How can you tell if two functions are inverses of each other? Be sure to discuss how to graphically and algebraically.

Answer:

m = 3, n = 4

Step-by-step explanation:

Solve using the substitution process. First, start with the second equation:

2m + 2n = 14

Simplify. Divide 2 from all terms within the equation. What you do to one side, you do to the other:

(2m + 2n)/2 = (14)/2

m + n = 7

Isolate the variable m. Subtract n from both sides:

m + n (-n) = 7 (-n)

m = 7 - n

Plug in 7 - n for m in the first equation:

-5m + 9n = 21

-5(7 - n) + 9n = 21

Solve. First, distribute -5 to all terms within the parenthesis:

(-35 + 5n) + 9n = 21

Simplify. Combine like terms:

-35 + (5n + 9n) = 21

-35 + 14n = 21

Isolate the variable, n. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS. First, add 35 to both sides:

14n - 35 (+35) = 21 (+35)

14n = 21 + 35

14n = 56

Isolate the variable n. Divide 14 from both sides:

(14n)/14 = (56)/14

n = 56/14

n = 4

Plug in 4 to n in one of the equations, and solve for m.

2m + 2n = 14

2m + 2(4) = 14

2m + 8 = 14

Isolate the variable, m. Do the opposite of PEMDAS. First, subtract 8 from both sides:

2m + 8 (-8) = 14 (-8)

2m = 14 - 8

2m = 6

Divide 2 from both sides:

(2m)/2 = (6)/2

m = 6/2

m = 3

Your answers: m = 3, n = 4

~

Answer:

(3, 4)

Step-by-step explanation:

Please include the instructions.  I'm assuming that you want to solve this system of linear equations.

If that's the case, let's use elimination by addition and subtraction.

Multiply the first equation, -5m + 9n = 21, by 2:  -10m + 18n = 42, and

multiply the second equation, 2m + 2n = 14, by 5:  10m + 10n = 70

Next, combine these two "new" equations:

-10m + 18n = 42

10m + 10n = 70

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

          28n = 112.  Dividing both sides by 28, we get  n = 4.

Subbing 4 for n in the second equation, we get 2m + 2(4) = 14, or

2m = 6.  Then m = 3, and the solution is thus

(3, 4).

Ari will think that there is not enough ice cream for the amount of caramel.

3:5 and 6:8 are not equivalent

But let's prove that;

We know that 3 x 2 is 6, so let's multiply 3 x 2 and 5 x 2, when we do so, we get 6:10.

6:10 is greater than 6:8, so there is obviously less ice cream for the amount of caramel.

Answer:

b/x=y/b

Step-by-step explanation:

Switch it over and get the y.

Answer:

  ABCDEADBEC

Step-by-step explanation:

A path that traverses all streets exactly once is called an Euler path. It is only possible for a graph that has an even number of streets coming together at each vertex, or one that has an odd number of streets at only two vertices.

This map has an odd number of streets at vertices A and C, so those are suitable starting and ending points for the path. I find it convenient to travel the outside ring first, then fill in the inner paths that weren't previously traveled. The list of vertices for one possible path is shown above.

Answer:

[tex]f(x)=x^{4}+x^{3}-7x^{2}-x+6[/tex]

Step-by-step explanation:

The zeros of the polynomial are: -3, -1, 1, 2

According to the factor theorem, the factors of the polynomial will be:

(x - (-3)) = x + 3

(x - (-1)) = x + 1

(x - 1)

(x - 2)

Since we have the factors, we can multiply them to obtain the equation of the polynomial.

So,

[tex]f(x)=(x+3)(x+1)(x-1)(x-2)\\\\ f(x)=(x+3)(x^{2}-1)(x-2)\\\\ f(x)=(x^{2}-1)(x^{2}-2x+3x-6)\\\\ f(x)=(x^{2}-1)(x^{2}+x-6)\\\\ f(x)=x^{4}+x^{3}-6x^{2}-x^{2}-x+6\\\\ f(x)=x^{4}+x^{3}-7x^{2}-x+6[/tex]

The above equation give the polynomial with integer coefficients and a leading coefficient of 1

The polynomial of degree 4 that has -3, -1, 1, and 2 as its real zeros and integer coefficients with a leading coefficient of 1 can be expressed in its factored form as f(x) = (x + 3)(x + 1)(x - 1)(x - 2).

To form a polynomial with the given real zeros and degree, we must first understand that each real zero corresponds to a factor of the form (x - a), where a is the zero.

