A rectangle measuring 7 cm by 4 cm is enlarged by a ratio
of 2:1.
a) What is the area of:
i) the original rectangle?
ii) the enlarged rectangle?
b) By what ratio has the area been enlarged?

Answer:

700 and 600

Step-by-step explanation:

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The motion of a Ferris wheel, spinning about a fixed axis is rotational motion

a) Please find attached the height vs time graph of ONE cycle of Bert's motion on the ride, showing 5 Key points, including; The period, amplitude, the vertical shift, horizontal shift, the neutral axis

b) The equation to represent Bert's journey is h(t) = 6·sin(3.6·(t - 25)) + 7

The reason the above equation are correct are:

The given parameters of the Ferris wheel are;

Radius, r = 6 meters

The height of the axle above the ground, h = 7 metres

The time it takes to complete one revolution, T = 100 seconds

The level at which Bert enters the Ferris wheel = The lowest level

The time at which the ride starts = 0 seconds

a) The graph of a Ferris wheel is a graph sinusoidal function with the following details

The general form of the sinusoidal function is, y = a·sin(b·(t - h)) + D

Amplitude = The radius = 6 meters

The vertical shift, D = The elevation of the axle above the ground = 7 meters

The period, T = 360/b

∴ b = 360/T = 360/100 = 3.6

At t = 0, sin(b·(t - h)) = -1

Given that sin(-90) = -1

Therefore; (3.6·(0 - h)) = -90

π/50 = -π/2

-h = -25

∴ The horizontal shift, h = 25

The function of the Ferris wheel is y = 6·sin(3.6·(t - 25)) + 7

The graph of the function is created on MS Excel, using the above sinusoidal equation of the Ferris wheel

The 5 key points included in the graph are;

b) The appropriate equation of the sinusoidal function of the Ferris wheel is determined from the general sinusoidal function equation, y = a·sin(b·(t - h)) + D, as follows;

From part (a);

a = 6, b = 3.6, h = 25, and D = 7

The equation of the sinusoidal function h(t) to represent Bert's journey, is h(t) = a·sin(b·(t - h)) + D

Where;

h = The height of the Ferris Wheel

t = The time in seconds

a = The amplitude = 7

b = The 360/(The period) = 3.6

h = The horizontal shift = 25°

D = The vertical shift = 7 meters

The MOST appropriate equation of the sinusoidal function h(t) is therefore;

h(t) = 6·sin(3.6·(t - 25)) + 7

Learn more about Ferris wheel, and sinusoidal function equation here:

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Answer:

A.) w² + 3w in²

B.) 28 in²

Step-by-step explanation:

A.)

Let w = width and l = length.

    The area of a rectangle can be written as length · width (base · height). The problem informs us that the length of the rectangle is 3 inches greater than the width. Therefore, l can also be written as w + 3. We can use this to form a polynomial that represents the area of the rectangle.

A(rectangle) = lw = (w + 3) · w = w² + 3w

B.)

Use the polynomial we previously found to find the area.

A(rectangle) = (4)² + 3(4) = 16 + 12 = 28 in²

Model:

Answer:

12.75

Step-by-step explanation:

Given the equations

x - y = 3.5 → (1)

[tex]\frac{x+y}{2}[/tex] = 11 ( multiply both sides by 2 to clear the fraction )

x + y = 22 → (2)

Add (1) and (2) term by term to eliminate y

2x + 0 = 25.5

2x = 25.5 ( divide both sides by 2 )

x = 12.75

Substitute x = 12.75 into (2)

12.75 + y = 22 ( subtract 12.75 from both sides )

y = 9.25

The 2 numbers are 12.75 and 9,25

With the larger number being 12.75

Answer:

5d² - 3d

Step-by-step explanation:

Given

4d² + d² - 2d - d ← collect like terms

= (4 + 1)d² + (- 2 - 1)d

= 5d² + (- 3)d

= 5d² - 3d

[tex]\\ \rm\longmapsto \dfrac{5L}{250mL}[/tex]

[tex]\\ \rm\longmapsto \dfrac{5000mL}{250mL}[/tex]

[tex]\\ \rm\longmapsto \dfrac{20}{1}[/tex]

[tex]\\ \rm\longmapsto 20:1[/tex]

Answer:

A no. ans is 17a/20

B no. ans is 10c-7d/35

C no. ans is +1/−1⋅2/2⋅−1⋅3/2⋅−1⋅4

Answer: Rational number

It is a rational number because it is a fraction of two integers. Those two integers being -15 and 2.

