how do the average rates of change for f(x)= -0.5x2 and g(x)= -1.5x2 over the interval -3 < x < 3

The expression for the length of the rectangular prism is L = 9x² + 7x - 2

Given data ,

Let the length of the rectangular prism be L

Let the volume of the rectangular prism be V = 36x³ - 28x + 8

Let the height of the prism be H = 3x - 1

Let the width of the prism be W = 4

And , Volume of Rectangle = Length x Width x Height

On simplifying , we get

36x³ - 28x + 8 = L ( 3x - 1 ) ( 4 )

L ( 12x - 4 ) = 36x³ - 28x + 8

By long division , we get

       -----9x² + 7x - 2--------------------------------------

4(3x - 1) | 36x³ - 28x + 8

                  - (36x - 9x)

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

                           7x - 2

                           - (7x - 2)

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

                                          0

Hence , the length of the prism is L = 9x² + 7x - 2

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If Hi, Leon Sargetta, do you promise to pay Patrick Amina the sum of $3500. the minimum amount of Leon’s monthly payment is: c. $104.84.

Using this formula

Monthly Payment = (P * r * (1 + r)^n) / ((1 + r)^n - 1)

where:

P = Principal = $3500

r = Monthly interest rate =  (5.5% / 12) = 0.00458333

n = Number of months in the loan term = 3 years 36 months.

Let plug in the formula

Monthly Payment = (3500 * 0.00458333 * (1 + 0.00458333)^36) / ((1 + 0.00458333)^36 - 1)

Monthly Payment  = 104.84

Therefore the correct option is C.

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Answer:

6 cm

Step-by-step explanation:

let, missing side be x cm

then, x+x+3 = 15

=> 2x = 12

=> x = 6 cm

Thus, missing side is 6 cm long

Here, we can use the fact that ln(x) grows slower than any positive power of x. That means that as x approaches infinity, ln(x) approaches infinity slower than x. Therefore, (ln(x))/x approaches zero as x approaches infinity. Using this fact, we can see that the entire expression approaches zero as x approaches infinity. Therefore, the limit is equal to zero.

To get  the limit of lim (ln(x))²/3x as x approaches infinity, we can use l'Hospital's Rule. Taking the derivative of the numerator and denominator separately, we get: lim 2ln(x) * 1/x / 3
x→[infinity]
Simplifying this expression, we get: lim 2ln(x) / (3x)
x→[infinity]
Using l'Hospital's Rule again, we take the derivative of the numerator and denominator separately: lim 2 * 1/x / 3
x→[infinity]
Simplifying further, we get: lim 2/ (3x)
x→[infinity]
Since the denominator approaches infinity as x approaches infinity, the limit is equal to zero.
Alternatively, we can use an elementary method to find the limit. We can rewrite the expression as: (ln(x))^2 = (ln(x)) * (ln(x))
Then we can use the fact that ln(x) grows slower than any positive power of x. That means that as x approaches infinity, ln(x) approaches infinity slower than x. Therefore, (ln(x))/x approaches zero as x approaches infinity. Using this fact, we can see that the entire expression approaches zero as x approaches infinity. Therefore, the limit is equal to zero.

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The length of the arc shown in red is 5.2359 radians

We know that the formula for the length of the arc of a circle.

s = r × θ

where s represents the arc length (in radians)

r represents the radius

and θ is the central angle in radians

From the attached figure of the circle, the radius of the circle r is 10 cm.

Here, the arc length is given in degrees.

We know that central angle = arc measure

So, the central angle θ = 30°

θ = 0.52359 radians

Using above formula of the arc length,

s = r × θ

s = 10 × 0.52359

s = 5.2359 radians

Thus, the arc length = 5.2359 radians

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The approximation of g(-1.2) using the line tangent to the graph of g at x=-1 is 3.6.

We can use the formula for the equation of a tangent line to approximate the value of g(-1.2) using the given information:

y - y1 = m(x - x1)

m = g'(-1) = 2 (since g'(-1) = 2)

Substituting these values into the formula, we get:

y - 4 = 2(x + 1)

Simplifying:

y = 2x + 6

Now we can use this equation to approximate g(-1.2) by plugging in x=-1.2:

g(-1.2) ≈ 2(-1.2) + 6

g(-1.2) ≈ 3.6

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An equation that can be used to determine how many months Ely will need to save money to reach his goal of a total of $1,550 in his savings account is 200 + 150x = 1,550.

An equation is a mathematical statement showing the equality or equivalence of two or more algebraic expressions.

Equations use the equal symbol unlike mathematical or algebraic expressions, which combine variables with numbers, constants, and values using mathematical operands.

