Describe how to determine the average rate of change between x = 2 and x = 4 for the function f(x) = 2x3 + 1. Include the average rate of change in your answer.

Answer:

===========

Let the number of apples in each bag is x, then the number of bags is 20/x.

Since the number of apples in each bag is greater than one and number of bags is greater than one, we have the following conditions:

The factors of 20 between 1 and 20 are:

The possibilities are:

Marta’s equation has a positive y-intercept, but the scatterplot shows a negative correlation.

The scatter plot is a manner in which data is presented as dots on a cartesian axes, The line of best fit is a description of the data that is presented in the scatter plot.

Hence, Marta is incorrect because Marta’s equation has a positive y-intercept, but the scatterplot shows a negative correlation.

Missing parts;

Marta believes that the equation of the line of best fit for the scatterplot below is y=-5/9x+23/9. Which statement best summarizes why Marta is likely incorrect?

Marta’s equation has a positive y-intercept, but the scatterplot suggests a negative y-intercept.

Marta’s equation has a positive y-intercept, but the scatterplot shows a negative correlation.

Marta’s equation has a negative slope, but the scatterplot suggests a negative y-intercept.

Marta’s equation has a negative slope, but the scatterplot shows a positive correlation.

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Answer:

The highest number that divides each of the two or more numbers is the HCF or Highest Common Factor.

Step-by-step explanation:

Example: What is the HCF of {12,42,14}

Answer: The HCF is 2 as the biggest number they can all be divided by is 2. {12,42,14} = {2^2*3,2*3*7,2*7} The factors in each number is 2.

Answer:

3

Step-by-step explanation:

Start with the amount that he wants to pay with gigabytes and subtract the amount of his bill without gigabytes.

58.50-46.50=12

 Then divide that amount by the price of each gigabyte to determine how many gigabytes he can use while staying in budget.

12/4=3

Answer: 3

Inequalities help us to compare two unequal expressions. The gigabytes of data that Elijah should use while staying within his budget is 3 gigabytes.

Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed. It is mostly denoted by the symbol <, >, ≤, and ≥.

Given that Elijah pays a flat cost of $46.50 per month and $4 per gigabyte. He wants to keep his bill at $58.50 per month. Therefore, we can write the inequality for this condition as,

$46.50 + $4(x) ≤ $58.50

46.50 + 4x ≤ 58.50

4x ≤ 58.50 - 46.50

4x ≤ 12

x ≤ 12/4

x ≤ 3

Hence, the gigabytes of data that Elijah should use while staying within his budget is 3 gigabytes.

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Answer:

Step-by-step explanation:

6. The rate of change is essentially the slope. But in other words, it's how much the y changes as x increases by 1. If this rate of change is 0, that means the y-value is constant, while the x can be any real number. It can be generally given in the formula: y=b, which comes from simplifying the slope-intercept form: y=(0)x+b = b. You can also derive the same thing for a point-slope form: y-a = 0(x-b)=0 so y=a. In both cases, y is equal to some constant value. So graphing this makes a horizontal line.

7. To define a parallel line, you need the same slope, and a different y-intercept, which is under the assumption that the line has a slope that is definable. If the slope is definable, you'll have the equation: y=mx+b, where m is the same as the other line. Then you plug in the known values as x and y, to solve for b, which is the y-intercept. Now if the line is a vertical line, a parallel line can be defined as: x=a, where a doesn't equal the constant, the other vertical line is equal to. To make it pass through some point (c, d). Then you would simply set x=c, since the x is the only thing that matters, since the y-value is all real numbers, so it will eventually have the y-value d somewhere on the line.

