If f(x) = 3x + 7, which of these is the inverse of f(x)?

Answer:

Part A) The system has one solution

Part B) The solution is the point (4,4)

Step-by-step explanation:

step 1

Find the equation of the line A

we have

(0,6) and (6,3)

Find the slope

m=(3-6)/(6-0)

m=-0.5

Find the equation of the line into slope intercept form

y=mx+b

we have

m=-0.5

b=6 -----> the point (0,6) is the y-intercept

substitute

y=-0.5x+6 ------> equation A

step 2

Find the equation of the line B

we have

(0,0) and (6,6)

Find the slope

m=(6-0)/(6-0)

m=1

Find the equation of the line into slope intercept form

y=mx+b

we have

m=1

b=0 -----> the line represent a direct variation

substitute

y=x ------> equation B

step 3

Find how  many solutions does the pair of equations for lines A and B have

we have

y=-0.5x+6 ------> equation A

y=x ------> equation B

Solve the system of equations by graphing

Remember that the solution of the system of equations is the intersection point both lines

using a graphing tool

There is one point of intersection

therefore

The system has one solution

see the attached figure

step 4

What is the solution to the equations of lines A and B?

we know that

The solution of the system of equations is the intersection point both lines

The intersection point is (4,4)

therefore

The solution is the point (4,4)

so

x=4,y=4

Answer:

Step-by-step explanation:

Let's say the numbers are x and y, and y is larger than x.

x + y = 27

y = 6 + 2x

Substitute:

x + (6 + 2x) = 27

3x + 6 = 27

3x = 21

x = 7

So x = 7 and y = 20.

Answer:

y=3(0.8)x

Step-by-step explanation:

An exponential function is a function of the form;

[tex]y=ab^{x}[/tex]

The explanatory variable x is the exponent, a is the initial value and b the base of the exponential function.

The function is said to be an exponential decay function if the base is between 0 and 1;

0<b<1

Therefore, y=3(0.8)^x is the required function. The values of y become smaller as x increases.

Answer:

Step-by-step explanation:

The factors of each term are ...

So, the greatest common factor is 3a. Factoring that out gives ...

  3a(16a^2 -25) . . . . . . matches answer 2

The factor in parentheses is the difference of squares, so it can be factored. You have memorized the form for the difference of squares ...

  p^2 -q^2 = (p -q)(p +q)

so you know the factoring of this with p=4a and q=5 will be ...

  3a(4a -5)(4a +5) . . . . . . matches answer 4

__

Any pair of factors can be multiplied by -1 without changing the value of the expression. So, two more answers are equivalent:

   (-3a)(-(16a^2 -25) = -3a(25 -16a^2) . . . . . . matches answer 5

  (-3a)(-(4a -5)(4a +5) = -3a(5 -4a)(5 +4a) . . . . . . matches answer 6

Answer:

2 4 5 6

Step-by-step explanation:

The highest common factor is 3a That means that 48a^3 must be divided by 3a which means 48a^3 / 3a = 16a^2. Notice what happened. 48/3 = 16. a^3/a = a^2.

Now you have to pull out 3a from 75a. That wasn't done to Answer 1. So answer one is incorrect.

75a/3a = 25

So far what you answer looks like is

3a(16a^2 - 25) which is answer 2

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

Answer 3 is wrong because one of the factor has to be - 5. Neither one is.

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

Answer 4 is correct

16a^2 - 25 factors into (4a - 5)(4a + 5)

So what is written reflects those factors + the 3a

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

Now we come to the brutal ones.

If you take out a minus sign from the brackets, it has the effect of turning the two terms inside the brackets around.

-3a(25 - 16a^2) is what the above sentence means. so 5 is correct

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

The two terms inside the brackets still factor

-3a ( 5 - 4a)(5 + 4a) It is just that they are turned around.

6 is correct.

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

Each pack costs 5 dollars so you take 5 times 8 to get 45 dollars. Then you take to 8 and times it by 10 to get a total of 80 pens

Answer:

D

Step-by-step explanation:

The difference in the x-coordinates is Δx = 6 - 3 = 3.

The difference in the y-coordinates is Δy = 8 - 2 = 6.

