Fill in the missing number in this sequence:
324, 108, 36, 12, { }

[tex]\dfrac{7x^2+14}{(x^2+3)^2}=\dfrac{7x^2+21-7}{(x^2+3)^2}=\dfrac{7x^2+21}{(x^2+3)^2}-\dfrac{7}{(x^2+3)^2}=\dfrac{7(x^2+3)}{(x^2+3)^2}-\dfrac{7}{(x^2+3)^2}=\\=\dfrac{7}{x^2+3}-\dfrac{7}{(x^2+3)^2}[/tex]

Answer:

B

Step-by-step explanation:

(f + g)(x)

= f(x) + g(x)

= 2x + 1 + x² - 7 ← collect like terms

= x² + 2x - 6 ← in standard form

The value of (f + g)(x) is x² + 2x - 6.

Arithmetic operations are a set of four basic operations to be performed to add, subtract, multiply or divide two or more quantities. They include the study of numbers including order of operations which are useful in all the other parts of mathematics such as algebra, data handling, and geometry.

Given are two functions, f(x) = 2x+1 and g(x) = x²-7, we are asked to find

(f + g)(x),

So we know,

(f + g)(x) = f(x) + g(x)

Therefore,

(f + g)(x)

= f(x) + g(x)

= 2x + 1 + x² - 7

= x² + 2x - 6

Hence the value of (f + g)(x) is x² + 2x - 6.

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Answer:

The value of x is 30 degrees.

Step-by-step explanation:

We know that angle 1 is 60 degrees, and that angle two is a right angle (meaning 90 degrees.) 60+90 is equal to 150 degrees. 180 degrees - 150 degrees is equal to 30 degrees. I hope this helps! :)

[tex]~~~~~~\sin \theta = \dfrac{\text{Perpendicular}}{\text{Hypotenuse}}\\\\\\\implies \sin 60^{\circ} = \dfrac{x}{8}\\\\\\\implies x = 8 \sin 60^{\circ}\\\\\\\implies x = 8 \cdot \dfrac {\sqrt3}2\\\\\\\implies x = 4\sqrt 3[/tex]

The required total distance the ball travels, approximately, is 180 feet.

Let's denote the height of the first fall as a (initial height of 60 feet), and the distance covered during each rebound as r (two-thirds the distance of the previous fall).

The first fall distance (a) is 60 feet.

The first rebound distance (r) is (2/3) * 60 feet.

The total distance covered during the first fall and rebound cycle is:

60 + (2/3) * 60 = 60 + 40 = 100 feet.

Now, for the subsequent cycles, the ball will continue to fall and rebound in the same pattern:

Second fall distance = r * a
                                  = (2/3) * 60
                                  = 40 feet.

Second rebound distance = r*(2/3) * 60
                                            = (2/3) * 40
                                            = 80/3 feet.

The total distance covered during the second fall and rebound cycle is:

40 + (80/3) ≈ 66.67 feet.

The pattern will continue for the subsequent cycles.

To represent this as an infinite geometric series, we can write:

Total distance = [tex]a + (a * r) + (a * r^2) + (a * r^3) + ...[/tex]

Where:

a = 60 feet (height of the first fall)

r = 2/3 (rebound factor)

Using the formula for the sum of an infinite geometric series:

Total distance = a / (1 - r)

Total distance = 60 / (1 - 2/3)

Total distance = 60 / (1/3)

Total distance = 60 * 3

Total distance = 180 feet.

Therefore, the total distance the ball travels, approximately, is 180 feet.

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The measure of angle that is coterminal with 425° is 425° + (1440n)°

Coterminal angles are angles in multiples of the angles in standard positions examples(360°).

It is mostly gotten by adding  360° or multiples of 360 to the angle.

One of the unique behavior of coterminal angles is that their sine, cosine and tangent are equal.

Analysis:

From the options, the only one with an addition of 360 or multiples of 360 is 425 + 1440n

If we put n = 1, the coterminal angle gotten is 1865.

if we find the sine of 425°, we get 0.9063 which is same as the sine of 1865°.

In conclusion, the coterminal angle to 425° is 425° + (1440n)°.

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Answer:

B. 425° – (840n)°, for any integer n

Answer:

Yes! |-15| = 15

Step-by-step explanation:

Many people think of absolute value (the two bars symbol around the -15) as ALWAYS POSITIVE.