The intended monthly savings = $150

The amount already in Ely's account = $200

The total amount Ely needs = $1,550

Let the number of months required to reach $1,550 = x

200 + 150x = 1,550

150x = 1,550 - 200

150x = 1,350

x = 9 months.

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The trigonometric ratios of the angle are given as follows:

The three trigonometric ratios are the sine, the cosine and the tangent, and they are defined as follows:

Applying the Pythagorean Theorem to the terminal side, the hypotenuse is given as follows:

h² = 9² + 10²

h = square root(9² + 10²)

h = 13.45.

Hence the ratios are given as follows:

The inverse ratios are given as follows:

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The thing that will be always true about quadrilateral ABCD is C. m∠A+m∠B=180°

The coordinates of the center of the circle is B. (6, 4)

Based on the fact that opposite angles in an inscribed quadrilateral are always equal, then m∠A+m∠B=180°. As a result, ∠A + ∠C = 180 degrees and likewise for ∠B + ∠D = 180 degrees.

The intersection of the two lines, namely, the perpendicular bisector of AB (passing through midpoint (6, 3.5) with a slope -12/7) and the vertical line whose undefined own slope penetrates the midpoint (6, 0) of AC, is exactly the center of circle, which has its coordinates as (6, 4).

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To compute the distance dd from yy to the line through uu and the origin, we can use the formula for finding the distance between a point and a line. The line through uu and the origin can be represented by the equation

y = (u2/u1)x, where u1 and u2 are the x and y coordinates of uu, respectively.
To find the distance dd, we first need to find the coordinates of the point where the line through uu and the origin intersects with the line perpendicular to it that passes through yy. Let (a,b) be the coordinates of this point. Then we have:
b = (u2/u1)a  (since (a,b) lies on the line through uu and the origin)
u1a + u2b = 0  (since (a,b) lies on the line perpendicular to it that passes through yy)
Solving these equations simultaneously, we get:
a = -u1u2/(u1^2 + u2^2)
b = u1^2/(u1^2 + u2^2) * y
Now we can use the distance formula to find dd:
dd = sqrt((x - a)^2 + (y - b)^2)
where x and y are the coordinates of yy.

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Grantly must place the chairs close enough so that people can easily speak with one another

Grantly is designing a sitting area that will be located outside of his client's master bedroom. He intends to furnish the area with a few rugs, an end table, and chairs.  The seats should be spaced apart just enough to allow for easy conversation while seated, but not too much that it seems crowded. For easy access, end table should be positioned close to the seats. The placement of rugs should be such that they both define seating area and add to overall attractiveness of the space.

To make sure that chairs, end table, and rugs fit properly without giving area a claustrophobic feeling, Grantly should take measurements of the available space in the sitting room. He should also consider how the master bedroom is organised as well as any existing furnishings or fixtures that could have an impact on how the sitting room furniture is arranged. Additionally, seating should be set up so that conversing with one another while seated is simple. Conversation can be facilitated and a cosy environment can be created by positioning chairs in a circula configuration, facing one another.

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Two possible values for the meteorologist's prediction are  $35.24$ inches and $50.76$ inches.

Let's denote the meteorologist's rainfall prediction by x.

The percent error can be calculated using the formula:

percent error = |(actual value - predicted value) / actual value| x 100%

We can use this formula to set up an equation and solve for x.

Since we want to find two possible values for x, we can use both the positive and negative versions of the percent error:

18.02% = |(43 - x) / 43| x 100% or

-18.02% = |(43 - x) / 43| x 100%

We have to find the values of x

18.02% = |(43 - x) / 43| x 100%

0.1802 = |(43 - x) / 43|

0.1802 x 43 = |43 - x|

7.7566 = |43 - x|

43 - x = 7.7566 or 43 - x = -7.7566

x = 35.2434 or x = 50.7566

Therefore, two possible values for the meteorologist's prediction are  $35.24$ inches and $50.76$ inches.

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The true statements are (A) 30×400 ml equal the total number of milliliters for 30 bowls of soup

(B) 30 bowls of soup hold 12,000 ml, which is same as 12 Litres

(C) Noah can multiply the number of bowls of soup by 1,000 to find the number of litres

(D) If each family member has 2 bowls of soup , Noah need to make 24 litres of soup

There are 30 people and each person is served soup in a 400 ml bowl, so the total amount of soup needed is 30 × 400 ml = 12,000 ml.

Option A is true

30 bowls of soup hold 30 × 400 ml = 12,000 ml, which is the same as 12 litres (since 1 litre = 1,000 ml).

Option B is true

Since 1 litre = 1,000 ml

Noah can multiply the number of bowls of soup by 1,000 to find the number of litres.

For example, 30 bowls of soup hold 12,000 ml = 12 litres.

Option C is true

If each family member has 2 bowls of soup, then the total amount of soup needed is

30 × 2 × 400 ml

= 24,000 ml, which is 24 litres (since 1 litre = 1,000 ml).

