Which of the following functions is graphed below?
O A. y - x - 61+3
O B. y - x + 61-3
O C. y = x +61+3
D. y - x - 61-3

Answer:

18 is the first multiple of 3,6, and 9.

Step-by-step explanation:

Answer:

18

Step-by-step explanation:

We need to find the LCM (lowest common multiple) of 3, 6, and 9. Let's count by multiples of 3 to find it.

3 (not a multiple of 6 or 9), 6 (not a multiple of 9), 9 (not a multiple of 6), 12 (not a multiple of 9), 15 (not a multiple of 6 or 9), 18.

Since 18 is the first number that is a multiple of 3, 6, and 9, that is the answer.

This question is incomplete

Complete Question

The function s(V) = ∛V describes the side length, in units, of a cube with a volume of V cubic units.

Jason wants to build a cube with a minimum of 64 cubic centimeters.

What is a reasonable range for s, the side length, in centimeters, of Jason’s cube?

a) s > 0

b) s ≥ 4

c) s ≥ 8

d) s ≥ 16

Answer:

b) s ≥ 4

Step-by-step explanation:

From the above question, we are given Volume of the cube = 64cm³

We are given the function

s(V) = ∛V

Hence,

The range for the side length s =

s(V) ≥ ∛V

s(V) ≥ ∛64 cm³

s(v) ≥ 4 cm

Therefore, the reasonable range for s, the side length, in centimeters, of Jason’s cube

Option b) s ≥ 4

Answer:

s≥ 4

Step-by-step explanation:

Answer:

work is pictured and shown

Answer:

Infinitely many solutions.

Step-by-step explanation:

To solve the system of equation using the substitution method, the problem has already given us a solution for x:

x = -4y - 9

Using this, we can plug that into the first equation and solve for y:

3x + 12y = -27

3(-4y - 9) + 12y = -27

-12y - 27 + 12y = -27

-27 = -27

The fact that our solution indicate -27 = -27 means that these two equations have infinitely many solutions for the value y.  This simply means that no matter what we put in for y, the statement will always be true.

Notice that these two equations are in fact the same equation:

x = -4y - 9 ==> x + 4y = -9 ==> 3x + 12y = -27

Since these two equations are the same, then there are infinitely many solutions.

I'm not sure quite what they want for the form in terms of y, but let's solve for y since they already solved for x:

x = -4y - 9

x + 9 = -4y

y = (-1 / 4) (x + 9)

Cheers.

Answer:

3/8

Step-by-step explanation:

There are 72 students.  27 students choose football, and 18 choose tennis, which means 27 choose running.

So the probability that a student chooses running is 27/72, which reduces to 3/8.

Answer:

[tex] y'' =12x^2 -72=0[/tex]

And solving we got:

[tex] x=\pm \sqrt{\frac{72}{12}} =\pm \sqrt{6}[/tex]

We can find the sings of the second derivate on the following intervals:

[tex] (-\infty<x< -\sqrt{6}) , y'' = +[/tex] Concave up

[tex]x=-\sqrt{6}, y =-180[/tex] inflection point

[tex] (-\sqrt{6} <x< \sqrt{6}), y'' =-[/tex] Concave down

[tex]x=\sqrt{6}, y=-180[/tex] inflection point

[tex] (\sqrt{6}<x< \infty) , y'' = +[/tex] Concave up

Step-by-step explanation:

For this case we have the following function:

[tex] y= x^4 -36x^2[/tex]

We can find the first derivate and we got:

[tex] y' = 4x^3 -72x[/tex]

In order to find the concavity we can find the second derivate and we got:

[tex] y'' = 12x^2 -72[/tex]

We can set up this derivate equal to 0 and we got:

[tex] y'' =12x^2 -72=0[/tex]

And solving we got:

[tex] x=\pm \sqrt{\frac{72}{12}} =\pm \sqrt{6}[/tex]

We can find the sings of the second derivate on the following intervals:

[tex] (-\infty<x< -\sqrt{6}) , y'' = +[/tex] Concave up

[tex]x=-\sqrt{6}, y =-180[/tex] inflection point

[tex] (-\sqrt{6} <x< \sqrt{6}), y'' =-[/tex] Concave down

[tex]x=\sqrt{6}, y=-180[/tex] inflection point

[tex] (\sqrt{6}<x< \infty) , y'' = +[/tex] Concave up

Answer: 14

Step-by-step explanation:

12/4 times 3 +5

= 3 times 3 + 5

= 9 + 5

= 14

Answer:

1800

Step-by-step explanation:

Hello,

First of all we need to find the prime factorisation of the numbers.