Therefore, given the zeros -3, -1, 1, and 2,

the corresponding factors of the polynomial are (x + 3), (x + 1), (x - 1), and (x - 2).

The polynomial of degree 4 with these zeros can then be written as the product of these factors,

obtaining f(x) = (x + 3)(x + 1)(x - 1)(x - 2).

Since it's required that polynomial has integer coefficients and a leading coefficient of 1,

we leave it in this factored form.

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Answer: its the third one try that

Step-by-step explanation:

Answer:

It's C

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

5/12, 1, 1/3, 5/6. 1/3 is the smallest.

Answer with Step-by-step explanation:

Mixture A-

Blue Paint - 5 cups

White Paint - 12 cups

Ratio of blue paint to white paint=5:12

Mixture B-

Blue Paint- 6 cups

White Paint- 6 cups

 Ratio of blue paint to white paint=6:6=12:12  

(on multiplying numerator and denominator by 12 i.e.6/6=12/12)

Mixture C-

Blue Paint - 4 cups

White Paint - 12 cups

 Ratio of blue paint to white paint=4:12

Mixture D-

Blue Paint - 5 cups

White Paint - 6 cups

Ratio of blue paint to white paint=5:6=10:12

(on multiplying numerator and denominator by 12 i.e.5/6=10/12)

The denominator of the ratios are same in each mixture now,to determine the lowest ratio we have to see the numerator with smallest value which is 4

Hence, Mixture C has the lowest ratio of blue paint to white paint

Since the graph above shows a proportional relationship between x and y, an equation of the line is y = -1/4(x).

In Mathematics and Geometry, a proportional relationship is a type of relationship that passes through the origin (0, 0) and produces equivalent ratios as represented by the following mathematical equation:

y = kx

Where:

Next, we would determine the constant of proportionality (k) by using various data points as follows:

Constant of proportionality, k = y/x

Constant of proportionality, k = -1/4 = -2/8 = -12/3

Constant of proportionality, k = -1/4.

Therefore, the required linear equation for y(x) is given by;

y = kx

y = -1/4(x)

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Answer:

x-intercept (-3,0)

y-intercept  (0,-9)

Step-by-step explanation:

The x-intercepts can be found by setting y to 0 and solving for x.

y=-3x-9

0=-3x-9

Add 9 on both sides:

9=-3x

Divide both sides by -3:

9/-3=x

-3=x

The x-intercept is (-3,0).

The y-intercepts can be found by setting x to 0 and solving for y.

y=-3x-9

y=-3(0)-9

y=0-9

y=-9

The y-intercept is (0,-9).

Answer:

Step-by-step explanation:

x-intercept is for y = 0.

y-intercept is for x = 0.

y = -3x - 9

x-intercept (put y = 0):

0 = -3x - 9            add 9 to both sides

9 = -3x          divide both sides by (-3)

-3 = x → x = -3

y-intercept (put x = 0):

y = -3(0) - 9

y = 0 - 9

y = -9

Answer:

2y

Step-by-step explanation:

-2y + 3y x 2  – 3y + y

= -4y + 3 x 2y

= 4y + 6y

= 2y

Answer: I hope it's right :3

Step-by-step explanation:

Answer:

(a) Five

(b) Thirteenth

Step-by-step explanation:

We have the mean is 12.6 and

that 11 occurs 4 times, 12 occurs 7 times, 13 occurs 9 times, and 14 occurs f times.

How many children are there in all (that is the sum of the frequencies).

4+7+9+f

20+f

Alright so the mean could be found by doing:

[tex]\frac{4(11)+7(12)+9(13)+f(14)}{20+f}[/tex]

But we are given this is also equal to: 12.6.

So we have

[tex]\frac{4(11)+7(12)+9(13)+f(14)}{20+f}=12.6[/tex]

I'm going to simplify what I can on top.

[tex]\frac{245+14f}{20+f}=12.6[/tex]

I'm going to write 12.6 as [tex]\frac{12.6}{1}[/tex] because I want to cross multiply:

[tex]\frac{245+14f}{20+f}=\frac{12.6}{1}[/tex]

[tex](245+14f)(1)=12.6(20+f)[/tex]

Distribute:

[tex]245+14f=252+12.6f[/tex]

Subtract 12.6f on both sides:

[tex]245+1.4f=252[/tex]

Subtract 245 on both sides:

[tex]1.4f=7[/tex]

Divide both sides by 1.4:

[tex]f=5[/tex]

There are five 14 years old.

(b) I would say 13 is good age to represent this bunch.

The means was 12.6 which when rounded is 13.

