Find the derivative

An arrangement of the order the numbers would appear on a number line from least to greatest is: -31/3, -10, -9/8, 0, 1, 1/4, 9/8, 8.

In Mathematics, a number line can be defined as a type of graph with a graduated straight line which is composed of both positive and negative numbers that are placed at equal intervals along its length.

Generally speaking, a number line typically increases in numerical value towards the right from zero (0) and decreases in numerical value towards the left from zero (0).

In order to arrange the given numbers in order from least to greatest, we would convert them into a decimal number as follows:

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The point P is on the perpendicular line to AB that passes through its midpoint.

We know perpendicular lines have opposite-reciprocal slopes.

So the line we are looking for has a slope of 7/5.

Use the point-slope equation to find the line:

Choose any form above of the same line.

Answer:

[tex]\textsf{Slope-intercept form}: \quad y=\dfrac{7}{5}x-\dfrac{19}{5}[/tex]

[tex]\textsf{Standard form}: \quad 7x-5y=19[/tex]

Step-by-step explanation:

A perpendicular bisector is a line that intersects another line segment at 90°, dividing it into two equal parts.

To find the perpendicular bisector of segment AB, find the slope of AB and the midpoint of AB.

Define the points:

Slope of AB

[tex]\textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{-6-4}{9-(-5)}=\dfrac{-10}{14}=-\dfrac{5}{7}[/tex]

Midpoint of AB

[tex]\textsf{Midpoint}=\left(\dfrac{x_2+x_1}{2},\dfrac{y_2+y_1}{2}\right)=\left(\dfrac{9+(-5)}{2},\dfrac{-6+4}{2}\right)=(2,-1)[/tex]

If two lines are perpendicular to each other, their slopes are negative reciprocals.

Therefore, the slope of the line that is perpendicular to line segment AB is ⁷/₅.

Substitute the found perpendicular slope and the midpoint of AB into the point-slope formula to create an equation for the line that is the perpendicular bisector of line segment AB:

[tex]\implies y-y_1=m(x-x_1)[/tex]

[tex]\implies y-(-1)=\dfrac{7}{5}(x-2)[/tex]

[tex]\implies y+1=\dfrac{7}{5}x-\dfrac{14}{5}[/tex]

[tex]\implies y=\dfrac{7}{5}x-\dfrac{14}{5}-1[/tex]

[tex]\implies y=\dfrac{7}{5}x-\dfrac{19}{5}[/tex]

Therefore, the formula that expresses the fact that an arbitrary point P(x, y) is on the perpendicular bisector of segment AB is:

[tex]\textsf{Slope-intercept form}: \quad y=\dfrac{7}{5}x-\dfrac{19}{5}[/tex]

[tex]\textsf{Standard form}: \quad 7x-5y=19[/tex]

Step-by-step explanation:

If x = 3 :

x³ ÷ 3 = y

3³ ÷ 3 = y

27 ÷ 3 = y

y = 27 ÷ 3 = 9

Answer:

d /c

Step-by-step explanation:

if its rotated at an 270 angle then its d or c cause they are the same

Answer: the one on the top left corner

Answer: the third one (bottom left) but also the second one (top right)

Step-by-step explanation: 2. there are 8 total parts to the figure and four of those parts are shaded. 4/8

3. There are four total parts to the figure but only 2 are shaded. 2/4

2/4 and 4/8 are both EQUIVALENT to 1/2. Therefore, that is the correct answer.

The given phrase on translation to math expression is (6 ÷ 3) + 12 , the correct option is (a) .

In the question ,

an mathematical phrase is given , that is "Twelve more than the quotient of six divided by three" .

we have to translate it into mathematical expression ,

So , the term quotient of six divided by three is written as 6 ÷ 3 .

and phrase " more " is represented by " + " ,

Hence the given phrase,  "Twelve more than the quotient of six divided by three" is  (6 ÷ 3) [tex]+[/tex] 12 .

Therefore , The given phrase on translation to math expression is (6 ÷ 3) + 12 , the correct option is (a) .