You can also think of absolute value as a distance. If you move 15 units, it doesn't matter in what direction you go. 15 units travelled is 15 units.

Lastly, absolute value has a V-shaped graph, that is because its always positive.

The coterminal angle to -ㅠ/2 in the range between 0 and 2ㅠ radians is 3ㅠ/2.

For any angle A, all the coterminal angles are of the form:

B = A + n*(2ㅠ).

Where n is an integer different than zero.

In this case, the angle is A = -ㅠ/2

So the coterminal angles are of the form:

B = -ㅠ/2 + n*(2ㅠ)

We want it to be between 0 and 2ㅠ, so we can define n = 1, then we get:

B = -ㅠ/2 + (2ㅠ) = -ㅠ/2 + ((4/2)ㅠ) = 3ㅠ/2

Then we can conclude that the correct option is b.

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By applying knowledge on complex analysis, the complex numbers that satisfy the three conditions defined in the statement are z₁ = 4 - i 3 and z₂ = 5 + i 12.

In this question we must derive two complex numbers such that the following conditions are fulfilled:

a² + b² = 5²     (1)

c² + d² = 13²     (2)

13 · (a + i b) - 5 · (c + i d) = 27 - i 99     (3)

If we assume that a, b, c, d are integers, then we can suppose that (a, b) = (4, -3) and (c, d) = (5, 12) and we check if these values satisfy (3):

13 · (4 - i 3) - 5 · (5 + i 12)

52 - i 39 - 25 - i 60

27 - i 99

By applying knowledge on complex analysis, the complex numbers that satisfy the three conditions defined in the statement are z₁ = 4 - i 3 and z₂ = 5 + i 12.

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Answer:

Negative; it describes a violent reaction based on rage.

Step-by-step explanation:

[tex]\text{Apply Pythagorean theorem,}\\\\~~~~~~~~\text{Hypotenuse}^2=\text{Base}^2 + \text{Perpendicular}^2\\\\\implies 9^2 = \text{Base}^2 + \left(2\sqrt{14} \right)^2\\\\\implies 81 = \text{Base}^2 + 56\\\\\implies \text{Base}^2 = 81-56\\\\\implies \text{Base}^2 = 25\\\\\implies \text{Base} = \sqrt{25}\\\\\implies \text{Base} = 5\\\\\text{The length of the third side is 5 units.}[/tex]

To better give a visual, I drew it out instead.

The attachment is the solution.

Answer:

(4, 5)

(4, 2)

(6, 2)

Step-by-step explanation:

add 3 in "x" and 1 in "y"

(1, 4) ⇒ (1+3, 4+1) = (4, 5)

(1 , 1) ⇒ (1+3 , 1+1) = (4, 2)

(3, 1) ⇒ (3+3, 1+1) = (6, 2 )

Hope this helps

Answer:

0.25m or 1/4m

Step-by-step explanation:

Given Height of Dorsal Fin = 1/6 of Length of whale Sculpture,

and given length of whale sculpture = 1.5m or [tex]1\frac{1}{2} m\\[/tex]

Height of Dorsal fin on scuplture = [tex](\frac{1}{6})(1\frac{1}{2} )\\[/tex]

= [tex](\frac{1}{6} )(\frac{3}{2}) \\= \frac{3}{12} \\= \frac{1}{4}m or 0.25m[/tex]

The measure of the radius of the cylinder to the nearest tenth is 1.7cm

The formula for calculating the surface area of a cylinder is expressed as:

S = 2πr(r+h)

Given the following

S=. 125cm²

h = 10cm

Substitute

125 = 2πr(r+10)

Expand

125 = 2(3.14)r² + 20(3.14)r
6.28r² + 62.8r - 125 = 0

Factorize

On factorizing, the measure of the radius of the cylinder will be 1.7cm

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mean is average, add all numbers and divide by quantity of numbers.

Median is the middle value, list the numbers from smallest to largest and find the middle number.

mode is the number that appears the most.

1. Mean = 6

Median = 5

Mode = 6

2. Mean = 86.1

Median = 86.5

Mode = 85

When the sum of two angles measures up to 180° then these angles are known as supplementary angles of each other. The supplementary angles are 153° and 27°. The Complementary angles are 34° and 56°.

When the sum of two angles measures up to 180° then these angles are known as supplementary angles of each other.

for example, ∠x + ∠y = 180°, therefore, the ∠x and ∠y are the supplementary angles of each other.

