How do the graph of f(x) and f^(-1)(x) relate?
A.They are rotations of each other.
B.They are reflections of each other.
C.They are the exact same graph.
D.They are translations of each other.

The linear equation that represents the line that passes through the points (4,5) and (0,-3) is given by:

B. y = 2x - 3

A linear function is modeled by:

y = mx + b

In which:

The line passes through (0,-3), that is, when x = 0, y = -3, hence the y-intercept is of b = -3.

The slope is given by the change in y divided by the change in x, hence:

m = (5 - (-3))/(4 - 0) = 2

Hence the equation is:

y = 2x - 3.

Which means that option B is correct.

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Answer:

17

Step-by-step explanation:

5x+5x+10=180

10x=170

x=17

Answer:

Answer is 17

Step-by-step explanation:

It is done in this step

5x +5x+10=180

10x=170

x=17

Answer:

576 m

__________________________________________________________ The surface area of the triangular prism is (Perimeter of the base × Length of the prism) + (2 × Base Area) = (S1 + S2+ S3)L + bh

For this question,
you know that the perimeter of the base is 6+10+8 which is 24.
and the length of the prism is 22,
so (22x24) + Base Area which is (6x8)/2-> 24x2
(22x24)+(24x2)= 528 + 48 = 576
so your answer is 576
__________________________________________________________

Hope this helped!

The figure that shows the reflection of the letter Z is C

The figure shows the letter Z and four of its transformed images—A, B, C, and D

Which of the four images was formed by a reflection of the letter Z?

A   B   C    D

From the graph, see attachment, we have the following highlights:

The letter Z is in the second quadrant.

Also, B and D are letter Z.

So, they cannot represent the reflection

When reflected across the x-axis, the reflection is C

Hence, the figure that shows the reflection of the letter Z is C

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Answer:

-1 and -11

Step-by-step explanation:

"sum" means we're adding.

-1 + -11 = - 12

"product" means we're multiplying.

-1 × -11 = 11

Answer:

Slope =  - 1

Step-by-step explanation:

The equation is in form [tex]y=mx+c[/tex], [tex]m[/tex] s the slope and [tex]c[/tex]  is the intercept on [tex]y[/tex] axis.

Hence, in [tex]y=-x+3[/tex] , slope is -1  and intercept on [tex]y[/tex] axis is 3.

Answer:

D. 11

Step-by-step explanation:

Take the two horizontal line measurements and subtract them.

13-9=4

That is how much it changed between these two numbers. Since x is exactly halfway between, simply divide 4 and 2.

4/2=2

Now, add that to 9 or subtract it from 13.

9+2=11

or

13-2=11.

Hope this helps!

If not, I am sorry.

Answer:

D. 11

Step-by-step explanation:

Since segment AC bisects segments ED and BF, the length of AC is the average of the lengths of EB and DF.

AC = x = (EB + DF)/2 = (9 + 13)/2 = 22/2 = 11

Answer: D. 11

Answer:

slope = [tex]\frac{1}{3}[/tex]

Step-by-step explanation:

calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (6,3) and (x₂, y₂ ) = (9,4) ← 2 ordered pairs from the table

m = [tex]\frac{4-3}{9-6}[/tex] = [tex]\frac{1}{3}[/tex]

x = 90°

2x = 180°

Step-by-step explanation:

angle VTS= angle TSR (alternate angle)

now in ∆TRS,

2x + x + x = 360° (angle sum property of ∆)

4x = 360°

x = 90°

Answer: [tex]\frac{r^9}{r^3} = r^{9-3} = r^6[/tex]

We subtract the exponents when dividing terms with the same base.

The general rule is [tex]\frac{a^b}{a^c} = a^{b-c}[/tex]

Hii!

___________________________________________________________

[tex]\rightsquigarrow\circ\boldsymbol{Answer}\circ\leftharpoonup[/tex]

r^6

[tex]\rightsquigarrow\circ\boldsymbol{Explanation}\circ\leftharpoonup[/tex]

To simplify this we need to use the division property of exponents:

[tex]\large\boxed{\mathtt{\frac{x^m}{x^n} =x^{m-n}}}[/tex]. So if we divide two numbers with the same base, we subtract their exponents.