18 = 2 * 3 * 3

40 = 2 * 2 * 2 * 5

75 = 3 * 5 * 5

It means that the LCM should have 5 * 5 , 2 * 2 * 2 and 3 * 3

Then LCM = 3 * 3 * 2 * 2 * 2 * 5 * 5 = 1800

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

1800

Step-by-step explanation:

→ First of all we need to find the prime factorisation of the numbers.

18 = 2 × 3 × 3 or 2 × 3²

40 = 2 × 2 × 2 × 5 or 2³ × 5

75 = 3 × 5 × 5 or 5² × 3

→ Now find the number that appear twice or more and write them down

3 and 3 from 18

2, 2 and 2 from 40

5 and 5 from 75

→ Now multiply all of these numbers together

3 × 3 × 2 × 2 × 2 × 5 × 5 = 3² × 2³ × 5² = 1800

Answer:

  As x increases, y decreases and then increases

Step-by-step explanation:

You need only understand your own description of the graph:

  begins above the x-axis, extends below the x-axis, and ascends above the x-axis

This is a description of decreasing, then increasing:

  As x increases, y decreases and then increases

Answer:

C. As x increases, y increases and then decreases.

Step-by-step explanation:

Just took the Unit Test and got it correct on Edge.

Answer:

For 3^-6 = 1/3^6 = 726 and for 3^-4 = 1/3^4 = 81

Step-by-step explanation:

ARE THE NUMBERS SEPARATED OR THEY ARE TO BE JOIN TOGETHER,IF THERE ARE SEPARATED THE SOLUTION IS GOING TO BE...

3^-6

using law of indices x^-a = 1/x^a

So 3^-6 = 1/3^6

Now find the power of 3^6

which is the same as 3×3×3×3×3×3 = 729

therefore 1/3^6 = 729

For 3^-4

using the above method

3^-4 is same as 1/3^4

which is equal to

finding the nominator

3×3×3×3 = 81

so the answer is 81

Answer:

Going from up to down

Box #1=0

Box #2=3

Box #3=5

Step-by-step explanation:

Answer:

Step-by-step explanation:

Going from up to down

Box #1=0

Box #2=3

Box #3=5

Answer:

[tex]\boxed{\sf k=6}[/tex]

Step-by-step explanation:

[tex]\sf kx (x-2)+6=0[/tex]

Expand brackets.

[tex]\sf kx^2 -2kx+6=0[/tex]

This is in quadratic form.

[tex]\sf ax^2 +bx+c=0[/tex]

Since this is for equal roots:

[tex]\sf b^2 -4ac=0[/tex]

[tex]\sf a=k\\b=-2k\\c=6[/tex]

[tex]\sf (-2k)^2 -4(k)(6)=0[/tex]

[tex]\sf 4k^2-24k=0[/tex]

[tex]\sf 4k(k-6)=0[/tex]

[tex]\sf 4k=0\\k=0[/tex]

[tex]\sf k-6=0\\k=6[/tex]

Plug k as 0 to check.

[tex]\sf \sf 0x^2 -2(0)x+6=0\\6=0[/tex]

False.

So that means k must equal 6.

Step-by-step explanation:

since you provided 1st and the last terms

the equation can be nth term

n/2 × ( a + l) = nth sum

n/2 × ( 1 + 121) = 671

n/2 × 122 = 671

61 n = 671

n = 11

a) so there are 11 terms

then,

so as 11th term is 121

let's find common diff

a + ( n-1) d = nth term

1 +( 11-1) d= 121

10d = 121 -1

10d = 120

common difference = 12

Answer:

8 colors

Step-by-step explanation:

There should be at least 8 different colors available for coloring the sections. The one color is used to color all the small triangles on the upper most and lower most lines, then there will be required another color so that the edges does not matches with the previous color. For the bigger hexagon shapes in the center we will require different colors for all of them because all of the hexagon shapes touches a line and an edge with each other.

Answer:

its 2 trust me

Step-by-step explanation:

its two cause if you think about it and color in the hexagons and triangles two different colors it works

Answer:

1. a = -31/9

2. -3/4

3. Different degree polynomials

4. Yes, of a degree 2n

5. a. Even-degree variables

b. Odd- degree variables

Step-by-step explanation:

1. Suppose f(x) = x^4-2x^3+ax^2+x+3. If f(3) = 2, then what is a?

Plugging in 3 for x:

f(3)= 3^4 - 2*3^3 + a*3^2 + 3 + 3= 81 - 54 + 6 + 9a = 33 + 9a and f(3)= 2

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

2. Let f, g, and h be polynomials such that h(x) = f(x) * g(x). If the constant term of f(x) is -4 and the constant term of h(x) is 3, what is g(0)?