In general, any rational number is of the form P/Q where P and Q are integers. The Q cannot be zero. Another example of a rational number is 2/3. In this example, P = 2 and Q = 3.

Going back to -15/2, we would have P = -15 and Q = 2.

The fraction -15/2 is not a whole number nor is it an integer. This is because -15/2 = -7.5 and this is sufficient to see we don't have an integer result. We would need to have nothing after the decimal point to get a whole number.

Answer:

I don't really know

Step-by-step explanation:

Err.. sorry but i am in grade 6

Answer: y = (-1/2)x + 2

Concept:

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

The reciprocal of a number is 1 divided by the number.

In other words, it is the image opposite of a term.

Solve:

Given information

Given line = y = 2x - 5

Point = (-4, 4)

Find the slope of the line

Given the line is perpendicular to the line y = 2x - 5, the slope of the line would be negative reciprocal of the line y = 2x - 5.

Slope of line [y = 2x - 5] = 2

Slope of new line = (-1/2)

Find the y-intercept by substituting the given point

Equation of the new line: y = (-1/2)x + b

y = (-1/2)x + b

4 = (-1/2) (-4) + b

4 = 2 + b

4 - 2 = 2 + b - 2

b = 2

Finalize the equation of the line

Slope = -1/2

Y-intercept = 2

[tex]\boxed{y=-\frac{1}{2}x+2 }[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer:

Step-by-step explanation:

[tex] \frac{(5m - 4)}{6} - 1 = 4m - \frac{(3m + 10)}{2} [/tex]

[tex] = > \frac{5m - 4 - 6}{6} = \frac{8m - 3m - 10}{2} [/tex]

[tex] = > \frac{5m - 10}{6} = \frac{5m - 10}{2} [/tex]

[Cross Multiplication]

=> 2(5m - 10) = 6(5m - 10)

=> 10m - 20 = 30m - 60

=> 60 - 20 = 30m - 10m

=> 40 = 20m

[tex] = > m = \frac{40}{20} [/tex]

=> m = 2 (Ans)

Answer:

c.15+2z/6x-12y

f.7a+b/4a-6b

Step-by-step explanation:

z+1/x-2y - 2x-3/2x-4y + z/3x-6y

z+1/x-2y - 2x-3/2(x-2y) + z/3(x-2y)

6(z+1)-3(2z-3)+2z

15+2z/6x-12y

3a/2a-3b - a+b/2(-3b+2a)

6a+a+b/2(2a-3b)

7a+b/4a-6b

Answer:

True

Step-by-step explanation:

Every number to the power of 0 is equal to one, so 2⁰ = 1 it's true

and every number to the power of 1 is equal to itself, so

5¹ = 5, also true

Answer:

Alice drives 168.26 miles daily and 841.3 miles per 5 days on her regular route when there is no detour.

Step-by-step explanation:

First, we need to divide 927.8 miles by 5.

927.8 ÷ 5 = 185.56 is her daily mileage, including the detour.

Since her detour added 17.3 miles to her daily mileage, we need to subtract this from her current daily mileage.

185.56 - 17.3 = 168.26 is her daily mileage when there is no detour.

Now, in order to find her mileage for 5 days, we need to multiply this number by 5.

168.26 x 5 = 841.3

Therefore, Alice drives 168.26 miles daily and 841.3 miles per 5 days on her regular route when there is no detour.

Since you're trying to find f(-3), your function that you have to plug -3 into will be f(x).

f(-3) = -2(-3)^2+(-3)+3

f(-3) = -2(9)+(-3)+3

f(-3) = -18-3+3

f(-3) = -18 is your final answer

Answer:

Heya mate....

Step-by-step explanation:

This is ur answer.....

Hope it helps!

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Answer:

Technically, it could be one. since one goes into everything but I'm not sure if you're teacher accepts that answer. So 2. 2 goes into 4 two times and 2 goes into 20 ten times

Step-by-step explanation:

Answer:

2a - 2b - 11ab

Step-by-step explanation:

2a + 4b - 11ab- 6b

subtracting:

simplify like terms by subtracting or adding.

➡️ 2a - 2b - 11ab

Answer:

Remove the radical by raising each side to the index of the radical.

n= 25.

Answer:

The hourly charge for labor is $11.10.