The mode is 13 because it is the most occurring

The median is also 13. Why? If you list out the data 13 will be the middle number. Or you could say there are 25 kids and if I divide it by 2, I get 12.5.  This means you only need to count to the 13th kid with the ages in order to tell with the median is.

There are 4 eleven yr olds.

There are 7 twelve yr olds.  That is 11 kids so far.

So the median has to be included in the 9 thirteenth yr olds.

Answer:

Shaded to the left

Step-by-step explanation:

I cannot see the illustration, but I know for a fact that after using the zero-interval test [plug 0 in for BOTH y and x], you get 0 < 4, which is a genuine statement, so it gets shaded on the left hand side, otherwise shaded on the right of it were false statement.

I am joyous to assist you anytime.

Answer:

Angles congruent to angle 2 is first. Angles congruent to angle 6 is second. Angles congruent to angle 1 is third. Angles congruent to angle 7 is last.

Step-by-step explanation:

Opposite angles are always equal. Alterbate interior/exterior angles are always equal.

Answer:

The correct option is C.

Step-by-step explanation:

Using the given box plots:

The data set for Asian elephant is

6, 6, 7, 7, 7, 8, 8, 8, 8, 8, 8, 9, 9, 9, 10

Divide the data set in 4 equal parts.

(6, 6, 7), 7, (7, 8, 8), 8, (8, 8, 8), 9, (9, 9, 10)

[tex]Q_1=7, Median=8, Q_3=9[/tex]

IQR of the Asian elephant is

[tex]IQR=Q_3-Q_1=9-7=2[/tex]

IQR of the Asian elephant is 2.

If the data set lies in interval [tex][Q_1-1.5(IQR),Q_3+1.5(IQR)][/tex], then the data set has no outliers.

[tex][Q_1-1.5(IQR),Q_3+1.5(IQR)]=[7-1.5(2),9+1.5(2)]=[4,12][/tex]

All the data lie in [4,12], therefore Asian elephant  has no outliers.

The data set for African elephant is

4, 6, 7, 7, 8, 8, 8, 9, 9, 9, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 13, 13, 14, 14

Divide the data set in 4 equal parts.

(4, 6, 7, 7, 8, 8, 8), 9,( 9, 9, 10, 10, 10, 10, 11), (11, 11, 11, 11, 11, 12, 12), 12, (12, 12, 12, 13, 13, 14, 14)

[tex]Q_1=9, Median=11, Q_3=12[/tex]

IQR of the African elephant is

[tex]IQR=Q_3-Q_1=12-9=3[/tex]

IQR of the African elephant is 3.

[tex][Q_1-1.5(IQR),Q_3+1.5(IQR)]=[9-1.5(3),12+1.5(3)]=[4.5,16.5][/tex]

All the data lie in [4.5,16.5] except 4, therefore African elephant has lower outliers.

African have a greater IQR because there were some very short elephants.

Therefore the correct option is C.

Answer:

African Elephants have a greater IQR because there were some very short elephants (low outliers).

Step-by-step explanation:

Apex

Answer:

164 legs all together

Step-by-step explanation:

There are 144 legs out of all the numbered creatures together.

Spiders = 8 legs

8 x 8 = 64

Cockroaches = 6 legs

6 x 5 = 30

Bees = 6 legs

7 x 6 = 42

Deer = 4 legs

3 x 4 = 12

Cows = 4 legs

4 x 4 = 16

Answer:

  C.  0.006 g/cm³

Step-by-step explanation:

As the units tell you, density is the ratio of mass to volume. The volume of the container is found from ...

  V = πr²h = π(10 cm)²(25 cm) = 2500π cm³

Then the density is ...

  ρ = (50 g)/(2500π cm³) = 1/(50π) g/cm³

  ρ ≈ 0.006 g/cm³

_____

Comment on the problem

The "liquid" has about the same density as air pressurized to 75 psi.

Can someone confirm is this answer is right?

Answer:

GCF of 36x^3 and 48x^4 is 12x³....

Step-by-step explanation:

To find the GCF of 36x3 and 48x4 we have to perform prime factorization of both the terms:

Prime Factorization of 36x³ = 2*2*3*3*3*x*x*x

Prime factorization of 48x^4 = 2*2*2*2*3*x*x*x*x

Thus the common factors are 2*2*3*x*x*x

Therefore GCF of 36x^3 and 48x^4 is 12x³....