One third the difference is Δx/3 = 3/3 = 1 and Δy/3 = 6/3 = 2.

So the one-third point is at (3 + 1, 2 + 2) = (4, 4).

In general the segment from A to B has parametric equation

X = (1-t)A + tB

t=0 gives point A, t=1 gives point B, and in between we move linearly with t from A to B.

So if we want AX:BX=1:3, that's 1/(1+3)=1/4 of the way along from A to B, so corresponds to t=1/4.  So the point we seek is

X = (1 - 1/4)(3, 2) + (1/4)(6,8) = ((9+6)/4, (6+8)/4)=(15/4, 7/2)

Answer: Choice C

The ratio of areas of similar triangles is the square of the ratio of their linear dimensions. If the smaller triangle is 1/2 the area of the larger, then its linear dimensions are √(1/2) those of the larger triangle.

  smaller side length = √(1/2) × larger side length

  = (√2)/2×36 = 18√2 ≈ 25.4558

Answer:

2.3 and 3.6

Step-by-step explanation:

Final answer:

To solve the equation x^2 - 9|||-3 = log3 x, simplify both sides of the equation and then find the values of x that satisfy the equation.

Explanation:

To find the values of x that satisfy the equation, we can start by simplifying both sides of the equation.

On the left side, we have x^2 - 9|||-3. To simplify this, we first evaluate the absolute value of -3, which is 3. Then we have x^2 - 9(3), which simplifies to x^2 - 27.

On the right side, we have log3 x.

Setting the two sides equal to each other, we have x^2 - 27 = log3 x.

To solve this equation, we can graph both sides and find the intersection points, or we can use numerical methods like iteration or Newton's method to find the approximate solutions.

Answer:

Step-by-step explanation:

2*pi - sqrt(3)

pi = 3.14159

2pi = 6.283184

sqrt(3) = 1.73205

Answer

6.283184 - 1.73205

4.51133

Answer:

Sorry about being so late, but the answer is

4.55

OR

4.55113449961

Step-by-step explanation:

here the centre of circle(h,k) is (-2,4)

and its radius(r) is 6 uints.

now the equation of circle is,

(x-h)^2 +(y-k)^2 =r^2

or, (x+2)^2 + (y-4)^2=6^2

or, x^2 + 4x + 4+y^2 -8y+16=36

or, x^2 +y^2 + 4x -8y -16=o

Explanation:

___

Similar relationships pertain to the diagonal BD and segments EH and FG. You can also conclude that area EFGH is half of area ABCD by considering the various triangles you get by connecting midpoints different ways.

Answer:

  500

Step-by-step explanation:

A sequential search starts with the first item on the list, making a comparison with every item until the desired one is found. It takes 500 comparisons to find the 500th item.

Answer:

  36

Step-by-step explanation:

The total number of options is the product of the numbers of independent options: 3×3×4 = 36.

__

For each of the bedroom options, she can choose any parking option, so can have ...

  1 br, street parking

  2 br, street parking

  3 br, street parking

  1 br, assigned parking

  2 br, assigned parking

  3 br, assigned parking

  1 br, garage spots

  2 br, garage spots

  3 br, garage spots

That is, 3×3 = 9 options. Any of these can be put with any of the four lease options, for a total of 9×4 = 36 options altogether.

The answer would be 36

Answer:

No.

Step-by-step explanation:

Because x²-5x+7, as x = 9 is 9²-5·9+7 = 81-45+7 ≠ 0

f(x) = x²-5x+7 is divisible by x-9 only if f(9) = 0.

Answer:

250/3π cubic inches

Step-by-step explanation:

we know that

The volume of the space between the cylinder and the sphere is equal to the volume of the cylinder minus the volume of the sphere

step 1

Find the volume of the cylinder

The volume of the cylinder is equal to

[tex]V=\pi r^{2} h[/tex]

we have

[tex]h=10\ in[/tex]

[tex]r=5\ in[/tex]

substitute

[tex]V=\pi (5)^{2} (10)[/tex]

[tex]V=250\pi\ in^{3}[/tex]

step 2

Find the volume of the sphere

The volume of the sphere is equal to

[tex]V=\frac{4}{3}\pi r^{3}[/tex]

we have

[tex]r=5\ in[/tex]

substitute

[tex]V=\frac{4}{3}\pi (5)^{3}[/tex]

[tex]V=(500/3)\pi\ in^{3}[/tex]

step 3

Find the difference

[tex]250\pi\ in^{3}-(500/3)\pi\ in^{3}=(250/3)\pi\ in^{3}[/tex]

Answer:  B) 115

Step-by-step explanation:

S₅ means the sum of the first 5 numbers in the sequence.

