Find the explicit form of the arithmetic function of p if the first term is 12 and the common difference is 2. Then find the seventh term.

Answer:

1.ABC is equilateral triangle because all sides are equal

3.because they are the joined figure of a triangle

The number of pieces of card stock which would result upon the process repetition is; 256 pieces.

According to the task content, it follows that since, there are 8 pieces of the 8 inches per side cards initially, the resulting number of cards after carrying out the process of cutting cards into half five, 5 times is;

No of cards = 8 (2)⁵

No. of cards = 256 pieces.

The size of each of the cards in discuss provided that all cuts will be made along and not across the longer edge is; 8 by 1/4 inches.

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Answer:

[3,0]

[0,9]

Step-by-step explanation:

9x+3y=27

9x+3(0)=27

9x=27

x=3

9(0)+3y=27

3y=27

y=9

It has been estimated that every year 20,000 species are going extinct and 72 species are going extinct on an average day.

Species exist as organisms that contain similar characteristics and exist capable of interbreeding. A common example is human beings.

It has been observed that over the years, species have been going extinct due to human reasons such as excessive hunting, environmental factors such as natural disasters, global warming, and also due to changes in their genetic makeup or reduced reproduction.

It has been estimated that every year 20,000 species are going extinct and 72 species are going extinct on an average day.

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Answer: Edge 2022, B. 72

Since the product of AB and BC is -1, hence the ABC is a right triangle and the length AC is the hypotenuse

A right angles triangle is a triangle that has 3 sides and angles with one of its angles to be 90 degrees.

For the given coordinates to be a right angled triangle, one of the line must be perpendicular to the other and for two lines to be perpendicular, the product of its slope must be -1.

Find the slopes of AB, BC and AC

Slope of AB = 5-11/1-6
Slope of AB = -6/-5 = 6/5

Slope of BC = 0-5/7-1
Slope of BC = -5/6

Slope of AC = 0-11/7-6
Slope of AC = -11/1. = -11

Take the product of AB and BC
AB * BC = 6/5 * -5/6
AB * BC = -1

Since the product of AB and BC is -1, hence the ABC is a right triangle and the length AC is the hypotenuse

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The correct option regarding the point at which the linear functions intersect is given by:

C) The lines don't intersect.

A linear function is modeled by:

y = mx + b

In which:

For line m, we have that the y-intercept is of b = 8. When x changes by 4, y changes by 8, hence the slope is of 2, and the equation is:

y = 2x + 8.

Line n, in slope-intercept format, is given by:

-8x + 4y = 24

4y = 8x + 24

y = 2x + 6

Hence:

2x + 8 = 2x + 6

0x = -2

Which is impossible, hence they do not intersect and option C is correct.

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Answer:

b. (y - 4)(y - 8)

Step-by-step explanation:

The shape of a bst approaches that of a perfectly balanced binary tree, (log2n) is the time complexity for a balanced binary search tree in case of insertions and search.

In computing, binary bushes are mainly used for looking and sorting as they offer a way to save statistics hierarchically. a few common operations that may be conducted on binary trees encompass insertion, deletion, and traversal.

A binary tree has a special situation that each node could have a most of two youngsters. A binary tree has the benefits of each an ordered array and a linked listing as search is as brief as in a taken care of array and insertion or deletion operation are as fast as in related listing.

In pc science, a binary tree is a tree information shape in which every node has at maximum two youngsters, that are known as the left baby and the proper toddler.

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1st quartile: 11

median: 38.50000

3rd quartile: 45

Measure descriptive statistics

1st quartile: 11

median: 38.50000

3rd quartile: 45

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I understand that the question you are looking for is :

2 Drag the tiles to the boxes to form correct pairs. Match the values associated with this data set to their correct descriptions.  {6, 47, 49, 15, 43, 41, 7, 36} first quartile 38.5  median 11  third quartile 10.5 the difference of the largest value and the median 45

Answer:

$0.95/lb

Step-by-step explanation:

1 ton = 2000 lb

3 tons = 3 × 1 ton = 3 × 2000 lb = 6000 lb

$5700/(6000 lb) = $0.95/lb

Answer: $0.95/lb

Step-by-step explanation:

3 tons = 6000 pounds

Therefore, using ratio and proportion rules,

6000/5,700 = 1/x

x = 5700/6000 = 0.95

The price is $0.95, or 95 cents per pound.

Formula for the circumference of a circle is

[tex]c = \pi \: d[/tex]

where c is the circumference, and d is the diameter.

When diameter is 27-in, then

[tex]c1 = \pi \times 27[/tex]

When diameter is 25-in, then

[tex]c2 = \pi \times 25[/tex]

.: 27π-in – 25π-in is the farther distance.

Finding the difference, we have:

2π ≈ 6.28

.: 6.28-in is our final answer.

