Diet cola was on sale last week; it cost $10 for every 4 liters of diet cola. How many liters do you get per dollar?

Answer:

x=75/4

Step-by-step explanation:

4x+3=8x-9

4x+3= -72

4x= -72-3

4x= -75

x=75/4

The points of inflection for the function [f(x) = (x⁴ - 6x²)] are (1, -5) and

(-1, -5).

As per the question statement, we are provided with a function

[f(x) = (x⁴ - 6x²)].

We are required to determine the points of inflection for the above mentioned function.

To solve this question, we will have to calculate the second derivative of the given function. Then, we will have to equate the derivative to zero and solve for x. The obtained values for "x" will be our abscissa, and substituting these values of "x" in f(x), we will obtain our respective ordinates [Since, {y = f(x)}].

[tex]f(x)=(x^{4} -6x^{2})\\or,\frac{d[f(x)}{dx} = \frac{d(x^{4} -6x^{2}) }{dx}\\ or, f'(x)=\frac{dx^{4}}{dx}-\frac{d(6x^{2})}{dx}\\ or, f'(x)=\frac{dx^{4}}{dx}-6\frac{d(x^{2})}{dx}\\or, f'(x)=4x^{(4-1)}-(6*2)[x^{(2-1)}]\\ or,f'(x)=4x^{3}-12x\\[/tex]

Therefore, the second derivative of f(x) = [tex]\frac{d^{2}f(x)}{dx^{2} }[/tex]

[tex]or,f"(x)=\frac{d[f'(x)]}{dx}\\or,f"(x)=\frac{d(4x^{3} -12x)}{dx}\\or, f"(x)=\frac{d(4x^{3}) }{dx}-\frac{d(12x)}{dx}\\ or, f"(x)=4\frac{d(x^{3}) }{dx}-12\frac{d(x)}{dx}\\or,f"(x)=(4*3)[x^{(3-1)}]-(12*1)[x^{(1-1)}]\\ or, f"(x)=12x^{2} -12[/tex]

Now, equating (12x² - 12) to Zero, we get,

[tex](12x^{2} -12)=0\\or,12x^{2} =12\\or,x^{2} =1\\or,x=(1, -1)[/tex]

Now, substituting (x = 1) in f(x), we get,

[tex]y=f(1)=[(1)^{4}-6(1)^{2}]\\ or,y=[1-(6*1)]\\or,y=(1-6)\\or,y=(-5)[/tex]
Hence, one point of inflection for the function [f(x) = (x⁴ - 6x²)] is (1, -5).

Again, substituting [x = (-1)] in f(x), we get,

[tex]y=f(-1)=[(-1)^{4}-6(-1)^{2}]\\ or,y=[1-(6*1)]\\or,y=(1-6)\\or,y=(-5)[/tex]

That is, another point of inflection for the function

[f(x) = (x⁴ - 6x²)] is (-1, -5).

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The scores on the test are centered around 66 and vary from 43 to 85.

A stemplot is a type of table where figures are divided into a stem and a leaf. The stem is the first number in the digit while the leaf is the last number. For example in the number 31, 3 would be the stem and 1 would be the leaf.

The range is used to measure variation. The range is the difference between the highest number and the smallest number. The largest number is 85 and the smallest number is 43.

The data would be centered around the median. The median is the number at the center of a dataset. The median is a measure of central tendency.

Median = (sum of numbers + 1) / 2

(26 + 1) / 2

= 27 / 2 = 13.5th number

(66 + 67) / 2 = 66.5

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Answer:

23m-18

Step-by-step explanation:

2(7m−5)+(−8+9m)

Remove parenthesis

2(7m-5)-8+9m

expand

14m-10

14m-10-8+9

simplify

23m-18

Ask me for more questions brainliest please.

The intervals over which the function is increasing are -

x ∈ (- ∞, - 2.5) and  x ∈ (0.5, ∞). We can write it as one single set (S) as -

S = (- ∞, - 2.5) ∪ (0.5, ∞).

The interval in which the y - coordinate of the points gets larger, or the graph gets higher as it moves from left to right over the interval is called increasing interval. Similarly, the interval in which the y - coordinate of the points gets smaller or the graph gets lower as it moves from left to right over the interval is called decreasing interval.