8. To define a perpendicular line, you get the reciprocal of the slope and change the sign. So if the slope is: [tex]\frac{a}{b}[/tex] then it becomes [tex]-\frac{b}{a}[/tex] and vice versa depending on the sign. In this example, let's just say m=a/b, then the perpendicular slope would be -b/a. You can then plug this into the slope-intercept formula: [tex]y=-\frac{b}{a}+c[/tex] where c is the y-intercept. Then you plug in the known point as (x, y) and solve for c, the y-intercept. Now let's say for example that you have a vertical line: x=a. In this case you can see the slope as: [tex]\frac{1}{0}[/tex][tex]\frac{y_2-y_1}{a-a}[/tex]. Of course this isn't definable, but if you take the reciprocal you get something that is: [tex]-\frac{0}{y_2-y_1}[/tex] which will always evaluate to 0. This means you get a horizontal line, since the slope is 0. This means if you have a vertical line, any horizontal line should be perpendicular, which makes sense, since it should form a 90 degree angle when they intersect, because they're straight lines. To make sure that horizontal line passes through the point (b, c), you simply set the y equal to c. So y=c, will pass through (b, c), since the c is constant, and the x can equal anything so somewhere on the line it will intersect (b, c). But let's say we had a horizontal line, the reciprocal can be defined as: [tex]\frac{a-a}{x_2-x_1}[/tex] where a is the y constant. If you take the reciprocal, then you have a-a in the denominator, which gives you an undefined slope, because the perpendicular line to a horizontal line, is a vertical line. To ensure this perpendicular line passes through the point (b, c). You simply set x equal to b. so that x=b.

#6

if m is 0

Hence line is parallel to x axis

#7

parallel lines have equal slopes

so we can use the point slope form of line to find the equation

#2

Same process like no 7 but

slope of perpendicular line is negative reciprocal of given line's slope

Answer:

9

Step-by-step explanation:

So first step is to subtract [tex]3x^2+4x[/tex] from [tex]7x^2+x+9[/tex]. In setting this up you get the following expression

[tex](7x^2+x+9)-(3x^2+4x)[/tex]

Distribute the negative

[tex]7x^2+x+9-3x^2-4x[/tex]

Group like terms

[tex](7x^2-3x^2)+(x-4x)+9[/tex]

Simplify:

[tex]4x^2-3x+9[/tex]

Now subtract [tex]4x^2-3x[/tex]. In setting this up you get the following expression

[tex](4x^2-3x+9)-(4x^2-3x)[/tex]

Distribute the negative:

[tex]4x^2-3x+9-4x^2+3x[/tex]

Group like terms

[tex](4x^2-4x^2) + (-3x+3x) + 9[/tex]

Simplify:

[tex]9[/tex]

Answer:

18 and 72

Step-by-step explanation:

the smaller part can be assigned as x while the larger will be 4x. Both numbers need to add up to 90, giving the equation: 4x+x = 90

Solve:

4x+x = 90

5x = 90

x = 18

4x = 72

The percent by volume of the resulting solution is 10L by 93 percent

The resulting solution = sum of the volumes of both solutions

Resulting solution = 6L × 33 percent + 4L × 60 percent

Resulting solution = 10 L × 93 percent

This is so because both solutions add up to form the resulting solution

Thus, the percent by volume of the resulting solution is 10L by 93 percent

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The solution is x=3/4

How can we solve given equation?

First, we will solve like terms. Then shift constant to other side and keep x on the same side to get the value of x.

We can solve given equation as shown below:

5/2-3x-5+4x=-7/4

(5-10)/2+x=-7/4

-5/2+x=-7/4

x=5/2-7/4

x= (10-7)/4

x=3/4

Hence, the solution is x=3/4.

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From the straight line AB and CD with point M as midpoint of both lines, AM = BM = 3.2 cm and CM = DM = 2 cm

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

m as the midpoint of both ab and cd, hence:

AM = BM = AB/2 = 6.4/2 = 3.2 cm

CM = DM = CD/2 = 4/2 = 2 cm

From the straight line AB and CD with point M as midpoint of both lines, AM = BM = 3.2 cm and CM = DM = 2 cm

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Answer:

[tex]6[/tex]

Step-by-step explanation:

The gist of modular arithmetic in a nutshell: the numbers [tex]a[/tex] and [tex]b[/tex] are considered to be congruent by their modulus [tex]m[/tex] if [tex]m[/tex] is a divisor of their difference.

In mathematics: [tex]a \equiv_{m} b \Leftrightarrow (a - b) \vdots m[/tex]

Exemplifying this: [tex]6 \equiv_{7} -1[/tex] because [tex]6 - (-1) = 6 + 1 = 7[/tex], [tex]7 \vdots 7[/tex].

