the sum of one-half t and one third s

So if you're asked to graph a function and its inverse, all you have to do is graph the function and then switch all x and y values in each point to graph the inverse. Just look at all those values switching places from the f(x) function to its inverse g(x) (and back again), reflected over the line y = x.

The equation of the line across which all inverses reflect is y = x. This reflection principle applies to linear functions, hyperbolas, and other mathematical relations where inverses can be found by interchanging the roles of x and y.

The equation of the line that all inverses reflect across is y = x. This is because when you are finding the inverse of a function, you swap the x and y variables, thus mirroring the original function across the line y = x. If you have a linear function in the slope-intercept form (y = mx + b), and you find its inverse, assuming the function is one-to-one and therefore has an inverse, you would essentially swap the x and y coordinates, resulting in the equation of its inverse. This process reflects each point of the original function across the line y = x.

As an example, for a line with an equation y = -x + 1, the inverse when reflected across the line y = x would result in swapping x and y to get x = -y + 1, which when solved for y, gives the inverse function's equation. Conversely, for a function expressed in another form, such as a hyperbola or a set of simultaneous linear equations, the principle is the same: to find the inverse, interchange the roles of the dependent and independent variables. For instance, a hyperbola described by y = a - b/x could have its inverse derived by interchanging x and y, leading to the inverse relation x = a - b/y.

Answer:

5

Step-by-step explanation:

Answer:

32

Step-by-step explanation:

multiply 25×6 =150

subtract 150-22 = 128

128÷4

32

Answer:

[tex]\displaystyle (3, 6)[/tex]

Step-by-step explanation:

{x -4y = −21

{8y - x = 45

_________

[tex]\displaystyle \frac{4y}{4} = \frac{24}{4} \\ \\ [/tex]

[tex]\displaystyle y = 6[/tex][Plug this back into both equations above to get the x-coordinate of 3]; [tex]\displaystyle 3 = x[/tex]

I am joyous to assist you anytime.

Answer:

When the denominator is an irrational number in order to make the denominator a rational number we rationalize the denominator.

Step-by-step explanation:

For example,

[tex]\frac{1}{1+\sqrt{2} }[/tex] (here the denominator is an irrational number)

Multiply the numerator and denominator by [tex]1-\sqrt{2}[/tex]

We get [tex]\frac{1-\sqrt{2} }{(1+\sqrt{2})(1-\sqrt{2}) }[/tex]

Here (1+\sqrt{2})(1-\sqrt{2}) = -1

Thus we get [tex]\sqrt{2} -1[/tex]

Here the denominator has become a rational number.

When we are isolating a variable we are only taking the required variables to one side thus it doesn't require rationalization.

[tex]a = \frac{x}{1+\sqrt{2} }[/tex]

Then we can say,

[tex]x = a(1+\sqrt{2})[/tex]

No rationalisation required

Answer:

B

Step-by-step explanation:

in B, the expression can be writting in variation form as

y∝1/x

this indicate an inverse variation

Answer:

B) y=6/x

Step-by-step explanation:

I took the test.

Answer:

see the explanation

Step-by-step explanation:

we know that

To find out how many people voted for each option multiply the percentage in decimal form of each option by the total number of people

so

[tex]84\%=84/100=0.84[/tex] ---> [tex]0.84(6)=5.04=5\ people[/tex]

[tex]16\%=16/100=0.16[/tex] ---> [tex]0.16(6)=0.96=1\ people[/tex]

Answer:

30 miles

Step-by-step explanation:

We know

D = RT

Where

D is the distance

R is the rate

T is the time

Towards Island:

R = 15

Let time be x

So, we can write:

D = 15x

Return from Island:

R = 10

Let time be y

So, we can write:

D = 10y

Also, total time is 5 hours, so we can write:

x + y = 5   [equation 2]

Now, since the distance for both legs of the journey is equal, we can write:

Distance 1 = Distance 2

15x = 10y

Now we replace this equation with equation 2, so we get:

