b) The diagram shows a thin square sheet of metal measuring 24 cm by 24 cm. A square of side x cm is cut off from each corner. The remainder is then folded to form an open box, x cm deep, whose square base is shown shaded in the diagram. Write the volume, cm³, of the box as V=4x³-96x² +576x [3]
(ii) Compute the maximum cost paid to fill up the box with sand if RM 0.30 per cubic centimeter of sand charged. [2] ​

The minimum and maximum of the function f(x)=2x³+15x²-36x+1 are 38 and 39 respectively

The maximum value of a function f(x) is also called the absolute maximum value, or the  greatest value of the function f on the closed interval [0, 1]. on the other hand, the minimum value of f(x) at x = 0 is called the absolute minimum value,  or least value of the function f on the closed interval [0, 1)

How to find the minimum and maximum functions?

From the function f(x) = 2x3 − 15x2 + 36x + 1.

Using differential calculus , dy/dx = 6x2 - 30x + 36

= 6(x2 - 5x + 6)

f(x) is a maximum when x = 2 and the maximum value of f(x) = f(2).

This implies that f(2) = 2(23) − 15(22) + 36(2) + 11 = 39

d2y/dx2|x=3 = 12 x 3 - 30 = 6 > 0

This also implies that  f(x) is a minimum when x = 3 and the minimum value of f(x) = f(3) = 2(3)3 − 15(3)2 + 36(3) + 11 = 38

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Answer:

18 in. x 10 in.

Step-by-step explanation:

Squares will always have equal lengths. So, you need to figure out what will multiple by itself to get 196, and it’s 14.

Since you know in the equation that if 4 were to be taken away from the length and added to the width, it would make the 14 x 14 square, you can subtract 4 from one of the 14’s and add 4 to the other 14.

So, then you get (14-4) 10 in. x (14+4) 18 in.

The amount of the first application that has been downloaded is 6.48 megabytes

The size of the second application is 7.35 megabytes

The first application has a size of 10.8 megabytes and out of this 10.8 megabytes, only 60% has completely downloaded. The amount that has already downloaded is therefore:

= Size of application x Percentage downloaded

= 10. 8 x 60%

= 6.48 megabytes

The second application is sized such that it is 3.45 MB less than the first application. The size of the application is therefore:

= 10.8 - 3.45

= 7.35 megabytes

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A number line which represents the given inequality (-1 ≥ x) is: number line C.

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

This ultimately implies that, a number line primarily increases in numerical value towards the right from zero (0) and decreases in numerical value towards the left from zero (0).

Next, we would determine a solution for the given inequality (-1 ≥ x) in order to graph it on a number line:

-1 ≥ x

x ≤ -1

In conclusion, we can logically deduce that the value of x is less than or equal to -1 as shown in number line C, which is shaded because of the less than or equal inequality symbol.

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The width of Lewis´s rectangular cage as a mixed number in simplest form is equal to 14.86 inches.

Mathematically, the perimeter of a rectangle can be calculated by using this formula;

P = 2(L + W)

Where:

For the perimeter of Becky's rectangular cage, we have:

Perimeter, P = 2(L + W)

Perimeter, P = 2(15 + 11)

Perimeter, P = 2(26)

Perimeter, P = 52 inches.

For the perimeter of Lewis's rectangular cage, we have:

Length, L = 0.75W

Perimeter, P = 2(L + W)

52 = 2(0.75W + W)

26 = (0.75W + W)

1.75W = 26

Width, W = 26/1.75

Width, W = 14.86 inches.

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h(n) = -17·0.2^(n-1)

Step-by-step explanation:

The explicit formula for a geometric sequence with first term a1 and common ratio r is ...

an = a1·r^(n-1)

Your sequence h has first term a1 = -17 and common ratio r = 0.2. Then the explicit formula is ...

h(n) = -17·0.2^(n-1)

$225 was earned from the craft sales

and $40 was earned from the play.

Given, During a school carnival, students from the middle school raised money by selling crafts, food, game tickets, and school play admissions.

Of each dollar earned, $0.15 came from games. Craft sales earned 3 times as much as games. Food sales were 4 times the amount earned from the play.

Let the amount earned by play be x,

Now, Games earned = 0.15×500 = $75

Also, crafts earned 3×75 = $225

Now, as play earned x, then food earned 4x.

According to question,

x + 75 + 225 + 4x = 500

5x + 300 = 500

5x = 200

x = 40

So, the amount earned by Play be, $40

and the amount earned by Food be $160.