Step-by-step explanation:

Assuming there is no flat rate

166.50/15 = h

h represents the hourly charge

h = 11.10

Answer:

let the number of snacks bought be x

f(x) = 7 +2.5(x)

=> f(x) is the amount you spend in total

We have that The height as a linear function of time is

[tex]x=-27.5T+500[/tex]

From the Question we are told that

Time t=8 minutes

Height h=500

Descended height h_d= 280 feet.

Generally the equation for the linear function  is mathematically given as

Let

Height as a linear function =x

[tex]x=\frac{h_d-h}{t}*T+h[/tex]

[tex]x=\frac{280-500}{8}*T+500[/tex]

[tex]x=-27.5T+500[/tex]

In conclusion

The height as a linear function of time is

[tex]x=-27.5T+500[/tex]

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Answer:

303/25 is an equivalent fraction form for decimal 12.12.

Here we have some given restrictions that affect the number of medals, using these, we want to find the maximum number of bronze medals that can be awarded.

We will find that:

The maximum number of bronze medals that can be awarded is 535

Now let's see how we can get that.

Let's define the variables:

G = number of gold medals.

S = number of silver medals.

B = number of bronze medals.

Now we can see what information we have.

There are 2021 participants.

The number of silver medals is at least twice the number of gold medals.

S ≥ 2*G

The number of bronze medals is at least twice the number of silver medals:

B ≥ 2*S.

The number of all medals is not more than 40% of the number of participants.

The total number of medals is (G + S + B)

40% of the total number of participants is:

(40%/100%)*2021 = 0.4*2021 = 808.4

Then we have:

G + S + B ≤ 808.4

We can rewrite the above inequality as:

G + S + B ≤ 808.

Then we have 3 inequalities:

S ≥ 2*G

B ≥ 2*S

G + S + B ≤ 808

Now we want to maximize the number of gold medals.

This means that the total number of medals should be exactly 808 (the maximum number of total medals) so we have:

G + S + B = 808.

Also, if we want to maximize the number of gold medals, then we need to minimize the number of silver medals and the number of bronze medals, such that we get:

S = 2*G

B = 2*S

Now we have 3 equations:

G + S + B = 808

S = 2*G

B = 2*S

Replacing the third equation in the first one, we get:

G + S + 2*S = 808

G + 3*S = 808

Now we can replace:

S = 2*G

in the above equation to get:

G + 3*(2*G) = 808

G + 6*G = 808

7*G = 808 =

G = 808/7 = 115.43

But we can have 0.43 of a gold medal, so we need to round down to the next whole number:

G = 115

Now, with this restriction, we want to find the maximum number of bronze medals.

This means that we need to minimize the number of silver medals, so we use:

S = 2*G = 2*115 = 230

And the number of bronze medals will be such that:

B + G + S  = 880

B + 115 + 230 = 880

B = 880 - 115 - 230 = 535

The maximum number of bronze medals that can be awarded is 535

If you want to learn more, you can read:

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Answer:

yes this quote isabsolutely right as

life is very innocent , we can make our life whatever we like

(x+3)(x^2-3x+27)

x^3-3x^2+27x+3x^2-9x+81

x^3+19x+8

Answer:

area= 9 pi km²

circumference= 6 pi km

Step-by-step explanation:

area = pi r ²

so pi × 3²

area = 9 pi km²

circumference = d × pi

so 6 pi km

Step-by-step explanation:

gof(x)= g(f(x))

gof(x)= g(4x-1)

gof(x)= (4x-1)²+7

gof(x)=16x²-8x+1+7

gof(x)=16x²-8x+8

Answer:

We can cancel out A and B because there is no distributive property, and then I would say its C or the 3rd one.

Step-by-step explanation:

I used the cancelling out method.

Hey there! I'm happy to help!

This glass is most likely a cylinder. To find the volume of a cylinder you take the area of the circle base and multiply it by the height.

To find the area of a circle, you square the radius and multiply it by pi (we will use 3.14 for pi).

Our radius is 3cm.

3

We square it.

3²=9

Multiply by 3.14.

9×3.14=28.26

Now that we have our circle base area, we multiply it by the height (7 cm).

28.26×7= 197.82

This is how many cubic centimeters the glass can hold if it is completely full. However, we want half full, so we can just divide by 2.

197.82/2=98.91

We can also multiply our circle base by 3.5, which will give us half of the full height.

So, the height of the water is 3.5 cm and the volume of the water is 98.1 cm³.

Have a wonderful day and keep on learning! :D