Answer: (8,0) and (0,-4)

Step-by-step explanation:

The x-intercept of an equation is when the equation touches the x-axis which is also where y = 0

So the x coordinate of the x-intercept is -2x + 0 = -16 as y = 0

x = 8 so the x-intercept is (8,0)

The y-intercept of an equation is when the equation touches the y-axis which is also where x = 0

So the y coordinate of the y-intercept is 0 + 4y = -16 as x = 0

y = -4 so the y intercept is (0,-4)

The word complementary describes the their measures of ∠1 and ∠2.

According to the statement

we have given that the some conditions like

Angles 1 and 2 form a right angle. 2 lines form a right angle. another line extends between the 2 lines to form 2 angles. the top angle is labeled 1, and the bottom angle is labeled 2.

And we have to find the word that describes all about the given angles.

So, For this purpose,

According the given conditions, we recall that:

Angles that are complementary angles whose sum equals 90 degrees.

A right angle equals 90 degrees.

From the information given, we know that:

m∠1 and m∠2 forms a right angle.

Since a right angle = 90 degrees, therefore:

m∠1 + m∠2 = 90° (complementary)

So, The word complementary describes the their measures of ∠1 and ∠2.

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Answer: complementary

Step-by-step explanation: took the test on edge!

Answer:

632

Step-by-step explanation:

So we can define decreasing x% in two ways: we can define 20% off as 80% of the original value, or we can define subtracting 20% from the original value, and both representations are useful.

In this case it's more useful to define 20% as subtracting 20%, from the original value. The reason for this, is because since we're subtracting 20% of the original value, we then know that 126.40 is 20% the original value.

So to find x% of some value, you generally use the following equation: [tex]A*\frac{x}{100}[/tex] where A=original amount, and x is the percent. This equation is simply converting the x% to a decimal value. Since 126.40 is 20%, we can derive the following equation.

[tex]0.20A = 126.40[/tex]

We can solve for A, by dividing by 0.20

[tex]A=632\\[/tex]

It's also important to note, you didn't really have to set up this entire equation, since you know that the 126.40 is 20%, you simply could've multiplied by 5, since 20% is really just 1/5 of the entire value, so get the entire value, or original value you multiply by 5

Answer:

Side AB = [tex]9\sqrt{2}[/tex]

Side AB = [tex]9\sqrt{2}[/tex]

Side CB = 36

Step-by-step explanation:

This is a special right triangle and it's also an isosceles triangle

therefore the measure of AC = AB and they are both = [tex]9\sqrt{2}[/tex]

for this special triangle the measure of hypotenuse (CB in here) is represented with [tex]x\sqrt{2}[/tex] and the legs are represented with x, each

since legs' lengths are given as = [tex]9\sqrt{2}[/tex] then x = [tex]9\sqrt{2}[/tex]

replace the x in front of [tex]x\sqrt{2}[/tex] with  [tex]9\sqrt{2}[/tex]

[tex]9\sqrt{2}[/tex] *  [tex]\sqrt{2}[/tex] = 36

Answer:

The cable length will have to be at least 30.51936ft

Step-by-step explanation:

[tex]c= \frac{25}{ \sin( 55 ) } = 30.51936[/tex]

C = Cable

Answer:

  (a)  x = -1.10 and x = 1.10

Step-by-step explanation:

A straightforward square root will give the value of x.

Divide by the coefficient of x^2:

  x^2 -30/25 = 0

  x^2 -1.20 = 0

Add 1.20, and take the square root.

  x^2 = 1.20

  x = ±√1.20 ≈ ±1.0954

  x ≈ -1.10 and 1.10 . . . . . round to hundredths

__

Additional comment

For small values of x, the root of (1+x) is approximately 1+x/2. For a root accuracy to the nearest hundredth, x < 0.21 (as here). For accuracy to the nearest thousandth, x < 0.064.

The radius of the circle is 24 hectometers.

Remember that the circumference of a circle of radius R is given by the equation:

[tex]C = 2*\pi*R[/tex]

In this case, we know that the circumference is: C = 150.7968 hm

And π = 3.1416

Replacing that and solving for R, we get:

[tex]R = \frac{C}{2*\pi} = \frac{150.7968hm}{2*3.1416} = 24hm[/tex]

The radius of the circle is 24 hectometers.

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Answer:

you need all of them?

Step-by-step explanation:

The minimum distance between the origin and the plane 3x + y + 2z = 28, using the Lagrange Multipliers is 8.73 units.

In the question, we are asked to use Lagrange multipliers to find the minimum distance between the origin and the plans 3x + y + 2z = 28.

Lagrange multipliers state that if we want to minimize a function, f(x, y, z), subject to a constraint g(x, y, z) = constant, then ∇f = λ∇g.

We want to minimize the distance, and the distance formula says that the distance from the origin to a point (x, y, z), is given as:

D = √(x² + y² + z²), which can also be shown as:

D² = x² + y² + z².