Hence, $225 was earned from the craft sales

and $40 was earned from the play.

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Considering the quadratic equation, it is found that:

a) The initial height of the object is of 58.8 meters.

b) The object first hits the ground after 39.2 seconds.

c) The maximum height reached by the object is of: 1912 meters.

The quadratic equation that models the projectile's height is defined as follows:

s(t) = -4.9t² + 190.6t + 58.8.

Which has the coefficients given as follows:

a = 4.9, b = 190.6, c = 58.8.

The initial height is obtained as follows:

s(0) = -4.9(0)² + 190.6(0) + 58.8 = 58.8 meters.

It hits the ground at the positive root for which s(t) = 0, hence, using a quadratic equation calculator, this root is of:

t = 39.2 seconds.

The maximum height obtained by the object is the y-coordinate of the vertex, hence:

hMAX = -(b² - 4ac)/4a = -(190.6² - 4(-4.9)(58.8))/(4(-4.9)) = 1912 meters.

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Answer:

There are two pairs of numbers:

-8      -18

and

18        8

Step-by-step explanation:

a * b = 144      EQ. 1

a - b = 10         EQ. 2

From EQ. 2:

a = 10 + b          EQ. 3

Replacing EQ. 3 in EQ. 1:

(10+b)b = 144

10*b + b*b = 144

b² + 10b - 144 = 0

b = {-10±√((10²)-(4*1*-144))} / (2*1)

b = {-10±√(100+576)} / 2

b = {-10±√676} / 2

b = {-10±26} / 2

b₁ = {-10-26} / 2 = -36/2 = -18

b₂ = {-10+26} / 2 = 16/2 = 8

a₁ - b₁ = 10

a₁ - (-18) = 10

a₁ + 18 = 10

a₁ = 10 - 18

a₁ = -8

a₂ - b₂ = 10

a₂ - 8 = 10

a₂ = 10 + 8

a₂ = 18

Check:

a₁ * b₁ = -8 * -18 = 144

a₂ * b₂ = 8 * 18 = 144

The equation of line in slope intercept form is y=−9/8x+7.

In the given question we have to write the equation of the graph line in slope intercept form.

The give points are(0,7) and (8,−2)

Let x(1)=0, y(1)=7, x(2)=8 and y(2)=−2.

The slope intercept form of equation is

y−y(1)=m(x−x(1))+c.........(1)

Before finding the equation we find the slope of equation.

Slope(m)={y(2)−y(1)}/{x(2)−x(1)}

Now putting the value

m=(−2−7)/(8−0)

m= −9/8

Now putting the value in equation 1

y−7=−9/8(x−0)

Now the equation is

y−7=−9/8x

Add 7 on both side

y−7+7=−9/8x+7

y=−9/8x+7

Hence, the equation of line in slope intercept form is y=−9/8x+7.

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The graph of the polar curve r = 3 – 2cos(θ) is in the attachment

A graph is a diagram representation on a coordinate system.

A polar curve is a curve represented by the equation r = a + bcosθ where

To find the graph of the polar curve r = 3 – 2cos(θ), we need to determine its maximum and minimum values and also the value as it crosses the axis.

Since r = 3 – 2cos(θ), the maximum value of r is obtained at the minimum value of cos(θ) = -1 at θ = π

So, substituting this into the equation, we have

r = 3 – 2cos(θ)

r = 3 – 2(-1)

r = 3 + 2

r = 5

Since r = 3 – 2cos(θ), the minimum value of r is obtained at the maximum value of cos(θ) = 1 at θ = 0

So, substituting this into the equation, we have

r = 3 – 2cos(θ)

r = 3 – 2(1)

r = 3 - 2

r = 1

Since r = 3 – 2cos(θ), the value of r at the origin is when θ = π/2 and θ = 3π/2

So, substituting this into the equation, we have

r = 3 – 2cos(θ)

r = 3 – 2cos(π/2)

r = 3 – 2(0)

r = 3 - 0

r = 3

So, in polar form, the points we require for the polar curve graph are

Find the graph of the polar curve in the attachment

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Answer:

C: The third graph.

Step-by-step explanation:

Took the quiz

Round 8.879 to the nearest tenth is 8.9.

Rounding to the nearest tenth:

The combination of a whole number and a fraction, separated by a decimal point, is known as a decimal number in mathematics. The place value of the digits is divided by 10 starting from left to right. Determining the place values of tenths, hundredths, and thousands will therefore be aided by the decimal place value. For instance, the definition of the place value tenth is 1/10.