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

3. Suppose the polynomials f and g are both monic polynomials. If the sum f(x) + g(x) is also monic, what can we deduce about the degrees of f and g?

If the sum of monic polynomials f(x) + g(x) is also monic, then f(x) and g(x) are of different degree and their sum only change the one with the lower degree, leaving the higher degree variable unchanged.

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

4. If f(x) is a polynomial, is f(x^2) also a polynomial?

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

5. Consider the polynomial function g(x) = x^4-3x^2+9

a. What must be true of a polynomial function f(x) if f(x) and f(-x) are the same polynomial?

b.What must be true of a polynomial function f(x) if f(x) and -f(-x) are the same polynomial?

Answer:

Step-by-step explanation:

The null hypothesis is usually the default statement. The alternative is the opposite of the null and usually tested against the null hypothesis

In this case study,

The null hypothesis in would be that the mean time between clicks of the second hand on a particular clock is 1 second. In symbolic form it would be u = 1

The alternative hypothesis would be that the mean time between clicks of the second hand on a particular clock is 1 not second. In symbolic form, it would be: u =/ 1

Answer:

61 and -87

Step-by-step explanation:

If the numbers are x and x - 148, we can write the following equation:

x + x - 148 = -26

2x - 148 = -26

2x = 122

x = 61 so x - 148 = 61 - 148 = -87

Answer:

[tex] a = 2.7 [/tex]

Step-by-step explanation:

Distributive property can be used to solve the equation, by multiplying [tex] \frac{2}{3} [/tex] with [tex] 6a, [/tex] and [tex] 9 [/tex]

Thus,

[tex] (\frac{2}{3}*6a) + (\frac{2}{3}*9) = 16.8 [/tex]

[tex] 2*2a + 2*3 = 16.8 [/tex]

[tex] 4a + 6 = 16.8 [/tex]

Subtract 6 from both sides.

[tex] 4a + 6 - 6 = 16.8 - 6 [/tex]

[tex] 4a = 10.8 [/tex]

Divide both sides by 4 to solve for a

[tex] \frac{4a}{4} = \frac{10.8}{4} [/tex]

[tex] a = 2.7 [/tex]

Answer:

Largest integer in the interval [−∞, 31] is 31.

Step-by-step explanation:

Given the interval: [−∞, 31]

To find: The largest integer in this interval.

Solution:

First of all, let us learn about the representation of intervals.

Two kind of brackets can be used to represent the intervals. i.e. () and [].

Round bracket means not included in the interval and square bracket means included in the interval.

Also, any combination can also be used.

Let us discuss one by one.

1. [p, q] It means the interval contains the values between p and q. Furthermore, p and q are also included in the interval.

Smallest p

Largest q

2. (p, q) It means the interval contains the values between p and q. Furthermore, p and q are not included in the interval.

Smallest value just greater than p.

Largest value just smaller than q.

3. [p, q) It means the interval contains the values between p and q. Furthermore, p is included in the interval but q is not included in the interval.

Smallest value p.

Largest value just smaller than q.

4. (p, q] It means the interval contains the values between p and q. Furthermore, p is not included in the interval but q is included in the interval.

Smallest value just greater than p.

Largest value q.

As per above explanation, we can clearly observe that:

The largest integer which belongs to the following interval: [−∞, 31] is 31.

Answer: Estimated the standard deviation α  = 5.35

Step-by-step explanation:

According to Empirical rule, the largest value is approximately:

ц + 3α

And the smallest value is approximately:

ц + 3α

Based on the given figures in the question, we can say

ц + 3α = 140.6

ц - 3α = 108.5

Now subtracting these two; we have

ц + 3α - ( ц - 3α  ) = 140.6 - 108.5

ц + 3α - ц + 3α = 32.1

6α = 32.1

α = 32.1 / 6

α = 5.35

Estimated the standard deviation α  = 5.35

Answer:

The value of  annuity is [tex]P_v = \$ 32058[/tex]

Step-by-step explanation:

From the question we are told that

    The periodic payment is  [tex]P = \$ 1500[/tex]

     The  interest rate  is   [tex]r = 8\% = 0.08[/tex]

     Frequency at which it occurs in a year is  n = 2 (semi-annually )

      The number of years is  [tex]t = 22 \ years[/tex]

The  value of the annuity is mathematically represented as

             [tex]P_v = P * [1 - (1 + \frac{r}{n} )^{-t * n} ] * [\frac{(1 + \frac{r}{n} )}{ \frac{r}{n} } ][/tex](reference EDUCBA website)

 substituting values

             [tex]P_v = 1500 * [1 - (1 + \frac{0.08}{2} )^{-22 * 2} ] * [\frac{(1 + \frac{0.08}{2} )}{ \frac{0.08}{2} } ][/tex]