Let us have following equivalences: [tex]a \equiv_{m} b[/tex] and [tex]c \equiv_{m} d[/tex], then:  [tex](a - b) \vdots m[/tex] and [tex](c - d) \vdots m[/tex] by definition.

Properties:

1. [tex]a + c \equiv_{m} b + d \Leftrightarrow ((a + c) - (b + d)) \vdots m \Leftrightarrow (a + c - b - d) \vdots m \Leftrightarrow ((a - b) + (c - d)) \vdots m[/tex].

2. [tex]a - c \equiv_{m} b - d \Leftrightarrow ((a - c) - (b - d)) \vdots m \Leftrightarrow (a - c - b + d) \vdots m \Leftrightarrow ((a - b) - (c - d)) \vdots m[/tex].

3. [tex]ac \equiv_{m} bd \Leftrightarrow (ac - bd) \vdots m \Leftrightarrow (ac - bc - bd + bc) \vdots m \Leftrightarrow (c(a - b) + b(c - d)) \vdots m[/tex].

4. What if we have [tex]a \equiv_{m} b[/tex] twice? If we abide by property 3, we can come to the conclusion that [tex]a^2 \equiv_m b^2[/tex]. It is fair enough that there is room for the equivalence [tex]a^n \equiv_{m} b^n[/tex].

[tex]3^{51} = (3^3)^\frac{51}{3} = 27^{17} \equiv_{7} (-1)^{17} \equiv_{7} -1 \equiv_{7} 6[/tex].

We used property 4.

Keep in mind that any remainder cannot be a negative number.

Therefore, the remainder equals [tex]6[/tex].

[tex]\Large\maltese\underline{\textsf{Our problem:}}[/tex]

What is [tex]\bf{\bigg(\dfrac{2}{5}\bigg)^2[/tex]?

[tex]\Large\maltese\underline{\textsf{This problem has been solved!}}[/tex]

When we have a fraction that is raised to a specific power, we raise both the numerator and the denominator to that power.

[tex]\bf{\dfrac{2^2}{5^2}}=\dfrac{4}{25}[/tex]

[tex]\rule{300}{1.7}[/tex]

[tex]\bf{Answer:}[/tex]

                    [tex]\bf{=\dfrac{4}{25}[/tex]

[tex]\boxed{\bf{aesthetic \not101}}[/tex]

Step-by-step explanation:

There cannot be such a question because the difference of half of the big number and the small number will automatically be zero, but we can find it with the equation I circled on the paper I gave you. achievements

Answer:

1.19x = 12

Step-by-step explanation:

To write an equation, we multiply the cost of each song by the number of songs, x

1.19 * x

This is equal to the total amount he is allowed to spend

1.19x = 12

Answer:

D

Step-by-step explanation:

If Doug can download new songs for $1.19 each, then he will be able to download 12 songs.

Answer:

5/6

Step-by-step explanation:

The numbers on a six-sided die are as shown:

1, 2, 3, 4, 5, 6

The even numbers are:

2, 4, 6

The numbers greater than 3 are:

3, 4, 5, 6

Both lists together are:

2, 3, 4, 5, 6

Because 5 out of 6 numbers satisfy these conditions, the probability of satisfying these conditions is 5/6.

Answer:

[tex](-\infty, -1)\ \cup\ (0, 2)[/tex]

Step-by-step explanation:

So if you expand out the two binomials (k-2)(k+1), you'll get: [tex]k^2+k-2k-2[/tex]. which simplifies to: [tex]k^2-k-2[/tex]. Multiplying this by the k gives you: [tex]k^3-k^2-2k[/tex]. As you can see the degree is odd, this means that this polynomial will have two opposite end behaviors. And as you can see the leading coefficient is positive, meaning that this function will go towards positive infinity as k goes towards positive infinity. Also we if look at the original equation given, it's in factored form, with the zeroes as k=0, k=2, and k=-1. So given this we can draw a simple graph to see when the value of the equation is negative. If you look at the graph I drew you'll see that it's negative from (-infinity, -1) and then negative from (0, 2)

Answer:

ok so we can just add 20 + 45 then divide by 2

20+45=65/2=32.5

32.5

Hope This Helps!!!