Option D is true.

Noah needs to make 24 litres of soup, and each pot contains 6 litres of soup.

Therefore, he would need to make 24 ÷ 6 = 4 pots of soup to serve each family member 2 bowls of soup.

Option E is false.

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Noah is making soup for a family reunion of 30 people. Each pot he makes contains 6 liters of soup. He uses bowl that 400mL to serve the soup to his family

Select all the true statements

(A) 30×400 ml equal the total number of milliliters for 30 bowls of soup

(B) 30 bowls of soup hold 12,000 ml, which is same as 12 Litres

(C) Noah can multiply the number of bowls of soup by 1,000 to find the number of litres

(D) If each family member has 2 bowls of soup , Noah need to make 24 litres of soup

(E) Noah would need to make 2 pots of soup for each family member to have 2 bowls of soup

There were 4 speed bumps installed on the road leading into the house development.

What is the formula of speed when time and distance have given?

The formula is speed = distance/time

Here given,

The length of the road is 3/4 miles or 12/16 miles and the distance between each speed bump is 3/16 miles.

Now we want to obtain the number of speed bumps,

So, Number of speed bumps = (Total distance of road) / (Distance between each speed bump)

Number of speed bumps = [tex] \frac{ \frac{12}{16} }{ \frac{3}{16} } [/tex]

Number of speed bumps = [tex] \frac{12}{16} \times \frac{16}{3} [/tex]

Number of speed bumps = 4

Therefore, there were 4 speed bumps installed on the road leading into the house development.

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The percent of students in grade 8 those who like to join dance club is equal to 25%.

Total number of students in grade 8 = 20

Total number of students of grade 8  join in dance club = 5

Percent of students of grade 8 prefer to join dance club

= ( total number of students prefer dance club ) / ( Total number of students in grade 8 ) × 100

Substitute the value in the formula we get,

⇒ Percent of students of grade 8 prefer to join dance club

= ( 5 ) / ( 20 ) × 100

⇒ Percent of students of grade 8 prefer to join dance club  = 0.25 × 100

⇒ Percent of students of grade 8 prefer to join dance club  = 25%

Therefore, percent of grade 8 students who preferred to join dance club is equal to 25%.  

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The above question is incomplete, the complete question is:

What percent of students in grade 8 prefer to join a dance club?

                      Dance club      Hiking club     Total

Grade 7               15                       15                 30

Grade 8               5                        15                  20

Total                    20                     30                    50

Answer:

The original recipe calls for 1 1/4 cups of dip and 1/2 cup of veggies, so you + both together which is a total of 1 3/4 cups of ingredients.

If Austin wants to use 1 cup of veggies instead of 1/2 cup, he needs to double the recipe. To keep the same ratio of dip to veggies, he will also need to double the amount of dip.

1 3/4 cups (original recipe) x 2 = 3 1/2 cups

Therefore, Austin will need 3 1/2 cups of dip to make the recipe using 1 cup of veggies.

The change in the allocation of congressional seats based on changes in the population is called redistricting.

The process of altering the borders of electoral districts or constituencies in response to population changes is known as redistricting. The census is taking a note of the population in an interval of ten years to check the population of the united states nationally and also in each and every state.

Further on the data from the census will be helping to calculate the number of the states in the house of representative from the states. This is done to make sure the one person one vote agenda. Redistricting has the potential to significantly affect political power and representation.

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Answer:

The answer to your problem is, A. Larger

Step-by-step explanation:

First in order to know to the answer lets learn about different types of fractions:

For example, 1/4, 3/4, 3/8, are all proper fractions.

4/3, 5/2, are all improper fractions.

When we have to multiply a whole number with fractions less than 1, then the resulting number will be less the number originally

Example; 3 x [tex]\frac{3}{4}[/tex]

If we then multiplying numerators together and the denominators together.

3 x [tex]\frac{3}{4}[/tex] = [tex]\frac{3}{1}[/tex] x [tex]\frac{3}{4}[/tex] = [tex]\frac{9}{4}[/tex] = 2[tex]\frac{1}{4}[/tex] < 3

Example /\

Thus the answer to your problem is, A. Larger OR Multiply.

The ratio of the volume of the first cube to the volume of the second cube is 1:27. The correct option is (C).

Let's represent the length of the edge of the first cube "n" and the length of the edge of the second cube "3n".

The volume of the first cube is:

V1 = n³

The volume of the second cube is:

V2 = (3n)³ = 27n³

To find the ratio of the volume of the first cube to the volume of the second cube, we divide V1 by V2:

V1/V2 = n³ / (27n³) = 1/27

Therefore, the required ratio is 1:27.