The gradient of this function is: (2x + 2y + 2z), which needs to be equal to the gradient of the constraint equation multiplied by the constant, λ, that is, λ(3, 1, 2), which gives:

2x = 3λ, or, x = (3/2)λ,

2y = λ, or, y = λ/2, and,

2z = 2λ, or, z = λ.

Substituting these in the equation of the plane, 3x + y + 2z = 28, we get:

3(3/2)λ + λ/2 + λ = 28,

or, 6λ = 28,

or, λ = 28/6 = 14/3.

Thus, we get:

x = (3/2)λ = 7,

y = λ/2 = 7/3, and,

z = λ = 14/3.

Substituting these in the distance formula, we get:

D = √(7² + (7/3)² + (14/3)²) = √(49 + 49/9 + 196/9) = √(686/9) = 8.73.

Thus, the minimum distance between the origin and the plane 3x + y + 2z = 28, using the Lagrange Multipliers is 8.73 units.

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The total surface area of this shaded region is 1000 units²

An equation is an expression that shows the relationship between two or more numbers and variables.

The total surface area of a polygon is the sum of the individual areas of each surface.

Total area of the figure = 2(20 * 10) + 2(10 * 10) + 2(20 * 10) = 1000 units²

The total surface area of this shaded region is 1000 units²

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The statement that is true about two ordered pairs that are the same except for the signs of the numbers is their points are in different quadrants. Option D

Ordered pairs are known to be pairs of numbers that are used locate a point in the rectangular coordinate plane

They are written as (x ,y)

where

It is important to note that the location of the ordered pair in the quadrants determines the sign of the x and y coordinates.

The signs of the ordered pairs are given as;

When (x , y)  is in Quadrant I then both x and y are positive

Therefore, the statement that is true about two ordered pairs that are the same except for the signs of the numbers is their points are in different quadrants. Option D

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Answer:

At least 18 solid balls

Step-by-step explanation:

    [tex]\sf \boxed{\bf Volume \ of \ rectangular \ tank = length* width * height}[/tex]

Volume of empty space = Volume of the full tank - Volume of the tank till the water.

                                        = 20*10*13 - 20*10*11

                                        = 2600 - 2200

                                        = 400 cm³

Volume of 1 solid ball = 23 cm³

Number of solid ball to make the tank overflow = 400 ÷ 23

                                                                               ≈ 18 solid balls

The probability of selecting an ace or a heart when one card is drawn from 52 cards is 1/52.

Given that there are 52 cards in which there are 13 cards each for spades,clubs,hearts and diamonds.

We are required to find the probability of getting an ace or a heart when one card is drawn from 52 cards.

Probability is basically the chance of happening an event among all the events possible. It lies between 0 and 1. It cannot be negative. The probability can be calculated through following formula:

Probability=Number of items/total number of items.

Number of hearts=13

Number of ace=4

Probability of getting an ace or a heart when one card is drawn=P(X=heart)*P(X=ace)

=13/52 * 4/52

=52/(52*52)

=1/52

Hence the probability of getting an ace or heart when one card is drawn from standard deck of cards is 1/52.

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Answer:

Step-by-step explanation:

(14 - 7x)/7 =

[7(2-x)]/7 =

2-x

The difference between the 6th term and the 9th term of the sequence is 135

Given that the nth term is;

3n² + 11

For the 6th term, the value of n is 6

Let's solve for the 6th term

= 3( 6)^2 + 11

= 3 × 36 + 11

= 108 + 11

= 119

For the 9th term, n = 9

= 3 (9)^2 + 11

= 3( 81) + 11

= 243 + 11

= 254

The difference between the 6th and 9th term

= 254 - 119

= 135

Thus, the difference between the 6th term and the 9th term of the sequence is 135

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The solution to the system of equation is x < 44/3

Inequality expressions are expressions not separated by an equal sign. An example of an inequality is a < b

Given the inequality expression below;

x  + 2x + 6 < 50

Simplify to have:

3x + 6 < 50

Subtract 6 from both sides

3x + 6 - 6 < 50 - 6

3x < 50 - 6

3x < 44

Divide both sides by 3

3x/3 < 44/3

x < 44/3

Hence the solution to the system of equation is x < 44/3

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Answer:

4c+2d+10

Step-by-step explanation:

7+4c+2d+3

4c+2d+(3+7)

4c+2d+10

Answer: 4c+2d+10

Step-by-step explanation:

There are 680 combinations of four teachers include Mrs. Vera(only)

The given parameters are

Teachers, n = 18

Selected teachers. r = 4

The selection must include Mrs. Vera.

So, the remaining parameters are:

Teachers, n = 17

Selected teachers. r = 3

The combination is then calculated as:

Ways = nCr

This gives

Ways = 17C3

Apply the combination formula

Ways = 17!/(14!3!)

Evaluate the expression

Ways = 680

Hence, there are 680 combinations of four teachers include Mrs. Vera(only)

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