Answer:

c.) 38

Step-by-step explanation:

[tex]\sum\limits_{n=3}^6 a_n[/tex]   means "summation of the all the elements starting from the 3rd element to the 6th element".

The 3rd element in the series is 14, and the 6th element is 5; we have to add these and all the elements between them together.

∴    [tex]\sum\limits_{n=3}^6 a_n[/tex]    =  14 + 11 + 8 + 5

                   = 38

The statement that's true about the triangle is that WXY + YXZ = 180°.

It should be noted that in the question, the options are related to a linear pair.

According to the linear pair, when a line cuts another line at a point, then the sum of the adjacent angles formed at the point will be 180°.

Therefore, WXY + YXZ = 180°.

The correct option is C.

The complete question is:

Which statement regarding the diagram is true?

m∠WXY = m∠YXZ

m∠WXY < m∠YZX

m∠WXY + m∠YXZ = 180°

m∠WXY + m∠XYZ = 180°

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Answer:

f(x)=x²-3x-10

Step-by-step explanation:

[tex]f(x) = x {}^{2} - 3x - 10 \\ to \: find \: x \: intercept \:o r \: zero \: substitute \: f(x) = 0\: \\ 0 = x {}^{2} - 3x - 10 \\ x {}^{2} - 3x - 10 = 0 \\ x {}^{2} + 2x - 5x - 10 = 0 \\ x(x + 2) - 5x - 10 = 0 \\ x(x + 2) - 5(x + 2) = 0 \\ (x + 2).(x - 5) = 0 \\ x + 2 = 0 \\ x - 5 = 0 \\ x = - 2 \\ x = 5[/tex]

therefore the zeros of the equation are x₁=-2,x₂=5

Answer:

16 to the power of 5

y to the power of 4

(7a) to the power of 3 or 7 times a to the power of 3

Answer:

55

Step-by-step explanation:

To find the average you add up all numbers given then divide by the amount of numbers there were. The mean, or average, of the original 5 people was 13 since their ages added was 65, which you divide by 5 for 13. The new mean once the 6th person entered the room was 20. So, you do 6 [number of people] times 20 [average] to get 120. Taking 65 [added amount of original ages of the 5 people] away from 120 [the new added up ages of all 6 people], you get 55. This means 55 would be the 6th person's age.

Sorry if the explanation is confusing!

Call the total ages of the 6 people, x

To calculate the mean age of 6 people, we take the total age (x) and divide by the amount of people (6)

So, x : 6 = 20

-> The total ages of the 6 people are 20 x 6 = 120

We can calculate the 6th person's age by taking 120 and minus the total age of the other 5

-> 120 - (13+12+13+15+12) = 55

So, the 6th person's age is 55.

Using the Central Limit Theorem, the standard deviation of the sampling distribution of sample means would be of 0.86.

It states that the standard deviation of the sampling distribution of sample means is given by:

[tex]s = \frac{\sigma}{\sqrt{n}}[/tex]

In which:

The parameters for this problem are given as follows:

[tex]\sigma = 6.8, n = 63[/tex].

Hence:

[tex]s = \frac{\sigma}{\sqrt{n}}[/tex]

[tex]s = \frac{6.8}{\sqrt{63}}[/tex]

s = 0.86.

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The system of equations has (d) 0 real solutions

The system of equations is given as:

y = x^2+1

y=x

Substitute y=x in y = x^2+1

x = x^2+1

This gives

x^2 - x + 1 = 0

Calculate the discriminant using:

d = b^2 - 4ac

So, we have:

d = (-1)^2 - 4 * 1 * 1

Evaluate

d = -3

Because the discriminant is negative, the equation has no real solution

Hence, the system of equations has (d) 0 real solutions

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The table below is a quadratic function.

A quadratic function is an Algebraic function with the power of its variable as 2.

This function normally has three algebraic terms, the x-square term, the x-term and the constant term.

Analysis:

The X-column values increases from -2 to 1, while the f(x) column which is the y-column increase from -9, until it gets to 1, where the value falls to -5.

A typical behavior of an inverted-v curve which is a quadratic curve.