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The correct question is as follows:

One cube has edges n meters long. Another has edges 3n meters long. What is the ratio of the volume of the first cube to the volume of the

second cube?

A 1:3

B. 1:9

C. 1:27

D. 1:6

E. 1:81

The breadth of the cuboid is 0.5 m

The volume of a cuboid is given by the formula:

V = l * b * h

Where l is the length, b is the breadth and h is the height of the cuboid

We have:

length (l) = 60 cm = 0.6 m

volume (V) = 1.2 m³

height (h) = 4 m

Substituting:

1.2 = 0.6 * b * 4

1.2 = 2.4b

b = 1.2/2.4

b = 0.5 m

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The value of x is 7.99 centimeters to the nearest hundredth.

As per the given diagram, the value of x sits as the base length of the triangle.

And it is given that the hypotenuse's side length is 10 cm.

As per the cosine function,

The adjacent side to hypotenuse ratio is known as the cos function.

Adjacent Side/Hypotenuse = CosA.

Here, A = 37 degrees, adjacent side = x, and hypotenuse = 10cm.

So,

cos37° = x/10

x = 10 × cos37°

x = 7.9863551

x ≈ 7.99 cm.

Therefore, the value of x to the nearest hundredth can be described as x = 7.99 cm.

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The complete question:

Solve for x. x = [ ? ] cm, round to the nearest hundredth.

The image is attached below.

Answer:

1760

Step-by-step explanation:

10 x 16 x 11

160 x 11 = 1760

Step-by-step explanation:

6 blocks ÷ 14 sudents =    6/14 =   3/7  of a block each

Triangles ΔKLM and ΔXYZ are congruent using the ASA criteria.

Given are two triangles as shown in the image given.

The given triangles are ΔKLM and ΔXYZ.

∠L = ∠Y

KM = XZ

∠M = ∠Z

So, by ASA criteria, the triangles ΔKLM and ΔXYZ are congruent.

Therefore, triangles ΔKLM and ΔXYZ are congruent using the ASA criteria.

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The absolute value of  |-8 +12| is number  4.

We have to find the value of |-8 +12|

The absolute value | x | of a real number x is the non-negative value of x without regard to its sign.

Let us solve the value inside the mod

When eight is subtracted from twelve we get 4

|-8 +12|

|4|

The absolute value is 4.

Hence, the absolute value of  |-8 +12| is 4.

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The value of expression is, 4

We have to given that;

The expression is,

⇒ | - 8 + 12 |

Now, We can simplify the expression as;

⇒ | - 8 + 12|

⇒ | 4 |

⇒ 4

Thus, The solution of expression is, 4

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The number of miles driven if the cost of renting a car is $130 with a cost function of c(m) = 0.05m + 30 is 2000 miles.

We can start by setting up an equation to solve for the number of miles driven, m

c(m) = 0.05m + 30 (where c(m) is the cost of renting a car)

We know that the cost is $130, so we can substitute that into the equation

130 = 0.05m + 30

Now we can solve for m

130 - 30 = 0.05m

Subtract the numbers

100 = 0.05m

m = 100/0.05

Divide the numbers

m = 2000 miles

Therefore, the number of miles driven is 2000 miles

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The given question is incomplete, the complete question is:

If c(m)=0. 05m + 30 represents the cost of renting a car, how many miles were driven if the cost is 130$?

The speed of the car traveling is 42.96km/hr, under the condition  if d=0. 05v²+2. 2v.

The distance a car travels is 200. We can perform the formula d = 0.05v² + 2.2v to evaluate the speed of the car.
Staging d = 200 in the above equation, we get:

0.05v² + 2.2v - 200 = 0

Evaluating this quadratic equation gives us two values of v:

v = (-2.2 ± √(2.2² + 4 × 0.05 × 200)) / (2 × 0.05)

v ≈ -44.96 or
v ≈ 42.96

Since speed cannot be negative, we take v ≈ 42.96 as the speed of the car.
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t = 18, -18

To solve, we will isolate the variable t.

Given:

      0.5t² = 162

Divide both sides of the equation by 0.5:

      t² = 324

Square root both sides of the equation:

      t = 18, -18

The required solution to the equation [tex]0.5t^2 = 162[/tex] is t = ±18, as of the given condition.

To solve the equation [tex]0.5t^2 = 162[/tex], we need to isolate the variable t.

First, we can start by dividing both sides of the equation by 0.5 to eliminate it on the left side:

[tex]0.5t^2 / 0.5 = 162 / 0.5[/tex]

Simplifying:

[tex]t^2 = 324[/tex]

Next, we take the square root of both sides to solve for t:
[tex]\sqrt(t^2) = \sqrt(324)[/tex]

t = ±18

Therefore, the solution to the equation [tex]0.5t^2 = 162[/tex] is t = ±18.

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