             [tex]P_v = 1500 * [1 - (1.04 )^{-44} ] * [\frac{(1.04 )}{0.04} ][/tex]

             [tex]P_v = 1500 * [1 - 0.178 ] * [\frac{(1.04 )}{0.04} ][/tex]

            [tex]P_v = \$ 32058[/tex]

Answer:

-7/5

Step-by-step explanation:

We can find the slope using the slope formula

m = ( y2-y1)/(x2-x1)

   = ( -3 -4)/(8-3)

   = -7/5

Answer:

-7/5

Step-by-step explanation:

Hey there!

To find the slope of a line with 2 given points we'll use the following formula,

[tex]\frac{y^2-y^1}{x^2-x^2}[/tex]

-3 - 4 = -7

8 - 3 = 5

-7/5

Hope this helps :)

Answer:

Note Due Date Interest due at Maturity

1 Mar 6 $500

2 Apr 23 $360

3 July 20 $840

4 Sept 6 $945

5 Nov 29 $270

6 Dec 30 $300

Step-by-step explanation:

Calculation to Determine the due date and the amount of interest due at maturity for Flush Mate Co.

Using this formula to Calculate for the amount of interest due at maturity.

Interest due at Maturity= [Face amount * Numbers of days to maturity / 360 * Interest rate]

Note, Due Date,  Face Amount, No of days to maturity,  Interest rate, Interest due at Maturity

1 Mar 6 80,000× 45/360 ×5% =$500

2 Apr 23 24,000 × 60/360 ×9% =$360

3 July 20 42,000×120/360 ×6% =$840

4 Sept 6 54,000× 90/360 ×7% =$945

5 Nov 29 27,000× 60/360 ×6% =$270

6 Dec 30 72,000× 30/360 ×5% =$300

Therefore  the due date  and the amount of interest due at maturity for Flush Mate Co are:

Note Due Date Interest due at Maturity

1 Mar 6 $500

2 Apr 23 $360

3 July 20 $840

4 Sept 6 $945

5 Nov 29 $270

6 Dec 30 $300

Answer:

The new car travels 247.5 miles more than the old one on 30 gallons of gas.

Step-by-step explanation:

The fuel consumption of the old car was:

[tex]car_{old} = 18 + \frac{1}{4} = \frac{73}{4} \text{ miles per gallon}[/tex]

The new one can travel a distance of 390 7/8 miles by using 14 3/4 gallons of fuel, therefore the consumption is:

[tex]car_{new} = \frac{390.875}{14.75} = 26.5 \text{ miles per gallon}[/tex]

If the tank holds 30 gallons, on the old car the distance would be:

[tex]distance_{old} = 18.25*30 = 547.5 \text{ miles}[/tex]

On the new one it will be:

[tex]distance_{new} = 26.5*30 = 795 \text{ miles}[/tex]

So the new car is able to travel 247.5 miles more than the old one on 30 gallons of gas.

Answer:

Don

Step-by-step explanation:

1. We make the fractions have common denominators so it is easier to compare them. We can do this buy multiplying 2/3 by a factor of 16, so it becomes 32/48. For 11/16, we multiply by a factor of 3 so it becomes 33/48. It is now apparent that Don has the longer pipe.

Don has the longest section of pipe because the fraction number 11/16 is greater than the fraction number 2/3.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The decimal number is the sum of a whole number and part of a fraction number. The fraction number is greater than zero but less than one.

David says he has 2/3 of a line length left, while Wear says he has 11/16 of a length left.

Convert the fraction numbers 2/3 and 11/16 into the decimal number. Then we have

2/3 = 0.6667

11/16 = 0.6875

The decimal number 0.6875 is greater than 0.6667. Then the fraction number 11/16 is greater than the fraction number 2/3.

Don has the longest section of pipe because the fraction number 11/16 is greater than the fraction number 2/3.

More about the Algebra link is given below.

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Answer:

9a^2sqrt(ab)

Step-by-step explanation:

The first noticable thing is that 81 has a perfect square of 9.