If it were a linear function, as x values increase, y value would either keep increasing or decreasing, it does not change its orientation.

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[tex]\Large\maltese\underline{\textsf{A. What is Asked}}[/tex]

Which ordered pairs make the equation [tex]\bf{3x+2y=-7}[/tex] true? Select all that apply. 3 options are given

[tex]\Large\maltese\underline{\textsf{B. This problem has been solved!}}[/tex]

We can tell which ordered pairs make equations true by plugging in the coordinates.

[tex]\mathbb{ORDERED\;PAIR\;NUMBER\;ONE}[/tex]

[tex]\bf{3(3)+2(-8)=-7}[/tex] | simplify

[tex]\bf{9-16=-7}[/tex] |simplify

[tex]\bf{-7\equiv-7}[/tex] | this one checks

[tex]\mathbb{ORDERED\;PAIR\;NUMBER\;TWO}[/tex]

[tex]\bf{3(-2)+2(-1)=-7}[/tex] | simplify

[tex]\bf{-6-2=-7}[/tex] | simplify

[tex]\bf{-8\neq-7}[/tex] | this one does not check

[tex]\mathbb{ORDERED\;PAIR\;NUMBER\;THREE}[/tex]

[tex]\bf{3(1)+2(-4)=-7}[/tex] | simplify

[tex]\bf{3-8=-7}[/tex] | simplify

[tex]\bf{-5\ne-7}[/tex] | this one does not check

[tex]\rule{300}{1.7}[/tex]

[tex]\bf{Result:}[/tex]

              [tex]\bf{=The\;First\;Option[/tex]

[tex]\boxed{\bf{aesthetic \not101}}[/tex]

The value of x will be equal to 33.94 units.

Trigonometry is the branch of mathematics that set up a relationship between the sides and angle of the right-angle triangles.

Given that:-

Given that the radius of the circle is 12 units which are PO = 12 and OR = 12, QR = x , ∠O = 60 So ∠Q = 30.

First, we will calculate the Length OQ by angle property in triangle OQR.

[tex]Sin 30=\dfrac{Perpendicular}{Hypotenuse}[/tex]

[tex]Sin 30 = \dfrac{12}{OQ-12}[/tex]

[tex]\dfrac{1}{2}=\dfrac{12}{OQ-12}[/tex]

OQ - 12 = 24

OQ = 36

Now applying the Pythagorean theorem in the triangle OQR.

H² = P² + B²

36² = 12² + x²

x² = 1296 - 144

x = √1152

x = 33.94

Therefore the value of  x will be equal to 33.94 units.

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Step-by-step explanation:

I assume

SR = 2x + 23

RQ = x + 21

if that is true, then the situation is completely simple :

14 = (2x + 23) + (x + 21) = 3x + 44

3x = -30

x = -10

SR = 2×-10 + 23 = -20 + 23 = 3

RQ = -10 + 21 = 11

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \:x = -10 [/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

[tex] \qquad \tt \rightarrow \: SR + RQ = SQ[/tex]

[tex]\qquad \tt \rightarrow \: 2x + 23 + x + 21 = 14[/tex]

[tex]\qquad \tt \rightarrow \: 3x + 44 = 14[/tex]

[tex]\qquad \tt \rightarrow \: 3x = 14 - 44[/tex]

[tex]\qquad \tt \rightarrow \: 3x = - 30[/tex]

[tex]\qquad \tt \rightarrow \: x = - 10[/tex]

Now,

[tex] \qquad \tt \rightarrow \: SR = 2x + 23 [/tex]

[tex] \qquad \tt \rightarrow \: SR = 2(-10) + 23 [/tex]

[tex] \qquad \tt \rightarrow \: SR =-20+ 23 [/tex]

[tex] \qquad \tt \rightarrow \: SR = 3 \:\: units [/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

The angle of y in the triangle is 30 degrees.

∠O = 180 - 30 - 70 (angles in a triangle)

∠O = 180 - 100(angles in a triangle)

∠O = 80°

Using vertically opposite angle principle and sum of angle in a triangle,

80 + y + 70 = 180

180 - 150 = y

y = 30 degrees

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