2.1. Consider the following pattern. 2.1.1 complete the table. (match-sticks were used to make each shape) (6marks) Shape No. of match-sticks Rule 1 4 2 7 3 10 4 13 6 241 10 40 43 21 82​

Answer:

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To solve this problem, we can use a system of equations with two variables:

We have two equations based on the given information:

Solve the first equation for x:

Substitute the expression for x into the second equation:

Simplify and solve for y:

Substitute the value of y back into the expression for x:

So, you should mix 9.375 pounds of almonds with 10.625 pounds of peanuts to obtain 20 pounds of mixture that will sell for $4.50 per pound.

Answer:

Step-by-step explanation:

You should mix 9.375 pounds of almonds with 10.625 pounds of peanuts to obtain 20 pounds of mixture that will sell for $4.50 per pound.

The angle that is supplementary to the angle DEA is angle DEC

From the question, we have the following parameters that can be used in our computation:

Also from the question, we have

Angle = DEA

As a general rule;

Two angles are said to be supplementary if their sum add up tp 180 degrees

This means that the angles are on a straight line

The angle are on the same straight line with ange DEA is DEC

Hence, the angle is angle DEC

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The three angles of the triangle are 48 degrees, 60 degrees, and 72 degrees and it is a acute triangle.

The three angles of the triangle 4x, 5x, and 6x, where x is a constant of proportionality.

We know that the sum of the angles of a triangle is always 180 degrees, so we can set up an equation:

4x + 5x + 6x = 180

Simplifying, we get:

15x = 180

Dividing both sides by 15, we get:

x = 12

So the three angles of the triangle are:

4x = 4(12) = 48 degrees

5x = 5(12) = 60 degrees

6x = 6(12) = 72 degrees

all three angles are less than 90 degrees, the triangle is an acute triangle.

Therefore, the three angles of the triangle are 48 degrees, 60 degrees, and 72 degrees and it is a acute triangle.

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Answer:

Step-by-step explanation:

We can start by solving the second equation for y:

1/2y - x = 1

1/2y = x + 1

y = 2x + 2

Now we can substitute this expression for y into the first equation:

y = 2 - 6x

2x + 2 = 2 - 6x

Adding 6x to both sides, we get:

8x + 2 = 2

Subtracting 2 from both sides, we get:

8x = -0

Dividing both sides by 8, we get:

x = 0

Now we can use this value of x to find y:

y = 2x + 2

y = 2(0) + 2

y = 2

Therefore, the solution to the system of equations is x=0 and y=2.

Answer:

400% of 2 is 8, so it would be less than 10

Step-by-step explanation:

Answer:

MN and ML are on the same straight line.

Phil owns a ranch business and uses four-wheelers to do much of his work the allowable depreciation for year 2 is $4,096.

To calculate the allowable depreciation for year 2, we need to determine the depreciation basis of the four-wheeler and then apply the appropriate MACRS depreciation rate.

The depreciation basis is the original cost of the asset minus any Section 179 expense deduction and any bonus depreciation claimed.

Since we are ignoring these deductions in this case, the depreciation basis is simply the original cost of the four-wheeler:

Depreciation Basis = $12,800

To determine the MACRS depreciation rate for year 2, we need to consult Table 2 from the MACRS tables, which gives the percentage rates for assets in the 5-year class for each year of the recovery period. According to Table 2, the depreciation rate for year 2 is 32%.

Using this information, we can calculate the allowable depreciation for year 2 as follows:

Depreciation for Year 2 = Depreciation Basis × MACRS Depreciation Rate for Year 2

Depreciation for Year 2 = $12,800 × 32%

Depreciation for Year 2 = $4,096

Therefore, the allowable depreciation for year 2 is $4,096.

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Answer:

-4 < -2.3 < -0.43 < 69

Step-by-step explanation:

If you look at a number line,

-4 is the first to come and as we approach 0, it's -2.3 and then -0.43. After 0 is only 69 leftover.

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The maximum height of the ladder on the wall is given as follows:

h = 8.7 m.

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

For the angle of 60º, the parameters are given as follows:

Hence the maximum height is obtained as follows:

tan(60º) = h/5

h = 5 x tangent of 60 degrees

h = 8.7 m.

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The estimated rating of chips whose cost is $1.10 is 2.25.

From the question, we have the following parameters that can be used in our computation:

y = 2.5x - 0.5

To estimate the rating of chips whose cost is $1.10, we can substitute x = 1.10 into the equation y = 2.5x - 0.5 and solve for y.

y = 2.5x - 0.5

y = 2.5(1.10) - 0.5

y = 2.75 - 0.5

y = 2.25

Therefore, the estimated rating of chips whose cost is $1.10 is 2.25. Rounded to the nearest hundredth, it is 2.25.

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Answer:

7.5 kilometers

Step-by-step explanation:

[tex]\frac{40}{5}[/tex] = [tex]\frac{60}{x}[/tex]

[tex]\frac{40}{5}[/tex] can be simplified to 8

8 = [tex]\frac{60}{x}[/tex]  Multiply both sides by x

8x = 60  Divide both sides by 8

[tex]\frac{8x}{8}[/tex] = [tex]\frac{60}{8}[/tex]

x = 7.5

Helping in the name of Jesus.

Answer:

57.89%

Step-by-step explanation:

Implied probability = (1 / (odds + 1)) x 100%

Using the odds of 8/11 for Hillary Clinton:

Implied probability = (1 / (8/11 + 1)) x 100% = 57.89%

There is a 57.89% chance that Hillary Clinton will win the presidency.

Answer:

C. d= 163t represents the relationship between d, the number of dollars Rajindri earns, and t, the amount of time Rajindri works, in hours. This is because Rajindri earns $163 for every two hours that she works, which means she earns $81.50 for each hour that she works. Therefore, the equation that relates the number of dollars earned to the number of hours worked is d = 163t.

Step-by-step explanation:

Applying the circumference formula, the strip of aluminum foil should be about 38 inches long, which corresponds to answer choice D.

To determine the length of the aluminum foil strip, we need to find the circumference of the pie pan, which is the distance around the edge of the pan.

The formula for the circumference of a circle is:

C = 2πr

where C is the circumference, π is a mathematical constant approximately equal to 3.14, and r is the radius of the circle (which is half the diameter).

Since the pie pan has a diameter of 12 inches, the radius is 6 inches. Therefore:

C = 2π(6)

C ≈ 37.7 inches

This is approximately, D. 38 inches.

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Step-by-step explanation:

Subtract the 99 from 949 then    divide by 2

949-99= 425 dollars = price of dryer

( then washer is  425 + 99 )

The hiking trial at the state park that is the longest would be D. Hilltop

To find the hiking trail that is longest, convert the lengths shown to one form so as to see which is the longest.

Mammoth = 8.005 kilometers

Brookside = 8. 7 kilometers

Wild Rose = 8, 080 meters = 8. 08 kilometers

Hilltop = 8 kilometers 800 meters = 8. 8 kilometers

This then shows that the hiking trail that is the longest in the state park is the Hilltop trail which goes for 8. 8 kilometers.

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The sum of geometric series 3+2.55+2.1675+1.842375+...

Hence, the correct option is B.

To find the sum of a geometric series, we can use the formula

S = a(1 - [tex]r^{n}[/tex]) / (1 - r)

Where

S = sum of the geometric series

a = first term of the series

r = common ratio of the series

n = number of terms in the series

In this case, we can see that the first term is 3 and the common ratio is 2.55/3 = 0.85. We can also see that there are an infinite number of terms in the series.

Using the formula for an infinite geometric series, we can simplify the formula to

S = a / (1 - r)

By putting these values we have, we get

S = 3 / (1 - 0.85) = 20.

Hence, the sum of the geometric series is 20.

Hence, the correct option is B.

The question is incomplete and the complete question is '' FIND THE SUM OF GEOMETRIC SERIES 3+2.55+2.1675+1.842375+...

A. 8

B. 20

C. 12

D. 4 ''

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Answer: 2304.0 cm³

Step-by-step explanation: V = length x width x height

V = 18 cm x 8 cm x 16 cm

V = 2304 cm³

The height of box for the given cuboid satisfied the relation through which the volume of cuboid is satisfied is,  height = x+2

What about volume of cuboid?

A cuboid is a three-dimensional shape that has six rectangular faces, where each face has four sides and four right  angles. The volume of a cuboid is the amount of space that it occupies in three-dimensional space. It is measured in cubic units.

The formula to calculate the volume of a cuboid is given by multiplying its length, width, and height.

Volume of cuboid = Length x Width x Height

The volume of a cuboid can be used to determine the amount of space that it can hold or the amount of material required to fill it.

The volume of a cuboid can be calculated by multiplying its length, width, and height.

If the length of the cuboid is represented by "l", the width by "w", and the height by "h", then the volume can be calculated using the formula:

Volume of cuboid = l x w x h

According to the given information:

As, we know that the volume of cuboid = length x breath x height

Given volume of cuboid is = [tex]x^{3} + 6x^{2} +11x^{} + 6[/tex]

And width = x + 1 and length = x + 3.

Volume of cuboid = length x breath x height

⇒ [tex]x^{3} + 6x^{2} +11x^{} + 6[/tex] = (x + 1)(x + 3) x height

⇒ height = [tex]\frac{x^{3} + 6x^{2} +11x^{} + 6}{(x+1)(x+3)}[/tex]

⇒ height = [tex]\frac{(x+1)(x+2)(x+3)}{(x+1)(x+3)}[/tex]

⇒ height = (x+2)

So, the height of the given cuboid is (x+2)

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We can eulerize this graph in the most efficient way possible by making these vertices have even degree through  adding  an edge between them.

We can Eulerize a graph by ensuring  to add edges to the graph in a way that preserves its connectivity while ensuring that all vertices have even degree.

A good method to do this is by  adding  edges between pairs of vertices that have odd degree until all vertices have even degree.

In the scenario above,  all the  vertices have odd degree except for the first and last vertices. To make these vertices have even degree, we go ahead and add an edge between them.

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The frequency of the wave is 2.62 Hz

The equation of the line that is perpendicular to the line passing through the points (-3, 10) and (3, 8) is y = 3x + 9.

To find a line that is perpendicular to another line, we need to use the fact that the slopes of the two lines are negative reciprocals of each other.

The slope of a line passing through two points (x1, y1) and (x2, y2) can be found using the slope formula:

slope = (y₂ - y₁)/(x₂ - x₁)

Therefore, the slope of the line passing through the points (-3, 10) and (3, 8) can be found as follows:

slope = (8 - 10)/(3 - (-3)) = -1/3

Now, to find the equation of a line perpendicular to this line, we need to find the negative reciprocal of the slope -1/3, which is 3.

Therefore, the slope of the line perpendicular to the given line is 3.

Now, we can use the point-slope form of a linear equation to find the equation of the perpendicular line. The point-slope form of a linear equation is:

y - y₁ = m(x - x₁)

where m is the slope of the line, and (x₁, y₁) is any point on the line.

We know the slope of the perpendicular line is 3, and we can choose any point on the line. Let's choose the midpoint of the given points (-3, 10) and (3, 8), which is

=> ((-3+3)/2, (10+8)/2) = (0, 9).

So, using the point-slope form of the equation with m = 3 and (x1, y1) = (0, 9), we get:

y - 9 = 3(x - 0)

Simplifying this equation, we get:

y = 3x + 9

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Answer:

They barter, or trade (without using money). Economic systems are based on customs, traditions, and beliefs of the past.

Step-by-step explanation: -

The meaning of the given statement is concept of a cyclic subgroup in group theory.

What is cyclic group?

In group theory, a cyclic group is a group that can be generated by a single element. That is, it is a group that is generated by a single element a, where any element of the group can be expressed as a power of a.

The order of a cyclic group is equal to the order of its generator. If the generator has order n, then the cyclic group has n elements. The group operation in a cyclic group can be either additive or multiplicative, depending on the notation used.

The statement defines a cyclic subgroup is a subgroup of a group that is generated by a single element. The element used to generate the subgroup is called the generator of the cyclic subgroup. The set of all powers of the generator, including the inverse powers and the identity element, forms the cyclic subgroup.

In other words, the cyclic subgroup generated by an element a of a group is the smallest subgroup that contains a. It consists of all possible combinations of a and its inverse under the group operation.

A group or subgroup is called cyclic when it can be generated by a single element. In other words, if every element of the group can be expressed as a power of a single element, then the group is cyclic.

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Answer:

1. 17/8   2. 89/24   3. 47/12   4. 9/7

Answer:

1) 29

2) 57

3) 91

4) 15

Step-by-step explanation:

1) 7/8 + 11/4

find lcm

lcm=8

multiply through by 8

8×7/8+8×11/4

Gives: 7 + 22

 =29

2) 12/6+ 11/4

lcm=12

multiply through by 12

12× 12/6 + 12× 11/4

 24 + 33

 =57

3) 23/4 + 11/6

lcm=12

multiply through by 12

12× 23/4 + 12× 11/6

 =69 +22

 =91

4) 22/7 - 1

lcm=7

multiply through by 7

7 ×22/7 - 7 ×1

22-7

=15

When 70 to a z-score, the resulting z-score is 0

From the question, we have the following parameters that can be used in our computation:

Mean = 70

Standard deviation = 8

Score = 70

To convert 70 to a z-score, we make use of the following equation

z = (score - mean)/Standard deviation

Substitute the known values in the above equation, so, we have the following representation

z = (70 - 70)/8

Evaluate the expression

z = 0

Hence, converting 70 to a z-score. we get 0

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