Equation 2: x + y = 5 or x = 5 - y

15x = 10y

15(5 - y) = 10y

75 - 15y = 10y

75 = 25y

y = 75/25

y = 3

Distance 2 = D = 10y

Replacing y with 3, we get:

D = 10y

D = 10(3)

D = 30

So, the distance to island is 30 miles

Answer:

Option A. [tex]\frac{sin(45\°)}{7}=\frac{sin(40\°)}{b}[/tex]

Step-by-step explanation:

we know that

Applying the law of sines in the triangle ABC

[tex]\frac{sin(A)}{a}=\frac{sin(B)}{b}[/tex]

substitute the given values

[tex]\frac{sin(45\°)}{7}=\frac{sin(40\°)}{b}[/tex]

[tex]b=\frac{7}{sin(45\°)}sin(40\°)\\\\b=6.4\ units[/tex]

1.) 7+5 > 6+2

2.) g ≥ 8

3.) s = -2, -8

4.) from the middle and beyond (best way i can answer)

5.)

b < 11 = The board is shorter than 11 cm

b > 11 = The box contains more than 11 books

b < 12 = There are fewer 12 beetles in a jar

b > 12 = The building is taller than 12 ft.

Answer:

1. 6 times 5

2. 7/6 simplified

3. 4 times 13

4. 45 divided by 1 1/6

5. 10 as a proporation

Step-by-step explanation:

Answer:

4 is the greatest

Step-by-step explanation:

Answer:

NOT PROPORTIONAL

Step-by-step explanation:

The given two fractions are: [tex]$ \frac{5}{8} $[/tex] and [tex]$ \frac{8}{10} $[/tex].

Proportional fractions are those which have the same value when to reduced to the simplest form.

Consider two fractions [tex]$ \frac{p}{q} $[/tex] and [tex]$ \frac{x}{y} $[/tex].

We say they are proportional if [tex]$ p : q = x : y $[/tex].

Or, if [tex]$ py = qx $[/tex] then we can say the fractions are proportional.

Here the fractions are:  [tex]$ \frac{5}{8} $[/tex] and [tex]$ \frac{8}{10} $[/tex].

LHS: 5 X 10 = 50.

RHS: 8 X 8 = 64.

Clearly they are not equal. So, we can say these two fractions are not proportional.

Answer:

x is less than 6 so that is correct because 24 divided by 4 is 6

 Answer:

Number of Adult's tickets sold on Saturday = 3,356

Number of Children's tickets sold on Saturday = 2, 928

Total number of tickets sold over these two days is 8,938.

Step-by-step explanation:

Here, the number of tickets sold on FRIDAY:

Adult Ticket sold = 1,678

Children's Tickets sold = 976

So, the total number of tickets sold on Friday  

= Sum of ( Adult + Children's ) tickets  = 1,678  + 976 = 2,654 ....  (1)

The number of tickets sold on SATURDAY:

Adult Ticket sold =   2 times  the number of adult tickets sold on Friday  

                             =  1,678 x 2  = 3,356

Children's Tickets sold = 3 x the number of children's tickets sold on Friday.

                                      =  976  x 3 = 2, 928

So, the total number of tickets sold on Saturday  

= Sum of ( Adult + Children's ) tickets  = 3,356 + 2,928 = 6, 284 ....  (2)

Now, the total number of tickets booked in these two days :

Sum of tickets booked on (Friday + Saturday)

= 2,654 +  6, 284  =   8,938

Hence, total number of tickets sold over these two days is 8,938

Answer:

Step-by-step explanation:

- Predicting the gender of an arbitrarily picked craftsmanship educator if 1 of 3 workmanship / art instructors is female .

- Predicting the gender of a haphazardly picked science / biology instructor if 8 of 12 biology educators are female .

- Predicting the gender of a haphazardly picked health educator if 2 of 4 health instructors are female .