Answer:

it is 12x^3

Step-by-step explanation:

Answer:

y = 3(x + 2) + 2 and y = -3(x + 2) + 2

Step-by-step explanation:

* Lets revise the equation of the hyperbola with center (h , k) and

 transverse axis parallel to the y-axis is (y - k)²/a² - (x - h)²/b² = 1

- The coordinates of the vertices are  (h , k ± a)

- The coordinates of the co-vertices are (h ± b , k)  

- The coordinates of the foci are (h , k ± c) where c² = a² + b²

- The equations of the asymptotes are  ± a/b (x - h) + k  

* Lets solve the problem

∵ The equation of the hyperbola is (y - 2)²/9 - (x + 2)² = 1

∵ The form of the equation is (y - k)²/a² - (x - h)²/b² = 1

∴ h = -2 , k = 2  

∴ a² = 9

∴ a = √9 = 3

∴ b² = 1

∴ b = √1 = 1

∵ The equations of the asymptotes are y = ± a/b (x - h) + k  

∴ The equations of the asymptotes are  y = ± 3/1 (x - -2) + 2

∴ The equations of the asymptotes are  y = ± 3 (x + 2) + 2    

* The equations of the asymptotes of the hyperbola are

  y = 3(x + 2) + 2 and y = -3(x + 2) + 2

Answer: I just did this quiz in Plato the correct answer is in the pic I did this question 3 times because I listened to the other people and finally got the answer which is the correct one, Hope this helps :)

Step-by-step explanation:

Answer:

Factored form of A-B is: (5-3p^4)(25+15p^4+9p^8)

Option A is correct.

Step-by-step explanation:

Given:

A= 125

B = 27p^12

To find: A-B

A-B = 125 - 27p^12

A-B=(5)^3-(3p^4)^3

We know that, a^3 - b^3 = (a-b)(a^2+ab+b^2)

Using this formula and finding factored form of A-B:

=(5-3p^4)((5)^2+(5)(3p^4)+(3p^4)^2)

=(5-3p^4)(25+15p^4+9p^8)

So, factored form of A-B is: (5-3p^4)(25+15p^4+9p^8)

Option A is correct.

Answer:

-10.5 deg

Step-by-step explanation:

Yesterday's temp = 7-1/2 deg (or 7.5 deg)

Today's temp = -3 deg

net change = today's temp - yesterday's temp

= -3 - 7.5 = -10.5 deg

Answer:

-10.5

Step-by-step explanation:

I listened to the other person and they helped me get it right. I'm just here to confirm it. Stay safe!! <3

Answer:

D. 66.

Step-by-step explanation:

There has to be 3 even multiples in the 5 numbers so we try:

22+33+44+55+66

= 220.

Answer:

Option D. 66

Step-by-step explanation:

A multiple is an exact number of times to another number.

The five consecutive multiples of 11 are:

22 -> 11/22 = 2 times, no remainder

33 -> 33/11 = 3 times, without remainder

44 -> 44/11 = 4 times, without remainder

55 -> 55/11 = 5 times, without remainder

66 -> 66/11 = 6 times, without remainder

Of those five multiples of 11 (22, 33, 44, 55, 66), the greatest is 66.

Answer:

The inverse is g(x)=-x+5.

Both f and g have domain and range all real numbers.

In interval notation that is [tex](-\infty,\infty)[/tex]

Step-by-step explanation:

f(x)=-x+5 is a linear function.

Since isn't f(x)=constant then it is diagonal so this means the range is all real numbers.

For any linear function, the domain will be all real numbers.  

So to find the inverse of y=-x+5, you interchange x and y and resolve for y.

y=-x+5

(interchange)

x=-y+5

(solve for y)

Subtract 5 on both sides:

x-5=-y

Multiplying both sides by -1:

-x+5=y

So the inverse is g(x)=-x+5. To find find the domain and range of the inverse function given you already did it for the original function, the sets are swapped.  The sets were the same here because they were both all real numbers.

Answer:

Domain of this function become R

Step-by-step explanation:

Answer:

C. The system has no solution.

C. The system has no solution.

A system of linear equations has no answer whilst the graphs are parallel. A coordinate plane. The x- and y-axes both scale by way of one-1/2. A graph of a line is going through the factors 0, one and a half of and three, two.

No solution would suggest that there's no answer to the equation. it's miles not possible for the equation to be proper regardless of what price we assign to the variable. infinite answers would suggest that any value for the variable would make the equation authentic.

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Answer:

Step-by-step explanation:

It all depends upon what the terms are.  If each term of the 3 all have a variable you can factor out, then you'd do that first.  For example, if your trinomial looks like this:

[tex]x^3+3x^2+4x[/tex]

you would begin by factoring out the common x, reducing the third degree polynomial to a quadratic which can then be factored many ways.

