Describe the symmetry of these functions.

The numbers in the set can be compared by placing them in the number line, arranging the numbers from least to greatest as follows;

\(|-2\frac{1}{2} |\), \(-\frac{1}{2}\), \(1\frac{1}{2}\), \(|\frac{1}{2} |\) |-2|, \(-2\frac{1}{2}\)

A number line is a series of numbers placed on the a line at regular intervals that can be used to express mathematical operations.

The elements in the set includes;

|-2 1/2|, -1/2, 1 1/2, |1/2|, |-2|, -2 1/2

The numbers within the absolute sign have a positive result, therefore;

|-2 1/2| = 2 1/2

|-2| = 2

The numbers in the set can be arranged in the order from least to the greatest as follows;

The above ordered numbers indicates that the specified numbers arranged in order from least to the greatest are;

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The volume of the given triangular prism is 384 cm³.

Volume is the measure of the capacity that an object holds.

Formula to find the volume of the object is Volume = Area of a base × Height.

Here, the area of the base is

Area of a rectangle = 1/2 ×Base×Height

= 1/2 ×12×4

= 24 cm²

Now the volume is 24×16

= 384 cm³

Therefore, the volume of the given triangular prism is 384 cm³.

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Answer:

Step-by-step explanation:

In general, given the function, f(x), its zeros can be found by setting the function to zero. The values of x that represent the set equation are the zeroes of the function. To find the zeros of a function, find the values of x where f(x) = 0.

Answer:

Use the rational root theorem to list all possible rational zeroes of the polynomial P(x) P ( x) .

Evaluate the polynomial at the numbers from the first step until we find a zero. ...

Repeat the process using Q(x) Q ( x) this time instead of P(x) P ( x) . This repeating will continue until we reach a second degree polynomial.

By answering the presented question, we may conclude that Therefore, triangle the length of the base AB is approximately 20.88 centimeters.

A triangle is a closed, double-symmetrical shape composed of three line segments known as sides that intersect at three places known as vertices. Triangles are distinguished by their sides and angles. Triangles can be equilateral (all factions equal), isosceles, or scalene based on their sides. Triangles are classified as acute (all angles are fewer than 90 degrees), good (one angle is equal to 90 degrees), or orbicular (all angles are higher than 90 degrees) (all angles greater than 90 degrees). The region of a triangle can be calculated using the formula A = (1/2)bh, where an is the neighbourhood, b is the triangle's base, and h is the triangle's height.

the length of the base AB,

Area = (1/2) * base * height

\(CB^2 = CD^2 + BD^2\\9^2 = x^2 + (AB - x)^2\\81 = x^2 + (AB^2 - 2ABx + x^2)\\AB^2 - 2ABx + 2x^2 = 81\\\)

We also know that the area of the triangle is:

\(46 = (1/2) * AB * CB\\46 = (1/2) * AB * \sqrt(x^2 + 81)\\Now we can solve for AB in terms of x:AB = (2 * 46) / \sqrt(x^2 + 81)\\AB = 92 / \sqrt(x^2 + 81)\\(92 / \sqrt(x^2 + 81))^2 - 2(92 / \sqrt(x^2 + 81))x + 2x^2 = 81\\\)

\(8464 / (x^2 + 81) - (184x) /sqrt(x^2 + 81) + 2x^2 = 81\\8464 - 184x(x^2 + 81) + 2x^2(x^2 + 81) * sqrt(x^2 + 81) = 81(x^2 + 81)\\2x^4 - 181x^2 + 7743 = 0\\x^2 = (181 + \sqrt(181^2 - 427743)) / (2*2)\\x^2 = (181 + sqrt(129961)) / 4\\x^2 = (181 + 361) / 4\\x^2 = 90^2 / 4\\x = 45\sqrt(2) / 2\\\)

\(AB = 92 / \sqrt(x^2 + 81)\\AB = 92 / \sqrt((45sqrt(2) / 2)^2 + 81)\\AB = 92 / \sqrt(4050)\\AB ≈ 20.88 cm\\\)

Therefore, the length of the base AB is approximately 20.88 centimeters.