So it is now 9sqrt(a^5b)

you can split the a^5, to a^4 × a.

you can now take the sqrt of a^4, which is a^2, and pull it out from the sqrt

You are now left with 9a^2sqrt(ab)

Answer:

9a^2sqrt(ab)

Step-by-step explanation:

Answer:  Focus = (-2, 3)

Step-by-step explanation:

[tex]y=-\dfrac{1}{4}x^2-x+3\\\\\rightarrow a=-\dfrac{1}{4},\ b=-1[/tex]

First let's find the vertex. We do that by finding the Axis-Of-Symmetry:

[tex]AOS: x=\dfrac{-b}{2a}\quad =\dfrac{-(-1)}{2(\frac{-1}{4})}=\dfrac{1}{-\frac{1}{2}}=-2[/tex]

Then finding the maximum by inputting x = -2 into the given equation:

[tex]y=-\dfrac{1}{4}(-2)^2-(-2)+3\\\\y=-1+2+3\\\\y=4[/tex]

The vertex is: (-2, 4)

Now let's find p, which is the distance from the vertex to the focus:

[tex]a=\dfrac{1}{4p}\\\\\\-\dfrac{1}{4}=\dfrac{1}{4p}\\\\\\p=-1[/tex]

The vertex is (-2, 4) and p = -1

The focus is (-2, 4 + p) = (-2, 4 - 1) = (-2, 3)

Answer:

Step-by-step explanation:

Probability is defines as the likelihood or chance that an event will occur.

Probability = expected outcome of event/total outcome.

Since a single die with 9 sides was rolled, the total event outcome will be 9*9 = 81

Expected outcome will be the event that the sum of the two rolls equals 3. The possible outcomes are {(1,2), (2,1)}. The expected outcome is 2

Probability that the sum of the two rolls equals 3 = 2/81

The probability that the sum of the two rolls equals 3 is [tex]\dfrac{2}{81}[/tex].

Important information:

We need to find the probability that the sum of the two rolls equals 3.

If a die with 9 sides is rolled twice, then the number of total possible outcomes is:

[tex]9\times 9=81[/tex]

The sum of the two rolls equals 3, if we get 1, 2 and 2, 1. It means the number of favorable outcomes is 2.

[tex]P=\dfrac{\text{Favorable outcomes}}{\text{Total outcomes}}[/tex]

[tex]P=\dfrac{2}{81}[/tex]

Therefore, the probability that the sum of the two rolls equals 3 is [tex]\dfrac{2}{81}[/tex].

Find out more about 'Probability' here:

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Hello!

Answer:

Table B.

Step-by-step explanation:

An inverse of a function means that the x and y values are swapped in comparison to the original function. For example:

We can use points on the table:

[tex]f(x)[/tex] = (7, 21)

The inverse of this function would 7 as its y value, and 21 as its x value:

[tex]f^{-1} (x)[/tex] = (21, 7)

The only table shown that correctly shows this relationship is table B.

Answer: You have the correct answer. It is y = 150x-50

Nice work on getting the correct answer. For anyone curious, the explanation is below.

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

x = number of hours the stand is open

y = amount earned

(1,100) is from the fact the stand is open 1 hour and earns $100

(3,400) is due to the stand earning $400 after 3 hours.

Slope Formula

m = (y2 - y1)/(x2 - x1)

m = (400-100)/(3-1)

m = 300/2

m = 150 is the slope, and it is the amount earned per hour. It is the rate of change.

Use m = 150 and (x,y) = (1,100) to find the value of b as shown below

y = mx+b

100 = 150(1) + b

100 = 150 + b

100-150 = b

-50 = b

b = -50 is the y intercept and it is the starting amount they earn. The negative earning indicates that they spent $50 to set up the stand, which is the cost of buying the food, equipment, etc.

So we have m = 150 as the slope and b =  -50 as the y intercept.

Therefore, y = mx+b turns into y = 150x-50.

-------

As a check, plugging in x = 1 should lead to y = 100

y = 150x-50

y = 150(1)-50

y = 150-50

y = 100 and indeed it does

The same should be the case with (3,400). Plug in x = 3 and we should get y = 400

y = 150x-50

y = 150(3)-50

y = 450-50

y = 400, we have confirmed the answer by showing that the line y = 150x-50 goes through the two points (1,100) and (3,400).

The equation for revenue earned from being opened for x hours will be y=150x-50 so it is absolutely correct.

Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.

In other words, an equation is a set of variables that are constrained through a situation or case.

Given,

$100 for 1 hour

So,

x = 1 and y = 100

And,

$400 for 3 hour

So,

x = 3 and y = 400

Now the slope of the linear equation is given by

m = difference in ys coordinate / difference in xs coordinate  

m = (400 - 300)/(3-1) = 150

So equation become

y = 150x + b

Now put (3,400) to find out b

400 = 150(3) + b

b = -50

So, equation

y = 150x - 50

Hence " The equation for revenue earned from being opened for x hours will be y=150x-50".

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