Answer:

1/3 8/12 2/4

Step-by-step explanation:

Because they involve 6

Answer:

42 years, 9 months

Step-by-step explanation:

Using the compound interest formula Accrued Amount = P (1 + r/n)^(nt)

where Accrued amount (A) which is quadruple the initial deposit

A = 4 x 500 = $2000

P = principal; $500

r = 3.25% = 0.0325

t = number of years

n = number of times interest is compounded = 12 for monthly

Therefore

2000 = 500 (1 + 0.0325/12)^(12t)

Therefore

(1.002708)^12t = 2000/500

(1.002708)^12t = 4

finding the log of both sides

12t x log 1.002708 = log 4

12t x 0.001174 = 0.6021

12t = 0.6021/0.001174

12t = 512.83

t = 512.83/12

t = 42.7

which is estimated as 42 years, (0.7 x 12 = 9) months

hence it takes about 43 years to quadruple the deposit

The number of years it will take to be the amount by quadruple will be 42.7 years.

Compound interest is applicable when there will be a change in the principal amount after the given time period.

As per the given,

The total amount will be,

A = 4 × 500 = $2000

Principle amount P = $500
Rate of interest r =  3.25% = 0.0325

The time period is t.

n = number of times interest is compounded

n = 12

By compound interest formula,

2000 = 500 [tex](1 + 0.0325/12)^{12t}[/tex]

(1.002708)^12t = 2000/500

(1.002708)^12t = 4

Take logs on both sides,

12t × log 1.002708 = log 4

12t × 0.001174 = 0.6021

12t = 0.6021/0.001174

12t = 512.83

t = 512.83/12

t = 42.7

Thus, the time period will be 42.7 years.

Hence "The number of years it will take to be the amount by quadruple will be 42.7 years.".

For more information about compound interest,

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Answer:

3. irrational

4. rational

5. rational

6. natural, whole, integer, rational

Step-by-step explanation:

Answer:

-88/85

Step-by-step explanation:

2 14/49=112/49

7 3/85=598/85

3 35/49=182/49

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

112/49-(598/85-182/49)

112/49-1976/595

-88/85

[A] 23w + 35 = 150 ; Sal will have enough money in 5 weeks.

We can see 35 as the starting value since he already has that amount when he started saving up money. We can subtract it (150 - 35 = 115). Then we can divide (115 / 23 = 5). It took Sal 5 weeks to save enough money for the bike. The first option makes the most sense because the expression can be solve to find how many weeks he save up his money.

_______

Best Regards,

Wolfyy :)

√6(7+√2)

Use the distributive property:

√6 * 7 + √6 * √2

Move the 7 to the left:

7 * √6 + √6 * √2

Use the product rule for radicals on  √6 * √2

7 * √6 + √(6*2)

Simplify:

7√6 + √12

Rewrite 12 as 2^2*3

7√6 + √(2^2*3)

Pull terms out from under the radical for final answer:

7√6 + 2√3

The kinetic energy (Ek) of the car with a mass of 1000 kg moving at a speed of 20 m/s is calculated using the formula Ek = 0.5 * m * v². Substituting the given values, we find the kinetic energy to be 2.00 x 10⁵ Joules.

To calculate the kinetic energy (Ek) of a car with a given mass and speed, you can use the formula Ek = 0.5 * m * v², where m is the mass, and v is the speed. In this case, the mass (m) of the car is 1000 kg, and the velocity (v) is 20 m/s.

Substituting the given values into the formula, we have Ek = 0.5 * (1000 kg) * (20 m/s)². This simplifies to Ek = 2.00 x 10⁵ J (Joules), which is the kinetic energy of the car.

It's important to note that kinetic energy always has units of Joules in the International System (or SI), and it represents the energy that an object has due to its motion.

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Answer:

Procedure in option C only works.

Step-by-step explanation:

We have to select the process in which Mrs. Smith can help her to work 30 divided by 3.