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Answer:

x=7.5

Step-by-step explanation:

Answer:

34 will go in the middle of the two, 80 is everybody who voted, end 64 is the people that own the dog. No people on the cat

Step-by-step explanation:

there

Solution:

the percent markdown of the iPad is 17.86%

Given:

Original Price = $700

Final price = $575

The markdown is gotten by;

\(Markdown=original~price-final~price\)

\(Markdown=700-575\)

Markdown = $125

Thus, the percent markdown is gotten by;

\(percent~markdown=\frac{markdown}{original~price}~x~ 100\)

percent markdown = \(\frac{125}{700}\) × 100%

percent markdown =\(\frac{12500}{700}\)

percent markdown = 17.857 %

percent markdown  ≈ 17.86%

Therefore, the percent markdown of the iPad is 17.86%

Hope this helps!!

If you have any questions please ask.

Answer:

B. 34.90°

Step-by-step explanation:

✔️First, find GF using Trigonometric function:

Reference angle = 58°

Adjacent length = GF

Hypotenuse = 6 cm

Apply CAH, thus:

Cos 58 = Adj/Hyp

Cos 58 = GF/6

GF = 6*Cos 58

GF = 3.17951558 ≈ 3.18 cm

✔️Find angle K using the Sine Rule:

\( \frac{sin(K)}{GF} = \frac{sin(G)}{KF} \)

Substitute

\( \frac{sin(K)}{3.18} = \frac{sin(64)}{5} \)

Multiply both sides by 3.18

\( sin(K) = \frac{sin(64)}{5}*3.18 \)

\( sin(K) = 0.5716 \)

\( K = sin^{-1}(0.5716) \)

K = 34.8618741° ≈ 34.90°

Answer:

The arc CD is: 114.64°

Step-by-step explanation:

The given triangle inside the circle, we can get the trigonometric ratio such as

sin x = opposite / hypotenuse

Here:

The opposite side of angle x = 36.7/2

The hypotenuse = 21.8

Thus,

sin x = [36.7/2] / [21.8]

sin x = 18.35 / 21.8

sin x  = 0.8417

x = arc sin (0.8417)

x = 57.32°

Thus, the angle formed at the center by CD is:

2 x 57.32 = 114.64°

Therefore, the arc CD is: 114.64°

Answer:

The arc CD would be 114.6°

We use- sin x = opposite / hypotenuse

In the problem the opposite side of angle x = 36.7/2 and the hypotenuse = 21.8

So:

sin x = [36.7/2] / [21.8]

sin x = 18.35 / 21.8

sin x = 0.8417

x = arc sin (0.8417)

x = 57.32°

So the angle formed at the center by CD would have to be 2 x 57.32 = 114.64°

BUT, it says to round to the nearest tenth, so the answer would therefore, the arc CD is: 114.6°

Answers:

A, B, D, E

Nearly everything except choice C is true.

====================================================

Explanation:

Answer:

Jennifer jogged the most, by 18 miles

Step-by-step explanation:

Given

Alan:

\(To\ School = 3.2\ miles\)

\(After\ School = 2.2\ miles\)

\(Days = 5\)

Jennifer:

\(Total= 45\ miles\)

Required

Who jogged most?

First, we calculate the distance covered by Alan daily

\(Daily = To\ School + After\ School\)

\(Daily = 3.2\ miles + 2.2\ miles\)

\(Daily = 5.4\ miles\)

Next, we calculate the distance covered in 5 days

\(Distance = 5.4\ miles * 5\)

\(Distance = 27\ miles\)

By comparison, Jennifer jogged the most because 45 > 27

And the difference is:

\(Difference = 45\ miles - 27\ miles\)

\(Difference = 18\ miles.\)

Answer: 2/90 = 1/45

Step-by-step explanation:

Answer:

Step-by-step explanation:

25.

x + 2x -75 = 90

3x = 90+75

3x = 165

x = 55

Measure of A = 55

Measure of B = 2(55) - 75 = 110 - 75 = 35

28.