When the sum of two angles measures up to 90° then these angles are known as complementary angles of each other.

for example, ∠x + ∠y = 90°, therefore, the ∠x and ∠y are the complementary angles of each other.

The supplementary angles are 153° and 27°.

The Complementary angles are 34° and 56°.

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Answer:

its the Pentagon, the other shaps have 2 lines if symmetry

Answer:

A) z

Step-by-step explanation:

(8z - 10) ÷ (-2) + 5(z - 1)

1. Rewrite:

 [tex]\large \textsf{$\dfrac{(8x-10)}{-2}+5(z-1)$}[/tex]

2. Distribute 5

[tex]\large \textsf{$5(z-1)$}\\\\\large \textsf{$5(z)+5(-1)$}\\\\\large \textsf{$5z-5$}[/tex]

Now we have:

[tex]\large \textsf{$\dfrac{(8x-10)}{-2}+\large \textsf{$5z-5$}$}[/tex]

3. Reduce the fraction:

[tex]\large \textsf{$\dfrac{(8x-10)}{-2}+\large \textsf{$5z-5$}$}\\\\\large \textsf{$-4x+5+5z-5$}[/tex]

4. Combine like terms:

[tex]\large \textsf{$-4x+5+5z-5$}=\large \textsf{z}[/tex]

Final answer: z

Hope this helps!

Answer:

15

Step-by-step explanation:

For this question you would need to do a squared + b squared so 9x9 is 91 + 12x12 which is 144. you add the two up then find the square root of that which should make your answer 15

The correct solution to the limits of x in the tiles can be seen below.

The limits of x approaching a given number of a quadratic equation can be determined by knowing the value of x at that given number and substituting the value of x into the quadratic equation.

From the given diagram, we have:

1.

[tex]\mathbf{ \lim_{x \to 9^+} (\dfrac{|x-9|}{-x^2-34+387}) }[/tex]

So, x - 9 is positive when x → 9⁺. Therefore, |x -9) = x - 9

[tex]\mathbf{ \lim_{x \to 9^+} (\dfrac{x-9}{-x^2-34+387}) }[/tex]

Simplifying the quadratic equation, we have:

[tex]\mathbf{ \lim_{x \to 9^+} (-\dfrac{1}{x+43}) }[/tex]

Replacing the value of x = 9

[tex]\mathbf{ = (-\dfrac{1}{9+43}) }[/tex]

[tex]\mathbf{ = -\dfrac{1}{52} }[/tex]

2.

[tex]\mathbf{ \lim_{x \to 8^-} (\dfrac{8-x}{|-x^2-63x+568|}) }[/tex]

Thus |-x²-63x+568| = -x²-63x+568

[tex]\mathbf{ \lim_{x \to 8^-} (\dfrac{1}{x+71}) }[/tex]

[tex]\mathbf{=\dfrac{1}{8+71} }[/tex]

[tex]\mathbf{=\dfrac{1}{79} }[/tex]

3.

[tex]\mathbf{ \lim_{x \to 7^+} (\dfrac{|-x^2-17x+168| }{x-7}) }[/tex]

[tex]\mathbf{ \lim_{x \to 7^+} (\dfrac{-x^2-17x+168 }{x-7}) }[/tex]

[tex]\mathbf{ \lim_{x \to 7^+} (-x-24)}[/tex]

[tex]\mathbf{ \lim_{x \to 7^+} (-7-24)}[/tex]

= -31

4.

[tex]\mathbf{ \lim_{x \to 6^-} (\dfrac{|x-6| }{-x^2-86x+552}) }[/tex]

[tex]\mathbf{ \lim_{x \to 6^-} (\dfrac{-x+6 }{-x^2-86x+552}) }[/tex]

[tex]\mathbf{ \lim_{x \to 6^-} (\dfrac{1}{x+92}) }[/tex]

[tex]\mathbf{ \lim_{x \to 6^-} (\dfrac{1}{6+92}) }[/tex]

[tex]\mathbf{ =\dfrac{1}{98}}[/tex]

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The domain of the function when Toni participates in a 10-mile charity walk will be [0, 9, 18, 27, 36, 45, 54, 63, 72, 81, 90]

It should be noted that a function simply means a relation that's used to express a variable with another variable.

In this case, it should be noted that a domain simply means the set of possible values of the independent variable. The function here is 9x. The domain is all x-values or inputs of a function. Therefore, the domain is depicted above.