Let's apply this rule here.

[tex]\twoheadrightarrow\sf r^9\div r^3[/tex].

[tex]\bullet[/tex] Since these two numbers have the same base, we subtract their exponents

[tex]\twoheadrightarrow\sf r^6[/tex]

[tex]\bullet[/tex] Great job! We found the answer

--

Hope that this helped! Best wishes.

[tex]\textsl{Reach far. Aim high. Dream big.}\\\boldsymbol{-Greetings!-}[/tex]

--

Answer:

(2.5, - 10 )

Step-by-step explanation:

given endpoints (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is

( [tex]\frac{x_{1}+x_{2} }{2}[/tex] , [tex]\frac{y_{1}+y_{2} }{2}[/tex] )

here (x₁, y₁ ) = (- 16, - 12 ) and (x₂, y₂ ) = (21, - 8 ) , then

midpoint = ( [tex]\frac{-16+21}{2}[/tex] , [tex]\frac{-12-8}{2}[/tex] ) = ( [tex]\frac{5}{2}[/tex], [tex]\frac{-20}{2}[/tex] ) = (2.5, - 10 )

Answer: c - (2 1/2 - 10)

Step-by-step explanation:

Answer: These ARE congruent to each other.

Step-by-step explanation: Do you see the ''tick marks?'' They both have 1 set of 2, and 1 set of 1. If that makes sense. They also have a "angle" in one of their acute angles.

A person can immigrate to another country for educational purposes.

A person can emigrate to another country for work.

A person can emigrate to another country due to war in their own country.

Migration is when a person moves from one geographical location or another. Immigration and emigration are types of migration.

Immigration is when a person moves to a foreign country. For example, when a US citizen moved to Italy for work. Emigration is when a person lives his home country.

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Answer:

88 sq. units

Step-by-step explanation:

1st. BxH

12-4 = 8 is our Base

8x8=64 that is out 1st area

and 2nd area is LxW which is 12x2 = 24

64+24= 88 sq. units

Answer:

x = 64

Step-by-step explanation:

Solve for x: √x + 3-4=7

√x + 3-4=7

= √x + 1 = 7

= √x = 7 + 1

= √x = 8

= (√x)² = 8²

x = 64

Answer:

angle A=angleB .…(समदिबाहु त्रिभुज भएर)

34°=(x-5)°

or, 34=34

angleA+angleB+angleC=180°

or, 34+34+4y=180

or, 68+4y=180

or, 4y=180-68

or, 4y=112

or, y=112÷4

or, y=28

Answer:

A. True

Step-by-step explanation:

One of the ways to check this is solving each side of the equation.

(5+4)+10=5+(4+10)

Remember PEMDAS.

Parenthesis first.

(9)+10=5+(14)

Now, you can drop the parenthesis and add the numbers together.

9+10=19

5+14=19

19=19

This is a true statement.

Hope this helps!

If not, I am sorry.

Answer:

A = 27π cm²

Step-by-step explanation:

the area (A) of the sector is calculated as

A = area of circle × fraction of circle

the central angle of the shaded sector = 360° - 90° = 270° , then

A = πr² × [tex]\frac{270}{360}[/tex]

  = π × 6² × [tex]\frac{3}{4}[/tex]

  = 36π × [tex]\frac{3}{4}[/tex]

  = 9π × 3

 = 27π cm²

Answer:

choice C

Step-by-step explanation:

x could be any number except -1.

Cause for x=-1 the denominator becomes undefined.

Answer: [tex]8\sqrt{5}[/tex]

Step-by-step explanation:

By the geometric mean theorem,

[tex]\frac{y}{16}=\frac{4}{y}\\\\y^{2}=64\\\\y=8[/tex]

Thus, by the Pythagorean thoerem,

[tex]8^2 +16^2=x^2\\\\320=x^2\\\\x=\boxed{8\sqrt{5}}[/tex]

Answer:

[tex]3a^2+12a+12[/tex]

Step-by-step explanation:

first, you have to plug in x = a+2 into the function, which would look like:

[tex]f(a+2) =3(a+2)^2[/tex]

then, you can first simplify [tex](a+2)^2[/tex]. to do this, use the rule [tex](a+b)^2 = a^2 +2ab + b^2[/tex], so it would be [tex]a^2+(2*a*2)+2^2 = a^2 + 4a + 4[/tex]

this means your new equation is:

[tex]3(a^2+4a+4)[/tex]

you can then distribute the 3:

[tex]3*a^2+3*4a + 3*4 = 3a^2+12a+12[/tex]

let me know if there's anything you want me to clarify!