The given question is incomplete , the complete question is

Translate the phrase into a math expression , "Twelve more than the quotient of six divided by three" .

(a) (6÷3)+12

(b) 6÷(3+12)

(c) (3÷6)+12

(d) 3÷(6+12)

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The difference between their ages one year ago was 2 years.

Difference in maths, the result of one of the important mathematical operations, which is obtained by subtracting two numbers.

Given that, Jack is 2 years older than Bob,

Let Bob's age be x then, Jack's age will be (x+2)

Their ages before 1 year was =

Bob's = x-1

Jack's = (x+1)

Difference = x + 1 - x + 1 = 2

Hence, The difference between their ages one year ago was 2 years.

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Step-by-step explanation:

if I understand your typing correctly, and there is nothing missing, we have

f(x) = 0.6x⁵ - 2x⁴ + 8x

the "end behavior" means the general tendency of the result values for very large or very low values of x (going to +infinity and -infinity).

the higher (or lower in the negative direction) x gets, the more the highest exponent will dominate the result values.

it does not matter, that it has a diminishing factor (or coefficient) like 0.6.

the much stronger progression of x⁵ vs. smaller exponents like x⁴ or x will easily compensate for that with sufficiently large x.

so, ultimately, the term with the highest exponent (in our case 0.6x⁵) defines the end behavior.

with x going to +infinity, so does the function result (+infinity).

with x going to -infinity, so does the function result (-infinity, because an odd exponent number like 5 will maintain the sign of the argument).

The maximum tangential speed that the ball can have is 3.89 m/s. Centripetal acceleration is 0.06561 and tangential speed of ball will be 0.243 m/s

The centripetal force is the force needed to keep a body moving in circular motion. It exists for circular motion. Example - rotation of earth around sun.

We have an athlete swings a 7.9 kg ball horizontally on the end of a rope. The ball moves in a circle of radius 0.9 m at an angular speed of 0.27 rev/s.

[A] -

Tangential speed of ball = v = rω = 0.9 x 0.27 = 0.243 m/s

[B] -

Centripetal acceleration = a[c] = rω² = 0.9 x 0.27 x  0.27 = 0.06561

[C] -

Maximum tension = Maximum centripetal force = mrω² = 132.3

ω² = 132.3/mr

ω² = 18.60

v² = 18.60r²

v = 3.89 m/s

Therefore, the maximum tangential speed that the ball can have is 3.89 m/s. Centripetal acceleration is 0.06561 and tangential speed of ball will be 0.243 m/s

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The measures of the arithmetic sequence are given as follows:

a. [tex]S_{10} = 350[/tex]

b. [tex]A_{n + 1} = 17 + 4n[/tex]

c. [tex]S_n = \frac{n(30 + 4n)}{2}[/tex]

d. [tex]A_n = 17 + 4(n - 1)[/tex]

An arithmetic sequence is a sequence of values in which the difference between consecutive terms is constant and is called common difference d.

The nth term of an arithmetic sequence is given by the rule shown below:

[tex]a_n = a_1 + (n - 1)d[/tex]

In which [tex]a_1[/tex] is the first term of the sequence.

The sum of the first n terms is given by the rule shown below:

[tex]S_n = \frac{n(a_1 + a_n)}{2}[/tex]

The equation given for this problem is:

[tex]a_{n + 4} = 4n + 17[/tex]

Hence the sequence can be written as follows:

17, 21, 25, 29, 33.

Then the first term and the common ratio are given as follows:

[tex]a_1 = 17, d = 4[/tex]

Then the nth term is of:

[tex]A_n = 17 + 4(n - 1)[/tex]

The (n + 1)th term is of:

[tex]A_{n + 1} = 17 + 4(n + 1 - 1)[/tex]

[tex]A_{n + 1} = 17 + 4n[/tex]

The sum of the first n terms is of:

[tex]S_n = \frac{n(a_1 + a_n)}{2}[/tex]

[tex]S_n = \frac{n(17 + 17 + 4(n - 1))}{2}[/tex]

[tex]S_n = \frac{n(30 + 4n)}{2}[/tex]

The sum of the first ten terms is of:

[tex]S_{10} = \frac{10(30 + 4(10))}{2} = 350[/tex]

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The equation of the tangent line of f at the point x = -3 will be y = -16x-48.