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The error in the distance if the uppermost portion of a 3. 0m long stadia rod is inclined 14 cm toward the observer and the rod intercept is 1. 75m on a horizontal sight is 8.167cm.

The tangent or tanθ in a right angle triangle is the ratio of its perpendicular to its base. it is given as,

Tan(θ) = Perpendicular/Base

where,

θ is the angle,

Perpendicular is the side of the triangle opposite to the angle θ,

The base is the adjacent smaller side of the angle θ.

Given the uppermost portion of a that is 3.0m long stadia rod is inclined 14 cm toward the observer, therefore, the angle of inclination, θ can be written as

tan(θ)=0.14/3

θ = 2.672°

Also, the rod intercept is 1.75m, therefore, t the error in distance in the distance is,

tanθ=x/1.75

x = 1.75 tan(θ)

x = 1.75 × tan(2.672°)

x = 0.08167 m = 8.167 cm

Hence, the error in the distance if the uppermost portion of a 3. 0m long stadia rod is inclined 14 cm toward the observer and the rod intercept is 1. 75m on a horizontal sight is 8.167cm.

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Answer:

a)  26 tickets

b)  £5

c)  chips, pastie and a soft drink

Step-by-step explanation:

Given:

Part (a)

Greatest number of tickets = total available to spend ÷ cost of one ticket

                                             = 200 ÷ 7.5

                                             = 26.66666...

                                             = 26 tickets

(We can't round up, as 27 tickets would cost £202.50)

Part (b)

Money left = Total available spend - cost of 26 tickets

                  = 200 - (26 × 7.50)

                  = 200 - 195

                  = £5

Part (c)

Cost of 3 items = £10 - change

                         = £10 - £4.70

                         = £5.30

One of the items can't be a burger, as £5.30 - £3.50 = £1.80
and £1.80 is not enough to buy 2 items.

If he buys chips, he has: £5.30 - £2.40 = £2.90 left to spend on the other 2 items.

Pastie + Soft Drink = £1.60 + £1.30 = £2.90

So he can buy: chips, pastie and a soft drink

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{20\% of 20000}}{\left( \cfrac{20}{100} \right)20000}\implies 4000\qquad \impliedby downpayment[/tex]

The expression that is equivalent to (-11/15)⁵ is (-11)⁵/(15)⁵

Given the expression as shown below

(-11/15)⁵

This expression means that we are to raise the value -11 and 14 raised to the power of 5 individually as shown:

(-11/15)⁵ = (-11)⁵/(15)⁵

Hence the expression that is equivalent to (-11/15)⁵ is (-11)⁵/(15)⁵

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The expression that signifies Katherine’s final cost F= P + T= $466

The number of pansies to be arranged around each tree = 15 pansies

The cost of pansies(P) = 15 × 8 × 2.50 = $300

The number of juniper trees available = 8

The cost of the trees available(T) = 8 × 20.75= $166

Therefore Katherine's final cost(F)= $300 + $166 = $466

The expression to find Katherine’s final cost = F= P + T

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Answer:

18

Step-by-step explanation:

Mode =  modal class (Recurring)
The number/value that appears the most which in this case is 18 because it can be seen twice.

The distance travelled from the starting point is 29 km , the bearing is 344 degree

The missing diagram is attached with the answer.

It is the horizontal angle between the object and another object.

It is given that the car starts from point travels for 30km on a bearing of 145, then 10 km on a bearing of 250

(a) the distance travelled from the starting point

It can be understood from the diagram that

To determine the distance , b is to determined4

By applying Cosine rule

b² = a² +c²-2ac cos[tex]\rm \theta[/tex]

b² = 10²  +30²  - 2* 30*10 cos75

b² = 100+900 -600* 0.2588

b² = 100-155.2914

b² = 844.7

b = 29 km

Therefore the distance travelled from the starting point is 29 km.

(b) the bearing of the starting point from the car.

To determine the bearing ,

angle C has to be determined

By sine rule

sin C / c = sin B / b

sin C = sin 75 * 30 / 29

sin C = 0.9970

C = sin⁻¹ 0.9970

C = 85.59 degree

angle C = α +70 degree

α  = 15.59 degree

Bearing = 70 + 20 + 9 0 + 90+74 = 244 degree

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Answer:

-0.5

Step-by-step explanation: