Directions: The soccer team at your school wants to spray paint a design on the middle of the
playing field. The design will include this soccer ball. You have been asked to enlarge the drawing of
this ball to use for the painting on the field. Using the Text Editor and information you learned in this
Unit, write a brief essay in which you explain how to accurately enlarge or reduce the size of objects
such as the soccer ball. Include the steps that should be taken in order to complete a project like this,
and use concepts discussed in this Unit to support your plan. For example, you may want to include
scale factor, proportions, dilations, and similarity.

Based on the given scenario, the kind of sequence explained is an arithmetic sequence

First term, a = 19

Second term, a + d

28 = 19 + d

28 - 19 = d

9 = d

Third term, a + 2d

= 19 + 2(9)

= 19 + 18

= 37

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Answer:

A. The Highest Points Of The Graph

Step-by-step explanation:

A nonperiodic function is one that generates a graph without a regular recurring pattern over a fixed time interval. A repeating section of a graph is called the period.

Jhon was between 6:12 p.m and 6:52 p.m. So, Jhon left home for exact 40 minutes. Using the angle made by the hands in the clock, the required value is calculated.

The general formula for finding the angle between the minute hand and the hour hand is

M = [tex]\frac{2}{11}[/tex] (H × 30 ± θ)

It is given that,

Jhon left home after 6 p.m with an angle of 110° formed by the minute hand and hour hand.

So,

M = [tex]\frac{2}{11}[/tex] (H × 30 - θ)

   = [tex]\frac{2}{11}[/tex] (6 × 30 - 110)

   = [tex]\frac{2}{11}[/tex] (180 - 110)

   = [tex]\frac{2}{11}[/tex] × 70

   = 140/11

So, he left after 6:12 p.m

Jhon returned home before 7 p.m with angle of 110° formed by the minute hand and hour hand.

M = [tex]\frac{2}{11}[/tex] (H × 30 + θ)

   = [tex]\frac{2}{11}[/tex] (6 × 30 + 110)

   = [tex]\frac{2}{11}[/tex] (180 + 110)

   = [tex]\frac{2}{11}[/tex] × 290

   = 580/11

So, he returned before 6:52 p.m

Then,

The time taken for returning home = 580/11 - 140/11 = 440/11 = 40 minutes.

Therefore, he took 40 minutes to return home.

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Answer: Vertex (-2,-15) and therefore the axis of sym will be -2

Step-by-step explanation: Using -b/2a you can deduce that 4x^2 is a, 16x is b and 1 is c. So -b/2a = -16/8 = -2. Then you plug -2 for y and yu should get -15. Then x will be your axis of symetry to x=-2

The area of the convex polygon is 21.5 square units

The vertices are given as:

(0,5), (-1,2), (4,4), (-3,-4) and (2,0)

The area is then calculated as:

A = 0.5 * |x1y2 - x2y1 +x2y3 - x3y2 + ....... |

So, we have:

A = 0.5 * |-1 * 5 - 2 * 0 + 0 * 4 - 5 * 4 + 4 * 0 - 4 * 2 +2 * -4 - 0 * -3 - 3 * 2 + 4 * 1|

Evaluate

A = 0.5 * |-43|

Remove the absolute bracket

A = 0.5 * 43

This gives

A = 21.5

Hence, the area of the convex polygon is 21.5 square units

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Distributive property is the term for breaking a larger number apart into smaller numbers that can be multiplied together to get a specific result.

Firstly, to distribute means to divide something or give a share or part of something.

Distributive property explains that multiplying the sum of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the products together.

Therefore, distributive property is the term for breaking a larger number apart into smaller numbers that can be multiplied together to get a specific result.

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Answer:

The answer options appear garbled.  If A is 4/9, then this is equal to 2/3.  The others I can't see/understand.

Step-by-step explanation:

Answer: C. the graph contains (1, 1/10)

Step-by-step explanation:

When x=1, [tex]y=(1/10)^1=1/10[/tex].

Answer: B

Step-by-step explanation:

[tex](4^{-5})^3=4^{-15}=\frac{1}{4^{15}}[/tex]

The value of x is (d) 1

The angle ABC is given as:

∠ABC = 43x

The line AB touches the tangent line BC at point B.

However, the line AB is not a radius.

This means that:

∠ABC < 90

So, we have

43x < 90

Divide by 43

x < 2.09

From the list of options, the number less than 2.09 is 1

Hence, the value of x is (d) 1

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Answer:

9.09 years

Step-by-step explanation:

Use the simple interest formula

A=P(1+rt)

18000=9000(1+.11*t), solve for t

t = 9.0909

Answer:

[tex]h(x)=-0.11(3)^{-x}[/tex]

Step-by-step explanation:

Given function:

[tex]f(x)=0.11(3)^x[/tex]

Reflection in the x-axis:

When reflecting a function in the x-axis, make the whole function negative:

[tex]\implies g(x)=-f(x)[/tex]

[tex]\implies g(x)=-0.11(3)^x[/tex]

Reflection in the y-axis:

When reflecting a function in the y-axis, make the x variable negative:

[tex]\implies h(x)=g(-x)[/tex]

[tex]\implies h(x)=-0.11(3)^{-x}[/tex]

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Answer:

the answer to this question is d

Step-by-step explanation:

h(x)=-0.11(3)^-x

The expanded form of the expression (x+3)(x-3) is x² - 9

Given the expression;

(x+3)(x-3)

We multiply each term in the second bracket by each term in the first bracket

x(x-3) + 3(x-3)

x² - 3x + 3x - 9

x² - 9

Therefore, the expanded form of the expression (x+3)(x-3) is x² - 9.

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Answer:

y = 7.25 + 0.65x

Step-by-step explanation:

y = total cost

x = each mile

it starts at 7.25

any mile after that is an extra $0.65

y = 7.25 + 0.65x

The amount of money Mario will have if he puts $1000 in a savings account earning 4% annually after 10 years is $1,480

A = p(1 + r)^t

A = p(1 + r)^t

= 1000(1 + 0.04)^10

= 1000(1.04)^10

= 1000(1.48)

A = $1,480

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Since the jet bomber arrived over its Target at the same time as its fighter jet escorted, it took the jet bomber 0.34 h to reach the target.

To find the number of hours, we need to solve simultaneous equations.

Simultaneous equations are pair of equations which contain two unknowns.

Let

So, D = vt

D = 500t  (1)

Also, D = VT

D = 60T  (2)

Since  jet bomber traveling 500 mph arrived over its Target at the same time as its fighter jet escorted which left the same fate 2.5 hours after the bomb took off.

T = t + 2.5

So, D = 60(t + 2.5)  (3)

D = 500t  (1)

D = 60(t + 2.5)  (3)

Equating equations (1) and (3), we have

500t = 60(t + 2.5)

500t = 60t + 150

500t - 60t = 150

440t = 150

t = 150/440

t = 15/44

t = 0.34 h

So, it took the jet bomber 0.34 hours to reach the target.

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The equation that is represented by the graph below is y = e^x - 4.

From the graph, it can be seen that the only exponential function n to hat intercept the function at equal to 3 is y = e^x - 4.

Let's equate y to 0.

y = e^x - 4.

e^x - 4 = 0

e^x = 4

In(e^x) = In(4)

x = 1.386

The x intercept is located at (1.386, 0).

In conclusion, the correct option is D.

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Answer:

y=-2/3x-7/3

Step-by-step explanation:

a parallel line has the same slope but different y intercept

so we need to solve for y=-2/3x+b

since it passes through 4,-5 we can plug it in for x and y

-5=-2/3(4)+b

-5=(-8/3)+b then add 8/3 to both sides

-5 is also -15/3

-7/3=b

so answer is y=-2/3x-7/3

The probability of winning 15 out of the 22 games is [tex]P = 0.099[/tex]

We know that the probability of winning on the arcade game is 0.568.

Then the probability of losing is:

P = 1 - 0.568 = 0.432

The probability of winning 15 out of 22 games is given by the equation:

[tex]P = C(22, 15)*(0.568)^{15}*(0.432)^{7}[/tex]

Where C(22, 15) is the number of combinations of 15 elements that we can make with a set of 22 elements, given by:

[tex]C(22, 15) = \frac{22!}{(22 - 15)!*15!} = \frac{22!}{7!*15!} = \frac{22*21*20*19*18*17*16}{7*6*5*4*3*2*1} = 170,544[/tex]

Then the probability is:

[tex]P = 170,544*(0.568)^{15}*(0.432)^7 = 0.099[/tex]

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Answer:

R = $2,120

Ticket price = $11

Step-by-step explanation:

Finding revenue when t = 10 :

The vertex of the graph will have the maximum revenue.

Hence, the revenue is maximum when the ticket price is $11.

Answer: There were 78 bags of chips.

the population of province is growing at the rate of 2.91%

the formula of the rate of growth of a population =

[(future population- initial population/initial population)*100]/time

population in 2016 = 4.2 milllion = 4200000

Population predicted in 20 years = 6.65 million = 6650000

so, initial population = 4200000

future population = 6650000

rate of growth = {(6650000- 4200000/4200000)*100]/20

                       = 58.33/20

                     = 2.91%

the population is growing at the rate of 2.91%

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Answer:

-70

Step-by-step explanation:

We are given this arithmetic sequence:

-2, -6, -10, -14, ...

And we want to find the 18th term in it.

The 18th term can be found using this formula:

1st term + common difference(desired term-1)

The desired term is the term that we are looking for. In this case, it would be the 18th term, so substitute 'desired term' with 18.

1st term + common difference(18-1)

So, let's find the first term and the common difference.

The 1st term is the first term (number) that appears in the sequence. In this case, that number would be -2.

The common difference can be found by doing second term minus first term.

Remember that we know that the first term is -2. The second term is the second number that appears in the sequence, which would be -6.

So, do -6 subtract -2.

-6 - - 2

-6 + 2

-4

The common difference is -4.

So, we can plug -2 and -4 into the formula.

-2 - 4(18-1)

Now, doing the order of operations, first, subtract 1 from 18.

-2-4(17)

Now multiply -4 and 17 together.

-2 -68

Subtract -68 from -2.

-70

The 18th term of the sequence is -70.

Answer:

Step-by-step explanation:

6^0 + 6^0 + 6^0 + 6

= 1+1+1+6

= 9.

Answer:

279

Step-by-step explanation:

The area of the square base is 9² = 81.

The area of each triangular face is (1/2)(9)(11)=99/2.

So, the total surface area is 4(99/2)+81=279

If they plan to split the cost evenly, the expression that could be used to find how much they each owe is 18/3

The given parameters are:

Total amount owed = 18 dollars

Number of friend = 3

If they plan to split the cost evenly, the expression that could be used to find how much they each owe is represented as:

Amount = Total/Friends

This gives

Amount = 18/3

Hence, the expression is 18/3

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1a. 10. 24

1b. 125/243

2a. 0. 0048

2b. 32/3125

3a. 0. 64

3b. 0. 0031

4a. 2/5

4b. 48. 735

5a. 2. 36

5b. 1. 39

1a. Given the values

(2/5)^2/(1/2)^6

Multiply both the numerator and denominator by the powers

⇒ [tex]\frac{\frac{4}{25} }{\frac{1}{64} }[/tex]

To find the common ration, multiply thus;

⇒ [tex]\frac{4}{25}[/tex] × [tex]\frac{64}{1}[/tex]

⇒ [tex]\frac{256}{25}[/tex]

= 10. 24

1b. (5/7)^2 × (5/7)^1

= [tex]\frac{25}{49}[/tex] × [tex]\frac{5}{7}[/tex]

= [tex]\frac{125}{343}[/tex]

= 125/243

2a. 0. 6^1  × 0. 2^3

= 0. 6 × 0. 008

= 0. 0048

2b. (2/5)^3 × (2/5)^2

= [tex]\frac{8}{125}[/tex] × [tex]\frac{4}{25}[/tex]

= [tex]\frac{32}{3125}[/tex]

= 32/ 3125

3a. 1^99 - 0. 6^2

= 1 - 0. 36

= 0. 64

3b. (0. 2 ) ^1 × (1/8)^2

= 0. 2 × 1/64

= 0. 2 × 0. 016

= 0. 0031

4a. (1/2)^2/ (5/8)^1

= [tex]\frac{\frac{1}{4} }{\frac{5}{8} }[/tex]

Take the inverse of the denominator

= [tex]\frac{1}{4}[/tex] × [tex]\frac{8}{5}[/tex]

= 2/5

4b. 7^2 - 0. 5^3

= 49 - 0. 125

= 48. 875

5a. 3^1 - 0. 8 ^2

= 3 - 0. 64

= 2. 36

5b. 0. 7^2 + 0. 9^1

= 0. 49 + 0. 9

= 1. 39

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The survey shows that adding up the daily media use figures to obtain a report of weekly media use leads to the staggering number of more than 60 hours a week of media use by 11- to 14-year-olds.

It should be noted that a survey simply means a list of questions that are used to get information about a group.

In this case, the daily media use figures to obtain a report of weekly media use leads to the staggering number of more than 60 hours a week of media use by 11- to 14-year-olds.

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If the time taken by 14 inches wide is one hour then the blade of 12 inches wide will take 1 hour 17 minutes to mow a lawn.

What is width?

The width of something is the measurement of one side of a body. It is generally less than length of that body or shape.

How to calculate time?

We have been given time of 1 hour if blade is 14 inches wide and we have to calculate time taken by 12 inches wide blade:

It will be as 14/12* 1 hour

=14/12

=1.167

=1.17 hour

Hence the time taken by the blade of 12 inches wide will be 1 hour and 17 minutes.

Answer:

70 mins

Step-by-step explanation:

This is called inverse proportion.

1hr : 14in

x hr : 12in

Ask yourself, what do you do to 14 to get 12? To find this out, we do:

14 / 12 = 1.16666667

Since the blade is smaller, it will take longer. So, we times 1hr by 1.16666667 to get

1.16666667 hrs =

1.17 hours (rounded)

This is 70.2 mins, or 1hr 10 mins

Hope this helps!