According to the question,

We have the following information:

f(x) = [tex]2x^{2} -4x-4[/tex]

Now, we will first find the derivation of this function with respect to x:

Let's take its derivation to be f'(x).

f'(x) = 4x-4

Now, finding the slope of the equation when x = -3:

f'(-3) = 4*(-3)-4

f'(-3) = -12-4

f(-3) = -16

Now, we know that following formula is used to find the equation of a line:

(y-y') = m(x-x')

y-0 = -16{x-(-3)}

y = -16(x+3)

y = -16x-48

Hence, the equation of the tangent line of f at the point x = -3 will be y = -16x-48.

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Any of the four terms of a discrete geometric proportion is called a proportional fourth.

[tex]\bold{5, 2 \: and \: 10.5}[/tex]

A geometric proportion is formed as follows:

[tex]\bold{5 : 2 :: 10 : x}[/tex]

Since the unknown term is an extreme and as we have seen before, one extreme is equal to the means divided by the other extreme, we will have:

[tex]\boxed{\bold{ \: x = \frac{2 \:∗ \: 10}{5} = 4} }[/tex]

Therefore, the geometric proportion is:

[tex]\bold{5 : 2 :: \: :: 10 :4}[/tex]

1. Two constants of proportionality representing the proportional relationship between distance in kilometers and number of hours are 400 km and 8 hours.

2. The relationship (ratio) between the two values is 50 km per hour or the equation, d = 50t.

3. Another equation that relates distance and time in this context is t = d/50 or 400/50.

The constant of proportionality is the ratio relating two given values in a proportional relationship.

Other names for the constant of proportionality include:

Distance, d = 400 km

Constant speed, t = 8 hours

d = 400/8

d = 50t

Constant of proportionality = 50.

t = d/s

Where d, distance = 400 km and s, speed = 50 km/h

= 400/50

= 8 hours

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The probability of the sets P(F or G) is; P(F or G)  = 0.67

We are given the following;

Sample Space; S = {3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14}

Set F = {6, 7, 8, 9, 10}

Set G = {10, 11, 12, 13}

Now, F or G, simple means; F ∪ G

Thus;

F or G = {6, 7, 8, 9, 10, 11, 12, 13}

Number of terms is (F or G) = 8

Number of terms is Sample space = 12

Thus;

P(F or G) = 8/12 = 2/3 = 0.67

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The number of the blueberries is 31.

In this case,  the only way that we can be able to obtain the number of the pints of the blueberries that she sold is by the use of a simultaneous equation.

Let the number of  the blueberries be x and the number of the raspberries be y.

We have

x + y = 57 ------ (1)

1.75x + 2.40y = 116.65 ------- (2)

x = 57 - y ------ (3)

Then we have;

1.75(57 - y) + 2.40y = 116.65

99.75 - 1.75y + 2.40y = 116.65

Collecting like terms;

- 1.75y + 2.40y = 116.65 - 99.75

0.65y = 16.9

y = 16.9/0.65

y = 26

To obtain the number of blueberries

x + 26 = 57

x = 57 - 26

x = 31

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The correct equation that could be used to solve for side x is x = sin52° × (Hypotenuse)

From the question, we are to determine the correct equation that could be used to solve for side x

From the given diagram, we observe that

Side x is the Opposite

Side z is the Adjacent

Side y is the Hypotenuse

Using SOH CAH TOA, we can write that

sin (angle) = Opposite / Hypotenuse

From the diagram,

Given angle = 52°

Hypotenuse = y = 13

Thus,

sin 52° = x/13

x = sin 52° × 13

OR

x = sin52° × (Hypotenuse)

Hence, the equation is x = sin52° × (Hypotenuse)

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Benchmark percentage of 1% = 9.6 & 10% = 24.