3 + 13 + 23 + 33 + 43 = 115

Answer:

Step-by-step explanation:

X has a binomial distribution when the probability of X is the same for each spin.

When the spinner is spun four times, X is the number of times the spinner does not land on an odd number.

When the spinner is spun five times, X is the number of times the spinner lands on 1.

Answer with explanation:

Total number of sections in the spinner = 1 to 5=5 in all

For, a Distribution to be a Binomial Distribution,

Number of trials  should be fixed.

All trials should be Independent of one another.

Only two outcomes  are Possible one is called Success and Other is failure.

Probability of each Outcome should remain constant irrespective of number of trials.

Probability of getting either of 1,2,3,4,or 5 when the spinner is spun once

    [tex]=\frac{1}{5}[/tex]

Option C

When the spinner is spun four times, X is the number of times the spinner does not land on an odd number.

Probability of Failure ={1,3,5}=Getting odd number on spinner

          [tex]=\frac{3}{5}[/tex]

Probability of Success={2,4}=Getting even number on spinner

       [tex]=\frac{2}{5}[/tex]

Number of trials is fixed and each trial is independent of another.

Option D

Total Number of Trials= 5

Probability of Success = When the Spinner is spun and it Lands on 1

Probability of Failure = When the Spinner is spun and it does not Land on 1

When the Spinner is spun five times ,Probability of each Outcome,that is either of 1,2,3,4,or 5 is constant which is [tex]\frac{1}{5}[/tex]

⇒⇒When the spinner is spun five times, X is the number of times the spinner lands on 1.

→≡Option C and D

Answer:

9

Step-by-step explanation:

coefficients = numbers in front of variables (x, x^2 etc)

so 5 + 3 + 1 = 9

In the expression 3x^4 + 5x^2 + x, the coefficients are 3, 5, and 1. Adding these values together gives a sum of 9.

In the expression 3x^4 + 5x^2 + x, the coefficients are 3, 5, and 1 respectively. The term x is implied to have a coefficient of 1 though it is not written explicitly. We find the sum of the coefficients by simply adding all these values together. So the sum would be 3 + 5 + 1 = 9.

The term x is implied to have a coefficient of 1 though it is not written explicitly. We find the sum of the coefficients by simply adding all these values together.

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well, the movie lasted 1:38   so.... and she finished it at 1:10pm.

1:10pm minus 1 hour?  12:10pm.

12:10 pm minus 10 and minus 28 minutes?   12:10 - 00:10 = 12:00pm, 12:00 - 00:28 minutes = 11:32am.

Answer: 11:32

Step-by-step explanation:

Answer:

(x-2)²+(y--2)²=9

Step-by-step explanation:

The center moves to the right by 2 so its x-2

The center moved down 2 so its y+2 or y--2

The radius is 3 so we square that to get what it equals (9)

Answer:

8

Step-by-step explanation:

First Step

Convert meters to centimeters

For every meter there are 100 (centi)meters

6 meters ×100=600 cm

Second Step

Find how many scarves can be made

We have 600 cm of fringe

It takes 70 cm to make 1 scarf

Divide 70 into 600

600÷70=8.571

Rounding down we get 8

Answer:

  Hari is 20; Harry is 28

Step-by-step explanation:

The ratio in 4 years is equivalent to the ratio 6:8, which has each of the original ratio unit numbers increased by 1. That means each of those ratio units stands for 4 years, and the present ages are ...

  Hari: 5·4 = 20

  Harry: 7·4 = 28

_____

Conventional method of solution

If you like, you can write equations for the ages of Hari (x) and Harry (y):

  x/y = 5/7

  (x+4)/(y+4) = 3/4

These can be solved a variety of ways. For some methods, it may be useful to write them in standard form:

These have solution (x, y) = (20, 28).