Given is the following function f(x) -

f(x) = x³ + 3x² - 4x - 12

First, we will plot the graph of this function. The graph is attached with the answer. On the graph, there are two black dots. From the definition of increasing functions, we know that the interval along which the y - coordinate gets larger is called increasing interval of the function. The first interval over which the function is increasing is-  x ∈ (- ∞, - 2.5). The second interval over which the function is increasing is- x ∈ (0.5, ∞).

Therefore, the intervals over which the function is increasing are -

x ∈ (- ∞, - 2.5) and  x ∈ (0.5, ∞). We can write it as one single set (S) as -

S = (- ∞, - 2.5) ∪ (0.5, ∞).

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Answer:

3

Step-by-step explanation:

Answer:

false true true true

Step-by-step explanation:

The equation for x = 6 is true and would be equal to 6x = 12. and the rest are false.

An equation represents the equality of two or more mathematical expressions. When someone asks you to solve an equation, then they usually mean to find the values of the unknowns for which that equation would be true (the equality between expressions should hold for those values). Solutions to an equation are those values of the variables involved in that equation for which the equation is true.

The given equations are;

6x = 12

Substitute x = 6 to check whether the solution satisfies the equation;

6(6)  = 36

Thus, it is False.

5 + x = 11

Substitute x = 6 to check whether the solution satisfies the equation;

5 + x = 11

5+ 6 = 11

Thus, it is True.

x ÷ 2 = 3

Substitute x = 6 to check whether the solution satisfies the equation;

6/2 = 3

Thus, it is True.

17 – x = 11

Substitute x = 6 to check whether the solution satisfies the equation;

17 - 6 = 11

Thus, it is True.

Hence, the equation for x = 6 is true and would be equal to 6x = 12. and the rest are false.

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Answer:

3.72 ft

Step-by-step explanation:

Height of the wall will be equal to the width of the wall because we are considering over surface area of the wall

Therefore,

Area of the wall = length * height

1534 = 412 * height

Height = 1534/412

Height = 3.72 ft

Answer:

In 8 minutes, she can jog 4000 feet.

Step-by-step explanation:

Davita jogs 2000 feet in 4 minutes.

Her rate is 2000/4 or 500 feet per minute.

500*8 = 4000

Answer:

x = 6

Step-by-step explanation: (See picture)

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Hope this helps!

Have a great day and God bless! :)

Answer:

baila como juana la cubana

Step-by-step explanation:

Answer:

Algebraic properties can be used as "reasons" in a two-column proof.

Step-by-step explanation:

Let's take an example:

Given: F = 9/5C + 32

Prove: C = 5/9(F-32)

Statements                                       Reasons

1) F = 9/5C + 32                               1) Given

2) F-32 = 9/5C                                 2) subtraction

3) 5/9(F-32) = C                                3) multiplication

4) C = 5/9(F-32)                                4) symmetric property

Therefore, we conclude that Algebraic properties can be used as "reasons" in a two-column proof.

Answer:

f(x)g(x) = 2x² - 6x

General Formulas and Concepts:

Algebra I

Step-by-step explanation:

Step 1: Define

f(x) = 2x

g(x) = x - 3

Step 2: Find f(x)g(x)

The constant of proportionality is 4, while the equation is given as y = 4x.

An equation is an expression that shows the relationship between two or more numbers and variables.

A variable can either be dependent or independent. A dependent variable depend on other variable while an independent variable does not depend on other variables.

Let x represent number of mines and y represent the number of gems. Since this is a proportional relationship, hence:

y = kx; where k is the constant of proportionality

From the table when y = 4, x = 1, hence:

4 = k(1)

k = 4

y = 4x

The constant of proportionality is 4, while the equation is given as y = 4x.

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Answer:

Bella can sell 13.78 glasses with 9 pieces of bling.

Step-by-step explanation:

Given the function

y=1.36x+1.54

Given that the number of pieces of bling = x = 9

Thus,

[tex]y = 1.36x+1.54[/tex]

 [tex]= 1.36(9)+1.54[/tex]

 [tex]=12.24+1.54[/tex]

 [tex]=13.78[/tex]

Thus, Bella can sell 13.78 glasses with 9 pieces of bling.

Answer:

hey ok

Step-by-step explanation:

a

Answer:

33 adult tickets and 21 student tickets

Step-by-step explanation:

We will create a system of equations.