[tex]x^3+3x^2+4x=x(x^2+3x+4)[/tex]

If that is not the case, then you are factoring higher degree polynomials, and the way I always recommend to my students is the Rational Root Theorem and then synthetic division.

Answer:

The top tag price you could pay for the shorts = $32.71....

Step-by-step explanation:

Total amount = $ 60.00

Cost of jacket = $25.50

Sales tax = 7% = .07

First of all find the total price of the jacket including sales tax.

25.50* .07 = 1.79( this is the sales tax)

Now add this sales tax into the original price.

25.5 + 1.79 = 27.29

Total price of a jacket = $27.29

Now subtract the total amount by the amount of the jacket.

$60.00 - $27.29 = $32.71

Thus the top tag price you could pay for the shorts = $32.71....

f(x)=(x-5)(x-4)(x-2)

x-5=0

x-5+5=0+5

x=5

x-4=0

x-4+4=0+4

x=4

x-2=0

x-2+2=0+2

x=2

Answer: 5,4,2 -C

The zeros of the function f(x) = (x-5)(x-4)(x-2) are 5, 4, 2

Option C is correct

Note that:

The zeros of a function f(x) are the values of x that makes f(x) to be equal to zero

If f(x)  =  (x - a)(x - b)(x - c), then the zeros of the function f(x) are:

x  = a,  x  =  b,  x  =  c

Therefore, the zeros of f(x)=(x-5)(x-4)(x-2) are found by equating f(x) to zero

(x - 5)(x - 4)(x - 2)  =  0

Equate each of the terms to zero

x  -  5  =  0

x  =   5

x  -  4  =  0

x   =  4

x  -  2  =  0

x   =  2

The zeros of the function f(x) = (x-5)(x-4)(x-2) are 5, 4, 2

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Answer:

0.88 feet

Step-by-step explanation:

The tire covers 0.88 feet in 1 rotation.

1 rotation means the whole tire moves, which is basically its circumference. So, the distance it covers in moving 1 rotation IS ITS CIRCUMFERENCE.

Hence, 0.88 feet is the circle's circumference.

Answer:

A parameter is a numerical measurement describing data from a population. A statistic is a numerical measurement describing data from a sample

Step-by-step explanation:

In statistics we have to deal with populations and samples to carry out our studies. A population is a large group under consideration and the elements or members of the population have some common features or attributes. For example, all the school going kids in a certain town will be considered a population. Sample on the other hand is a subset(a part) of the population. For example, all school going kids in the town aged 5-6 years will be considered a sample.

The term Parameter and Statistic are very similar as they represent some numeric description. Parameter represents the data of the entire population, while statistic represents that data of a sample. An easy way to remember this is to match the initials i.e. Parameter for Population and Statistic for Sample.

Considering this, we can say the correct answer is:

A parameter is a numerical measurement describing data from a population. A statistic is a numerical measurement describing data from a sample

A parameter is a numerical value describing a characteristic of a population whilst a statistic is a numerical value describing a characteristic of a sample. A population is any whole set, while a sample is a subset of the population.

The primary difference between a parameter and a statistic lies in the data they refer to. A parameter is a numerical measurement that describes a characteristic of a population. A population is the whole set of items or individuals that we are interested in. On the other hand, a statistic is a numerical measurement that describes a characteristic of a sample, where a sample is a subset of the population.

For example, if we were to measure the average height of all adult men in a certain city (the population), the resulting value would be a parameter. If we were to take a sample group of 100 men from that city and measure their average height, the resulting value would be a statistic.

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Answer:

Step-by-step explanation:

If you observe the image, you deduct that the polygon ABCD was increased in size, that means the scale factor applied dilated the figure. In other words, there was applied a factor of dilation.

To find the exact factor of dilation, we just have to divide each prime coordinate by the original ones.

For example, you can observe that coordinates [tex]A(3,0)[/tex] was changed to [tex]A'(6,0)[/tex], [tex]B(1,0)[/tex] was changed to [tex]B'(2,0)[/tex], [tex]C(1,2)[/tex] was changed to [tex]C'(2,2)[/tex] and [tex]D(3,2)[/tex] was changed to [tex]D'(6.2)[/tex].

Now, observe that the dilation was horizontal, that is, the scale factor was only applied to x-coordinates, and this factor is 2, beacuse each x-coordinate was increase by a factor of 2.

Therefore, this transformation is a horizonta dilation by a factor of 2.