Think about the decimal 12.345.

Tenth place value in this case is 3.

By substituting the actual number with an approximation, the decimal value can be rounded. To the nearest integer, the decimal number 5.8 is rounded to 6, for instance. The decimal number can also be rounded to the nearest tenths place value. The first integer that appears after the decimal point is the tenth place value. Look at the hundredth number to round the decimal number to the nearest tenth. If it's more than 5, add one to the tenth value. Remove all the numbers that are present after the tenth place and leave the tenth place value alone if it is less than 5.

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Answer:8 experiments

Step-by-step explanation:

she has 8 feet of copper and she needs one foot for each experiment she can do 8 experiments.

The positive co-terminal is 9π/4 and negative co-terminal is 25π/4 for the given angle 17π/4.

Coterminal angles are those with a common terminal side that are in standard position (angles with the initial side on the positive x-axis). Angles with the same initial side and terminal side are said to be coterminal angles. Depending on whether the given angle is in degrees or radians, finding coterminal angles is as easy as adding or subtracting 360° or 2 to each angle. Coterminal angles can be found in an infinite number of ways.

The negative co-terminal=17π/4-2π

=9π/4

The positive co-terminal=17π/4+2π

=25π/4

For the given angle 17π/4, positive co-terminal is 9π/4 and negative co-terminal is 25π/4.

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A system of linear equations to describe this situation is given by:

A + O = 11.

0.80A + 0.95O = 9.95.

Harry bought six (6) apples and five (5) oranges from this store.

In order to write a system of linear equations to describe this situation, we would assign variables to the amount of apples and oranges respectively, and then translate the word problem into algebraic equation as follows:

Since Harry bought a total of 11 pieces of fruit, we have:

A + O = 11              .....equation 1.

Since the cost of apples is $0.80 each and oranges cost $0.95 each, we have:

0.80A + 0.95O = 9.95      .....equation 2.

From equation 1, we have:

O = 11 - A                   .....equation 3.

Substituting equation 3 into equation 2, we have:

0.80A + 0.95O = 9.95

0.80A + 0.95(11 - O) = 9.95

Apples, A = 0.90/0.15

Apples, A = 6.

For the number of oranges, we have:

Oranges, O = 11 - A

Oranges, O = 11 - 6

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Complete Question:

At a store, apples cost $0.80 each and oranges cost $0.95 each. Harry buys some apples and oranges and spends $9.55 . He buys a total of 11 pieces of fruit.

Part a. Write a system of linear equations to describe this situation.

Part b. How many of each fruit did Harry buy?

The distance between the points (-5,4) and (1,0) is  7.21 .

In the question ,

it is given that ,

the two points are (-5,4) and (1,0) ,

we  have to find the distance between them .

we know that the distance between the points (x₁ , y₁) and (x₂ , y₂) is calculated using the distance formula

distance = √(y₂ - y₁)² + (x₂ - x₁)²

Substituting the values of the points , we get

distance = √(0 - 4)² + (1 -(-5))²

= √(-4)² + (1 + 5)²

= √16 + (6)²

= √16 + 36

= √52

= 7.21111

≈ 7.21

Therefore , The distance between the points (-5,4) and (1,0) is  7.21  .

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Answer:

Step-by-step explanation:

Let the required amount of 5% milk is x quartz, then the amount of 2% milk is 90 - x quartz.

Set equation for the fat content:

Answer:

volume is approximately 73.6 to the nearest tenth

Step-by-step explanation:

The volume of a pipe is volume = π * radius² * length

diameter = 2.5

radius = 2.5/2 = 1.25 inches

volume = π * 1.25² * 15

volume = π * 1.5625 * 15

volume =  π * 23.4

which is approximately 73.6 to the nearest tenth

Answer:

P = 84

Step-by-step explanation:

Area = length* width or A = lw

We know that the length is 5 times its width which can also mean

[tex]l = 5*w[/tex] or [tex]l=5w[/tex]

Use the formula for area and replace [tex]l[/tex] with [tex]5w[/tex] and the total area with 245

[tex]A = lw\\245=5w(w)[/tex]

Multiply:

[tex]245=5w^{2}[/tex]

Divide by 5

[tex]49=w^2[/tex]

Square root of [tex]w^2[/tex]

[tex]\sqrt{49}=\sqrt{w^2}[/tex]

Simplify

[tex]7=w[/tex]

Now that we know w = 7 we can input this into the Perimeter formula

(P = 2l +2w)

P = 2(5*7)+2(7)   // Note: Remember [tex]l[/tex] = 5*w and w = 7

P = 84

There is also a formula for this type of problem, but this explanation is for when you forget. Hope that explains things :)  

Answer:

whole triangle 180 degrees

y = 84 degrees

x = 36 degrees

Step-by-step explanation:

y = 180 - 96

x = y - 48. Reason: Exterior angle theorem

Substitute: x = 84 - 48

Answer:

180

36

84

Step-by-step explanation:

→ Find x

180 - (96 + 48) = 36

→ Find y

180 - 96 = 84

The money spent on the plates which are very expensive is: $133.44

Given,

The plates that mom bought are very fragile and expensive.