Let x = the number of adult tickets sold and let y = the number of student tickets sold

x + y = 54

3x + 2y = 141

We can cancel out the y by multiplying the first equation by -2.

-2x - 2y = -108

3x + 2y = 141

Adding these equations together we get:

x = 33

Plugging this into the equation, we have:

38 + y = 54

y = 21

There were 33 adult tickets and 21 student tickets

Answer: Rami saved 2004 pennies

Step-by-step explanation:

The mode of the given data set is 1.

The given data set is 5, 4, 0, 1, 1, 0, 2, 2, 3, 1, 0, 4, 1, 1, 5, 2, 4, 0, 1, 2, 3.

We need to find the mode of the given data set.

The mode is the value that appears most frequently in a data set. A set of data may have one mode, more than one mode, or no mode at all.

The order of the given data set is

0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 4, 4, 4, 5, and 5.

Here, mode=1 (appear 6 times)

Therefore, the mode of the given data set is 1.

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Answer:

1) Combine the x tiles to get: [tex]\mathbf{4x}[/tex]

2) Combine integer tiles to get: 3

3) The equivalent function is: [tex]\mathbf{4x+3}[/tex]

4) If we Substitute any value of x both expressions will be equivalent

Step-by-step explanation:

We are given expression: [tex]x+x+x+x++4-1\\[/tex]

We need to complete following statements.

1) Combine the x tiles to get:

[tex]x+x+x+x\\=4x[/tex]

Combine the x tiles to get: [tex]\mathbf{4x}[/tex]

2) Combine integer tiles to get:

[tex]+4-1\\=3[/tex]

Combine integer tiles to get: 3

3) The equivalent function is:

[tex]x+x+x+x++4-1\\\\4x+3[/tex]

The equivalent function is: [tex]\mathbf{4x+3}[/tex]

4) If we Substitute any value of x both expressions will be equivalent

Verifying:

[tex]x+x+x+x+4-1=4x+3\\Let\: x = 1\\1+1+1+1+4-1=4(1)+3\\4+4-1=4+3\\7=7[/tex]

So, Both expressions are equivalent.

The answer is "4x" for the first box

                        "3" for the second box

                        "4x + 3" for the third box

And "Substitution"  for the last box

                                               You're Welcome!

    PS: I want to thank the first person for answering, you are amazing,

                                                       thanks!

Answer:

$22.50

Step-by-step explanation:

Answer: No

Step-by-step explanation:

Because 52/1 is just plain 52

But 1/52 is one thing out of 52 of them.

So 52/1 is just the number 52 versus 1/52 is one of fifty-two.

Answer:

Yes, 1/52 is the same as 52/1 because 52/1 is the inversed fraction of 1/52. Inversed fractions is a fraction with the denominator and numerator swapped.

Step-by-step explanation:

Hope this helped and please tell me if I'm incorrect :)

Answer:

41/30

Step-by-step explanation:

To find the answer, all we need to do is plug in the slope and point they gave us into the Point Slope Formula!

The point slope formula is ...

[tex]y - y_{1} = m ( x - x_{1} )[/tex]

So lets put them in!

y - 4    =    2/3     (x - (-3))

Tip: remember when you subtract a negative number, it turns into adding !

So our final answer is probably D (I think you may have put a typo)

[tex]y - 4 = \frac{2}{3} (x + 3)[/tex]

Answer:

16

Step-by-step explanation:

Answer:

x² + 24x + 84

Step-by-step explanation:

4 * (x+3)(x+3) - 3 * (x+4)(x-4)

4(x²+6x+9) - 3(x²-16)

4x² + 24x + 36 - 3x² + 48

x² + 24x - 84

A. The equation for x is c - b/a

B. x = 4

x = 10

Given the equation;

ax + b  = c

Let's make 'x' the subject of formula by expressing it in terms of other variables

We have;

ax = c - b

Divide both sides by the coefficient of 'x'

ax/a = c - b/ a

x = c - b/a

B. 3x + 7 = 19

Let's solve for x

3x = 19 - 7

3x = 12

Make 'x' the subject

x = 12/ 3

x = 4

1/2x  = 5

cross multiply

x = 5 × 2

x = 10

Thus, the equation for x is c - b/a

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Answer:

(1, -3)

Step-by-step explanation:

Use Desmos! It's really useful.