What is Free Throw Percentage?

Free throw percentage (FT%) puts a player’s successful free throws in perspective to their total attempts.

In basketball, a free throw (or foul shot) is awarded to a player who has been fouled by the other team. The number of free throws depends on where on the court the player was while being fouled.

To find 1% of a number, we can move the decimal point of the number two places to the left.

Therefore, 1% of 120 is 1.2

To find 10% of a number, we can move the decimal point of the number one place to the left.

Therefore, 10% of 120 is 12

Since 10% of 120 is 12 and

20% = 2 x 10%

then 20% of 120 = 2 x 10% of 120

= 2 x 12 = 24

Since 1% of 120 is 1.2 and

8% = 8 x 1%

then 8% of 120 = 8 x 1%  of 120

= 8 x 1.2 = 9.6

Hence the answer is, Benchmark percentage of 1% = 9.6 & 10% = 24.

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The coordinates of point (1,5) after dilation is (3,3). Therefore, 4th option is correct.

It is given to us that -

The coordinates of the original point is (1,5)

=> [tex](x_{o},y_{o} )=(1,5)[/tex] ---- (1)

The dilating factor is 1/3

=> [tex]s=\frac{1}{3}[/tex] (say) ---- (2)

And, the center of dilation is at the point (4,2)

=> [tex](x_{cod},y_{cod})=(4,2)[/tex] ---- (3)

We have to find out the coordinates of point (1,5) after dilation.

Using the formula for dilation coordinates from original to image, we have

[tex][(x_{cod}+s(x_{o}-x_{cod}),y_{cod}+s(y_{o}-y_{cod})]\\=[4+\frac{1}{3}(1-4),2+\frac{1}{3}(5-2)]\\=[(4-1),(2+1)]\\=(3,3)[/tex]

Thus, the coordinates of point (1,5) after dilation is (3,3). Therefore, 4th option is correct.

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Answer:

2

Step-by-step explanation:

The slope of a line is defined by the formula:

[tex]m=\dfrac{\Delta \, y}{\Delta \, x} = \dfrac{y_2 - y_1}{x_2 - x_1}[/tex]

In this problem, we are given two points in the form [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex].

So, we can define the x's and y's as:

[tex]x_1 = 1[/tex], [tex]y_1 = 2[/tex], [tex]x_2 = 5[/tex], [tex]y_2 = 10[/tex].

Hence, the slope of the line can be solved for.

[tex]m = \dfrac{10-2}{5-1}[/tex]

[tex]m = \dfrac{8}{4}[/tex]

[tex]m = 2[/tex]

The slope of the line with points (1, 2) and (5, 10) is 2.

The pair of polygons that are similar to each other are all the pairs of polygons except the pair of rectangles.

Similar polygons are polygons that have corresponding side lengths that are proportional to each other, thus, they have the same shape by different sizes.

To determine if he given pairs of polygons are similar, check if their corresponding side lengths have the same ratio, that is, if they are proportional to each other.

For the trapezoids:

27/15 = 18/10 = 7.2/4 = 10.8/6 = 1.8

This means the trapezoids are similar.

For the rectangles:

18/10 ≠ 14/7

This means the rectangles are not similar.

For the right triangles:

32/24 = 24/18 = 40/30 = 1.33

This means the right triangles are similar polygons.

So also is the last pair of polygons similar to each other. Therefore, the only polygon that is not similar is the pair of rectangles.

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Answer:

The y-intercept represents the number of mammals when they were originally counted.

The line y = 0 is an asymptote of the graph.

The y-intercept is 120.

The asymptote indicates that as years pass, the number of mammals will approach 0.

The point S of line segment RT such that RS / ST = 2 / 5 is equal to (- 3, 0).