2x+10-x+55 = 90

x = 90-65

x = 25

measure of A = 2(25) +10 = 60

measure of B = -25+55 = 30

31.

2x+3+3x - 223 = 180

5x -220 = 180

5x = 400

x = 80

measure of A = 163

measure of B = 17

32.

-4x+40+x+50 = 180

-3x +90 = 180

-3x = 90

x= -30

measure of A = -4(-30) +40 = 160

measure of B = -30+50 = 20

Answer:

Step-by-step explanation:

2x^2 + 9x + 4=0

2x^2+8x+x+4=0

2x(x+4) +1 (x+4) =0

2x+1 = 0

x+ 4 =0

2x= -1

x= -1/2

x=-4

Therefore x = -4 and x = -1/2

Answer:

Non-linear

Step-by-step explanation:

While the difference in x terms remains constant at 1

The difference between y terms varies.

Answer:

Non-linear.

Step-by-step explanation:

Answer:

  42.5 square units

Step-by-step explanation:

Pick's theorem probably provides the simplest approach to finding the area of this figure. It tells you the area of a figure drawn on grid points is given by ...

  A = i + b/2 -1

where i is the number of grid points inside the figure, and b is the number of grid points on the boundary.

Here, we have three closed figures, shown in different colors in the attachment. The red figure has 31 boundary points and 26 internal points, so an area of ...

  Ared = 26 +31/2 -1 = 81/2 = 40.5 . . . . square units

Each of the blue "feet" is 1 square unit, so the total area is ...

  A = 40.5 + 1 + 1 = 42.5 . . . square units

Answer:

13:24

that is it

male:all

\(y \propto \dfrac 1x\\\\\implies y = \dfrac kx \\\\\implies \dfrac 14 = \dfrac k{8}\\\\\implies k=2\\\\\text{When}~ x =-4\\\\y = \dfrac{k}{x} = \dfrac{2}{-4}= -\dfrac 12\)

The answer choice which is a function among the given answer choices is; Choice B as they are all correct.

From conventional mathematics, a function from a set x to a set y assigns to each element of X exactly one element of Y.

The set of values x is called the domain of the function and the set of values y is called the codomain/range of the function.

Functions basically represents the idealization of how a varying quantity depends on another quantity.

It therefore follows from the paragraph above that all of the answer choices are functions.

Therefore, the answer choice which is a function among the given answer choices is; Choice B as they are all correct.

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Answer:

In week 1, 69.15% of sales were 10-inch pizzas, and the remaining 30.85% were 12-inch pizzas; while in week 2, 71.09% of sales were 10-inch pizzas, and the remaining 28.91% were 12-inch pizzas.

Step-by-step explanation:

Given that a takeaway sells 10 inch pizzas and 12 inch pizzas, to determine what proportion sold were 10 inch pizzas in week 1 and what proportion sold were 10 inch in week 2, the following calculation must be performed:

Week 1 = 736 total sales

10-inch pizzas = 509

736 = 100

509 = X

509 x 100/736 = X

50,900 / 736 = X

69.15 = X

100 - 69.15 = 30.85

Thus, in week 1, 69.15% of sales were 10-inch pizzas, while the remaining 30.85% were 12-inch pizzas.

Week 2 = 1076 total sales

10-inch pizzas = 765

1076 = 100

765 = x

765 x 100/1076 = X

76500/1076 = X

71.09 = X

100 - 71.09 = 28.91

Thus, in week 2, 71.09% of sales were 10-inch pizzas, while the remaining 28.91% were 12-inch pizzas.

Answer: Half of them are even and half of them are odd.

Step-by-step explanation:

The even numbers are 6, 12, 18, 24, and 30. An even number is defined as a number that is divisible by 2, meaning it has no remainder when divided by 2. For example, 6 divided by 2 equals 3 with no remainder, so 6 is even.

The odd numbers are 3, 9, 15, 21, and 27. An odd number is defined as a number that is not divisible by 2, meaning it has a remainder of 1 when divided by 2. For example, 9 divided by 2 equals 4 with a remainder of 1, so 9 is odd.

Therefore, out of the given numbers, half of them are even and half of them are odd.

________________________________________________________

Answer:

  19 or 26

Step-by-step explanation:

You want the value of 3n² -8n -9, given that n(n -3) = 10.

We recognize that 10 = 5·2 and that these factors differ by 3. This means n(n -3) = 10 is equivalent to saying n ∈ {-2, 5}.

The value of 3n² -8n -9 will be one of ...

  (3n -8)n -9 = (3(-2) -8)(-2) -9 = (-14)(-2) -9 = 19 . . . . for n = -2

or

  (3(5) -8)(5) -9 = (7)(5) -9 = 26 . . . . . . . for n = 5

The expression 3n² -8n -9 will be either 19 or 26.

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Answer:

2

Step-by-step explanation:

2 to the second power is 4 and 3 to the second power is 9 if you add 4 and 9 you will get 14. hope i could help:)!

Yes, I agree with Benito's approach to finding the quotient of 45 ÷ 9.

We have,

When we divide 45 by 9, we are essentially asking, "How many times does 9 go into 45?"

This can also be rephrased as "What is the result of multiplying 9 by some number to get 45?"

Now,

To find the quotient of 45 ÷ 9, we can recall the related multiplication fact that 9 times 5 is equal to 45.

Then, we can use the Commutative Property of Multiplication, which states that the order of multiplication can be changed without changing the result, to recall the other related multiplication fact that 5 times 9 is equal to 45.

Therefore,

The quotient of 45 ÷ 9 is 5, which we can obtain by recalling either the multiplication fact 9 times 5 equals 45 or 5 times 9 equals 45.

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After the double rotation, the vertices of the quadrilateral MNPQ are transformed to M'', N'', P'', and Q''. The shape of the quadrilateral may have changed, but the order of the vertices remains the same.

When a quadrilateral MNPQ is rotated counterclockwise at 90 degrees about the origin, each vertex undergoes a transformation.

The new positions of the vertices after this rotation can be denoted as M', N', P', and Q'. The order of the vertices remains the same.

Next, when the rotated quadrilateral M'N'P'Q' is further rotated counterclockwise at 270 degrees about the origin, each vertex undergoes another transformation.

The new positions of the vertices after this rotation can be denoted as M'', N'', P'', and Q''. Again, the order of the vertices remains the same.

It's important to note that a 270-degree counterclockwise rotation is equivalent to a 90-degree clockwise rotation.

The result of the double rotation is equivalent to a single clockwise rotation of 90 degrees.

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The value of c in the polynomial is - 7.

The polynomial is given as follows:

p(x) = 2x³ - x² +  cx + 2 . The value of c if x - 2 is a factor of p(x) can be computed as follows:

Therefore,

p(x) = 2x³ - x² +  cx + 2

when x - 2 is a factor, p(x) = 0

Therefore,

0 = 2x³ - x² +  cx + 2

Hence,

2(2)³ - (2)² +  2c + 2 = 0

16 - 4 + 2c + 2 = 0

12 + 2 + 2c  = 0

2c = - 14

divide both sides by 2

c = - 14 / 2

c = - 7

Therefore,

c = -7

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Answer:

9 m²

Step-by-step explanation:

The perimeter of a square is 4x, where is the length of one side (because all the sides have the same length).

This means that 4x = 12, so x = 3, in other words the length of one side of the square is 3 m.

To work out the area of the square, multiply the length and the width together: 3 x 3 = 9 m²

Hope this helps!