28 m

To find:

Final velocity, v = ?

Solution:

The given relation between v, u, a and s is:

[tex]v^2=u^2+2as[/tex]

We have the values of initial velocity, acceleration and distance traveled in the question statement. We just need to put all these values to find the value of final velocity.

Let us put all the values in the given equation and try to find final velocity, v:

[tex]v^2=9^2+2\times 7 \times 28\\\Rightarrow v^2=81+14 \times 28\\\Rightarrow v^2=81+392\\\Rightarrow v^2=473\\\Rightarrow v=\sqrt{473}\\\Rightarrow v=21.75\ m/s[/tex]

So, the answer is:

final velocity, v = 21.75 m/s

Answer:

C. Rectangle

Step-by-step explanation:

A parallelogram can not have a single 90° angle. This is because the opposite angles of a parallelogram are equal.

Therefore, the two opposite sides are equal.

In a parallelogram, neighboring angles add up to 180°. This therefore implies that all the angles are 90°.

This describes a rectangle.

1 Ampere = 1 Coulomb of charge per second

2.5 A  =  2.5 C of charge per second

Time to deliver 3.5 C of charge = (3.5 C) / (2.5 C / sec)

Time = (3.5 / 2.5) (C / C-sec)

Time = 1.4 sec

A current of 2.5 A delivers 3.5 C of charge in 1.4 seconds.

Answer:

1 out of 6 because you have only one chance to get 4.

Step-by-step explanation:

Answer:

50% chance

Step-by-step explanation:

A prime number is a number that a natural number greater than 1 that is not a product of two smaller natural numbers. And the only prime numbers between 1 and 6 are 2,3, and 5. This is 3 numbers. So he has a chance of 3/6 =.5=50%

Answer:

12 cm × 12 cm.

Step-by-step explanation:

It is given that a square tile has a piece broken off it with 7 cm². The area of the remaining rule is 137 cm².

Total area of square = 7 + 137 = 144 cm²    ...(1)

Area of a square is

[tex]Area=a^2[/tex]     ...(2)

where, a is side length of square.

From (1) and (2), we get

[tex]a^2=144[/tex]

Taking square root on both sides.

[tex]a=\sqrt{144}[/tex]

[tex]a=12\ cm[/tex]

Therefore, the dimensions of the original tile are 12 cm × 12 cm.