Answer:

√30/6 = √5

The correct answer would be E

The value of the expression √30/√6 is √5, option E is correct.

A number system is defined as a system of writing to express numbers.

The given property is √a/√b = √(a/b)

Now we have to find the equivalent to the quotient √30/√6

By the given property let us plug in a as 30 and b as 6

√30/√6

= √(30/6)

When we simplify the fraction inside the root we get 5

= √5

Hence, the value of the expression √30/√6 is √5, option E is correct.

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The events "male” and "buys lunch” are not independent because P(male | buys lunch) = 0.4 and P(male) = 0.3.

James surveyed people at school and asked whether they bring their lunch to school or buy their lunch at school more often. The results are shown below.

Bring lunch: 46 males, 254 females

Buy lunch: 176 males, 264 females

The events "male" and "buys lunch" are not independent because

The number of male students is:

Male = 46 + 176

Male = 222

The number of female students is:

Female = 254 + 264

Female = 518

The total student is:

Total = 222 + 518

Total = 740

Next, calculate the probability of selecting a male student

P(Male) = 222/740

P(Male) = 0.3

Of all the 440 that buy lunch, 176 are male,

So, we have:

P(male | buy lunch) = 176 / 440

P(male | buy lunch) = 0.4

Because

P(male | buy lunch) and P(male) are not equal.

Then, the events "male” and "buys lunch” are not independent

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The inverse of the function will be [tex]f(x) ^{-1}= 2x - 12\\[/tex]. option C is correct.

Suppose that the given function is

[tex]f:X\rightarrow Y[/tex]

Then, if function 'f' is one-to-one and onto function (a needed condition for inverses to exist),

then, the inverse of the considered function is

[tex]f^{-1}: Y \rightarrow X[/tex]

The function is given as

[tex]f(x) = \dfrac{1}{2} x - 6\\\\[/tex]

The inverse of the function will be

[tex]f(x) ^{-1}= 2x - 12\\[/tex]

Therefore, option C is correct.

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The number of peanuts ( x ) he could plant on 8,500 square meters of land = 95.6 kg

"It is a method of finding the value of a single unit, and based on that value we can find the required value."

For given question,

A farmer can plant 45 kg of peanuts on 4,000 square meters of land.

Using unitary method,

[tex]\frac{4000}{45}\\\\=88.8888 \\\\\approx 88.89[/tex]

This means, a farmer can plant 1 kg of peanuts on 88.89 square meters of land.

We need to find the number of peanuts ( x ) he could plant on 8,500 square meters of land.

Here, 1 kg = 88.89 square meters

          x kg = 8500 square meters

[tex]\Rightarrow x=\frac{8500}{88.89}\\\\ \Rightarrow x = 95.6~kg[/tex]

Therefore, the number of peanuts ( x ) he could plant on 8,500 square meters of land = 95.6 kg

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The probability of hitting the shaded area is 0.64

The diameters are given as:

D = 10

d = 6

The shaded area is calculated as:

Shaded = π((D/2)² - (d/2)²)

So, we have:

Shaded = π((10/2)² - (6/2)²)

Evaluate the exponents

Shaded = 16π

The area of the big circle is calculated as:

Area = π(D/2)²

So, we have:

Area = π(10/2)²

Evaluate the exponents

Area = 25π

The probability of hitting the shaded area is:

P = 16π/25π

Evaluate

P = 0.64

Hence, the probability of hitting the shaded area is 0.64

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Answer:

Step-by-step explanation:

Simplify the following expression:

Simplify the following expression:

7a + 5b - 2a + b =

5a + 6b

Answer:

if a line is parallel they have the same slope

so the slope is 5

Hope This Helps!!!