Herein we find a line segment whose endpoints are known (R(x, y) = (- 5, - 2), T(x, y) = (2, 5)) and in which we must determine the coordinates of a point S within line segment RT such that the partition ratio is observed:

RS / ST = 2 / 5

[tex]\overrightarrow{RS} = \frac{2}{5} \cdot \overrightarrow {ST}[/tex]

S(x, y) - R(x, y) = (2 / 5) · [T(x, y) - S(x, y)]

(7 / 5) · S(x, y) = (2 / 5) · T(x, y) + R(x, y)

S(x, y) = (2 / 7) · T(x, y) + (5 / 7) · R(x, y)

Now we determine the location of point S:

S(x, y) = (2 / 7) · (2, 5) + (5 / 7) · (- 5, - 2)

S(x, y) = (4 / 7, 10 / 7) + (- 25 / 7, - 10 / 7)

S(x, y) = (- 21 / 7, 0)

S(x, y) = (- 3, 0)

The location of point S is (- 3, 0). A representation of the geometric system is shown in the image attached below.

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Olivia made $288 last week from her 4 percent commission and an average of $14,976 in 52 weeks

The term "percentage" was adapted from the Latin word "per centum", which means "by the hundred". Percentages are fractions with 100 as the denominator. In other words, it is the relation between part and whole where the value of whole is always taken as 100.

In this question, she makes a commission of 4% on her weekly sales.

A) How much did she makes last week?

To find how much she made, we simply have to find 4% of 7200

0.04 * 7200 = 288

She made $288 last week.

B) If she made $288 each week, and we have 52 weeks in a year, we can multiply them and find how much she made in a year.

$288 * 52 = $14,976

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Answer:

57 half dollars and 169 quarters

Step-by-step explanation:

We will need a system of equations to solve this problem.

Given that the number of quarters is 2 less than three times the number of half dollars, we have Q = 3H - 2

Thus, we have 0.25Q + 0.50H = 70.75 and Q = 3H - 2.

The second equation allows us to use substitution:

[tex]0.25(3H-2)+0.50H=70.75\\0.75H-0.50+0.50H=70.75\\1.25H=71.25\\H=57[/tex]

We can plus this 57 into the second equation to find the number of quarters:

[tex]Q = 3(57)-2\\Q=169[/tex]

Answer: x - 5 is less than or equal to -25

Step-by-step explanation:

The loan's future value will be $6925 when Lynne pays a simple interest rate of 5.4%.

According to the question,

We have the following information:

Lynne needs to borrow $6250 for cosmetic surgery. She obtains a loan from her grandmother for 24 months at a simple interest rate of 5.4%.

We know that the following formula is used to find the simple interest:

Principal*rate*time/100

Principal = $6250

Rate = 5.4%

Time = 2 years

Simple interest = (6250*5.4*2)/100

Simple interest = 67500/100

Simple interest = $675

Now, the total amount of loan will be:

Interest + principal

675+6250

$6925

Hence, the loan's future value will be $6925 when Lynne pays a simple interest rate of 5.4%.

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LJ = 46 is the value when  LK  congruent MK .

What do you mean by congruent?

By given figure ,

        MK = MN - KN

               = 9x - 11 - ( x + 3 )

               = 8x - 14

now given LK ≅ MK

           LK = MK

8x - 14 = 7x - 10

8x - 7x = 14 - 10

 x = 4

length of LJ = LK + KJ

                    = 7x - 10 + 28

                    = 7(4) + 18

                    = 28 + 18  ⇒ 46

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The required measure of ∠P would be 76.825° in the given triangle PQR.

Given that two angles in triangle PQR are congruent, ∠P and ∠Q;

∠R measures 26.35°.

Let the measure of ∠P would be x

∠P = x = ∠Q

We know that the sum of interior angles is always 180 degrees in the triangle.

⇒ ∠P + ∠Q + ∠R = 180°

⇒ x + x  + 26.35° = 180°

⇒ 2x  + 26.35° = 180°

⇒ 2x = 180° - 26.35°

⇒ 2x = 153.65

⇒ x = 153.65/2

⇒ x = 76.825°.

Therefore, the required measure of ∠P would be 76.825° in the given triangle PQR.

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