Each  plate costs $16.68.

Total plates bought by her mom are = 8

we are asked to determine the total cost of the plates bought = ?

let y represent the total cost of the plates.

and x represent the number of plates bought.

based on the conditions, we can formulate:

total cost pf plates = 16.38(number of plates bought)

⇒ y = 16.68x

we know that plates bought = 8

⇒ total cost is:

⇒ y = 16.68(8)

⇒ y = 133.44

Hence total cost of 8 plates is $133.44

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The area of the given trapezium is 16x + 8

Area of trapezium:

The general formula to calculate the area (A) of a trapezium is written as,

A = ½ (a + b) h where,

where

a, b = bases of trapezium, and,

h = height

Given,

Here we have the figure of trapezium and the measures are written in it.

Now, we have to find the area of the trapezium.

According to the formula of the area of the trapezium,

We need the value of base and height.

By looking into the given figure, we have identified the value of

a = x cm

b = 3x + 2 cm

h = 8 cm.

Then the area of the trapezium is calculated as,

A = ½ (x + (3x +2)) 8

A = ½ (4x + 2) 8

A = 4 (4x + 2)

A = 16x + 8

Therefore, the area of the trapezium is 16x + 8.

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Answer:

Step-by-step explanation:

7 1/4 is what i think

The fraction of the shops t-shirt are blue t-shirt that are on sale and are size medium can be explained by

"Multiplying the fraction of T-shirt that are blue by the fraction of T-shirt that are on sale. Then, multiply the result by the fraction of the blue T-shirt that are on sale that are size medium".

The correct answer option is option C.

A fraction is a number which consists of a numerator and a denominator.

A numerator is the upper value of a fraction while a denominator is the lower value of a fraction.

Fraction of blue T-shirt = 2/3

Fraction of blue t-shirt on sale = 3/7 × 2/3

= 2/7

Fraction of the blue T-shirts that are on sale are size medium = 1/2 × 2/7

= 2/14

= 1/7

Therefore, Multiply the fraction of T-shirt that are blue by the fraction of T-shirt that are on sale. Then, multiply the result by the fraction of the blue T-shirt that are on sale that are size medium".

= 2/3 × 3/7 × 1/2

= 1/7

Complete question:

Two-thirds of the T-shirts in a T-shirt shop are blue. Three-sevenths of those T-shirts are on sale.

One-half of the blue T-shirts that are on sale are size medium. What fraction of the shop's T-shirts are blue T-shirts that are on sale and are size medium?5 Explain

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Answer:

[tex]m=38[/tex]

Step-by-step explanation:

An interior angle and its corresponding exterior angle are supplementary, so:

[tex]3m-12+2m+2=180 \\ \\ 5m-10=180 \\ \\ 5m=190 \\ \\ m=38[/tex]

Answer:

Roman numeral representing thousand (1000)

Answer:

C) The y-intercept of Function A is 1 unit greater than the y-intercept of Function B

Step-by-step explanation:

The y-int of Function A is (0,1), while the y-int of Function B is (0,0).

Answer:

C

Step-by-step explanation:

For Function A, the y-intercept occurs at 1. For B, it occurs at 0. Therefore, the y-intercept of Function A is 1 unit greater than the y-intercept of Function B.

The time that it took Zane to reach the edge of the volcano is of:

35 seconds.

The variables that are graphed in this problem are listed as follows:

The edge of the volcano is the point at which the elevation relative to the volcano is of 0, hence the coordinate is:

y = 0.

y = 0 is the x-intercept of the function, which is the value of x at which the function crosses the x-axis.

Hence, looking at the graph, the time that it took Zane to reach the edge of the volcano is of:

35 seconds.

(as 35 is the x-intercept of the graph, and we previously explained that the edge of the volcano is the x-intercept).

The question is:

How long did it take Zane to reach the edge of the volcano?

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