(A) (27 divided by 9) + (9 divided by 3) = 3 + 3 = 6  

But (30 ÷ 3) = 10 ≠ 6

(B) (24 divided by 4) + (4 divided by 4) = 6 + 1 = 7 ≠ 10

(C) (21 divided by 3) + (9 divided by 3) = 7 + 3 = 10

(D) (20 divided by 4) + (10 divided by 4) = 5 + 2.5 = 7.5 ≠ 10

So, procedure in option C only works. (Answer)

Again, we can prove the procedure in the following way:

[tex]\frac{30}{3} = \frac{21 + 9}{3} = \frac{21}{3} + \frac{9}{3}[/tex]  

{Which is the distributive property of division}

Answer:

The number of terms of the G.P. is 6

Step-by-step explanation:

Let the G.P. has first term a, common ratio r and the number of terms n.

The G.P. has first term 2, so a = 2.

Now, the fourth term is 54 i.e. ar³ = 54

⇒ 2r³ = 54

⇒ r³ = 27

⇒ r = 3

Now, the last term i.e. the nth term is= [tex]ar^{n - 1} = 486[/tex]

⇒ [tex]2 \times 3^{n - 1} = 486[/tex]

⇒ [tex]3^{n - 1} = 243 = 3^{5}[/tex]

Hence, (n - 1) = 5

⇒ n = 6

So the number of terms of the G.P. is 6 (Answer)

Answer:

4

Step-by-step explanation:

7-3 pretty much

Answer: x=-10

Step-by-step explanation:

let x be that number

so, 7+x=-3

subtract 7 on both sides and...

x=-10

Good evening ,

Answer:

The set of solutions is IR

Step-by-step explanation:

-2(2x+8)>-16-4x ⇌ -4x-16>-16-4x

Any x∈IR verify the inequality

then The set of solutions is IR.

:)

Answer:

aₙ = a₁ . 5⁽ⁿ⁻¹⁾

Step-by-step explanation:

The first term in the sequence is a₁ = 6.

a₂ = 30. a₃ = 150.

We see that each consecutive term is multiplies by 5 to arrive at the next term.

That is: a₂ = 30 = a₁ . [tex]$ 5^{2 - 1}  = 5 $[/tex] = 6.5 = 30.

Similarly, a₃ = 150 = 6 [tex]$ \times $[/tex] [tex]$ 5^{3 - 1} = 5^2 = 25 $[/tex]

Generalizing this, we have:

aₙ = a₁ . [tex]$ 5^{n - 1} $[/tex]

This is called the recursive formula of the sequence.

Answer:

g+4-5

Step-by-step explanation:

because the plus would go first anyways.

Answer:

Each dog toy costs $1.75.

Step-by-step explanation:

6x=10.5

x=10.5/6

x=1.75

Answer: The tip is $17. The total amount he paid is $102.

Step-by-step explanation: 85 times .2 gets the tip, then you add that sum to the subtotal.

Answer:

The relation to find base is, [tex]base=\frac{area\ of\ the \ parallelogram}{height}=\frac{86}{12}=7.16\ cm[/tex]

Step-by-step explanation:

Given

Area of the parallelogram [tex]=86\ cm^2[/tex]

Height of the parallelogram [tex]=12\ cm[/tex]

We know that the area of the parallelogram [tex]=base\times height[/tex]

So

To find base we have to divide the height on both sides of the equation.

[tex]base=\frac{area\ of\ the \ parallelogram}{height}[/tex]

Plugging the values.

[tex]base=\frac{86}{12} =7.1\ cm[/tex]

So the base in terms of area of the parallelogram and its height is [tex]b=\frac{area}{height} =\frac{86}{12}=7.16\ cm[/tex]

Answer:

The total amount of money Alex spends on 5 DVD = $ 35.

Step-by-step explanation:

Total number of DVD purchased by Alex = 5

The cost of each DVD = $9

So, the total cost of purchasing 5 DVD = 5 x ( csot of 1 DVD)

= 5 x ( $ 9) = $ 45

Now , the discount if 1 DVD = $ 2

So, the total discount of 5 DVD = 5 x ( Discount on1 DVD)

= 5 x ($ 2) = $ 10

⇒ The total amount Alex spends

= Total cost of 5 DVD - Discount on 5 DVD

= $ 45 - $ 10 = $ 35

Hence, the total amount of money Alex spends on 5 DVD = $ 35.