Answer:

[tex]\boxed{x = 8}[/tex]

Step-by-step explanation:

1. Jump discontinuity

In the graph, you can see that the left-hand limit of g(x) as x⟶ 8 is 3 and the right-hand limit is -3.

When the left- and right-hand limits at x = 8 exist but are different, we say that g(x) has a jump discontinuity at [tex]\boxed{\textbf{x = 8}}[/tex].

2. Other discontinuities

At x = 10, the left-hand limit is ∞ and the right-hand limit is -∞. Both one-sided limits are infinite, so this is an infinite discontinuity.

At x= 1, both one-sided limits are equal, but g(1) does not exist,

At x= 4, the limits are equal, and g(4) = 3.

In each case, the holes can be removed by redefining g(x), so the holes are removable discontinuities.

The domain is the X values and the range is the y values.

The blue line starts at X 0 and Y 0 and moves up and to the right.

This means the range and domain are equal to or greater than 0.

The 3rd choice is the correct one.

Answer:

B

Hope this helps!

Answer:

B

Step-by-step explanation:

The rate of change is the slope.  Function 1 has a slope of 4.  Function 2 has a slope of:

m = Δy / Δx

m = (10 - 6) / (3 - 1)

m = 4 / 2

m = 2

So function 1 has the greater rate of change.  Answer B.

Answer:

[tex]x^{1/4} y^{1/2}[/tex]

Step-by-step explanation:

When you have a power then a root like that, you have to divide the power by the root.

So, in this case, you have (x^2y^4) and a 8th root (8√).

So, you take your exponents from (x^2y^4) and divide them by the root (8), to get new powers of 2/8, or 1/4, and 4/8 or 1/2

As I already explained you in other questions, that leaves a fractional exponent that is equivalent to the regular exponent then rooted.

Answer is then: [tex]x^{1/4} y^{1/2}[/tex]

This function starts at 30 where x=0, and then gains 15 units each time x is increased by 1.

So, we deduce that renting the storage has a fixed price of 30, and then you have to pay 15 each month.

It will add 15 dollar for each month.

Answer:

B

Step-by-step explanation:

The domain is all possible values of x.  Here, x is the number of $5 nontaxable items.  So x must be an integer, and it can't be negative.  It is possible for x to be 0.  So x is all whole numbers.

The practical domain for the function f(x) which represents the total amount spent at a store is all whole numbers. Option B is correct.

Domain of a function is the set of all the possible input values which are valid for that function.

The function ​f(x) represents the total amount spent at a store.  The purchasing number of x items which are $5 each and the items which are not taxable is represented by x.

Thus, this function can be given as,

f(x)=5x

Now the domain of a function is the set of all the possible input values which are valid for that function. Thus, for this case the domain is,

-∞<x<∞

(-∞,∞)

For the practical domain, the numbers should be whole number to avoid negative amount value and integer amount.

Hence, the practical domain for the function f(x) which represents the total amount spent at a store is all whole numbers. Option B is correct.

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Answer:

346 trucks are needed

Step-by-step explanation:

We know that one acre equals 43560 feet ^ 2

In this case the area is 3 acres. So:

[tex]3\ acres * \frac{43,560\ ft^2}{1\ acre} = 130,680\ ft^2[/tex]

We know that 1 foot equals 12 inches. So:

[tex]24\ in * \frac{1\ ft}{12\ in} = 2\ ft[/tex]

So the volume of the contaminated area is:

[tex]V = 2* 130,680\ ft^3\\\\V = 261,360\ ft^3[/tex]

In a cubic yard there are 27 cubic feet. So:

[tex]28\ yard^2 * \frac{27\ ft^3}{1\ yard^3} = 756\ ft^3[/tex]

Finally if we have a volume of [tex]261,360\ ft ^ 3[/tex] and each truck can transport [tex]756\ ft ^ 3[/tex] then the amount of trucks x we need is:

[tex]x = \frac{261,360\ ft ^ 3}{756\ ft ^ 3} = 346\ trucks[/tex]